FIB Design of Anchorage in Concrete

Design g£ anChDraaes In CDncre~e

ISSN 1562-3610 ISBN 978-2-88394-098-7

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Design of anchorages in concrete Contents Part I: General provisions

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Scope - Terminology- Basis of design - Determination of action effectsDetermination of concrete condition - Verification of limit states - DurabilityProvisions for ensuring the characteristic resistance of the concrete member

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Part II: Characteristic resistance of anchorages with post-installed expansion anchors, undercut anchors, screw anchors and torque-controlled bonded expansion anchors Scope - Ultimate limit state - elastic design approach - Ultimate limit state - plastic design approach - Serviceability limit state - Fatigue loading - Seismic loading

Part III: Characteristic resistance of anchorages with bonded anchors and connections with post-installed reinforcing bars General- Anchorages with bonded anchors - Connections with post-installed reinforcing bars

Part IV: Characteristic resistance of anchorages with cast-in headed anchors Scope - Ultimate limit state - elastic design approach - Ultimate limit state - plastic design approach - Serviceability limit state - Fatigue loading - Seismic loading

Part

v: Characteristic resistance of anchorages with cast-in anchor channels

Scope - Determination of action effects - Ultimate limit state - elastic design approach - Serviceability limit state - Fatigue loading ~ Seismic loading

federation internationale du beton International Federation for Structural Concrete www.fib-international.org

Design of anchorages in concrete

Subject to priorities defined by the Technical Council and the Presidium, the results of fib's work in Commissions and Task Groups are published in a continuously numbered series of technical publications called 'Bulletins'. The following categories are used: cate20rv Technical Report State-of-Art Report Manual, Guide (to good practice) or Recommendation Model Code

minimum approval procedure required prior to publication approved by a Task Group and the Chairpersons ofthe Commission approved by a Commission approved by the Technical Council of fib approved by the General Assembly of fib

Any pUblication not having met the above requirements will be clearly identified as preliminary draft. This Bulletin N° 58 was approved'as a "Guide to good practice" by the Technical Council of fib in June 2011. This Guide was drafted by Special Activity Group 4, Fastenings to structural concrete and masonry structures. Rolf Eligehausen (Convener) Akiyama (Tokyo Soil Research, Japan), Asmus (lEA, Germany), Barthomeuf (SPIT, France), Bergmeister (Universitiit fur Bodenkultur, Austria), Cook (Univ. of Florida, USA), Elfgren (Luleii Univ. of Technology, Sweden), Fletcher (Australia), Genesio (Univ. Stuttgart, Germany), Grosser (Univ. Stuttgart, Germany), Hoehler (Hilti, Liechtenstein), Hofmann (Univ. Stuttgart, Germany), Klingner (Univ. of Texas, Hordjik (Adviesbureau, The Netherlands), USA), Hosokawa (Univ. of Tokyo, Japan), Kuhn (Adolf Wurth, Germany), Lange (DIBt, Germany), Li (fischerwerke, Germany), Lotze (MPA Stuttgart, Germany), Mallee (Germany), Matsuzaki (Science Univ. of Tokyo, Japan), Mattis (CEL Consulting, USA), Mesureur (CSTB, France), Michler (Techn. Univ. Dresden, Germany), Nakano (Tokyo Univ., Japan), Olsen (Powers, USA), Rieder (BBT, Austria), Roik (Halfen, Germany), Rutz (MKT, Germany), Silva (Hilti, USA), Sippel (VBBF, Germany), Spieth (fischerwerke, Germany), Stochlia (lCC-ES, USA), Turley (Simpson Strong Tie, USA), Vintzileou (National Technical Univ. Athens, Greece), Wall (Hilti, Liechtenstein), Wol1mershauser (USA), Yamamoto (Shibaura Institute ofTechnology, Japan), Ziegler (Powers, USA) The complete list of members and corresponding members who have contributed to this Design Guide over the years is given on pages iv-v.

Left cover photo: Anchorage of the column of a timber bridge (Courtesy of Institute of Construction Materials, University of Stuttgart) Right cover photo: Anchorage of a pipe (Courtesy of Hilti North America) © federation internationale du beton (jib), 2011

Although the International Federation for Structural Concrete fib - federation internationale du beton - does its best to ensure that any information given is accurate, no liability or responsibility of any kind (including liability for negligence) is accepted in this respect by the organisation, its members, servants or agents.

Preface Modern fastening technique is employed extensively for the transfer of concentrated loads into concrete and masonry structures. Cast-in-place anchors, placed in the formwork before casting of the concrete, and post-installed systems, which are installed in hardened structural concrete or masonry, are equally common. Loads are transferred into the concrete or masonry by mechanical interlock, friction, bond or a combination of these mechanisms. However, independent of the load-transfer mechanism, all anchorages rely on the tensile strength ofthe concrete or masonry, a fact which must be taken into account in both assessment and design. Despite the widespread use of cast-in-place and post-installed anchors in construction, the overall level of understanding in the engineering community regarding their behaviour remains quite limited. In order to improve the general state of knowledge in this field, Task Group III/S: "Fastenings to reinforced concrete and masonry structures" was formed within the Comite Euro-Intemational du Beton (CEB) in 1987. In 1996 the group published the CEB design guide "Design of Fastenings in Concrete". It covered expansion, undercut and headed anchors in concrete under predominately static loading, and has been a widely-referenced resource document for code deyelopment in this area. Following the transformation of the CEB into the International Federation for Structural Concrete (jib) in 1998, the group was re-named as Special Activity Group (SAG) 4 "Fastenings to Structural Concrete and Masonry Structures ". Since the publication of the original CEB guide ongoing research and additional application experience has led to an improved understanding and deepened knowledge in various areas of fastening technology. This publication "Design of Anchorages in Concrete" represents a substantial revision of the original I 996 design guide. It addresses a variety ofloading types and failure modes and takes into account the current state of the art for anchorages in new construction as well as for their use in the repair and strengthening of existing concrete structures. The following significant additions and revisions are incorporated in this document: a new section on the design of bonded anchors and connections with post-installed reinforcing bars; a new section addressing the design of anchor channels; a new section on the design of anchorages for fire; a new section on the design of anchorages under earthquake loading; inclusion of detailed design provisions for anchorages subjected to fatigue loading; significantly improved design provisions for the critical case of shear-loaded anchorages close to edges; and improved design provisions for combined tension and shear loading.

All rights reserved. No part of this publication may be reproduced, modified, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior written permission.

Among other topics, the group continues to investigate design provisions for shear lugs; this work will be included in a future edition.

First published in 2011 by the International Federation for Structural Concrete (jib) Postal address: Case Postale 88, CH-IOI5 Lausanne, Switzerland Street address: Federal Institute of Technology Lausanne - EPFL, Section Genie Civil Tel +4121 6932747· Fax +41216936245 fib@epfl.ch • www.fib-international.org

Rolf Eligehausen Chairman, SAG 4 "Fastenings to Structural Concrete and Masonry Structures" Stuttgart, November 2010

ISSN 1562-3610 ISBN 978-2-88394-098-7 Printed by DCC Document Competence Center Siegmar Kastl e.K., Germany

fib Bulletin 58: Design of anchorages in concrete

111

7

Contents

Durability

8 Preface

o

111

Introduction

x

Part I - General provisions 1 1.1 1.2 1.3 1.4 1.5 1.6 I. 7 1.8

Scope General Permissible anchor type and anchorage configurations Prequalification and quality control requirements for products Permissible anchor dimensions and materials Permissible anchor loading Permissible concrete strength Permissible loading of the concrete members Reliability classes

1 I I 9 10 II 15 15 16

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7

Terminology Definitions Indices (subscripts/superscripts) Actions and resistances Concrete and steel Notation - dimensional Greek symbols Units

21 21 26 28 31 32 35 35

3 Basis of design 3.1 General 3.2 Required verifications 3.3 Design format 3.4 Partial factors 3.4. I Partial factors for actions 3.4.2 Partial factors for resistance 3.5 Project specifications and anchor installation 3.5.1 Project specification 3.5.2 Installation

36 36 37 42 44 44 45 48 48 49

Determination of action effects 4 4.1 General 4.2 Effect of friction 4.3 Ultimate limit state 4.3.1 Elastic analysis 4.3.2 Plastic analysis 4.4 Serviceability limit state and fatigue 4.5 Seismic loading

52 52 52 55 55 96 102 102

5

102

Determination of concrete condition

6 Verification of limit states 6.1 Ultimate limit state 6.2 Serviceability limit state 6.3 Fatigue 6.4 Verification for load combinations including seismic actions 6.5 Fire 6.5.1 General 6.5.2 Partial factors 6.5.3 Resistance under fire exposure

VI

103 103 104 105 III 116 116 116 117

fib Bulletin 58: Design ofanchorages in concrete

Provisions for ensuring the characteristic resistance of the concrete member 8.1 General 8.2 Shear resistance of concrete member 8.3 Resistance to splitting forces

122 124 124 124 128

Part II - Characteristic resistance of anchorages with post-installed expansion anchors, undercut anchors, screw anchors and torque-controlled bonded expansion anchors 9

Scope

130

10 Ultimate limit state - elastic design approach 10.1 Resistance to tension load 10.1.1 Required verifications 10.1.2 Steel failure 10.1.3 Pullout failure 10.1.4 Concrete cone failure 10.1.5 Splitting failure 10.2 Resistance to shear load 10.2.1 Required verifications 10.2.2 Steel failure 10.2.3 Pullout failure 10.2.4 Concrete pryout failure 10.2.5 Concrete edge failure 10.3 Resistance to combined tension and shear load 10.3.1 Anchorages far from edges, anchorages close to edges with shear resisted by front anchors 10.3.2 Anchorages close to edges with shear resisted by the back anchors 10.3.3 Anchorages loaded by a tension load and a shear load with lever arm

136 136 136 137 137 137 143 145 145 146 148 148 149 163

11 Ultimate limit state - plastic design approach 11.1 Field of application 11.2 Resistance to tension load 11.2.1 Steel failure 11.2.2 Pullout failure 11.2.3 Concrete cone failure 11.2.4 Splitting failure 11.3 Resistance to shear load 11.3.1 Required verifications 11.3.2 Steel failure 11.3.3 Concrete pryout failure 11.3.4 Concrete edge failure 11.4 Resistance to combined tension and shear load

168 168 168 169 169 169 169 169 170 170 170 171 171

12

Serviceability limit state

171

13

Fatigue loading

172

14 Seismic loading

172


163 165 167

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Part III - Characteristic resistance of anchorages with bonded anchors and connections with post-installed reinforcing bars 15 General

173

16 Anchorages with bonded anchors 16.1 Scope 16.2 Ultimate limit state - elastic design approach 16.2.1 Resistance to tension load 16.2.2 Resistance to shear load 16.2.3 Resistance to combined tension and shear load 16.3 Ultimate limit state - plastic design approach 16.4 Serviceability limit state 16.5 Fatigue 16.6 Seismic loading

176 176 181 181 187 188 188 189 189 189

17 Connections with post-installed reinforcing bars 17.1 Scope 17.2 Prequalification testing 17.3 Design 17.3.1 General 17.3.2 Dimensioning of the connection 17.4 Design for fire 17.5 Installation and job site quality control

189 189 190 192 192 193 194 195

26.2 Anchor channels with anchor reinforcement 26.2.1 Resistance to tension load 26.2.2 Resistance to shear failure 26.2.3 Resistance to combined tension and shear loads

250 250 252 254

27 Serviceability limit state

255

28 Fatigue loading

255

29 Seismic loading

255

References

257

Part IV - Characteristic resistance of anchorages with cast-in headed anchors 18 Scope

196

19 Ultimate limit state - elastic design approach 19.1 Anchorages without anchor reinforcement 19.1.1 Resistance to tension load 19.1.2 Resistance to shear load 19.2 Anchorages with anchor reinforcement 19.2.1 Resistance to tension load 19.2.2 Resistance to shear loads 19.2.3 Resistance to combined tension and shear loads

202 202 203 208 209 209 214 220

20 Ultimate limit state - plastic design approach

221

21

222


22 Fatigue loading

224

23 Seismic loading

224

Part V - Characteristic resistance of anchorages with cast-in anchor channels 24 Scope

225

25 Determination of action effects 25.1 Derivation of forces acting on anchors of anchor channels 25.1.1 General 25.1.2 Tension loads 25.1.3 Shearloads

230 230 230 230 232

26 Ultimate limit state - elastic design approach 26.1 Anchor channels without anchor reinforcement 26.1.1 Resistance to tension loads 26.1.2 Resistance to shear loads 26.1.3 Resistance to combined tension and shear load

232 232 232 241 248

viii



IX

o Introduction

x

o. Anchorages are commonly used to transfer loads into concrete structures or to connect concrete elements. As illustrated in Figure 0-1, in general a connection (anchorage) to concrete is composed of the following basic components: a fixture that in connection with the attachment distributes loads to the anchors; the anchors which attach the fixture to the concrete; and the base material, consisting of the concrete surrounding each anchor. In some special cases the attachment may be anchored directly to the concrete, i.e., without a common fixture.

Anchors

Attachment

Fixture

Introduction

This Design Guide covers anchorages to concrete. The concrete may be assumed to crack during the service life of the anchorage or remain uncracked. The structure that is anchored may be either statically determinate or statically indeterminate. An anchorage (support) may consist of one anchor or a group of anchors. This Design Guide provides a method for the design of the anchorage and additional rules for the design of the concrete member to which the load is transferred. The provisions are based on the available research. The design of the fixture must be performed according to the relevant code of practice for the fixture material. The design methods provide an adequate level of safety for the given application conditions. The legal aspects of how these design rules are implemented in codes is beyond the scope of this document. However, throughout the Design Guide it is made clear where for proprietary products specific design resistances/parameters are required, the values given in the relevant Approval are decisive. There is an inherent assumption in this directive that Approval guidelines provide conservative recommendations. Although manufacturer recommendations may also be valid, no judgment regarding the adequacy of manufacturer recommendations for design is provided. This Design Guide is applicable provided that the following conditions are met:

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the anchorages are designed by qualified and experienced personnel; the installation is performed by personnel having the required skill and experience;

Base material

- the structure is adequately maintained during its intended service life; and

Figure 0-1:

Basic anchorage nomenclature

- the specified use of the anchorage is not changed in a manner that imposes more severe requirements on the anchors during their intended service life, unless redesign is carried out to verify their suitability for the new use. The anchorages should be fully described in the construction documents. The minimum required information that should be provided is described in Section 3.5.1.

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This Design Guide is subdivided into five parts: Part I

General provisions

Part II

Characteristic resistance of anchorages with post-installed expansion anchors, undercut anchors, screw anchors and torque-controlled bonded expansion anchors

Part III

Characteristic resistance of anchorages with bonded anchors and connections with post-installed reinforcing bars

Part IV

Characteristic resistance of anchorages with cast-in headed anchors

Part V

Characteristic resistance of anchorages with cast-in anchor channels

The design method given in this Design Guide is based on the safety concept adopted by the CEB-FIP Model Code 1990 (CEB, 1993). This safety concept is suitable for statically determinate systems, i.e., where failure of a single anchorage will result in failure of the entire system. It is also valid for statically indeterminate systems, e.g., continuous beam elements, distributed piping systems and ceiling support structures. It takes into account the current state of knowledge.

While Part I gives rules that are valid for all types of anchors, Parts II to V contain provisions that are valid for specific types of anchors. A flowchart for the design of anchorages is given in Figure 0-3. Flowcharts for calculating the resistance of specific types of anchorages are given in the respective part of this Design Guide.

The attachment usually consists of a structural steel element, and often includes a fixture (baseplate). However, attachments may also be made of timber, structural concrete or other structural materials.

This Design Guide replaces the CEB document "Design of Fastenings in Concrete" published in 1997 (CEB, 1997).

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The right side of each page contains design provisions. The left side provides commentary to these provisions.

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Durability (Seclion 7)

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Characteristic actions on fixture (Section 4)

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Fastener prequalification demonstrate suitability in cracked andlor uncracked concrete (Section 1.3)

Calculate design actions

on anchors (Section 4) I I I Elastic analysis I I Plastic analysis (Section 4.3.1) (Section 4.3.2)

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Serviceability

limit slale Fatigue

Seismic

Fire (Section 6.5)

I

Ensuring char. resistance of concrete member (Section 8)

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Flowchart Afar the design of anchorages

PART I: GENERAL PROVISIONS

1

Scope

1.1

General

The provlSlons of the Design Guide are addressed to connections involving the transmission of loads within the primary load-resisting frame of a structure. They are equally applicable, however, to the attachment of elements such as fayades, piping, etc., often referred to as non-structural components, and to temporary anchorages, e.g., for lifting precast elements or securing site equipment such as scaffolding and barriers.

This Design Guide provides requirements for the design of anchorages used to transmit loads to concrete. It is intended for applications in which the failure of the anchorage could:

The limiting criteria given here (collapse prevention, health and life preservation, economic protection) should be used as a guideline in detennining the scope of application. In all cases, it is assumed that the anchorage design will be carried out by a design professional competent in the field of reinforced concrete.

have significant economic, social or environmental consequences.

result in collapse or partial collapse of the structure, or cause injury or risk to human life, or The applications may be structural or non-structural in nature; that is, the connected elements may be part of the primary structural system or may consist of appurtenances such as guardrails, fayade elements or mechanical components. This Design Guide is applicable to pennanent anchorages in both new and existing structures. It may, however, also be applied to the design of temporary anchorages.

The design of the attachment (component, fixture, baseplate) is not addressed by the Design Guide, except where it may affect the distribution of loads to the anchors.

This Design Guide does not cover the design of the fixture (baseplate) or attached component (see Figure 0-1). The design of these elements should be carried out in accordance with applicable Standards. Requirements on the stiffness and ductility of the baseplate and/or attachment to ensure that the relevant assumptions for load distribution are met are given in Sections 4.3.1, 4.3.2 and 6.4.

1.2 Examples of anchor types covered by this Design Guide are given in Figure 1.2-1 to Figure 1.2-7. In these figures the predominant load transfer mechanism of the different anchor types is indicated.


Permissible anchor type and anchorage configurations

This Design Guide addresses the following anchor types: post-installed anchors (expansion anchors, undercut anchors, screw anchors, bonded anchors, torque-controlled bonded expansion anchors) and cast-in anchors (headed anchors and anchor channels). Furthennore, guidance is provided for the design of post-installed reinforcing bars.

1

Part I: 1 Scope

2

The installation, load-transfer mechanisms and behavionr in cracked and uncracked concrete of the different types of anchors are described in detail in eEB (1994) and Eligehausen et al. (2006-2).

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Figure 1.2-1:

Typical torque-controlled expansion anchors: a) single-cone sleeve type; b) bolt or wedge type

Figure 1.2-2:

Typical deformation-controlled expansion anchor: 'drop-in anchor'

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Typical undercut anchors: a) reversed undercut; b) to d) forward undercut; e) other interlocking system. a), b) and e): undercut formed before anchor installation; c) and d): undercutformed during anchor installation


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Typical headed anchors: a) headed bolt; b) embed plate with welded headed stud (embed plate placed in formwork); c) cast-in headed anchor with internal thread; d) anchor rod with bearing plate

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Figure 1.2-7:

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Typical anchor channels: a) anchor welded to channel bar; b) components of an anchor channel

The description of the behaviour of anchor groups in the Design Guide is predicated on the assumption that all anchors in the group exhibit roughly the same stiffness. This is most easily verified if the anchors are all of the same type, diameter and embedment. Note, that the characteristic spacings for the various failure modes may be different (see Parts II to V).


This Design Guide covers the design of single anchors and anchor groups. For the purpose of this Design Guide, anchor groups are assumed to be joined by a common structural element capable of distributing loads to the individual anchors of the group and the anchors spacing does not exceed the characteristic spacing for the failure mode under investigation. In addition, all anchors in a group are assumed to be of the same type, size and embedment.

5

--,

Part I: 1 Scope

6

Because the Design Guide makes certain assumptions with regards to load distribution and the behaviour of anchor groups, it does not directly address cases where interaction could occur between individual anchors not connected by a common attachment and/or fixture (Figure 1.2-8) and between anchor groups (Figure 1.2-9 and Figure 1.2-10). It may be assumed that interaction between individual anchors loaded in tension and tensionloaded anchor groups is precluded if the spacing between the outer anchors of adjoining tension-loaded groups or the distance between adjacent single anchors loaded in tension is not less than the minimum ofthe following:

The methods described in this Design Guide assume that single anchors not connected by a common structural element and anchor groups are spaced sufficiently to preclude interaction.

- the characteristic spacing for concrete cone failure (combined pullout and concrete cone failure for bonded anchors) and splitting failure; the characteristic spacing for concrete cone failure (combined pullout and concrete cone failure for bonded anchors) and splitting failure based on a reduced embedment required to resist the applied tension (Figure 1.2-9b). These requirements are also valid for single anchors or anchor groups loaded in shear with sufficient edge distance to preclude concrete edge failure. In the case of single anchors and anchor groups close to the edge loaded in shear it may be assumed that interaction is precluded if the spacing between the outer anchors of adjoining groups or between adjacent single anchors is not less than three times the minimum of the following:

the actual edge distance (Figure 1.2-10a); the edge distance corresponding to full utilization of the anchor steel capacity; and the reduced edge distance required to resist the applied shear (Figure 1.2-10b). When evaluating the reduced embedment depth and/or reduced edge distance of adjacent single anchor groups loaded by combined tension and shear loads, interaction of tension and shear loads should be taken into account. Where interaction between individual anchors or neighbouring anchors groups not connected by a common fixture may occur (Figure 1.2-8, Figure

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1.2-9 and Figure 1.2-10a), engineering judgement is required to adapt the rules given in this Design Guide to the specific geometry and loading in question.

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Example of an anchor configuration not directly addressed by this Design Guide - closely spaced single anchors with unequal loads (it is assumed that the critical distance is controlled by concrete cone failure)


7

Part I: 1 Scope

8

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Figure 1.2-9:

a) Example of an anchor configuration not directly addressed by this Design Guide - adjacent anchor groups loaded in tension; b) method of assessment to avoid interaction of neighboring anchor groups. This approach is valid if the anchorages with the reduced embedment depth h;j can safely transfer the design tension loads into the concrete member (it is assumed that the critical distance is controlled by concrete cone failure)

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Figure 1.2-10: Example for the assessment of adjacent shear-loaded anchor groups for applicability of the Design Guide: a) actual anchorage configuration; b) anchorages with reduced edge distance to avoid interaction. This approach is valid if the anchorages with the reduced edge distance can safely transfer the design shear loads into the concrete member (it is assumed that the critical distance is controlled by concrete edge failure)

c;

c;

1.3 Prequalification procedures may differ from country to country. At present, prequalification procedures that produce design data compatible with this Design Guide are included in: - European Technical Approval Guideline ETAG 00 I (EOTA, 1997), associated Technical Reports (EOTA, 2003-1) and Common Understanding of Assessment Procedures (CUAP) (EOTA, 2003-2 and EOTA, 2004-1) issued by the European Organisation for Technical Approvals (EOTA); - Acceptance Criteria AC193 (ICC-ES, 2010-1 and AC308 (ICC-ES, 2009) issued by the ICC Evaluation Service (ICC-ES); - ACI Standard 355.2 (ACI 355.2, 2007) issued by the American Concrete Institute (ACI). fib Bulletin 58: Design of anchorages in concrete

Prequalification and quality control requirements for products

This Design Guide is valid only for anchor products prequalified for the intended use whereby the manufacturer of the product is subject to a quality control system. The prequalification procedure should yield design data applicable to the design method provided in this document.

9

Part i: i Scope

10

Reports on prequalified anchors issued under ETAG 001 are referred to as European Technical Approvals (ETAs). Similarly, reports issued under AC193 or AC308 are referred to as Evaluation Service Reports (ESRs). In the following text these and other such documents are generically referred to as Approvals. Note, however, that ESRs are actually recommendations used by the authority having jurisdiction to help verifY code compliance. Other nationally-based prequalification procedures may be established. When products are prequalified in accordance with alternative criteria, verification of the conformance of such criteria with the requirements set by this Design Guide should be performed on a case by case basis. The required quality control system for the manufacture of the product is typically linked to the Approval and may vary regionally.

1.4 The minimum embedment depth of 40 mm is based on the following considerations: - in general, anchors should not be placed so that transfer of tension loads takes place within the cover layer of concrete. The quality of the cover concrete may vary considerably, depending on the reinforcement density, casting direction and method of consolidation. Cover concrete may also be subjected to spalling under adverse conditions (corrosion of reinforcing, structure overload, etc.); -

consider the flexural member shown in Figure 1.4-1. To reduce the degree of superposition of anchorage and bond stresses in the concrete, it is preferable that the load-transfer zone of the tension-loaded anchors be positioned beyond the innermost flexural reinforcement layer as shown. As a minimum the load-transfer zone should extend beyond the outermost layer of principal reinforcement.

Consideration of typical cover requirements and reinforcement configurations leads to a minimum embedment depth of 40 mm. Approvals may define embedment depths less than 40 mm on the basis of productspecific testing and restrictions on use. Lesser embedment depths may also be appropriate if increased factors of safety are applied.

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Permissible anchor dimensions and materials

This Design Guide applies to anchors with a minimum thread size of 6 mm (M6) or an equivalent cross-section. In general, the minimum embedment depth is taken as 40 mm. This Design Guide covers metal anchors made of carbon steel (ISO 898-2 (ISO, 1992)) or stainless steel (ISO 3506-1 (ISO, 2009-2) and ISO 3506-2, ISO, 2009-3)). The surface of the steel may be coated or uncoated. The anchors may include non-load bearing material, e.g., plastic parts. This Design Guide is valid for anchors with a nominal steel tensile strength, fuk:::: 1000 MPa. The bonding material of bonded anchors may be made primarily of resin, cement or a combination of the two. In addition, fillers and additives may be used. The grout used for bonded anchors may consist of organic or inorganic compounds used separately or in combination. The viscosity of the flowable bonding material or grout should be adequate to ensure correct placement (i.e., minimization of voids) considering: - drilled hole diameter and depth; - ratio of anchor element diameter to hole diameter (annular gap); and installation conditions (ambient and concrete temperatures and installation direction (downwards, horizontal or upwards)).

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Figure 1.4-1:

Example of an anchorage where the load-transfer area is beyond the innermost layer of reinforcement

Anchors may be produced from other materials than mentioned in Section 1.4, if these materials are shown to perfonn adequately. The limit on nominal tensile strength is intended to avoid the use of less ductile materials. Steel with strength fuk > 1000 MPa or hardened steel may be sensitive to stress corrosion or hydrogen embrittlement. The suitability of these steels for the intended application should be assessed by prequalification tests (see Section 1.3). Concrete screws may include locally hardened steel (e.g., in the threads) that exceeds 1000 MPa. The potential for hydrogen embrittlement or corrosion is checked in the appropriate suitability tests for the Approval (see EOTA, 1997; ICC-ES, 2010-1). The suitability of bonding materials and grouts used for bonded anchors is assessed via the prequalification test program. The degree to which grout shrinkage can be tolerated will depend on the thickness of the bond line (annular gap) associated with the anchor system. The use of highly expansive (as opposed to shrinkage compensating) grouts should be avoided in order to reduce the potential for premature splitting. Consideration should also be given to the ability of the grout to protect the anchor element from corrosion.

1.5 The actions on the anchor resulting from the actions on the fixture (tension, shear, bending or torsional moments or any combination thereot) will generally be axial tension and/or shear. When the shear force is applied with a lever arm, the anchor will be subjected to a bending moment as well.


Permissible anchor loading

This Design Guide applies to anchors subjected to predominately static loading. Certain types of anchors, however, may also be subjected to fatigue and/or seismic loads as stated in the respective Part of this Design Guide.

11

Part I: 1 Scope

12

Examples of loadings on anchorages are shown in Figure 1.5-1.

-LL

BL

V-

+N aj

bj

B o Figure 1.5-1:

Compression loads on a fixture are allowed provided that (i) they are transferred from the fixture to the concrete without loading the anchors or alternatively, (ii) the anchors are suitable to transfer compression loads (Figure 1.5-3).

\

F

~ Loading on anchorages and on anchors: aj tension load; bj shear load; cj combined tension and shear load; dj shear load with lever arm

Figure 1.5-2 represents conditions where compression forces are resisted by bearing at the concrete surface. Care should be exercised in cases where the compression forces are taken directly into the anchors, e.g., where levelling nuts are provided without bearing nut and washer as shown in Figure 1.5-3. There are two considerations in this case: - expansion anchors and some undercut anchors placed in direct compression may become dislodged and lose the ability to resist tension forces (Figure 1.5-4a); - where the member thickness is limited, resisting the compression loads through the anchor may result in concrete breakout failure at the backside of the member (Figure 1.5-4b).

·o:-:-~-_-"'~"-~-:---:---:-""'-:--·~-

-"---"'--

-.-~---~-.--.

F

~M ~

n!l.

,"" I I

I I I

~

f

I I

aj

bj Figure 1.5-2:

Examples of anchors where the anchors are not loaded by a compression force: aj anchorage loaded by a bending moment and/or a compression force; bj stand-off installation with bearing nut and washer


13

14

Part 1: 1 Scope

FI

....

,,

lI"'il

""'" I I I

u u

,

Base plate grout omitted or not in contact with base plate due to shrinkage, etc.

I I I

T I Figure 1.5-3:

F

I

Anchorage with anchors loaded by a compression force (base plate grout omitted)

,

F[

vertical

I displacement of anchor I

. . g, Wi>

I

!--~

l'm"P.,,,'"

-

loss of expansion force

)

\

'---'......, ~,

~,

~

Figure 1.5-4:

~

Possible failure modes for a compression-loaded anchor when the compression load is not transferred at the concrete surface: a) anchor becomes dislodged (loss of expansion force); b) concrete breakout failure at backside of member

-~~

1.6 Structural nonnal weight concrete of strength class C20 to C50 corresponds roughly to the range of 2500 psi to 7500 psi concrete. Insufficient data for anchors installed in lightweight concrete exist to provide general guidance for their design. Product-specific data may be developed for these cases in accordance with prequalification procedures. Concrete having a compressive strength less than 20 MPa may exhibit local variations in concrete density and quality that could lead to unacceptable scatter of anchor load-displacement behaviour and strength.

Permissible concrete strength

In general, this Design Guide applies to anchorages in structural nonnal weight concrete (concrete produced with normal weight aggregates) of strength class C20 to C50 in accordance with CEB-FIP Model Code 1990 (CEB, 1993). For particular anchor types the pennissible range of concrete strength classes may be less restrictive than given above (see Part IV and Part V). This Design Guide addresses anchorages in both uncracked and cracked concrete.

The upper limit of concrete strength is derived from the following considerations: - the equations included in this Design Guide for the calculation of the resistance associated with pullout may be unconservative for high strength concrete; - experience regarding the response of post-installed anchors to tension loading in high strength concrete (e.g., follow-up expansion and bond strength of bonded anchors) is limited. The Design Guide is organised around anchorages in concrete that is expected to remain uncracked over the service life of the anchorage based on the calculated stress state (uncracked concrete) and those in concrete that may be expected to crack in the anchorage vicinity over the anchorage seryice life (cracked concrete). The bond between non-structural layers (screeds and toppings, plaster) and concrete can be highly variable. As such these layers may not be able to transfer loads induced by the anchorage to the underlying structural concrete.

This Guide does not address anchorages in thin non-structural layers such as screeds and toppings. For the case where anchors project through screeds or toppings, this Design Guide considers the screed or topping to be incapable of transferring loads.

1.7 Cyclic loading of structural concrete members may imply cycles of opening and closing of cracks that may cause deterioration of anchor perfonnance. Knowledge regarding the behaviour of the various anchor types under these conditions is limited.


Permissible loading ofthe concrete member

This Design Guide addresses anchorages in concrete members SUbjected predominantly to static loading. Where certain anchor types are deemed pennissible for use in concrete members subjected to fatigue or seismic loading, this is stated in the relevant parts of the Design Guide.

15

~

Part I: 1 Scope

16

1.8 The establishment of factors of safety for structures is typically based on a concept of the consequences of failure. The Consequences Classes as defined in EN 1990 (CEN, 2002-1) are given in Table 1.8-1. The Consequences Classes CCl, CC2, and CC3 correspond to Reliability Classes RCl, RC2 and RC3 according to EN 1990 (CEN, 2002-1).

The safety factor concept used in this document is predicated on the approach according to CEB-FIP Model Code 1990 (CEB, 1993) as adopted by EN 1990 (CEN, 2002-1). The basic requirements of EN 1990 are deemed to be satisfied for anchorages, when the following requirements are satisfied: limit state design is carried out according to the partial factor method in conformity with EN 1990 (See Section 3) and -

For the application of these procedures with other Reliability Classes, it is recommended to use the relevant provisions of EN 1990. Table 1.8-1:

Definition of Consequences Classes according to EN 1990 (CEN, 2002-1)

Consequences Class

Description

Examples of buildings and civil engineering

CCI

Agricultural buildings where people do not normally enter (e.g., storage buildings), greenhouses

CC2

Medium consequence for loss of human life, economic, social or environmental consequences considerable

Residential and office buildings, public buildings where consequences offailure are medium (e.g., an office building)

CC3

High consequence for loss of human life, or economic, social or environmental consequences very great

Grandstands, public buildings where consequences offailure are high (e.g., a concert hall)

resistances, durability and serviceability are calculated on the basis of the models ofthis Design Guide.

In general, a design using the partial factors given in this Design Guide and the partial factors given for loads in EN 1990 Annex A is considered to lead to a structure in compliance with Reliability Class RC2 according to EN 1990 (CEN, 2002-1). Use of the loads and safety factors given in ASCE/SEI 7-05 (ASCE, 2006) and the strength reduction factors given in ACI 318 (2008) is also admissible. See Section 3.

Use of other safety factor concepts is admissible if appropriately adjusted to ensure a similar probability offailure.

works Low consequence for loss of human life and economic, social or environmental consequences small or negligible

Reliability classes

I

~

For other reliability classes than RC2, the actions should be adjusted in accordance with Table 1.8-2. For example, for the same design, supervision and execution inspection levels, a multiplication factor KF/ may be applied to the partial factors }'f

Table 1.8-2:

Adjustment of action for reliability classes ReI to RC3 according to EN 1990 (CEN, 2002-1)

KF/ factor for actions KF/

Reliability class RCI

RC2

RC3

0.9

1.0

1.1

Note: In particular, for Class RC3, other measures such as increasedjobsite inspection requirements are preferred to using KF/ . KF/ should be applied only to unfavourable actions In other countries different classifications for Consequences Classes may be used, e.g., in the U.S. the classification shown in Table 1.8-3 applies.


17

18

Part I: 1 Scope Table 1.8-3:

Occupancy categories of buildings and other structures for floor, wind, snow, earthquake and ice loads taken from ASCEISEI 7-05 (ASCE, 2006)

Nature of occupancy Buildings and other structures that represent a low hazard to human life in the event of failure, including, but not limited to: o Agricultural facilities o Certain temporary facilities

Occupancy category

I

• Minor storage facilities All buildings and other structures except those listed in Occupancy Categories I, III, and IV

II

Buildings and other structures that represent a substantial hazard to human life in the event offailure, including, but not limited to: o Buildings and other structures where no more than 300 people congregate in one area o Buildings and other structures with day-care facilities with a capacity greater than 150 o Buildings and other structures with elementary school or secondary school facilities with a capacity greater than 250 o Buildings and other structures with a capacity greater than 500 for colleges or adult education facilities o Health care facilities with a capacity of 50 or more resident patients, but not having surgery or emergency treatment facilities o Jails and detention facilities Buildings and other structures, not included in Occupancy Category IV, with potential to cause a substantial economic impact and/or mass disruption of day-to-day civilian life in the event offailure, including, but not limited to:

• o o • --

III

Power generating stations a) Water treatment facilities Sewage treatment facilities Telecommunication centres

Buildings and other structures not included in Occupancy Category IV (including, but not limited to facilities that

manufacture, process, handle, store, use, or dispose of such substances as hazardous fuels, hazardous chemicals, hazardous waste, or explosives) containing sufficient quantities of toxic or explosive substances to be dangerous to the public if released. Buildings and other structures containing toxic or explosive substances shall be eligible for classification as Occupancy Category II structures if it can be demonstrated to the satisfaction of the authority having jurisdiction by a hazard assessment as described in Section 1.5.2 that a release of the toxic or explosive substances does not pose a threat to the pUblic. Buildings and other structures designated as essential facilities, including, but not limited to: o Hospitals and other health care facilities having surgery or emergency treatment facilities

• Fire, rescue, ambulance, and police stations and emergency vehicle garages o Designated earthquake, hurricane, or other emergency shelters • Designated emergency preparedness, communication, and operation centres and other facilities required for emergency response o Power generating stations and other public utility facilities required in an emergency o Ancillary structures (including, but not limited to communication towers, fuel storage tanks, cooling towers, electrical substation structures, fire water storage tanks or other structures housing or supporting water, or other firesuppression material or equipment) required for operation of Occupancy Category IV structures during an emergency • Aviation control towers, air traffic control centers, and emergency aircraft hangars o Water storage facilities and pump structures required to maintain water pressure for fire suppression o Buildings and other structures having critical national defense functions


IV

19

Part I: I Scope

20

Buildings and other structures (including, but not limited to facilities that manufacture, process, handle, store, use, or dispose of such substances as hazardous fuels, hazardous chemicals, or hazardous waste) containing highly toxic substances where the quantity ofthe material exceeds a threshold quantity established by the authority having jurisdiction. Buildings and other structures containing highly toxic substances shall be eligible for classification as Occupancy Category II structures ifit can be demonstrated to the satisfaction of the authority having jurisdiction by a hazard assessment as described in Section 1.5.2 that a release of the highly toxic substances does not pose a threat to the public. This reduced classification shall not be permitted if the buildings or other structures as function as essential facilities. oj Cogeneration power plants that do not supply power on the national grid shall be designated Occupancy Category II

The classification according to Table 1.8-3 corresponds approximately with the classes given in Table 1.8-1 as shown in Table 1.8-4.

Table 1.8-4:

Comparison of Consequences Classes in Europe and U.S.

Consequences Class according Table 1.8-1

Occupancy categories according Table 1.8-3

CCI

I

CC2

II

CC3

III + IV

Use of the safety factors given in ASCE/SEI 7-05 (ASCE, 2006) and the strength reduction factors given in ACI 318 (2008) leads to a reliability level in line with that associated with Reliability Class 2 (RC2).

2

Terminology

The definitions, notations and symbols frequently used in this Design Guide are listed below. Further notation is given in the appropriate sections of the Design Guide.

2.1

Definitions

Anchor

Steel element either cast into cOncrete or postinstalled into hardened concrete and used to transmit applied loads (see Figure 1.2-1 to Figure 1.2-7). In the case of anchor channels, a steel anchor is rigidly connected to the back of the channel and embedded in concrete.

Anchor channel

Steel profile (called channel) with rigidly connected anchors (see Figure 1.2-7) (also called channel bar) installed prior to concreting.

Anchor channel· -loading: Tension

Load applied perpendicular to the surface of the base material.

Anchor channel loading: Bending

Bending effect induced in the channel by a tension load applied perpendicular to the longitudinal axis of the channel.

Anchor channel loading: Combined

Axial and shear load applied simultaneously (oblique loading).

Anchor channel loading: Shear

Shear acting parallel to the cOncrete surface and perpendicular to the axis of the channel.

Anchor group

A number of anchors with identical characteristics acting together to support a common attachment where the spacing of the anchors does not exceed the characteristic spacing.

Anchor loading: Bending


=

Bending effect induced by a shear load applied with a lever arm with respect to the surface of the base material (see Figure 1.5-ld).

21

22

Part I: 2 Terminology

Axial and shear load applied simultaneously (oblique loading) (see Figure 1.5-lc).

Anchor loading: Combined tension and shear Anchor loading: Shear

Load applied perpendicular to the surface of the base material and parallel to the anchor longitudinal axis (see Figure 1.5-1a).

Anchor reinforcement

Reinforcement used to transfer the design load from the anchors into the structural member.

Anchor spacing

Distance between the centre lines of the anchors.

Attachment

Metal assembly that transmits loads to the anchor. In this Design Guide 'attachment', 'baseplate' and 'fixture' are used synonymously.

=

See 'Attachment'.

Blowout failure

Spalling of the concrete on the side of the anchorage component at the level of the embedded head with no major breakout at the top concrete surface. This is usually associated with anchors with small side cover and deep embedment.

Bonded anchor

Anchor placed into a hole in hardened concrete which derives its resistance from a bonding material placed between the wall of the hole in the concrete and the embedded portion of the anchorage (see Figure 1.2-5a). Bonded anchors are also referred to as adhesive, chemical or resin anchors.

Bond failure

Failure that occurs at the interface between the bonding material and the base material or between the bonding material and the steel part (anchor element) of a bonded anchor.

Cast-in anchor


Load applied perpendicular to the longitudinal axis of the anchor (see Figure 1.5-lb).

Anchor loading: Tension

Baseplate

,

=

=

Headed bolt, headed stud or anchor channel installed before placing the concrete (see Figure 1.2-6 and Figure 1.2-7).

Channel bolt

T-bolt which connects the element to be fixed to the anchor channel (see Figure 1.2-7b).

Characteristic resistance

The 5% fractile of the resistance (value with a 95% probability of being exceeded, with a confidence level of 90%).

Characteristic spacing

Spacing required to ensure the characteristic concrete resistance of a single anchor.

Clamping force

Prestressing force resulting from tightening of the anchor against the fixture.

Concrete breakout failure

Corresponds to a volume or cone of concrete surrounding the anchor or group of anchors separating from the base material (see Figure 3.2-lb and Figure 3.2-2b). In tension and shear loading this failure mode is denoted as 'concrete cone failure' and 'concrete edge failure', respectively.

Concrete member

Structural or non-structural member in which the anchorage is placed or installed.

Concrete pryout failure

Corresponds to the formation of a concrete spall opposite to the loading direction under shear loading (see Figure 3.2-2c).

Concrete screw

Threaded anchor screwed into a predrilled hole where threads create a mechanical interlock with the concrete (see Figure 1.2-4). In this Design Guide 'concrete screw' and 'screw anchor' are used synonymously.

Concrete strength

Concrete compressive strength from uniaxial compression tests on cylinders with diameter 150 mm and height 300 mm.

23

Part 1: 2 Terminology

24 Displacement

Movement of the anchor at the concrete surface relative to the surface of the concrete member into which it is installed. In tension tests displacement is measured parallel to the anchor axis. In shear tests, displacement is measured perpendicular to the anchor axis.

Defonnationcontrolled expansion anchor

A post-installed anchor that derives its tensile resistance by expansion against the side of the drilled hole through movement of an internal plug in the sleeve or through movement of the sleeve over an expansion element (Plug). Once set, no further expansion can occur (see Figure 1.2-2).

Ductile steel element

A steel element with sufficient ductility. The ductility conditions are given in the relevant sections of this Design Guide.

Edge distance

Distance from the edge of the concrete member to the centre of the anchor. Distance between the concrete surface and the deepest point of effective load transfer. The definition of the effective embedment depth for the different types of anchors is given in Fignre 2.5-1 to Fignre 2.5-4. The effective embedment depth for post-installed anchors is provided in the Approval. See.' Attachment'.

Effective embedment depth

Fixture Headed anchor

=

Steel anchor that derives its tensile resistance from mechanical interlock at the anchor head and which is cast in place (see Fignre 1.2-6).

Hole clearance

Annular gap between anchor and fixture (see Fignre 4.3-12).

Installation safety factor

Partial factor that accounts for the sensitivity of an anchor to installation inaccuracies (see Section 3.4.2.1.2).

-, Mechanical interlock

Load transfer to a concrete member via interlocking surfaces.

Minimum edge distance

Minimum distance from the centre of the anchor to the concrete edge to allow adequate placing and compaction of concrete (cast-in anchors) and to avoid damage to the concrete during installation (post-installed anchors); provided in the Approval.

Minimum member thickness

Minimum thickness of the concrete member in which an anchor is allowed to be installed; provided in the Approval.

Minimum spacing

Minimum centre to centre spacing of anchors to allow adequate placing and compaction of concrete (cast-in anchors) and to avoid damage to the concrete during installation (postinstalled anchors), provided in the Approval.

Post-installed anchor

An anchor installed in hardened concrete (see

Fignre 1.2-1 to Fignre 1.2-5). Pullout failure

Pull-through failure


Failure mode in which the anchor pulls out of the concrete without development of the full concrete resistance.

=

Failure mode in which the anchor body pulls through the expansion sleeve without development of the full concrete resistance.

Spacing

Distance between anchors measured centreline to centreline.

Splitting failure

Concrete failure mode in which the concrete fractures along a plane passing through the axis of the anchor or anchors (see Figure 3.2-1c).

Steel failure of anchor

Failure mode characterized by fracture of the steel anchor parts (see Fignre 3.2-1d and Fignre 3.2-2a). 25


26 Torque-controlled bonded anchor

Bonded anchor designed such that the anchor bolt can move relative to the hardened bonding material (see Figure 1.2-5b) resulting in follow-up expansion.

Torque-controlled expansion anchor

Post-installed expansion anchor that derives its tensile resistance from the expansion of one or more sleeves or other components against the sides of the drilled hole through the application of torque, which pulls the cone(s) into the expansion sleeve(s) during installation (see Figure 1.2-1). After setting, tensile loading can cause additional expansion (follow-up expansion).

Undercut anchor

A post-installed anchor that develops its tensile resistance from the mechanical interlock provided by undercutting of the concrete at the embedded end of the anchor (see Figure 1.2-3). The undercutting is achieved with a special drill before installing the anchor or alternatively, by the anchor itself during its installation.

2.2

Indices (subscripts/superscripts)

F

load

G

permanent action

M

material

N

=

axial force

Q

variable action

R

resistance; restraint

S

action effects

V

shear force

b

bond

c cb

= =

concrete concrete blowout

cl

clearance-hole

cp

concrete pryout

cr

cracked

d

design value

el

=

elastic

eq

earthquake (seismic)

f

action in general, friction, fixture

fat

fatigue

fi

fire

fix

=

fixture

flex

bending

g

group of anchors in context of load or resistance

h

highest loaded anchor in a group

ind

induced deformation

inst

installation

k

characteristic value local maximum

max mill


=

IniniInum

nom

nominal

p,

pullout or pull-through

pi

plastic

re

reinforcement

s

steel

27

28


sp

splitting

u

ultimate

uncr

uncracked

y

yield

o

reference value

1.

perpendicular to the edge

II

parallel to the edge

2.3

c

Actions and resistances =

compression force

G

permanent action

F

force

M

bending moment on anchor

M,

=

bending moment on fixture around axis in direction 1

M,

bending moment on fixture around axis in direction 2

AIj,ex

bending moment on channel of an anchor channel

N

=

axial force (positive denotes tension force, negative denotes compression force)

Q

=

variable action

R

resistance

S

action

T

torsional moment on fixture, tension force on anchor

V

shear force Characteristic value of resistance of a single anchor or an anchor group (nonnal force, shear force). Only those anchors susceptible to the particular failure mode under investigation shall be included in the group.

FRk(NRk;VRk)

FRd(NRd;VRd)

Design value of resistance of a single anchor or an anchor group respectively (normal force; shear force). Only those anchors susceptible to the particular failure mode under investigation shall be included in the group.

FSk(NSk ;Vsk;Msk;Tsk)

Characteristic value of actions acting on a single anchor or the fixture of an anchor group (normal load, shear load, bending moment and torsional moment). In the case of anchor channels characteristic values of actions acting on the channel bolts.

FSd(NSd ;Vsd;MSd;TSd )

Design value of actions acting on a single anchor or the fixture of an anchor group (normal load, shear load, bending moment, and torsional moment); in the case of anchor channels, design values of actions acting on the channel bolts.

Fs~(NS;;V;)

Design value of action on one anchor of an anchor channel.

FS~,i(N;d,i; Vs:,i)

Design value of action on anchor i of an anchor channel.

N"Sd ("V") Sd

Design value of tensile load (shear load) acting on the most stressed anchor of a group.

N%AV!.t)

Design value of the resultant tensile (shear) load acting on an anchor group effective in taking up tension (shear) loads.

NSd,re

NRk,s,a


=

Design value of tension load acting on an anchor reinforcement (see Figure 23.2-1c and Figure 23.2-2). Characteristic steel tension resistance of one anchor of an anchor channel.

29


30

=

NRk,s,c

N Rk",/

Characteristic tension resistance for local failure of channel lips (anchor channel).

NRk,sJ1ex

Characteristic tension resistance for flexural failure of channel (anchor channel).

NRd,s,a

Design steel tension resistance of one anchor of an anchor channel. Design tension resistance of connection between anchor and channel (anchor channel).

NRd,s,c

NRd.,'!

Design tension resistance for local failure of channel lips (anchor channel).

NRd,sjlex

Design tension resistance for flexural failure of channel (anchor channel). Design steel tension resistance of channel of an anchor channel (minimum value of NRd",a, NRd.'" and N Rd",/). Characteristic steel shear resistance of one anchor of an anchor channel.

NRd.s,ch

VRk,s,a

Characteristic shear resistance of connection between anchor and channel (anchor channel).

VRk,s,c

Characteristic shear resistance for local failure of channel lips (anchor channel),

VRk",!

Design steel shear resistance of one anchor of an anchor channel.

VRd,s,a

Design shear resistance of connection between anchor and channel (anchor channel),

VRd,s,c

Design shear resistance for local failure of channel lips (anchor channel).

VRd",/

Design steel shear resistance of the channel of an anchor channel (minimum value of VRd,s,a, VRd,s,c and VRd,s.!'

VRd,s,ch

2.4

Concrete and steel

A,

ex hk !ck,cube


Characteristic tension resistance of connection between anchor and channel (anchor channel),

stressed cross section of steel

=

concrete strength class where x is given as the characteristic concrete compression cylinder strength in MPa characteristic compressive strength of concrete (strength class) measured on cylinders 150 mm x 300 mm, according to CEB-FIP Model Code 1"990 (CEB, 1993) characteristic compressive strength of concrete (strength class) measured on cubes with a side length 150 mm (usually the word "cube" is substituted by the side length measured in mm)

.hk

characteristic steel yield strength or steel proof strength respectively (nominal value)

juk

characteristic steel ultimate tensile strength (nominal value)

Iy

moment of inertia of the channel [mm4] relative to the yaxis (Figure 2.5-4)

Wei

elastic section modulus of anchor calculated from the stressed cross section of steel

31


32

2.5 c a c m <> x ~ ~ ,,<> .~

~.?>

2~

-SUi ~ ~

c

~

Q,

a

~

E:"

~ffi

c a c m <> x

al (a2)

.~

~

Notation - dimensional

~

-g% eo> =~

c w -" 8 ~

_ ~ u5 c c w'"

ID ...~

u=

~~ ~

.~§

::>1-

dnom

d

~

"<> c~

00

,I<---,(

u c

'" '5

.!!:!g

~ a E:"' au 1-15

5

~

u c

E" ~ ~

=

a3

5

~

d .hi'

5

5

'"

~N

w

~

0

"'uc '"~

'5

~

c

m

" "ac

~

~

"<> c~

0

::>1-

'"d

d .hi'

Hd I' I r-Tli

aJ

d .hl-

.hi'

hole clearance according to Figure 4.3-12

acl,l

normal hole clearance according to Table 4.3-1

b

width of concrete member

=

bell

N

.;,

''"" ••

width of channel (Figure 2.5-4)

bf "

width of fixture

c

edge distance of an anchor (Figure 2.5-5) or an anchor channel

Ii: U)

distance between concrete surface and point of assumed restraint of an anchor loaded by a shear force with lever arm (see Section 4.3.1.5)

a"

,

M

spacing between outer anchors in adjoining anchorages in direction I (direction 2) (Figure 2.5-5)

CI

(c,j

edge distance in direction 1 (direction 2) (Figure 2.5-5)

c" Note: For torque-controlled expansion anchors, h,! is measured to the end of the expansion element(s) in the untorqued condition.

characteristic edge distance for ensuring the transmission of the characteristic resistance of a single anchor

Cmill

minimum allowed edge distance

Figure 2.5-1:

d

diameter of anchor bolt or thread diameter (Figure 2.5-1 and Figure 2.5-2), diameter of the stud or shank of headed anchors (Figure 2.5-3)

do

nominal diameter of drilled hole

Effective embedment depth h,Jior post-installed anchors

=

df

A(thread pitch)

~,

d

d"

, d

h" I I --

11;';;;:;;;;;;;¥CiS"%~~'''!

t

Figure 2.5-3:

diameter of anchor head (headed anchor) (Figure 2.5-3) outside diameter of anchor (Figure 2.5-1)

diameter of reinforcing bar

el

distance between shear load and concrete surface (Figure 4.3-36)

eN

eccentricity of resultant tension force of tensioned anchors in respect to the centre of gravity of tensioned anchors

ev

eccentricity of resultant shear force of sheared anchors in respect to the centre of gravity of sheared anchors

h, I~hnom

h

thickness of concrete member in which the anchor is installed (Figure 2.5-5)

hel tfi)(

tnx

~

}..Q4 a)

d" dllom

lh

c;:::;J

-H-

normal"diameter of clearance hole in fixture according to Table 4.3-1

d,

Effective embedment depth for screw anchors

dh

dJ,1

d for anchors without sleeve

her = 0.85 (h nom - a.Sht - hJ

Figure 2.5-2:

b,> D.5h" or

b,';; D.5h" or

to,,> D.2h" b)

tfi? O.2ho'

c)

Definition of effective embedment depth h,! for cast-in headed anchors: a) without baseplate; b) with a large baseplate with b l > O.5h,! or tfix> O.2h,! in any direction; c) with a small baseplate b l :::: O.5h'f or tft.' :::: O.2h'f in each direction

hell

height of channel (Figure 2.5-4)

h'f

effective embedment depth (Figure 2.5-1 to Figure 2.5-4)

hmill

minimum allowed thickness of concrete member

hI/om

=

Anchor Connection between channel and anchor

distance between tip of screw anchor and beginning of the thread

hi

thread pitch

I

lever arm of the shear force acting on an anchor (Figure 4.3-36)

lill

influence length of an external load channel (Figure 25.1-1)

Iv

embedment depth of post installed reinforcing bars

nl (n,)

..

Y

SI

----rh~nna.1

bolt

S"

Channel lips

Definitions for anchor channels


S;

NSd

along an anchor .

number of anchors in a group in direction I (direction 2) spacing of anchors in a group (Figure 2.5-5) or spacing of reinforcing bars

S

~Nut

Figure 2.5-4:

=

Channel

! 7L~~\'-ti 1

nominal anchor length (Figure 2.5-2 and Figure 2.5-3)

h,

Z

xlM

diameter ofclearance hole in fixture

(s,)

=

spacing of anchors in a group in direction 1 (direction 2) (Figure 2.5-5) characteristic spacing for ensuring the transmission of the characteristic resistance of a single anchor distance between anchor under consideration neighbouring anchors in anchor channels

and

33


34 Smill

=

thickness of fixture (Figure 4.3-34 and Figure 4.3-35)

(fix tgrout

t:

minimum allowed anchor spacing

=

thickness of grout layer (Figure 4.3-34) thickness of anchor head (Figure 2.5-3)

t" x

depth of the compression zone below the fixture (Figure 4.3-2)

a) Definition of c, s, a and h for tension loaded anchorages

VSdj

D o

°

0

......

5 1,2

51.1 C 1,1

VSdj

~~ ~,

JJi::

5,

I

S

f

'

c,

c,

b) Definition ofc and s for shear loaded anchorages Figure 2.5-5:

Definitions related to concrete member dimensions, anchor spacing and edge distance: a) anchorages subjected to tension load; b) anchorages near to an edge subjected to shear load; indices 1 and 2 depend on the edge for which the verification for concrete breakout is' made: index 1 denotes the direction perpendicular to the edge for which the verification for concrete breakout is made; index 2 denotes the direction perpendicular to direction 1

2.6 a

ach,V

factor taking into account the influence of the channel on the concrete edge failure load of anchor channels

a,q

seismic reduction factor

'C 'CRk

'If

2.7

0.03937 inches

2

0.001550 square inches

3

0.00006102 cubic inches

1 mm 1 mm

fib Bulletin 58: Design ofonchorages in concrete

angle between resultant shear load on anchors and a line perpendicular to the edge for which the verification for concrete edge failure is made angle between resultant shear load on fixture and a line perpendicular to the edgeD for which the verification for concrete edge failure is made

Jl

1 millimetre

=

a'v

8

inch-pound equivalent

factor for interaction equation factor taking into account the influence of the channel on the concrete cone failure load of anchor channels

o r

SI unit

=

ach,N

av

Conversions:

Greek symbols

=

displacement partial factor strain coefficient of friction bond stress characteristic bond strength of bonded anchors factorDto account for various influences in the calculation of concrete failure modes

Units

In this document SI units are used. Unless stated otherwise in the equations, the following units are used: dimensions are given in mm, cross sections in mm2 , section modulus in mm3 , forces and loads in N, moments in Nmm and stresses in MPa (N/mm2). Equations containing the concrete compression strength assume the use of cylinder strength (f;k). Cube strength may be converted to cylinder strength using the conversion according to EN 206-1 (CEN, 2000) and CEB-FIP Model Code 1990 (CEB, 1993):

35

Part 1: 3 Basis of design

I newton (N)

=

36

0.2248 pound force

C20

j;k = j;k,150 /

1.25

I MPa

145.0 pounds per square inch

C50

j;k = j;k,150 /

1.20

INm

8.850 inch pounds

If cubes with a side length larger or smaller than 150 mm are used, the followings conversion factors may be used: j;k.J50 = j;k.J50

In this Design Guide a nominal service life of at least 50 years is assumed for the anchorage. Further details on service life may be given in the relevant product Approvals.

The serviceability limit state is defined in CEB-FIP Model Code 1990 (CEB, 1993) as: limited local structural damage such as excessive cracking or excessive compressive stress, producing irreversible strains and micro cracks; - deformations which produce unacceptable damage in non-structural elements or excessively affect the use or appearance of structural or non-structural elements; vibrations resulting in discomfort, alarm or loss of utility.

0.95 j;k,IOO

= 1.05 j;k,200

3

Basis of design

3.1

General

Anchors should sustain all actions (forces and deformations) and environmental influences likely to occur during execution and use with an appropriate degree of reliability (ultimate limit state). At service loads they should conform to the serviceability requirements of CEB-FIP Model Code 1990 (CEB, 1993) (serviceability limit state). Additionally, they should remain fit for the use for which they are required over the service life of the anchorage (durability). Anchorages should be designed according to the same principles and requirements applicable to structures designed according to relevant design codes. The design service life of the anchors should not be less than that of the fixture. Actions on the anchorage should be obtained from the relevant design codes.

Anchors under service loads may produce micro cracking in the load transfer area. In as much as this microcracking is implicitly included in the calculation of the anchorage capacity, it may be neglected from a serviceability standpoint. In many cases, anchorage design is limited to considerations for the local transfer of load from the attachment to the concrete. It may be necessary, however, to explicitly veritY the continuous load path in the supporting structure accounting for the local loads originating from the anchorage. Such verification should be conducted to the extent that such forces significantly influence the design of the supporting structural elements or their connections.

The local transmission of the anchor loads to the concrete is checked in accordance with this Design Guide. It is assumed that under the design action of the anchorage the supporting structure is still at the serviceability limit state. The further transfer of loads originating in the anchorage to the remainder of the supporting structure should be considered in the design of the structure. Requirements for the concrete member are given in Section 8.

Quality requirements valid for design and execution of the RC structure and of the attachment are applicable to the design and execution of anchorages.

3.2 The following failure modes can be distinguished for cast-in-place and post-installed anchors: Tension loading (Figure 3.2-1): - steel failure (Figure 3.2-ld) _ pullout or pull-through failure (Figure 3.2-lal_2), combined pullout and concrete cone failure for bonded anchors (Figure 3.2- la3) -

concrete cone failure (Figure 3.2-lb l_3) blowout failure (Figure 3.2-1 b4) splitting failure (Figure 3.2-lc)

Pullout failure occurs when the entire anchor is pulled out of the drilled hole. The definition of pull-through failure depends on the type of anchor as follows: In torque-controlled expansion anchors, the expansion cone is pulled through the expansion elements. In torque-controlled bonded expansion anchors, the anchor bolt is pulled through the hardened mortar. Pull-through failure is allowed for torque-controlled expansion anchors and for torquecontrolled bonded expansion anchors, since pulling the cone(s) into the expansion elements (torque-controlled expansion anchor) or into the mortar (torque-controlled bonded-expansion anchors) constitutes the working mechanism of these anchor types. The assessment of these failure modes is performed in the relevant approval process and one characteristic value is given, which is termed "pullout" resistance. The concrete cone breakout failure mode is characterised by the formation of a cone-shaped fracture surface originating in the load-transfer zone of the anchor and radiating towards the concrete surface.

Required verifications

Anchorages should be designed for the following limit states: ultimate limit state; - serviceability limit state. Design for fatigue, seismic and fire exposure should be performed if applicable. Furthermore, adequate durability of the anchors for the intended use should be ensured. In the ultimate limit state verifications are required for all appropriate loading directions and for all relevant failure modes. In the serviceability limit state, the requirements given in Section 6.2 should be fulfilled. The material of the anchor and the appropriate measures for corrosion protection should be selected taking into account: - the intended working life; the environmental conditions at the place of installation; the conditions of inspection, maintenance or possible replacement of the anchors. Guidance for ensuring durability is given in Section 7. Where applicable, the anchorage should have an adequate fire resistance (see Section 6.5). For the purpose ofthis Design Guide it is assumed that the fire resistance of the fixture conforms to the applicable fire design regulations.

Blowout failure is a result of high bearing pressure generated in the load-

37 fib Bulletin 58: Design of anchorages in concrete

Part I: 3 Basis ofdesign

38

transfer area of the anchor. These high bearing stresses cause bursting forces transverse to the load direction which create a concrete breakout on the side face of the member. Splitting failure is caused by the hoop stresses around the anchor. The hoop stresses originate from local load transfer and expansion forces.

, NSdl

N

a,) Pulloutfailure

Sd '

,

NSd

a2) Pull-through failure

a3) Combined pullout and concrete cone failure of bonded anchor

b,) Concrete cone failure

.~

(b,(~ N~"J~ (b,)

b2) Group breakout; b3) Edge breakout; b4) Blowout NSd

/Ns~

(~

C2) Splitting failure of a group; C3) Near-edge splitting failure

C1) Splitting failure I

N Sd •

..W~

'" 1 ,

~'-~ " ..-.'

Figure 3.2-1:

d) Steel failure

Failure modes associated with tension loading


39


40

Shear loading (Figure 3.2-2): - steel failure (Figure 3.2-2a) pryout (Figure 3.2-2c) or pullout failure (Figure 3.2-2d) concrete edge failure (Figure 3 .2-2b) Steel failure is often accompanied by crushing and spalling of the concrete ahead of the anchor. The effect of the resulting secondary tensile and flexural stresses in the anchor bolt is accounted for in the design model for steel resistance. Pryout failure is caused by rotation of the anchor and the catenary tension force generated in the anchor bolt as a result of lateral deformation and the eccentricity between the acting shear force and the resultant resisting force in the concrete. Pullout under shear load is generated by the catenary tension force when the pullout resistance of the anchor is insufficient to generate concrete breakout. Concrete edge failure mode is characterised by the formation of a coneshaped fracture surface originating at the anchor shaft and radiating towards the concrete edge.

;~~~

The failure modes of anchor channels are explained in Section 24.

v"

VSd

b,) Edge breakout; b,) Group edge breakout; b3) Corner edge breakout

a) Steel failure

VSd

bs) Narrow member edge breakout

b4) Thin rnernber edge breakout I I

I

VSd , . ,..-~---

,

VSd

•

<.l

\....-

\....-

c,) Group pryout

Cl) Pryout I I

VSd , . r-- ____ _

=="Sl,"",~]

\....-

C3) Pryout at an edge

Figure 3.2-2:

d) Pullout (catenary action)

Failure modes associated with shear loading


41

--'-=

Part 1: 3 Basis ofdesign

42

3.3

Design format

For the design of anchorages, the safety concept of partial factors according to the CEB-FIP Model Code 1990 (CEB, 1993) is applied. According to this concept, in the ultimate limit state and for all relevant combinations of actions (including fatigue and seismic, where applicable) the value of the design actions Sd should not exceed the value of the design resistance Rd.

Sd ~Rd

(3.3-1)

where: In Load and Resistance Factor Design (LRFD), design actions are denoted as factored loads.

Sd = value of design actions on anchors Rd = value of design resistance of anchors In the serviceability limit state Equation (3.3-1) applies as well. In this case, the design action Sd as well as the design resistance Rd are generally expressed in terms of displacement or rotation (see Section 6.2).

The design actions on anchors may also be calculated according to corresponding standards, e.g., CEN (2002-2).

The design actions on the anchorage should be calculated according to CEB-FIP Model Code 1990 (CEB, 1993).

In the simplest case (permanent load and one variable load acting in the same direction as the permanent load) the following equation applies:

Sd=YO·Ok+YQ·Qk

(3.3-2)

where:

GiQk) = characteristic value of permanent (variable) actions YO(YQ) = partial factor of permanent (variable) actions For more complex loading situations refer to CEB (1993). If deformations imposed on the anchored element, e.g., due to temperature variations, are restrained by the anchorage, then the corresponding actions on the anchorage (Qind) multiplied by an appropriate safety factor (Yind) should be added in Equation (3.3-2).

If LRFD or strength design is used e.g., in ACI 318 (ACI 318, 2008) the basic requirement is expressed as follows: Design strength::: required strength

(3.3-4)

In the ultimate limit state, the value of the design resistance is obtained from the characteristic resistance of the anchor or anchor group as follows: Rd

= Rk

(3.3-3)

YM The required strength is derived from the design actions and is expressed in terms of actions (loads) multiplied by load factors (usually greater than 1) corresponding to specific load combinations specified in the applicable building code. The design strength (or design resistance) is obtained by multiplying the nominal strength (characteristic resistance) by a strength reduction factor ¢ (with ¢~ 1) instead of dividing it by a partial factor YM (with YM::: 1). Hence the basic requirement can be expressed as:

¢. (nominal strength) ::: required strength

where: Rk = characteristic resistance of single anchor or anchor group to the examined action effect (e.g., NRk or VRk)

yM= partial factor for material

(3.3-4a)

The strength reduction factors are given in the corresponding design Standard and in the Approval. Theoretically, the conversion of y",factors given in this Design Guide into rjJ-factors can be accomplished as follows using as an example the basic load combination of ASCE/SEI 7-05 (ASCE, 2006) and EN 1990 (CEN, 2002-1):

1.2D+1.6L =Sd

~Rd

=¢·Rk

1.350k +1.5Qk =Sd ~Rd

=Rk/YM

(3.3-5a) (3.3-5b)

with: D, Gk = dead load, permanent load

L, Qk

=

live load, variable load

For example, resolving Equations (3.3-5a,b) with respect to ¢ for the case Sd = Rd yields:

¢=

1.2D+1.6L YM. (1.35Gk + 1.5Qk)

(3.3-5c)

For various ratios of variable to permanent action the following equivalent strength reduction factors ¢ are obtained assuming YM= 1.5:


43


44

LID = QtlGk

rf;for YM= 1.5

0.4

0.63

1.0

0.67

10.0

0.70

Equation (3.3-5c) is valid for the simplest case (permanent load and one variable load acting in the same direction as the permanent load). For more complicated loadings, Equation (3.3-5c) should be modified accordingly. Note that the partial factors YM may address different safety aspects than the strength reduction factors rf;.

The partial factors for actions are independent of the materials used. In the absence of a generally accepted code for actions, they should be taken from CEB-FIP Model Code 1990 (CEB, 1993). Default values for the ultimate limit state are given in Table 3.4-1.

3.4

Partial factors

3.4.1

Partial factors for actions

The partial factors for actions depend on the type of loading and should be taken from CEB-FIP Model Code 1990 (CEB, 1993).

Table 3.4-1: Partialfactorsfor actions (ultimate limit state) Actions

Unfavourable effect

Favourable effect

Permanent, Ya

1.35

1.0

Variable, YQ

1.5

Usually neglected

1.0 1.0 oj 1.3 bj

Usually neglected

Accidental, YA

oj

Induced deformations, nnd

Usually neglected

Suggested value ifthe characteristic resistance is governed by ductile steel failure bj Suggested value if the characteristic resistance is governed by any other failure mode oj E.g., impact caused by vehicles

.J

In case of accidental loading safety is normally ensured by the design values of the accidental action or by other parameters describing the accidental situation. Therefore, YA = 1.0 is recommended. For serviceability limit state, as well as for fatigue actions, all partial factors for actions may be assumed to be 1.0. For seismic actions refer to the relevant design code, e.g., EN 1990 (CEN, 2002-1), Section 6.4.3.4.

3.4.2

Partial factors for resistance

The partial factor for materials given here are valid for Reliability Class RC2 according to EN 1990 (CEN, 2002-1) (see Section 1.8). Partial factors for Reliability Classes RCI and RC3 should be determined depending on the guidelines in each country.

3.4.2.1

Ultimate limit state

3.4.2.1.1 Partial factors for steel failure

In the absence of more accurate information, the values for YM, given in Equations (3.4-1) through (3.4-7) are recommended. Equations (3.4-1) through (3.4-5) were derived taking into account that the ultimate strength of steel!". is used for the calculation of the characteristic resistance of an anchor (including an anchor that is part of an anchor channel, see Figure 2.5-4) or of an anchor group. Equations (3.4-6) and (3.4-7) take into account that J;k should be used for calculating the characteristic bending resistance of the channel of anchor channels and the characteristic resistance for steel failure of anchor reinforcement.

The partial factors for steel YMs, YM,." YM,,l, YM'Jb and YM"" should be taken from the relevant AiJproval.

Tension load on anchors and channel bolts of anchor channels:

YMs

= 1.2.1,,· ~ 1.4 /y.

(3.4-1)

Shear loading on anchors and channel bolts of anchor channels with and without a lever arm: YM,

= f"k ~ 1.25 (f". ,;:;800 MPa and!,,. ,;:;0.8/',k)

(3.4-2)

/y.


45


YJill

46

=1.5 (f.,k > 800 MPa or!"k > 0.8!.,k)

(3.4-3)

Connection between anchor and channel of anchor channels assuming current channel fabrication steels and methods: (3.4-4)

YJill., =1.8

Local failure of the anchor channel by bending of the lips in tension and shear:

YJill,!

=1.8

(3.4-S)

Bending of the channel of anchor channels: (3.4-6)

YJill.!'", = 1.15 Steel failure of anchor reinforcement:

(3.4-7)

YJill,,.,, =1.15

3.4.2.1.2 Partial factors for concrete failure In order to provide uniformity in the recommended values for the partial factors YM" YM,p and YMp, the partial factor YM, takes into account not only the concrete quality, but also the sensitivity of the anchor to installation conditions and the coefficient of variation of the failure loads.

The partial factor YMc covers concrete breakout failure modes (cone failure, blowout failure, pryout failure and edge failure). The partial factor YM,p covers splitting failure. These partial factors' should be taken from the relevant Approval.

The value for YM, is therefore determined as follows: YMc =

(3.4-8)

Yc . rills! "Ycov

with:

Yc

Partial factor for concrete recommended value is Yc = 1.S.

YI,,"

=

under

compression.

The

Partial factor taking into account installation safety of the anchorage system. It is given in the Approval and represents a characteristic of the anchor. For information the following values YI,," for post-installed anchors are given:

Tension loading:

YI",'

1.0 for systems with high installation safety 1.2 for systems with normal installation safety 1.4 for systems with low but still acceptable installation safety

Shear loading:

1.0 For cast-in anchors and anchors channels a partial factor YI,," = 1.0 may be taken if the conditions of Section 3.S are fulfilled,

Yilisl =

The factors given above or in the relevant Approval are valid only if after installation the actual values of the effective embedment depth, spacing and edge distance are not less than the values used in the design (only positive tolerances are allowed on site), Partial factor taking into account the coefficient of variation of the failure loads in the service condition tests of the prequalification procedure

Ycov

=

1.0 (COV::: lS%)

>

1.0 (lS% < COV::: 20%) It is typically calculated according to Equation (3.4-9): Ycov =1.0+(COV[%]-15).0.03

(3.4-9)

In any case, the coefficient of variation of the failure loads in the service condition tests should be COV::: 20%.

For the partial factor of YM,p the value for YM, is reconunended. The partial factor for friction between fixture and concrete may be taken as YMj= 1.S.


47


48 3.4.2.1.3 Partial factor for pullout/pull-through failure

In the absence of specific information, the partial factor YMp should not be taken less than the value for YMo. This assumes that the effect of the concrete properties on the pullout/pull-through failure mode is similar to that associated with concrete cone breakout failure.

The partial factor for pullout/pull-through failure the relevant Approval.

3.4.2.2 The

It is reconunended to take the partial factor for material as YM'Jat = 1.35 (steel failure) and YMoJat = YM,pJat = YMpJat (concrete cone failure, splitting failure and pullout failure) according to Equation (3.4-8). For the partial factor for friction between the fixture and concrete a value YMjJat = 1.5 is recommended.

partial

factors

The description of the anchors should include the manufacturer (if applicable), make, model, dimensional and material characteristics and the embedment depth. Adherence to the specified edge distances, spacing and anchor embedment depth can be critical for the performance of an anchorage.

Specification of tolerances is useful in this regard. Where tolerances are specified, only positive tolerances should be used (exception: for the annular gap negative tolerances should be used). In general, tolerances should be specified for anchorages close to edges.

for 1.0.

resistance

should

be

taken

as

Fatigue loading

Partial factors for fatigue loading should be taken from the relevant Approval.

3.4.2.4 For seismic strengthening and repair of existing structures the partial factor for concrete Yo in Equation (3.4-8) may be modified according to the relevant Standards.

should be taken from


YAh = YMo = YMp = YMj= YM,p =

3.4.2.3

YMp

Seismic actions

Partial factors for the calculation of resistances, when seismic actions are considered, are assumed to be the same as for the ultimate limit state under static actions (see Section 3.4.2.1), unless otherwise stated in the relevant Approval.

3.5

Project specifications and anchor installation·

3.5.1

Project specification

Project specification should typically include the following information with regard to anchorages: strength class of the concrete used in the design; environmental exposure assumed in the design;

- construction drawings that include: - location of the anchors in the structure - number and detailed description of anchors including the grade and the type of steel, e.g., galvanized or corrosion resistant steel

Where stand-off installations are specified, the project specification for mechanical anchors should include provision of a nut and washer at the concrete surface.

- spacing and edge distances of the anchors thickness of fixture and diameter of holes in the fixture (as applicable) all relevant dimensional characteristics of the attachment maximum thickness of grout pads (if applicable) and maximum stand-off dimension (if applicable) (special) installation instructions (if applicable) - reference to the manufacturer's installation instructions; a note indicating that the anchor specification should not be changed without checking the original design.

3.5.2

Installation

The resistance and reliability of anchorages are significantly influenced by the manner in which the anchors are installed. The partial factors given in Section 3.4 are valid only when the following conditions are fulfilled: Often the anchor installation instructions are referenced in the Approval. These should be checked against the installation instructions provided with the product. Instructions should be explicit and direct. Perfonnance specifications (e.g., "Holes shall be free of all dust and debris" or "Air bubbles in the bonding material should be avoided") are generally not acceptable if not accompanied by clear instructions for achievement of the required condition. Gross errors are variations from the manufacturer instructions that result from carelessness or deliberate disregard and can significantly influence the performance of the anchor. This varies depending on the anchor type. Some examples of gross errors may be:


the manufacturer's published instructions for installation of the anchor are followed. The installation instructions and all necessary information for correct installation should be available where the installation takes place; - gross errors on site are avoided; - inspection and verification of the correct installation of the anchors is carried out by appropriately qualified personnel. The provisions of this Design Guide are based on assumptions as given in this section with respect to installation of the various anchor types. Installation instructions provided with specific proprietary products should be in conformity with these assumptions.

49

/~

50


- use of an anchor diameter or embedment depth other than specified; use of a drill bit with the incorrect diameter, especially for mechanical expansion anchors, undercut anchors or screw anchors; incorrect placement of cast-in anchors or channel anchors in the formwork; omission of installation torque, especially for torque-controlled anchors; - omission or incorrect placement of anchor reinforcement where required; - improper cleaning of the hole, in particular for bonded anchors. To avoid gross installation errors, anchors should be installed by trained personnel under adequate supervision. Job-site proof loading, whereby a specified number of installed anchors are loaded to some percentage beyond the design tension resistance to verify their correct installation, is one method to improve anchor installation quality. Because proof loading typically involves loads that are significantly below the expected anchor failure load, it may not detect minor defects in installation. Proof loading may be useful, however, to detect gross installation errors and to encourage quality control procedures on the job site.

3.5.2.1

Post-installed mechanical and chemical anchors

The following prOVlSlons apply to the installation of post-installed mechanical and chemical anchors. The concrete should be adequately consolidated in the region of the anchorage. This should be checked prior and during installation via a visual inspection. - Requirements for drilling operation and drilled hole: holes should be drilled perpendicular to the surface of the concrete unless otherwise required by the manufacturer's installation instructions or in the project specification

-

drilling should be carried out by the method specified in the manufacturer's installation instructions and in the project specification

Many drill bits exhibit a mark indicating that they are in accordance with a national Standard. If the drill bits do not bear a conformity mark, conformity with the Approval should be provided.

Carbide drill bits should comply with the relevant product Standards or specification, e.g., ANSI B212.15 (ANSI, 1994) and DIBt (2002).

Where holes are drilled in reinforced concrete or in concrete containing embedded items (electrical conduit, etc.), care should be exercised at the planning phase to reduce the degree of interference. While it may be permissible to interrupt existing reinforcing (e.g. by core drilling) in specific cases, damage to flexural or shear reinforcing should in general be avoided. Due to the potentially extreme consequences associated with damage to prestressing tendons, it is advisable to specify in the project specifications a minimum clearance, e.g., 50 mm, between the drilled hole and the prestressing tendon location.

Reinforcement should not be damaged during drilling of holes for anchors unless specifically permitted in the project specifications. Special care should be exercised when drilling in the vicinity of prestressing tendons. A suitable device, such as a pacometer or other non-destructive reinforcement detector should be used to determine the position of the reinforcement in the structure prior to drilling.

- Core bit diameter should comply with the prescribed diameter.

- Holes should be cleaned according to the instructions given in the relevant Approval or manufacturer's installation instructions. Abandoned drilled holes close to the final anchor location should be filled with high-strength non-shrink mortar.

In the process of installing post-installed anchors it may be necessary to relocate the anchor, e.g., if reinforcement is encountered. In general,

abandoned holes filled with high strength non-shrinking mortar do not adversely influence the anchorage resistance. Where damage to the concrete is excessive, other measures may be required.

3.5.2.2

Cast-in headed anchors and anchor channels

The following provlSlons apply to the installation of cast-in headed anchors and anchor channels: - the anchor or anchorage assembly should be secured in the formwork such that the anchor will remain in the specified location during placement and compacting of the concrete; Adjustment. of anchor or anchorage posItIOn after placement of the concrete but prior to curing should be avoided as it may lead to voids and localised weakness in the concrete.

the correct position of the anchorage or anchor should be verified prior to concrete placement in accordance with codes of practice for the control of reinforcement;

It may be advisable, depending on anchorage geometry and orientation, to

- the concrete should be adequately consolidated in the area of the anchorage, particularly around the head of the stud or anchor and under the fixture;

provide vent openings in base plates larger than 400 mrn x 400 mm to prevent air pockets from forming under the base plate during concrete placement.


- in general, placement of anchors or anchorages subsequent to concrete placement is not permitted unless tested procedures that ensure correct

51

l ~

52

Part I: 4 Determination ofaction effects

anchorage position and concrete consolidation in the anchorage vicinity are provided in the project specifications;

Placement of baseplates with welded anchors and anchor channels with vibration following concrete placement may be acceptable under the following conditions: the size of the baseplate (length of the anchor channel) is small enough that proper consolidation of the concrete can be assured, that air voids can be avoided and that correct placement of the fixture is assured;

welding of headed studs to an embed plate to create a group should be performed in accordance with the provisions given in the relevant Standard; -

welding of attachments to the anchorage should be performed in accordance with relevant Standards. In specific cases, measures to avoid transmission of excessive heat to the base plate or anchors may be required;

-

size and positioning of anchor reinforcement should be performed in accordance with the project specifications.

the installation should be performed according to a quality control system and the anchorages should not be moved after vibrating. In particular, the positioning of anchor reinforcement for shear loading may be particularly critical for the performance of the anchorage.

4

Determination of action effects

4.1

General

In general, when calculating the actions on the fixture, the displacement of the anchors is neglected. However, when anchoring statically indeterminate components, the effect of anchor displacements (support settlements) on the support reactions and bending moments of the anchored component may be significant and should be considered in the design.

This section provides guidance for the determination of the design actions on the anchors from the design actions on the fixture.

Deformations imposed on the anchored element, e.g., due to temperature variations, may be restrained by the anchors.

When calculating the design actions on the fixture, actions due to restraint of deformations should be taken into account.

4.2 An example where friction resistance is developed is shown in Figure 4.2-1.

Effect of friction

When a bending m0trlenf and/or a compression force acts on an anchorage that is in direct contacf with the concrete or baseplate grout, friction forces between the baseplate and the concrete or grout will develop. In general, it is conservative to neglect this friction in the design of the anchorage, although it may in some cases lead to an underestimation of concrete cracking at the serviceability level.

NSd I

M,/T" Sd I VSd

l

) Figure 4.2-1:

[

b

TSd

-- [j

V

RdJ

Ii, CsdiYMf

CSd

-------

Frictionforce due to a resulting compression reaction on the fixture

For anchorages located near a free edge, friction forces should not be considered to act in the design when they occur within the assumed fracture body. Consider an anchorage located close to an edge and loaded with a moment and compression force as shown in Figure 4.2-2. For the case shown in Figure 4.2-2a, the frictional resistance can mainly be developed in the edge breakout and should not have any appreciable effect on the shear resistance of the anchorage. Theoretically, if the moment is reversed, as shown in Figure 4.2-2b-c, and the edge failure is assumed to originate at the lead anchors, the resistance ofthe anchorage is increased by the friction force acting outside of the concrete failure cone (Figure 4.2-2b). However, if the fracture is assumed to originate at the back-most anchors (Figure 4.2-2c), the frictional resistance cannot be added to the resistance associated with edge breakout, because it is located within the fracture body. For these reasons, and since in general shear and moment generally act in combination as shown in Figure 4.2-2a (and not as shown in Figure 4.2-2b,c), the friction between concrete and fixture should be neglected.

As a rule, frictional resistance should be neglected if: the thickness of the grout layer exceeds one-half the anchor diameter d; -

the anchorage capacity is governed by a near-edge condition; or

-

the anchorage is intended to resist earthquake loads.

Where frictional resistance is taken into account, the design value of shear resistance corresponding to friction may be estimated as follows:

VRk ./ J1 VRd ./ =--=--,CSd YM! YM!

(4.2-1)

with: f.I

coefficient of friction

CSd

compression force under the fixture

YMj

partial factor for friction = 1.5 (see Section 3.4.2)

Note also, however, that the existence of frictional resistance may reduce the load at which cracking initiates at the front anchors, even if the strength of the anchorage is based on the capacity associated with fracture from the back-most anchors. This may have consequences for the serviceability check of the anchorage design.


53

54

Part I: 4 Determination of action effects

In general, the coefficient of friction between a flat steel element (base plate, etc.) and the concrete may be taken as f1 = 0.4. N"

N"

MT

Assumed faliure plane

VJ

r-

CSd

V" VRd,f

0

rfM

Assumed faliure plan

/1

\

t T"

V"

-

VRd ,/

~

T"

CSd ------.J

a)

b) N"

rfM

Assumed

faliure Planes~

I I

Ji=-r-Y

Sd

VRdf

~O

c)

Figure 4.2-2:

Actions and resulting shear failure patterns for a near edge anchorage a),c) friction force should not be considered in the design; b) for this combination of forces and failure pattern, friction force may be considered in the design

When the friction force calculated according to Equation (4.2-1) is taken into account in the design, it is treated as follows: In the elastic design approach the frictional force is usually subtracted from the shear force acting on the fixture; in the plastic design approach, it is added to the design shear resistance of the anchorage. Note that both of these approaches assume that the frictional resistance remains constant for all levels of anchorage displacement.

4.3 The degree of load redistribution assumed in the analysis should be in conformity with the available ductility of the anchors. For example, in a plastic analysis, anchor ductility shall be sufficient to ensure that all anchors on the tension side can achieve their full design resistance.


In general, the distribution of design actions to the anchors in an anchor group is predicated on linear elastic material behaviour. Under certain conditions (see Section 4.3.2.1), however, distribution of actions may be based on assumptions of plastic material behaviour.

In addition to verifications for acting forces and moments, it may also be necessary to check the rotation of the connection for conformity with the analysis of the attached structure. For example, if the analysis assumes fixity at the connection, it should be verified that the calculated rotation of the connection due to the design actions is sufficiently small to support this assumption. This may be particularly relevant if the design of the anchorage is based on plastic analysis. Similarly, an assumption of zero fixity (hinging) at the connection may be unconservative for the anchorage design if the detailing of the connection is inappropriate to ensure this condition.

4.3.1 Brittle failure modes include concrete fracture (breakout, splitting) and fracture of brittle steel elements. The elastic design approach is conservative for ductile failure modes.

Elastic analysis

The action effects on an anchor at the concrete surface may be derived from the action effects on the fixture using an elastic analysis. The use ofthis method is compulsory when the expected mode offailure of the anchorage is brittle. In this section, anchorages with post-installed anchors and cast-in headed anchors are considered. For the determination of action effects on anchor channels Part V ofthis Design Guide applies.

4.3.1.1 Tests have shown that the design method given in this Design Guide yields satisfactory strength predictions for large (6 x 6) anchor groups subjected to concentric tension loading that exhibited concrete cone failure. In these tests, the fixture was sufficiently stiff to ensure equal distribution of the tension force to all anchors.

Scope ofthe design method

For anchors loaded in tension, the design concept described in this Design Guide applies to any number of anchors in a group provided that the fixture is sufficiently stiff to ensure that the distribution of loads to the anchors is in conformity with the theory of elasticity (e.g., equal axial tension to all anchors, when a cOl)centric tension load is applied to the anchorage). For the design of anchors loaded in shear, the number of anchors in a group that may be considered as effective in resisting the shear load should be limited depending on considerations of hole clearance and edge distance. Anchor configurations as shown in Figure 4.3-1 and loaded in tension, shear or in combined tension and shear are covered by this Design Guide.


55


56 A distinction is made between anchors installed in fixtures with and without hole clearance. Hole clearances need not be considered in the design in the following cases: bolts that are welded to or threaded into the fixture, or assemblies in which the annular gap between the anchor and the fixture is filled with a mortar of appropriate flowability and compression strength or eliminated by other suitable means.

For shear loading, the pennissible anchor configurations given in Figure 4.3-la are intended to prevent excessive shear lag (non-uniform shear distribution in the direction of the shear load over the length of the connection).

D· ..

Anchor \

a)

m

~ (baseplate) """t:::.J

Fixture

I-l ~

D·· · DD

The limitations regarding configurations of anchors with hole clearance close to an edge (Figure 4.3-1 b) are based on the following considerations: at the onset of concrete failure, the displacement of each individual anchor within a group may be equal to or smaller than its hole clearance. This situation may lead to high uncertainties in the load distribution in groups with more than one anchor row perpendicular to the edge and more than two anchors per row located close to a free edge. Such configurations with more than two anchors in a row close to an edge or more than two anchor rows perpendicular to the edge have not been sufficiently investigated.

•• ••

• •

• • • • • • • • •

• • •••

No hole clearance: all edge distances Normal hole clearance: c!~ max (10ho!. aDd""",)

b)

Fixture (baseplate)

Thus, in case of anchor groups exceeding the limits indicated in Figure 4.3-1, the provisions of this Design Guide should be applied with engineering judgement.

t E.l-l

~

B

,Anchor

,

•• '.CJ-. GJ ...._-..

•

~

-~

c! < max (1 Oh~f' 60d nom )

Concrete edge Normal hole clearance: cj < max (10h Q1 • 60dnom )

Figure 4.3-1: Anchor configurations under tension, shear or combined tension and shear loading covered by this Design Guide: a) anchorages without hole clearance for all edge distances and anchorages with normal hole clearance (ac/~ae/,1 with ae/,J according to Table 4.3-1)) situatedfar from edges (CI ?max(10h'fi 60dnn"J) (coriflgurations valid also for CI ? cm;" if only tension loads are acting); b) anchorages with normal hole clearance (according to Table 4.3-1) having an edge distance CI < max(10h'fi 60dnm,J

4.3.1.2 The assumption of a linear distribution of strains across the fixture (Figure 4.3-2a) is analogous to the Bernoulli hypothesis of plane sections used in the analysis of reinforced concrete members. This assumption is valid only if the flexural rigidity of the fixture is large compared to the axial stiffness of the anchors so that at the design load the deformation of the fixture in the vicinity of the tension-loaded anchors is small compared to the anchor axial displacement. This requires, among other considerations, that the fixture remains elastic under design actions. In general, the approach described above calls for an iterative solution procedure to calculate the position of the neutral axis and the tension forces on the anchors. To avoid this iterative solution procedure it might be assumed that the resultant compression force is located at the toe of the attachment (see Figure 4.3-2b). For further discussion see Cook, Klingner (1992).

As a simplification, the modulus of elasticity of concrete may be assumed as Ee = 30,000 MPa.

Tension loads on anchors

The design value of tension loads on each anchor can be calculated from the design values of normal forces and bending moments acting on the fixture based on the assumption that the distribution of tensile strains across the fixture is linear. Furthermore, a linear relationship between strains and stresses is assumed. If the fixture bears on the concrete (directly or through a grout layer), the compression forces are transmitted to the concrete by the fixture. The distribution of tension loads to the anchors may be calculated by applying the method of reinforced concrete sections using the following assumptions: The axial stiffness E,A, of all anchors is equal. The cross-sectional area of the anchor, A" may, in general, be calculated using the nominal diameter of the anchor, d,wm. E, is the modulus of elasticity of the anchor material. For threaded anchors the stressed cross section according to ISO 898-1 (ISO, 2009-1) should be taken. The modulus of elasticity of the concrete may be taken from relevant Standards .... In general, anchors do not resist compressive forces.


57

58


N"

N"

M'Yf-

M'Yf-

II

II

II TSd3

~

T",

TSOl

=0

C"

j ICsd

T,",

TSdl

I m, ---

""'lJ

=0

I

I

£"',

TSd3

'

£",Ukl

£,

ft a) Figure 4.3-2:

b)

Examples of elastic load distribution for an anchorage with a rigid fIXture loaded by a bending moment and a normal force: a) distribution according to theory of elasticity; b) simplifYing assumption of compression reaction at toe of column

Fixtures that exhibit large defonnations under the design load may also be used, provided that the resultant non-linear load distribution (Figure 4.3-3a) and associated potential prying forces are taken into account (Figure 4.3-3a, b). In this Design Guide no guidance is given regarding the determination of the design actions on anchors in these applications.

"

"

-M

Prying

forc~

I

N", Sdrp

Prying force P

NSd/2+P

I IIN",'2+p c

~

T",

I I

r~!~d

I

T SdJ=O

TSd2

j;

P

I

~' £Sdl~1 ,

N",

I

-.;;:::::::] £ c

a) Figure 4.3-3:

b)

Examples of anchorages with flexible attachment: a) column baseplate subjected to a moment; b) hanger connection

For anchor groups loaded in tension and/or a bending moment, only the anchors loaded in tension are included in the group resistance. In the example in Figure 4.3-4b, only the anchors to the right of the neutral axis are considered. The anchors located in the zone of compression are neglected.

For anchor groups with different levels of tension forces NSdJ acting on the individual anchors of a group, the eccentricity eN of the tension force Nffd of the group of tensioned anchors with respect to their centre of gravity should be calculated.

An eccentricity due to non-equal tension forces in the individual anchors affects the concrete cone resistance of the anchor group. If the tension-loaded anchors do not fonn a rectangular pattern (example see Figure 4.3-4c) the group of tensioned anchors may be reorganised into a rectangular group to calculate the centre of gravity, which is point 'A' in Figure 4.3-4c. This simplification will lead to a larger eccentricity and a reduced concrete resistance.


59

Part I: 4 Determination of action iffects

60 N'

eNl

~--~--~--1 Nl Nl (' .N~1 •

5,

I

N~

i

51

~

•

eN1 N~=LNsd,1

NSd,l;::N~

a)

Ngd NSd ,2

NSd.1

N§d=l:Nsd,i NSd,1=N~d

U e N1

Compressed area

b) •

f-0..:£:'--~i~---1\

I

X

-

iJ

j

Tensile anchors

$ Centre of gravity of tensile anchors

t;}

X Point of resulting tensile force of tensile anchors

c)

Figure 4.3-4:

Examples of anchorages subjected to an eccentric tensile load: a) eccentricity along one axis - all anchors in tension; b) eccentricity along one axis only some of the anchors of the group are in tension; c) eccentricity along two axes - unsymmetrical tension loading of the anchors

4.3.1.3

Shear loads on anchors

4.3 .1.3.1 Distribution of shear loads - general method

') rf-"'

• V? I • •

T Iv,,"

s

T--fT

•

I/(>~I "TSd /

v" 4

~

Figure 4.3-5:

Vs,

•

•

Figure 4.3-6:

Examples of distribution of applied shear load and torsional moment acting on the fixture to anchors of a group if hole clearances have not been provided in the fixture or if the hole clearance is small (ael:S ael.1 with ael.l according to Table 4.3-1), and the resistance to edge failure need not to be verified (because the edge distance is large)

. [TI VSd.l.

•

•

TSd

+

---

•

•

.VSdJI •

+

= VSd '8v

181 ~

Resolution of a shear force on the fixture acting inclined to the edge and with an eccentricity in respect of the centre of gravity of the anchor into orthogonal shear loads and a torsional moment

The anchors participating in the shear resistance in a group will depend on a number of factors such as hole clearance, edge distance of the anchors, orientation of the applied forces and the assumed location of concrete fracture pattern in relation to anchor positions (i.e., when the anchors are located within the volume of the concrete that is assumed to have failed).


(1) General Determine the shear forces on the anchors of the group from the shear forces and/or torsional moments acting on the fixture in accordance with the theory of elasticity assuming equal stiffness for all anchors of a group that participate in the resistance of shear forces. When distributing the shear forces to anchors, equilibrium should be satisfied (examples see Figure 4.3-5). Where the assumption of participating anchors results in an eccentricity of the shear component relative to the centre of gravity of the participating anchors, include the corresponding eccentric torsional moment in the distribution of loads (examples see Figure 4.3-l6a and Figure 4.3-25).

If the shear load acting on the fixture is inclined to the edge and/or with an eccentricity in respect to the centre of gravity of the anchors, in general the determination of the distribution of the shear loads to the anchors of a group is done for each of the orthogonal shear components acting centrically on the fixture, i.e., perpendicular (VSd •L ) and parallel (VSd, II) to the edge, and a torsional moment (Tsd) (where applicable) (see Figure 4.3-6). Subsequently, the calculated anchor shear forces are added vectorially.

For determination of the anchors that participate in reslstmg shear forces the provisions (2) to (5) are valid. Furthermore, for the verification of steel failure, pryout failure and concrete edge failure the provisions in Section 4.3.1.3.2 should be observed.

61

62


For anchorages without hole clearance close to an edge (Figure 4.3-7) the shear force is initially distributed to all anchors. When the distance between the front and back anchor is large (s, > l.Oc),)), a crack occurs first at the front anchor closest to the edge (see Figure 4.3-7a). Often in the ultimate limit state this crack is taken as the failure crack. This assumption leads to a conservative estimation of the resistance with respect to concrete edge failure, but is conversely associated with the maximum resistance with respect to steel and pryout failure (greatest number of anchors active).

(2) Determination of anchors participating in shear for anchorages without hole clearance All anchors located in the line of the assumed failure plane and further away from the edge are assumed to resist shear forces. Examples are shown in Figure 4.3-5 for anchorages, where resistance to edge failure need not to be evaluated (because the edge distance is large) and in Figure 4.3-7 for a shear force acting perpendicular to the edge.

The maximum resistance in the ultimate limit state with respect to concrete edge failure is reached after a redistribution of the shear loads from the front anchors to the back anchors and the formation of a failure crack originating at the back anchors (Figure 4.3-7b). However, in general the front anchors do not take up a significant part of the shear load acting on the fixture due to the prior formation of the failure crack and in this case the resistance with respect to steel and pryout failure should be calculated with the back anchors only. The failure of the front anchor may have consequences for the structural member from either a strength or serviceability standpoint. Therefore, in general, the shear resistance associated with the concrete edge breakout strength of the back anchors in a near-edge anchor group should be accompanied by a serviceability check for front anchor edge breakout (see Section 6.2). For cases where combined tension and shear loading is present and where the shear resistance is assumed to be provided entirely by the back anchors, see Section 10.3.2.

r-----------------

,

' ,,,

!,, ,,

, ,,

'L____

51}

,

-----, r-----------------------------------, d

!'' ,

iC12=C12+S1 •

I'

' , ,' ,: ~C~1~1~~==~~---------' I

,,, ,, ,1 : ' I

.Q

/, ..

"

I

• Loaded anchor

o Unloaded anchor a)

Figure 4.3-7:

b)

Example of distribution of applied shear VSd to anchors in a group for verification ofsteel, pryout and edge breakout failure, anchorage without hole clearance: a) edge breakout failure assumed to initiate at front anchor; b) edge breakout failure assumed to initiate at back anchor (front anchor assumed to have failed)

The described anchor shear load redistribution is shown in the examples in Figure 4.3-8 to Figure 4.3-10, in which it is assumed that only the diameter of the anchor is varied. In this case, the steel resistance varies significantly whereby the concrete edge breakout and pryout resistances are nearly constant. In Figure 4.3-8 it is assumed that the steel and pryout resistance of the back anchor is higher than the concrete edge resistance of this anchor. In Figure 4.3-9 failure is caused by steel failure of the back anchor because of the assumed higher concrete edge resistance. In Figure 4.3-10 the assumed low steel resistance could theoretically lead to progressive steel failure after the formation of an edge breakout at the front anchor without additional load resistance.


63

64


• Loaded anchor

~

.3

o Unloaded anchor

Resistance to pryout

S

~a~u!eJ~~ ~n9!?~L -

~

Resistance to steel

c

i

-1

,-v~~

,,r

failure (two anchors)

v~

•

IV•J/2

cut

,G.,

''''-

/'"

Failure state I

Failure stale II

,

L __ ~e~~tallgljO.Jl.D'Quj @i~f!! ...b1!c!,!!n_cilor. _________________ __ ,. Resistance to steel failure. back anchor

..

r ___ J!~1.s!a_n.f~!('- C!.o_n.f[.ellt~..931J!!~ajl.9ylJ. Q~c~_a.!l~t:!.ol _ _______ _

,

Reslsl3ncc 10 concrele

edge breakout, front ~E£~O!

I

_________ _

......-:==

,, ,, I

,.

Failure slate I

Figure 4.3-8:

~ ~

--------11>

,,, ,

Failure slate II

t

Example of an anchor group loaded in shear near a free edge, transition of failure states from concrete edge breakout at front anchor to concrete edge breakout at back anchor

• Loaded anchor

I Resistance 10 pryout

o Unloaded anchor

~ . _f~il~r: ~~ ~~c~o~sl __ 1

~

"T cut

Resist..1nce 10 steel failure (two anchors)

Q

Steel failure of back anchor

,G.,

~,/

Failure stale I

"' ...,

failuro state II

~ __~e~is..ta~l~ ~o_P~u~ ~i~~:..b~C! ~r:.~o!. _________________ __ •

,,

____'3.~slsl'!.n~!~ <:'O.!lE~e!~ ~~g~_b.!~~p~~ ~~~k3l..!1~q:__________ _________ •

,i,-__"R",",,;,""~,,"~m"'~I'O,;,,~,II~"'~.~>b~'O"~'"'oh~OC'__________________________•

Resistance to concrete: edge breakout, front : anchor I ----------------

6\1~

\f\~ \OZ!

\f\C(c3.S

Failure state I

Figure 4.3-9:

,/

Failure stale II

Example of an anchor group loaded in shear near a free edge, transition of failure states from concrete edge breakout at front anchor to steel failure of back anchor


65

66

Part 1: 4 Determination of action effects • Loaded anchor

~ ~ Resistance 10 :ors) ______ ~>d12 ) _f~I~!(~~~____ 1- : I.

o Unloaded anchor

out

"0

-"l

&

i I IVJI2

"

,j -'~ ,

C 1•1

~,"

,

Failure stale I

""-

Failure statc II

,

l_l!e~i~..ta!1~oJo"'p!Y.QuJ

~~I~i~~(~~ ~On~~e:~)

Stool failure of back

anchor

,Q,

I

I

[J V~

(iliLu& ....bi!C.511llctlO[ ___________ __ ",

r- B.9!~!!l!!!?! l.OJ:9!!q.!lLe_e.9.9.!l.pr.ejl~QlJJ,-~as1511!!
Resistance to concrete edgo breakout, front anchor

-------------------------~

II

Resistance to stoel failure, back anchor

\O,..J,p ~\f>f/J

,
Failure St.ltO I & II

Figure 4.3-10: Example of an anchor group loaded in shear near afree edge, progressive failure of concrete edge breakout at front anchor followed by steel failure of back anchor However, in the case of anchorages with an anchor spacing in the direction perpendicular to the edge that is small relative to the edge distance of the front anchors (St / Ct,t < 1.0), the formation of a crack originating from the front anchors is suppressed by the compression stress field originating from the back anchors (Anderson, Meinheit, 2005, 2007; Hofmann, 2005; Periskic, 2006 and Grosser, Cook, 2009) and, at failure, the front anchors still resist a fraction of the total shear force, Note that the behaviour of groups under shear load inclined in respect to the edge has not been investigated, Therefore, for reasons of simplicity this behaviour as it applies to the steel and pryout capacity is neglected in this Design Guide, Figure 4.3-11 shows an anchorage close to a comer for which both edges should be verified, When calculating the resistance for concrete failure of the bottom edge (shear load perpendicular to the edge) and of the right edge (shear load parallel to the edge), the same number of anchors for transmitting the shear load should be assumed for each considered case,

v" 3"• )

•

a)

j

~ICl" l--c,+ v"

_~IF'

C z.,

-----.J~J'dc" I---cf,

v"

v"

~}, I---cf, •

o Figure 4,3-11:

I

2

l--c,+

c)

!

v'"

2 b)

\

--~I-c-',(

~lc" l---c-I,

Loaded anchor Unloaded anchor

Anchorage without hole clearance in a corner for which verification of both edges is required: a) Shear load is assumed to be transferred by all anchors; b) front anchor is assumed to have failed; c) shear load is assumed to be transferred by back anchor only

For anchor groups loaded in shear it is generally preferable to ensure that no annular gap exists between the anchors and the fixture in order to promote a uniform load distribution to the anchors, This may be accomplished as described in Section 4.3,\.\. In many cases, however, it is not practical or possible to provide for zero hole clearance,


(3) Determination of anchors participating in shear for anchorages with normal hole clearance a) In this Design Guide normal hole clearances are defined in Table 4.3-1.

67

68


Table 4.3-1: Anchor diameter cf} or dnomb}[mm] Diameter df,l of 2 clearance hole in fixture [mm]

Normal hole clearance ael.l (see definition of hole clearance, ael, in Figure 4.3-12) 6

8

W Q

~

ffi

ffi

~

II

~

~

~

>~

7

9

Q

M

ffi

ffi

~

II

~

~

~

B

l.lcf}or 1.1dllom b)

2

2

2

2

2

2

2

2

3

3

O.ld"m b}

O.lcf}or

3 Clearance ael, I [mm] oj

acl=df-d

acl

= df - dnom

b}

Bolt projects through fixture (Figure 4.3-12a) Bolt and sleeve project through fixture (Figure 4.3-12b)

b)

a)

Figure 4.3-12: Definition of hole clearance, ael, of anchors: a) bolt projects through fIXture; b) sleeve and bolt project through fixture

For hole clearances ael:5 ael.l (with ael.l = df,l - d or ael.l = df,l - d,wm) the requirement for "normal hole clearance" as defined in Table 4.3-1 is met. The basis for determining the distribution of shear loads in anchor groups provided with normal hole clearance is the degree of anchor displacement associated with concrete edge failure relative to the hole clearance in the fixture. Test results show that with a large edge distance c ~ lOh'i and c ~ 60d (if bolt projects through the fixture) or c ~ 60d",m (if sleeve projects through the fixture) shear displacements at failure are much larger than the normal hole clearances according to Table 4.3-1. Therefore, all anchors take up shear loads.

b) Anchorages with a large edge distance in all directions: c ~ 10h'iand c ~ 60d (if bolt projects through the fixture) or c ~ 60d",m (if sleeve projects through the fixture).

For cases involving small edge distances, the displacements associated with concrete edge failure resulting from loading perpendicular to the edge may be smaller than the normal hole clearances according to Table 4.3-1 (see Figure 4.3-13a).

c) Anchorages close to an edge: Cl < max(lOh'i' 60d) (if bolt projects through the fixture) or Cl < max(10h'i' 60d",m) (if sleeve projects through the fixture) loaded by a shear force perpendicular to the edge.

Therefore, for anchor groups in fixtures provided with normal hole clearances and loaded by a shear force perpendicular to an edge, often only the anchors closest to the edge are assumed to carry shear loads, when checking the resistance against concrete edge failure (Figure 4.3-14a). This

The determination of the anchors that resist shear loads depends on the failure mode:

approach is conservative in cases, where the anchor displacement may be estimated to be much larger than the provided hole clearance. When checking the resistance against steel and pryout failure, anchor shear displacements may be expected to be much larger than the allowable hole clearances according to Table 4.3-1. Therefore, all anchors may be assumed to resist shear forces (Figure 4.3-14b). Steel or pryout failure will govern the design for relatively large edge distances only.

All anchors are assumed to resist shear loads. Examples are shown in Figure 4.3-5.

Concrete edge failure: only the anchors generating the assumed failure plane should be assumed to take up shear forces (see Figure 4.3-14a,c). Steel and pryout failure: the anchors located in the assumed failure plane and further away from the edge may be assumed to take up shear loads (Figure 4.3-14b,c).

As with anchorages without hole clearances, the maximum resistance in respect to concrete edge failure is reached when the load is redistributed to the back anchor and the failure crack is generated from this anchor (crack 2 in Figure 4.3-14c). Because the front anchor has lost its resistance, only the back anchor should be taken into account, when calculating the resistance against concrete edge-, steel- and pryout failure. However, according to results oftests described in Grosser, Cook (2009) for anchorages with a small edge distance and a ratio Sl / Cl.l :5 1 the concrete edge failure load of the back anchor(s) may be negatively influenced (up to 20%) by the crack generated at the front anchor(s). Sd 1 •

V

~

VSd ,lI

cI~

cJZS=Vu,1I

~

~

Vu,l

I

?

k

-~

al:I,1 ;?!Ou,l

8 cl ,1
'j

~

Ou.u

OU.l

a)

b)

Figure 4.3-13: Relative anchor displacements associated with shear loading perpendicular and parallel to the edge


69

70


" m -

r----------------------,

, ,r----------------------, , ,

"~ ,I

I

I

I

I

, ,

:: I

.

5"

I

, ,

Cl1

VSd

~

I,

•

VSd 2

_

c1.1

I

~

~

r----------------------,

I~ crack 2

/' crack 1... 1~! " ...

• Loaded anchor o Unloaded anchor

, .,

C12=C 11 1+ 51

.

"

c) Figure 4.3-14: Example of distribution of applied shear load VSd to anchors in a group with normal hole clearance (ael:S; ael.J: a) verification for edge breakout failure when edge breakout is assumed to initiate at the front anchor; b) verification for steel and pryout failure when edge breakout is assumed to initiate at the front anchor; c) verification for steel, pryout and edge breakout failure when edge breakout is assumed to initiate at the back anchor Under otherwise constant conditions, the concrete edge failure load of anchorages loaded in shear parallel to the edge is about two to three times the value valid for anchorages loaded in shear perpendicular to the edge. As a consequence, the displacements at failure are significantly larger compared to loading perpendicular to the edge (increased resistance = increased displacement at failure). In general, the displacements at failure are larger than the allowable hole clearance according to Table 4.3-1 (see Figure 4.3-13b). For this reason it is assumed that all anchors resist shear forces. The influence of the possible uneven distribution of the shear load acting on the fixture to the anchors is taken into account in the resistance model.

d) Anchorages close to an edge: Cl < max(IOh,[. 60d) (if bolt projects through the fixture) or Cl < max(10h,[, 60dnom ) (if sleeve projects through the fixture) loaded in shear parallel to the edge or by a torsional moment: All anchors located in the line of the assumed failure plane and further away from the edge are assumed to resist shear forces (see examples in Figure 4.3-15). Figure 4.3-16 shows cases, where the failure crack is assumed to occur at the back anchors.

Vs ,

4"

-+ ~

1--

5,

TSd 5

-

r

.r5,~·

a)

b) V --"T-

VSd ,
Sd.8'lcllor

'.

y. Uso

-h

-5, I

C1'1~ j

Sd

cL2~iL

Cl.1~

5,

T

1:

,r

5,

A

~ I VSd,
I

C1.1

5,

c)


TSd

ijS;"

~~

>

, /, /

B----e.

5,

I

-....,"

Ie,.,

C l ,1

TSd VSd,ollchor

I

2

2

2·"SI +s,

d)

Figure 4.3-15: Distribution of shear forces for anchorages with no hole clearance or normal hole clearance (a,,:S; ael.J: a) shear load parallel to the edge, concrete edge failure assumed to originate at the front anchors; b) torsional moment on a group of two anchors; c) torsional moment on a group offour anchors, edge failure assumed to originate at the front anchors; d) torsional moment on a group offour anchors, edge failure assumed to originate at the back anchors and no torsional restraint


71


72

When a shear load acting on the fixture parallel or inclined to the edge is distributed to the back anchors, a torsional secondary moment is generated. If the fixture is not restrained (e.g., in case of a cantilever without connection to another sufficiently stiff strnctural element) this torsional moment must be resisted by the back anchors (see Figure 4.3-16a). In the case of an anchorage with two anchors oriented perpendicular to the edge, the loss of the front anchor leads to the failure of the anchorage. However, with a group of four anchors the shear resistance might be increased due to redistribution of the shear forces to the back anchors. If the torsional secondary moment is taken up by another strnctural element (e.g., by a floor or a cross beam) the back anchors are loaded by the shear load only (Figure 4.3-16b). When designing the element that is attached to the fixture and the element(s) that takes up the torsion moment, the torsional secondary moment must be taken into account.

v~l

v~1 v" -2- 1 •

•

0

I

5

l' -. tJi l' v"2

•

,I

I

5,

I

I

Rotation unrestrained

a)

'I

v,,1

V

"

:01 1,--4Q} I

<

I

L..J

Rotation restrained by decking

b) •

Loaded anchor

o

Unloaded anchor

Figure 4.3-16: Anchor group close to an edge loaded by a shear load parallel to the edge (after failure of the front anchors): a) without torsional restraint; torsional moment TSd = VSd 'sl2 is taken up by the back anchors; b) with torsional restraint, torsional moment is taken up by the beam attached to the fixture in connection with another structural element(s) restraining the beam (e.g., floor) (in a) and b) the bending moment on the anchorage resulting from the load shown in the 3D-sketches is disregarded)


73

74

Part I: 4 Determination of action effects When a torsional moment acts on the fixture of a group of four anchors, in the extreme case only the two front anchors may resist shear forces (see Figure 4.3-17). However, in practice the position of the anchor as shown in Figure 4.3-17 is considered as highly unlikely. Therefore, in general it may be assumed that all anchors contribute to resist the torsional moment (see Figure 4.3-15c). ,---------------------------------------------------~

• Loaded anchor

ix

o Unloaded anchor

0

6)

max. possible gap based on specified hole

~

clearance

Figure 4.3-17: Possible distribution of torsional moment to a group of four anchors with urifavourable anchor positions relative to holes in baseplate for evaluation of concrete edge breakout (normal hole clearances (a,,';; a".J exaggeratedfor clarity) • Loaded anchor o Unloaded anchor

+V

Sd

al· IT5J o

0

I . I

•

a)

•

t ~ ~

\k 2

(4) Determination of anchors participating in shear for anchorages with a large hole clearance (a" > a",1 according to Table 4.3-1) Only the most unfavourable anchors (having the highest ratio between design actions and design resistance due to combined loading and/or positioning) should be assumed to carry shear loads. Examples are shown in Figure 4.3-18 and Figure 4.3-19.

'rj

b)

c)

Figure 4.3-18: Examples of distribution of shear load and torsional moment to anchors of a group (where concrete edge failure need not to be verified because the edge distance is large) in fixtures provided with large hole clearance (a" > a",1 according to Table 4.3-1)

Figure 4.3-19 shows an anchorage with four anchors with large hole clearance close to an edge loaded by a bending moment and a shear load towards the edge. The bending moment causes tension forces in the back anchors. For the verification of steel and pryout resistance it should be assumed that the shear force is taken up by the back anchors (unfavourable anchor loading), while for the verification of concrete edge failure the front anchors should be assumed to take up the shear force (unfavourable anchor positioning). MSdr\ VSd

r"'Il

'If'" "

a)

b)

fI.:l

~-

v"

'2 VSd 2

c)

00 °

MSd ~Sd

•

°

Vsd' 2

• Anchor loaded in shear o Anchor unloaded in shear

Figure 4.3-19: Example of an anchorage close to an edge with large hole clearance (a" > a",1 according to Table 4.3-1): a) loading pattern (the two back anchors are loaded by a tension force); b) distribution of shear forces for verification of steel failure; c) distribution of shear forces for verification of concrete edge failure fib Bulletin 58: Design of anchorages in concrete

75

Part I: 4 Determination of action e.!Jects

76 (5) Determination of anchors that resist shear forces for anchorages with slotted holes in the fixture oriented parallel to the direction of the shear load


VSd VSd

I

""2

The anchors not located in slotted holes are assumed to take up shear loads. Slotted holes can be used to relieve anchors close to an edge which may otherwise cause a premature edge failure (Figure 4.3-20). In this case no check in the serviceability limit state is necessary.

VSd

""2

§ slotted or oversized hole

Figure 4.3-20: Example for the use of oversized or slotted holes to prevent participation of near edge anchors in resisting shear forces In Table 4.3-2 through Table 4.3-4 examples are given for the distribution of concentrically applied shear loads to a far- and near-edge orthogonal sixanchor array (anchorage with no hole clearance) or orthogonal four-anchor array (anchorage with normal hole clearance (ad::; ad.1) close to an edge). Table 4.3-2 addresses shear loads acting perpendicular to the edge, Table 4.3-3 shear loads acting parallel to the edge on an anchor group without torsional restraint, and Table 4.3-4 handles torsional moments. Note that for checking concrete edge failure the provisions in Section 4.3.1.3.2b) should additionally be taken into account in Table 4.3-3 and Table 4.3-4.

Table 4.3-2:

Edge

distance

Anchors resisting shear forces in the case of an applied shear load acting perpendicular to the edge. Note, that for anchors with normal hole clearance only anchorages with two anchor rows perpendicular to the edge are covered by this Design Guide (see Figure 4.3-1)

Considered failure plane

Sufficient

to not

require verification of concrete

Npt applicable

edge breakout

Steel and pryout failure.

No and ncnnal hole

Concrete edge failure. No hole

clearance (ael S DcU)

clearance

j

j

•j

•j VSd

•j •

•j •

6

Concrete edge failure. Normal hole clearance (ad S ad.l)

Not applicable

Not applicable

resistance 0

0

o

0

VStc 1,J:::Concrete

edge breakOut resistance

applicable

• I •

1

".'-<>.

,

,

• * VSd ' -6

• I •,

·

.l.

I;'

,

, •

. ~

,

....

VSd

-

Not covered

6

rEi Ifl tJ tJ ra! •j

VSd

C1.2

0

0

o

0

/"

•

.1

0

0

o

0

o

0

•j

VSd

~

/"

f V"

0

o~ ,;r:::

o

0

1.2

C 1.3

It:1t,, 2

0

0"2

• Loaded anchor

o Unloaded anchor


77

78

Part 1: 4 Determination of action effects

Table 4.3-3: Anchor resisting shear forces in the case of an applied shear load acting parallel to the edge (figure valid for case without rotational restraint). Note, that for anchors with normal hole clearance only anchorages with two anchor rows perpendicular to the edge are covered by this Design Guide (see Figure 4.3-1) Edge distance


Steel and pryout failure. No and nonnal hole clearance

Concrete edge failure. No or nonnal hole clearance (ac/S ael.1)

(ae/Sac/,v

Sufficient to not require verification of

EJ' --

Not applicable

concrete edge

--

breakout resistance

a

1r

VSd

c"G

-f--<>

00 ~

H

s,.,[ ...........

VSd

Concrete edge breakout resistance

Not applicable

6

c,r~

/0'

VSd

4"'

o~

~hear due to torsion: (VSd' SI,2/2 )/( 2'~S~2 + si )

applicable

"

rft0 "'1-<>

C 1,3

o

-

H

/:

VSd

:~

Shear due to torsion: Vsd' S1,2/ S2 • Loaded anchor o Unloaded anchor

Table 4.3-4: Anchors resisting shear forces in the case of an applied torsional moment. Note, that for anchors with normal hole clearance only anchorages with two anchor rows perpendicular to the edge are covered by this Design Guide (see Figure 4.3-1) Edge distance


Sufficient to not require verification of concrete edge breakout resistanDe

Not applicable

Steel and pryout failure. No and nonnal hole clearance (ael::; ael.v

a "

No or nonnal hole clearance (ael::; ael.l)

Not applicable

V"""t /

o

TSd 0

0+0.., f;'\

cuG Concrete edge breakout resistance applicable

Concrete edge failure.

~

/' C 1.3

....

•

t I)

./

fi0

C1{~

,t

of;'\

f;'\ ofo

0 0"" sd

,t

/0

.... 'o~

I)

~


For concrete edge failure further distribution of shear loads according to FIgure 4.3-27


79


80 4.3,1.3.2 General aspects for verification of failure modes

, •

5,

, ~ •

VSd,2= VSd/2- MSd/s\

(1)

Determine the highest loaded anchor in the group of anchors that are assumed to resist shear.

I ", ••

I

VSd,1 = VSd/2+ MSd/Sj

VS
2'lS<:I,1

(2)

b)

Verification of pryout failure Determine the resultant shear load acting on the anchors that are assumed to resist shear, Where applicable, determine the eccentricity of the resultant shear force with respect to the centre of gravity of the anchors resisting shear, An example is shown in Figure 4.3-21.

e,,= MSd I VSd

a)

Verification of steel failure

c)

Figure 4.3-21: Example of the resolution of unequal shear forces on anchors in the group into an eccentric shear force: a) forces acting on fixture; b) determination of shear forces on anchors; c) resolution of anchor shear forces into an eccentric shear force If an anchorage is loaded by a combination of a shear force perpendicUlar and/or parallel to the edge and a torsion moment, the shear loads on the anchors are calculated for each individual load case as explained in Section 4,3,1.3,1 (I) to (5) and then superimposed, This approach has been chosen for reason of simplicity even if it may not be considered as fully consistent in all cases,

(3)

Verification of concrete edge failure a) Determine the resultant shear load of the anchors located in the assumed line of failure plane according to Section 4.3,1.3,1 (I) to (5) and taking into account b) and c) below, Examples are shown in Figure 4.3-22 to Figure 4.3-27,

1VSd

+ rD

o

2! ! 2 VSd

5,

.I

VSd

----+

y

t

J

5,

s[ 1-+ ~IVSd

a)

VSd

~-

~

j.

J

5,

VSdO

o ----+

o

+ ..

VSd

...·1-2

b)

{ I';~;· -~uU 4" <;>

VSdl

•

.I

•

5,

d,1I '" \'sd sine\.

2~_

ir-

V

--~

<;>

<;>

VSd'.L~VSd IVSd,l1 ".

..

9

...

2

---.:---

J •

o o

Loaded anchor Unloaded anchor

Anchor load neglecled

c)

Figure 4,3-22: Examples of distribution ofshear forces on anchors of a group with normal hole clearance (ad';; ad, I, with ad.! according to Table 4.3-1) for verification of concrete edge failure assumed to be generated at the front anchors: a) shear load perpendicular to the edge; b) shear load parallel to the edge; c) shear load acting inclined to the edge


81

82


Various investigations (Mallee, 2001, 2002 and Hofmann, 2005) have shown that in general shear components acting perpendicular and away from an edge do not significantly influence the concrete edge breakout resistance of the group. Therefore, these components may be neglected in the assessment of the concrete breakout resistance. If in the case of shear loads with opposed directions (see Figure 4.3-23c), the ratio between spacing and edge distance of the anchors resisting the shear force is small and the ratio between the characteristic resistances for pryout and concrete edge failure is high, the above approach may be unconservative up to 20% as reported in Grosser (2008). Further research is required to provide specific guidance for these cases.

b) Components of the resultant shear forces on anchors acting perpendicular away from the edge may be neglected. Examples are shown in Figure 4.3-23 through Figure 4.3-25. c) Where applicable, determine the eccentricity of the resultant shear force with respect to the centre of gravity of the anchors resisting shear and the angle av (the angle between the resultant shear force on the anchors and a line perpendicular to the edge). Examples are given in Figure 4.3-21, Figure 4.3-22c and Figure 4.3-24 through Figure 4.3-27.

Note that the verification of steel and pryout failure should be performed with all loads acting on the anchors (omission of shear component acting perpendicular and away from the edge is not permitted).

s,

C1

I VSd I ,, 2

t

,

-r

!

!

'

No proof for concrete edge failure needed, components directed away from the edge

IVSd 2

I

VSd

a)

Action

e,

"

!

,;

II

VSd,1I

tt ~. "_Ii.

V~d

Components neglected, because directed away from the edge

I

-~:'~~~---

Load on anchor group for calculation

c,

b) This load is neglected for the analysis

~

I T" I

e,r--P7}OJ

e,dtJJ • Loaded anchor '" Anchor loads neglected for the analysis

c) Figure 4.3-23: Examples of anchor groups at the edge loaded by a shear force or torsional moment for verification of concrete edge failure: a) group of two anchors at an edge loaded by VSd directed away from the edge; b) group of two anchors at an edge loaded by VSd with an angle 90° < a', < 180°; c) group of two anchors at the edge loaded by a torsional moment


83


. rE£lj , TSd

Action

c

s,

I·

r:9

.~

c,

f

Load on anchor group

VSd

--.:.

•

J Load on each anchor

84

c,l

s,

Neglected, because sum of components directed away from the edge

,I

-I

11

l-I· 52

'I

e,


c,

J

j.

s,

a)

a,

Action

c,

I

,

Load on each anchor

I· ~

c,

J Load on anchor group

52

Considered, because sum of components directed toward the edge

s, of

-J

c, .

I·

52

of

t"vi' I /,VSd


c,

lEg r

S2

J b)

Figure 4.3-24: Examples of anchor groups at the edge loaded by a shear force and a torsional moment for verification of concrete edge failure: a) shear component due to torsional moment larger than component of shear force; b) shear component due to torsional moment smaller than component ofshear force


85

Part J: 4 Determination of action effects

r

s

v,

v,

.:ia,~

VSd,~ 0

0

,l

VSd,l

VSd .1

-

•

86 VSd.1

2~ VSd,1I ~~++ ---z 2

•+vs~'"j ~

0"'-iIi, -r 0

-+-

Ts =VSd,1I2

o

0

VSd

o

u2L

, 2s,

J

S2

MVSd.

a)

S -2' - VSd,lI~

VSd.L

25 2

c)

ev

-2- + VSd,II-2-s, 52 .l

VSd,1I

--

sr

b)

-..

-+-

o

W"':d

VSdU

2

-+-

o

G----<)

J s'T d1)

This load is neglected for the analysis

V

VSd,1I

VS,.l ~r-2 - VSd,11 ~ ___"I 2s, I -+-

o

Sdl 2+VSd ,U.2.L 2s

~~t S,

o

,l

s,

.-,1/) ~ ~ !a

2

-

v

'V/

,(

9

VSd

-+G----<)

J • Loaded anchor o Unloaded anchor

dv Figure 4.3-25: Distribution of an inclined shear load to a group of four anchors with no or normal hole clearance (ael:S; ael,J without torsional restraint for verification of concrete edge breakout failure assumed to be generated at the back anchors: a) inclined shear load acting at centroid of anchor group; b) shear load

.., resolved in a centric shear load and a torsional moment on back anchors; c) resulting shear components applied to back anchors; dd combination of shear components resulting in both anchors loaded in shear towards the edge and resultant shear load on group; dV combination of shear components resulting in only one anchor loaded in shear towards the edge and resultant shear load on group

,

s1[lv~d'"

VSd,l

"'2

"'2

.J ... ... -

8,

a)

• J

2 o

Vs,

ti

-

VSd, II

VSd,1I ...

VSd,1I

I.

.,f

Vs,

av~.

VSd,l

0

b)

2

/'

a\/""u:~

-+0

0

c)

Figure 4.3-26: Example of distribution of shear load to the back anchors of a group with four anchors with no or normal hole clearance (ael:S; ael,J with torsional restraint, Shear load inclined with respect to the edge: a) resolution of load into orthogonal components; b) distribution of load to back anchors assuming edge breakout failure originating at the back anchors; c) resultant shear load on back anchors


87

Part J: 4 Determination ofaction effects

88 Load on these anchors neglected for the analysis

VSd

-$-

VSd

2

.f

s,

=t

Vsd,anchor,ntl

J

V.Sd,anchor

2 1____

Vsd,anchor,l

TSd

2' IT, s +8 2 V 1

=

a)

b)

'r[] ,

j.

VSd

5,

\9 v

\9

J

c)

d) • Loaded anchor (\l Anchor loads neglected

Figure 4.3-27: Distribution of shear load and torsional moment to a group of four anchors with normal hole clearance (ael:S; ael.J, failure is assumed to be initiated at front anchors: a) shear resisted by front anchors, torsional moment by all anchors; b) loads on back anchors neglected; c) load components on front anchors combined; d) orthogonal loads resolved into an inclined load with eccentricity and angle av for assessment of concrete edge breakout resistance With regard to the distribution of a shear load and a torsional moment to the anchors of a group with four anchors with s, » S l (see Figure 4.3-28a) it should be noted, that the shear loads resulting from the torsional moment, VSd.anelw, act almost perpendicular to the concrete edge. In such a situation one

may consider a different distribution of the shear loads resulting from the torsional moment than shown in Figure 4.3-27 by assuming that the back anchors do not contribute to take up the torsional moment. This results in the distribution of shear forces shown in Figure 4.3-28b. Since no research is available regarding this aspect, a specific value for the ratio s, / SJ, which requires a distribution of shear loads according to Figure 4.3-28b cannot be provided and engineering judgement is necessary. Note, that the assumption according to Figure 4.3-28b is conservative. sd,a1 hor

sC

VSd

- 4

a)

-

•

-.-

J

C\d

Tc.9.../

1-1-

•

r )

sC.r~d+ b)

-~

r

S2

S2

I--Ys d 2

~~

---.A.. 52


Figure 4.3-28: Distribution of shear load and torsional moment to a group of four anchors with normal hole clearance (ael:S; ael.J and s,» Sl, failure is assumed to be initiated at front anchors: a) shear resisted by front anchors, torsional moment by all anchors; b) shear and torsional moment resisted by front anchors only


8.9


90 4.3 .1.3.3 Distribution of shear loads - alternative approach (I) For the verification of steel and pryout failure Section 4.3.1.3.1 applies without modifications.

When an anchor is loaded in shear parallel to the edge, concrete edge failure is initiated by the splitting forces perpendicular to the edge. The failure surface is rather similar to the failure surface when the shear load acts perpendicular to the edge (compare Fignre 4.3-29a with Figure 4.3-29b). In an alternative approach (Mallee, Pusill-Wachtsmuth, 2007) a shear load acting parallel to an edge (Figure 4.3-30a) is substituted by a virtual shear load perpendicular to the edge (Fignre 4.3-30b). This virtual shear load is equal to the splitting force shown in (Fignre 4.3-29b). If the load acts under an angle towards the edge (Figure 4.3-3Ia), the component of the shear load acting parallel to the edge is substituted by a virtual shear load, which is added to the component of the shear load acting perpendicular to the edge (Figure 4.3-3Ib). Mallee, Pusill-Wachtsmuth (2007) propose the factor a~ according to Equation (4.3-lb):

a.L =0.4.(1-d/(2c,))

VSd•

.L = a.L . V Sd. II

a.L =ljlf/90'.V' with If/,o'.V according to

Section 10.2.5.1.1f), is assumed as:

a.L = 0.4

anchorage with 3 anchors in the considered failure plane, see Figure 10.2-5

a.L = 0.5

anchorage with 2 anchors in the considered failure plane, see Figure 10.2-5

a ~ = 0.67

single anchor

When using the approach with virtual shear loads acting perpendicular to the edge, the same assumptions for the distribution of shear loads to the anchor of a group should be used as given in Section 4.3.1.3.1. In addition general aspects for verification of failure modes as given in Section 4.3.1.3.2 should be taken into account.

t

(4.3-1)

with:

.L =

virtual design shear force on anchor acting perpendicular to the edge

II

design value of shear force on anchor acting parallel to the edge

VSd .

VSd,

(4.3-1b)

In this Design Guide the factor

VSd ..L

(2) For the verification of concrete edge failure, the shear forces on the shear carrying anchors are calculated according to Section 4.3.1.3.1 (2) to (4). Components of the resultant shear forces on anchors acting perpendicular away from the edge may be neglected (see 4.3.1.3.2(3)b). Components of the shear force acting parallel to the edge are substituted by a shear force acting perpendicular to the edge according to Equation (4.3-1)

(4.3-la)

a~

ljlf/90'.V

If/,o'.v =

factor according to Equation (lO.2-5f) or Equation (10.2-5f,)

The real and virtual shear forces on anchors acting perpendicular to the edge are superimposed. <

<

The calculation of the virtual shear loads is exemplified in Figure 4.3-32 using the example of Fignre 4.3-25 as well as in Figure 4.3-33 using the example of Figure 4.3-26.

Ul·V Sd •1I

VSd •1I

~ b)

a)

Figure 4.3-29: Single anchor at an edge loaded in shear

,•

Ul'V Sd II

. ..

VSd •1I

~

b)

a)

Figure 4.3-30: Substitution of a shear load acting parallel to the edge (a) by a virtual shear load acting perpendicular to the edge (b).

VSd'COS(Iy

~ U,l 'VSd ·sinG. v I

.:-> . f

Uy/VSd

~~.~

V,Sd 'SlIlG.

~,

VSd'cosG. V

v

a)

b)

Figure 4.3-31: Substitution of a shear load acting with an angle o.v to the edge (a) by a superimposition of a real and a virtual shear load acting perpendicular to the edge (b)


91


92

VSd

VSd

•

Sn.

,e

~,.

-+-

VSd,11

•

o

0

I~ aJ. VSd .U

VSd,l

"2

S,

o -Iv"", 2s,

o

~IGI' o

a)

b l)

"VSd,~ 25 s,

0

2

e.

Neglected, because sum of components is directed away from the edge

~ U

NVid II

r"--

/' ,

0---..Q

,

,

e,

<--..!,

Vid

-

-+o

o

bz)

f"

/' &---0

,

,


Figure 43-32: Example of distribution of shear load to the back anchors of a group with four anchors without torsional restraint with no or normal hole clearance (ad S, ad.J loaded by a shear load inclined with respect to the edge using the virtual load method'

a) resolution of load into orthogonal components (compare with Figure 4.3-25a,b,c); b l ) resultant shear forces on both back anchors act toward the edge; bz) resultant shear force on one back anchor acts away from the edge

V~1~

.1Z.

VSd

VSd,l

VSd,1I

VSd,n

•

•

o

0

2

b)

a)

!

T ~

VSd.l

(1.1 VSd.U

VSd,l

t l G2

+-

(l.1VSd•1I

o

0

0

~ • Loaded anchor o Unloaded anchor

Figure 43-33: Example of distribution of shear load to the back anchor of a group with four anchors with torsional restraint with no or normal hole clearance (ad S, ad,l) using the virtual load method. Shear load inclined with respect to the edge: a) resolution of load into orthogonal components (compare Figure 43-260); b) redistribution of shear load to back anchors; c) substitution of shear load components acting parallel to the edge by a virtual shear load acting perpendicular to the edge; d) resultant shear load on back anchors


93


94

4.3.1.4

In general, static shear loads acting on anchors may be assumed to act without a lever arm if all of the following conditions are fulfilled:

fixture / VSd

grout

/g / ~

~

:::ttn, ~

I.,

Shear loads without lever arm

tgrout

if tgrout ~dJ2 and fc groul;:: 30 MPa, not necessary to include lever arm in design for static shear loads

anchor

a) the fixture is made of metal and in the area of the anchorage is fixed directly to the concrete without an intermediate layer or with a levelling layer of mortar with a compressive strength:::: 30 MPa and a thickness tg,",,,:5 d/2 (Figure 4.3-34); b) after anchor installation and prestressing the fixture is in contact with the anchor over a length of at least 0.51j;x (relevant for sleeve anchors, see Figure 4.3-35) and the bearing pressure between sleeve and fixture is smaller than the value allowed by the code for steel design (e.g., EN 1993-1-8:2005 (CEN, 2005)).

Figure 4.3-34: Anchorage with baseplate and grout

With load cases including fatigue and seismic loads it should only be assumed that shear loads act without a lever arm, when the fixture bears directly against the concrete (no levelling mortar is present or if the thickness of the grout is not larger than approximately 3 mm).

bearing length f;:: O.5tlix

anchor sleeve

Figure 4.3-35: Bearing length of a sleeve anchor inflXture

Shear loads with lever arm

4.3.1.5 Anchor bolt

\,' ,

,

'0'

-1~'

. -\;

Anchor bolt

V"

,...1'>.

;; n'

V"

t ,Fixture

Fixture

3

..•

,.I

with:

I

,f.{t",

;,..;' tfile

~a*_eLt ;

I

tf=t

I

~~---'-(

bj

aj Figure 4.3-36:

If one of the conditions a) and b) of Section 4.3.1.4 is not fulfilled, it should be assumed that the shear force acts on the anchor with a lever arm. The lever arm I is calculated according to Equation (4.3-2): (4.3-2) I =a +e,

e, = distance between shear load and concrete surface a3

= 0.5d for post-installed and cast-in-place anchors (see Figure 4.3-36a) =

0 if a washer and a nut are directly clamped to the concrete surface (see Figure 4.3-36b)

The design moment acting on the anchor is calculated according to Equation (4.3-3):

Anchorage with lever arm

MSd

v'"

v"

a. .;=1.0

t jFixture

!F~=~ .:s:::

=6-

a. M=2.0 tjFixture

,.....--

CE\'~~=IC> I

E

a,

a, aj

bj

Figure 4.3-37: Examples of anchorages aj without and bj with full rotational restraint of the anchorage at the end of the fixture


I

= VSd ' aM

(4.3-3)

The value aM depends on the degree of restraint of the anchor at the side of the fixture of the application in question and should be determined according to good engineering practice. No restraint (aM= 1.0) should be assumed, if the fixture can rotate freely (see Figure 4.3-37a). This assumption always is on the safe side. aM= 1.0 should always be assumed, if the diameter of the hole in the fixture is greater than the value df" according to Table 4.3-1 or if the hole clearance is ael::; ael.' and the fixture is not clamped to the anchor by nut and washer. In general full restraint (aM = 2.0) may be assumed only if the fixture cannot rotate (see Figure 4.3-37b) and either:

(1) the anchor is welded to, or threaded into the fixture, or (2) is clamped to the anchor by nut and washer (see Figure 4.3-36b) and the hole clearance in the fixture is ael:5 ael.! with ael.' according to Table 4.3-1. If restraint of the anchor is assumed, the fixture and/or the anchored element should be able to take up the restraining moment.

95

96


4.3.2

Plastic analysis

4.3.2.1

Field of application

The plastic design approach may enable the use of anchors with a smaller cross sectional area compared to the elastic design approach. However, the required embedment depth and edge distance may be larger than for the elastic design approach to preclude a concrete failure.

Currently there is only limited information regarding the plastic behaviour of anchor groups loaded by moments acting in two directions and/or by torsional moments. Therefore, these cases are not covered by this Design Guide. The attachment shown in Figure 4.3-38 is for illustration purposes. Other forms of the attachment are permissible.

In a plastic analysis it is assumed that significant redistribution of anchor

tension and shear forces will occur in a group. Therefore, this analysis is acceptable only when the failure is governed by ductile steel failure of the anchor. Anchor configurations covered by this Design Guide are shown in Figure 4.3-38. The number of anchors parallel to the axis of bending may be larger than two. ~M

~M ~a

a,r-

b

b,r-

n

0

I

c:,

~

I

(

---

-

I-I§ll-r

-

Fixture

"'I' - II

Anchors

-

-

/

I _

I

Axis of bending

_

--II _ I I

I

,

FH] I

-

fI

-

a-a

Figure 4.3-38: Examples of anchor configurations covered by this Design Guide for plastic design.

The use of bonded anchors in cases where plastic design is to be used presents special problems. It is necessary to ensure that the unbonded length is adequate to guarantee the necessary elongation associated with plastic design. This may be accomplished by de-bonding a length of the anchor, or by providing sufficient rod length between the surface of the concrete and the fixture (e.g., as in an anchor chair). The use of screw anchors and other anchor types where sufficient stretch length cannot be provided is not recommended for plastic design.

Anchorages loaded by normal and shear forces and by a bending moment around one axis may be assumed to exhibit ductile steel failure if the following conditions are met:

Pullout failure may occur at large displacements allowing for some redistribution of tension forces. However, redistribution of shear forces may not be significant. Due to the lack of relevant information, plastic analysis should not be applied for this type of failure. (1) The number of anchors in the plane of the moment is limited to 3. The Equation (4.3-4) is based on evaluations of Hoehler (2006) (Section 8 - Probability of Brittle Failure During an Earthquake) whereby the probability that concrete failure occurs prior to steel failure is taken as 10.2 • Plastic analysis is also allowed for anchorages with anchor reinforcement to take up tension or shear forces acting on the fixture. When anchor reinforcement is provided, this reinforcement should be dimensioned such that it is able to carry the tension forces in the concrete associated with concrete cone or a concrete edge failure.

(2) The strength of the anchorage is governed by ductile steel failure of the anchors. To ensure ductile steel failure of the anchorage Equation (4.3-4) should be satisfied:

Rk .,

:0;

0.6. ~k.'

(4.3-4)

rinst

with: R k.,

Rk.,

Yinst

=

characteristic resistance of the anchors against steel failure minimum characteristic resistance against relevant concrete failure modes. For anchorages without anchor reinforcement: pullout, concrete cone, splitting, blowout failure (tension loading), concrete pryout or edge failure (shear loading). In case of anchor reinforcement, the value R k., corresponding to concrete cone failure (tension loading) or concrete edge failure (shear loading) should be replaced by the characteristic resistance of the anchor reinforcement. partial factor for installation safety according to Section 3.4.2.1

(3) Equation (4.3-4)) should be checked for tension, shear and combined tension and shear forces on the anchors.


97


Sufficient ductility of the anchor may be assumed if the following conditions are fulfilled (Cook, Klingner, 1992):

98 (4) The ductility of the anchor should be adequate to allow the assumed redistribution of forces.

(I) The nominal anchor steel strength should not exceed juk = 800 MPa, the ratio of nominal steel yield strength to nominal ultimate strength should not exceed J;k / j.,k = 0.8, and the rupture elongation (measured over a length equal to 5c1) should be at least 12%. ASTM AI93 (ASTM, 2009) B7 steel may be assumed to fulfil these requirements. (2) Anchors that incorporate a reduced section (e.g., bolt with partial thread) should satisty the following conditions: a) For anchors loaded in tension, the strength Nuk of the reduced section should be adequate to permit yielding over the balance of the anchor length and sufficient stretch length should be provided. In cases where the steel at the reduced section meets the minimum requirements outlined in (1) above, the plastic steel elongation should be roughly the same as for an anchor without a reduced section. For cases involving multiple reduced sections (e.g., threads as well as deformations in the expansion zone), it may be necessary to conduct an analysis for the critical anchor segment, and to establish that the strength of this critical element is sufficient to induce yielding in the other, non-critical sections. Note that many steels used in anchor fabrication do not exhibit a clear yield point, and that the yield strength is determined by convention based typically on the 0.2% offset method. For this reason, it may be necessary to develop some multiple of the yield strength at the critical section. This is product and materialdependent. b) For anchors which are assumed to redistribute shear forces, the reduced section should begin at a distance 2: 5d below the concrete surface. In the case of threaded anchors, the threaded part should extend for a length 2: 2d into the concrete. c) For anchors loaded in combined tension and shear, the conditions a) and b) above should be met.

(5) The steel fixture should be embedded in the concrete or fastened to the concrete without an intermediate layer or with a layer of mortar with a thickness :s d/2 (d = anchor diameter) and a compressive strength, j;k 2: 30 MPa. In case of seismic or fatigue loading, the thickness of the mortar should be not larger than approximately 3 mm. (6) The diameter of the clearance hole in the fixture should be df:S df.l with df.l as given in Table 4.3-1.

4.3.2.2

Loads on anchors

It may be assumed that all anchors are stressed up to their design resistance without taking into account compatibility conditions. However, the following conditions should be met:

(1) Tension and shear acting on each anchor should lie within the tension-shear interaction diagram for that anchor (see Parts II to IV of this Design Guide). O",d = 6j;k / rM, is 50% larger than the maximum value according to CEB FIP Model Code 1990 (CEB, 1993) for partial loading. This increase is based on the results of tests by Cook, Klingner (1992). The assumed stress distribution is indicated in Figure 4.3-39 and Figure 4.3-40. For both rigid and flexible baseplate behaviour, the distribution of compressive stress between the baseplate and concrete is non-linear. It is assumed that the stress distributions shown in Figure 4.3-39 and Figure 4.3-40 are conservative.


(2) For design purposes, a rectangular compressive stress block between fixture and concrete may be assumed; the compressive stress can be taken as O",d:S 6j;k / rM,' (3) The location of the resultant compressive force CSd should be determined based on rigid or flexible baseplate behaviour in accordance with (a) or (b) below.

99


100

MS~

/

n

rt-h

I

'\R/_

If,~

Myd>CSd " 8 4 No yielding allowed

/1 fC

ck ,r -6f

0: <

Y~

-

rN~ ~~

(a) Rigid baseplate behaviour: For rigid baseplate behaviour, the compressive force is assumed to act at the extreme edge of the baseplate (see Figure 4.3-39). To ensure this behaviour, the baseplate should be of sufficient thickness to prevent yielding of the fixture at the edge of the attached member on the compression side of the fixture. The minimum baseplate thickness may be determined on the basis of Equation (4.3-5)

CSO=~NSd

a,

MYd

> CSd a 4

(4.3-5)

with:

Figure 4.3-39: Rigid baseplate behaviour

Attached member Yielding of plate allowed

M~ P":

_fI"~!Ii\;i")D

a

"

-'c

"1 6fY.."

CS<1= l:NSd

a

Myd

design moment that causes yielding of the fixture calculated with/yd = /yk / YMs (rM, may be taken as 1.1)

CSd

design resultant compressive force

a4

distance from the edge of the attached member to the resultant compressive force

(b) Flexible baseplate behaviour: If the baseplate is not stiff enough to obtain rigid baseplate behaviour, a hinge will form on the compression side of the baseplate at the edge of the attached member. This will cause the compressive reaction to move inward toward the attached member. The distance a4 between the edge of the attached member and the resultant of the compressive reaction may be calculated according to Equation (4.3-6) (compare Figure 4.3-40). MYd a,=--

(4.3-6)

CSd

with Myd and'Csd defined in Equation (4.3-5).

Figure 4.3-40: Flexible baseplate behaviour

Equations (4.3-5) and (4.3-6) can only be used if the thickness of the baseplate is known. If this is not the case, designers may assume that the compressive reaction is located at either the edge (a4 = 0) or centroid of the compression element of the attached member. This conservative assumption simplifies design calculation. Equation (4.3-7) is valid for one row of tensioned welded member. Myd>NSd" as \ No yielding allowed "',

Ms~

n rrn

.=.

l';

, ilEiilli&=_Gmt'

a

y

t

t:P

C,,= ~NSd

, N~

, Nso

(4) Both for rigid and flexible baseplate behaviour, the formation of a hinge in the baseplate on the tension side of the connection should be prevented. This is necessary to ensure that prying action between the baseplate and the concrete (see Section 4.3.1.2) does not develop. Prying action may be prevented by satisfying Equation (4.3-7).

with Myd as defined in Equation (4.3-5) and NSd

a6

Figure 4.3-41: Prevention ofprying action

MSd

~

"9:(1'::

-

(4.3-8)

with:

a,

a,

C NSd

distance between outermost tension anchors and edge of -the attached member (see Figure 4.3-41)

a, > O.4as

rP

tbA }

L

sum of the design tension forces of the outermost row of anchors

(5) Only those anchors which satisfy Equation (4.3-8) should be assumed to transfer a tension force.

,

.j2!

(4.3-7)

Myd >NSd a 6

J

j,

-'-"'1 NSd

C~=LNSO

a, (ag )

distance between the resultant compression force and the innermost (outermost) tensioned anchor (see Figure 4.3-42)

------- -----------

Figure 4.3-42: Condition for anchors transferring a tension force equal to the design yield resistance

(6) It may be assumed that all anchors or only part of the anchors carry shear loads. The shear load acting on the individual anchors of a group may not be equaL f----.,---· . ~.~ ~:.~-R-_.\


I .:,'.:.~-:;.;" I \.~-~--.. ,~ .. --.-~..'"-~

101

102

Part I: 5 Determination of concrete condition

4.4

Serviceability limit state and fatigue

In the serviceability limit state and for fatigue loading the forces on anchors should be determined according to Section 4.3.1 (elastic analysis) with YG = YQ = Y;nd = 1.0.

4.5 The assumption of elastic distribution of loads is generally conservative for the case of seismic loads. The use of the plastic analysis methods described in Section 4.3.2 should be applied with caution, since the low-cycle fatigue behaviour of anchors yielding in tension and subject to cyclic shear is poorly understood.

Seismic loading

When considering seismic loading, load distributions in accordance with either the elastic or plastic analysis procedures described in this document are admissible provided that the specific conditions of Sections 4.3.1 and 4.3.2 are fulfilled.

Note that in general this Design Guide limits the size of anchor groups loaded in shear due to the concern for excessive shear lag. In practice, much larger groups are typically used (e.g., for collectors, perimeter anchorage of braced frame elements, etc.). In these cases, there may be some justification for the assumption of uniform load distribution (i.e., due to progressive softening of the anchor response under cyclic shear) however, these cases are not addressed further in this Design Guide.

5

Determination of concrete condition (I) The designer should check whether the concrete in the region of the anchorage is cracked or uncracked. The check on the condition of the concrete can be avoided by assuming that the concrete is cracked. (2) For seismic design situations the concrete should always be assumed to be cracked in the region of the anchorage. (3) For non-seismic design situations uncracked concrete may be assumed in the design of anchorages, if for each anchor it is proven that under service conditions of the concrete member the anchor with its entire embedment depth is located in uncracked concrete. The concrete may be assumed to be uncracked, if Equation (5-1) is observed:

UL

(5-1)

+uR::;;O

with: stresses in the concrete induced by external loads including anchor loads

O"L

If no detailed analysis is conducted, then O"R should be assumed to be equal to 3.0 MPa. This value is used in EN 1992-1-1:2004 (CEN, 2004-1) when calculating the minimum reinforcement to limit crack widths.

O"R

=

stresses in the concrete due to restraint of intrinsic imposed deformations (e.g., shrinkage of concrete) or extrinsic imposed deformations (e.g., due to displacement of support or temperature variations)

The stresses O"L and concrete is uncracked.

O"R

should be calculated assuming that the

(4) For anchorages in slabs, walls and shells, Equation (5-1) should be checked for both mutually perpendicular directions in the plane of the structure.

The characteristic resistance is defined as the 5%-fractile ofthe strength of the total population for a confidence level of 90%. Often in codes, the nominal steel yield strength and nominal steel ultimate strength are given. These nominal values may be assumed as characteristic values for tension and shear, respectively. The characteristic concrete breakout resistance under tension and shear for any anchor should be based on design models which result in prediction of strength in good agreement with results of comprehensive tests, accounting for size effects as well. The models should take into account factors which affect anchor strength, such as embedment depth, spacing and edge distance, depth of the structural member, and the presence or the absence of concrete cracking. Limits on edge distance and anchor spacing in the design model fib Bulletin 58: Design ofanchorafJes in concrete

6

Verification of limit states

6.1


For each anchorage the characteristic resistance to all possible failure modes should be calculated. Specifically, the following characteristic resistances should be calculated: steel failure under tension and shear, concrete cone, blowout, concrete splitting and pullout failure under tension loading, concrete edge and concrete pryout failure under shear loading of the anchors. Where anchor reinforcement is provided, the calculation of the characteristic resistances associated with the concrete cone and concrete edge failure modes is replaced by a check ofthe characteristic resistance associated with the anchor reinforcement (steel and bond resistance). The minimum of the above mentioned resistances divided by the appropriate partial factor for resistance (see Section 3.4.2) should be taken as the design resistance of the anchorage.

103

104

Part I: 6 Verification of limit states

should be consistent with the tests that have verified the model. Interaction of tensile and shear loads should be considered in the design using an interaction expression which results in prediction of strength in substantial agreement with results of comprehensive tests. The above requirements are satisfied by the Concrete Capacity Method (CC-Method) described in the following parts of this Design Guide.

For combined tension and shear forces, the effect of their interaction on the resistance should be taken into account. The design models adopted in this Design Guide for the determination of the characteristic resistances for the different concrete failure models are valid under the assumption that the structural element that takes up the loads transferred by the anchorage is at or below the serviceability limit state, when the anchorage reaches the ultimate limit state.

Possible failure modes for anchorages are shown in Figure 3.2-1 (tension) and Figure 3.2-2 (shear).

6.2 It may also be necessary to limit the rotation of the fixture, if excessive rotations could lead to aesthetic or non-structural damage. If the design is done according to the elastic design approach, this condition is satisfied when the partial factors in the ultimate limit state proposed in this Design Guide both for actions and for the resistance to steel failure are applied. If the design is performed according to the plastic design approach, then a check that this condition is satisfied may be necessary.


In the serviceability limit state it should be shown that the displacements occurring under the design actions do not exceed the admissible displacement and that no excessive cracking occurs.

It should be demonstrated that Equation (3.3-1) is fulfilled for all loading directions (tension, shear, combined tension and shear), assuming design action and resistance are expressed in terms of displacements. The admissible displacement, Od, depends on the application in question and should be evaluated by the designer. For the determination of displacements, Os, resulting from loads acting on the anchorage, a linear function between loads and displacements may be assumed. In the case of combined tension and shear loads, the displacements for the shear and tension components of the resultant load should be added vectorially. The characteristic displacements under tension and shear loads of the anchor are given in this Design Guide (for headed anchors and anchor channels) or in the Approval.

Using the partial factors for steel failure given in this Design Guide (see Section 3.4.2.1.1) will prevent yielding under service loads.

The resultant stress in the most loaded anchor under the design tension or shear actions should not exceed yield.

In the case of anchor groups near a free edge and loaded towards or parallel to the edge, particular consideration should be given to the potential for premature cracking of the concrete originating from the near-edge anchors leading to excessive crack widths under service loads. Such premature

If it is assumed in the verification of the concrete edge resistance in the ultimate limit state that the failure crack does not start from the front anchor(s) of a group (those anchors nearest the edge), it should be verified that in the serviceability limit state the crack widths do not exceed the

cracking may occur if it is assumed in the design that the failure crack does not start from the front anchor(s). The likelihood of premature failure of the near-edge anchors is influenced by the hole clearance, the ratio of edge distance to anchor spacing in the direction orthogonal to the edge and the absence or presence of anchor reinforcement. In general, welded headed studs with close spacing (SI:S Cl.l) are not susceptible to such premature edge failure. Where hole clearances are present, the check according to Equation (6.2-1) should be done independent of the ratio Sl / Cl.l·

serviceability crack width limits. This is accomplished' by checking for concrete breakout starting from the near edge anchors (see Equation (6.2-1)).

Theoretically, the first crack can occur at a row beyond that nearest to the edge. However, the occurrence of an initial crack at a row beyond the near edge row has so far not been experimentally verified. Therefore, it is assumed that an SLS check for the anchors nearest to the edge is sufficient. If anchor reinforcement designed according to Section 19.2.2 is provided to take up shear loads, it may be assumed that the width of cracks starting from the front anchors is limited to acceptable values. Therefore, the check according to Equation (6.2-1) may be omitted. Furthermore, for cases where combined tension and shear loading is present and where the shear resistance is assumed to be provided entirely by the back anchor(s), a reduction in the calculated resistance of the front anchor(s) in tension due to the formation of a shear crack at the near-edge anchor(s) must be taken into account (see Section 10.3.2).

Vsd :;;

with: VSd

VRd (C1,1)


=

design shear force acting on the front anchor(s) calculated according to Section 4.3.1.3 with rG = rQ = 1.0

=

design concrete edge resistance ofthe front anchor(s) with an edge distance Cl,1 calculated with rMc = 1.0

For anchor groups loaded in both tension and shear, additional considerations apply (see Section 10.3.2).

6.3 Figure 6.3-1 illustrates a pulsating action. Figure 6.3-2 illustrates an alternating shear action.

(6.2-1)

VRd ( C1,1)

Fatigue

This Design Guide covers applications with anchors subjected to pulsating tension load, alternating shear load and combinations thereof. For load combinations including seismic loading see Section 6.4.

105

106

Part I: 6 Verification of limit states Load

J.,"

NSk,m

+--

Time

1 cycle

Figure 6.3-1:

Definition ofpulsating actions Load

,

{

{. , ,{ ,

I

.~l:NS'

Time

1 cycle

Figure 6.3-2:

Definition of alternating shear actions

Alternating axial loads on the anchor are not addressed for fatigue loading, because in general compression loads are transferred directly from the fixture to the base material (Figure 1.5-2). Loosening of the nut or bolt under fatigue loading may be prevented by the use of lock nuts, counter nuts or other suitable means. Elimination of hole clearance in the connection can be accomplished through the use of e.g., welded anchors, weld washers or by filling the annular gaps with suitable grout. It is advisable to maintain some level of prestress in the connection in order to avoid secondary effects associated with anchor displacements.

In general, fatigue verification is not required when:

•

•

•

Fewer than 1000 load cycles are expected for pulsating loads on the anchor with a load range LJNsk = N Sk.max - N Sk.mh, less than or equal to NRd / YQ where NRd is the design resistance for steel failure and YQ = 1.5. Fewer than 10 load cycles of alternating shear are expected with a load range LlVSk = V Sk.ma, - VSk.mia less than or equal to V Rd / YQ where VRd is the design resistance for steel failure and YQ = 1.5. For smaller amplitudes of the shear load the number of load cycles where no verification is required may be increased. Load cycles are imposed by climatic variations and the stress range caused by the restraint forces in the most stressed anchor is limited to LlcrSk = crSk.ma. - crSk.mia:S 100 MPa or, in the case of shear loading, if the maximum stress range of the most stressed anchor is limited to LlTsk = TSk,ma. - TSk,mia:S 60 MPa (7 = shear stress in the anchor), These values have historically been used for the design of fa,ade anchorages,

The values of M 2 ,10 6 load cycles,

Rk,,, MRk,p,

!l V Rk" and !l VRk"m should be established for

Fatigue verification should be carried out, when anchors are subjected to regular load cycles (e.g., anchorage of cranes, reciprocating machinery, guide rails of elevators). Fatigue loading may also arise due to restraint of members subjected to temperature variations, e.g., fa,ades. Anchors used to resist fatigue loading should be prequalified by appropriate tests. Anchorages subjected to fatigue shear loading should be constructed such that there is no annular gap between the anchors and the baseplate. Loosening of the nut or bolt should be avoided.

The verification under fatigue loading consists of both the verification under static and fatigue loading, Under static loading, the anchorage design should be based on the design methods given in the relevant Sections of this Design Guide, The verifications under fatigue loading are given below, The required verifications for all load directions are summarised in Table 6,3-1 and Table 6.3-2 Table 6.3-1: Required verifications - tension loading Failure mode

2

Steel failure

r F,fat MSk

Pullout failure

r F ,fat MSk

s:;

Rk

M

"

rF,fat M;k

s:;

IfRN M

s:; M

Rk ,p

r F,fat M;k

s:;

r F,fat MSk

s:;

failure

M

Rk

r

.,

rMp,fat

YF,fa' MIk

s:;

Mc,fat

M

Rk

"

YMc,Jat

4

Concrete splitting failure

rF,fat MSk

s:;

MRk"P

rF,fat MIk

s:;

MRk.,p

5

Concrete blowout failure

r F,Jat MSk

s:;

MRk"b

YF,fat MIk

s:;

MRk"b

rMc,fat

"

If RN MRk,p

YMp,Jat

cone

Rk

r "',fat

r "',fat

Concrete 3

Anchor group ,)

Single anchor

YMc,fat

rMc,fat

YMc,Jal

,) For steel and pullout failure modes, check critical anchor (anchor that experiences the largest stress range)

with: YFJat

=

partial factor for action (see Section 3.4.1) 1.0

YMsJal


=

partial factor for steel failure (see Section 3.4.2.3)

107


108 YMpJal

= partial factor for pullout failure (see Section 3.4.2.3)

YMc/at

=

partial factor for concrete failure (see Section 3.4.2.3) factor for anchor groups; taken from relevant Approval or determined from the results of suitable prequalification tests

'l/RN

< LO NSk,ma, - NSk,m;n; twice the amplitude of the fatigue tensile

MSk

action, see Figure 6.3-1

Tests by Lotze (1993) indicate that the fatigue resistance corresponding to concrete cone failure is roughly 60% of the static resistance. It is assumed that this ratio is also valid for other concrete failure modes.

M Rk"

characteristic fatigue resistance in tension to steel failure; taken from the relevant Approval or determined from the results of suitable prequalification tests

MRk,p

characteristic fatigue resistance in tension to pullout failure; taken from the relevant Approval or determined from the results of suitable prequalification tests

M Rk"

characteristic fatigue resistance in tension to concrete cone failure 60% of the characteristic resistance corresponding to concrete cone failure under static loading, i.e" N Rk" characteristic fatigue resistance in tension to concrete splitting failure

MRk"p

60% of the characteristic resistance corresponding to splitting failure under static loading, i.e" NRk"p characteristic fatigue resistance in tension to blowout failure

MRk,'b

60% of the characteristic resistance corresponding to blowout failure under static loading, i.e" NRk"b The values N Rk." NRk"p and NRk"b should be evaluated according to the corresponding parts of this Design Guide,

Required verifications - shear loading

Table 6.3-2:

To account for the potential non-uniform loading of anchors in a group arising from differences in anchor stiffness, the fatigue resistance of the most loaded anchor is reduced by 'l/RN for tensile loading or by 'l/RV for shear loading, The factors 'l/RN and 'l/RV should be evaluated from prequalification tests, For the special case of groups of two anchors subjected to shear loading perpendicular to the axis of the anchorage when the fixture is able to rotate, the value of 'l/RV may be taken as LO, In many applications 0.70:S 'l/RN ('l/RV) :s 0,85 may be used,

Failure mode Steel failure without

YF ,fal

Ll.VRk ,

Ll. VSk s:; - - ' -

3

4

F,fat

Ll.V,"

< If'RVLl.VRk "

Sk -

YMs,Jal

Ms,fat

Steel failure with lever ann Concrete pryout failure

Y F,fat

Ll. V, < Sk

Ll.V, Rk.,m

Ll. V," < If'RV Ll.VRk.,m

Y F,fat

rF,fat Ll. V,Sk <

Y Ms,fal

Ll.V Rk,'p

YF,Jar

YF,fal

Ll.VRk" Ll.VSk s:; - Y - -

Ll.V Ll.V,g <~ Sk-

YMc,far

YMc,Jat

Concrete edge failure

Sk

YMs,fal

Mc,fat ,j

Y

r

lever arm

2

Anchor group "

Single anchor

YF,fal

Ll.V, Ll.V,if s:; ~

rMe,lat

For steel failure modes, check critical anchor (anchor that experiences the largest stress range)

with: YMs/at YMc/at

'l/Rv ilVSk ilVRk"

!J.VRk,sm

The values VRk"p and VRk" should be evaluated according to the corresponding parts of this Design Guide,


ilVRk"P

partial factor for steel failure (see Section 3.4.2.3) partial factor for concrete failure (see Section 3.4.2.3) < LO; for anchor groups; taken from relevant Approval or determined from the results of suitable prequalification tests VSk,ma, - VSk,m;n; twice the amplitude of the fatigue shear action, see Figure 6.3-2 characteristic fatigue resistance in shear to steel failure; taken from the relevant Approval or determined from the results of suitable prequalification tests characteristic fatigue resistance in shear to steel failure with anchor bending (see relevant sections in the following Parts) characteristic fatigue resistance in shear to concrete pryout failure 60% of the characteristic resistance corresponding to concrete pryout failure under static loading, i.e" VRk"p 109

llO


It should be noted that limited testing indicates that anchors subjected to alternating shear near free edges may exhibit a reduced fatigue capacity associated with concrete edge failure as compared to anchors loaded in pulsating shear. In these cases, it may be appropriate to limit the load amplitude LtVRk = VSk,ma, - V,k.ml" to 0.3 VRk.,.

=

t;.VRk"

characteristic fatigue resistance in shear to concrete edge failure 60% of the characteristic resistance corresponding to concrete edge failure under static loading, i.e., VRk.,

For combined tension and shear loading the Equation (6.3-1) should be satisfied: (J3N./.,)"

(6.3-1)

+ (J3v./.,)" Sl.O

with: r J3N/at

F./"

. /::,N Sk < 1.0

YF,[al'

/::,N"Sk

< 1.0

If/RN . /::,NRk / r M,jat

r

F./at

./::,Ng Sk < 1.0

/::,NRk / r M./"

r fiv/at

F./at

. t;.v. Sk < 1.0

·t;.V;~

<1.0

If/RV' t;.VRk/rM./at g r F./at . t;.v.Sk < 1.0 t;.VRk/rM./at

Alternatively, the interaction Equation (6.3-1) may be checked separately for steel failure modes and concrete failure modes (including pullout failure) under tension and shear loads. The corresponding factors should be evaluated from appropriate prequalification tests. In general a = 1.0 may be taken.

(6.3-laJ)

steel and pullout failure of anchor groups

(6.3-la,)

concrete failure of anchor groups (concrete cone, splitting and blowout failure)

(6.3- la3)

single anchors

(6.3-1b J)

steel failure of anchor groups

(6.3-1b,)

concrete pryout and concrete edge failure of anchor groups

(6.3-1b 3)

t;. VRk / r M,jat

rF./"

a

single anchors

/::,NRd r M,j"

factor taken from the relevant Approval or determined from the results of suitable prequalification tests (see Section 1.3). In general a= 1.0 should be taken.

The largest value of fiN/at and fiv/at calculated according to Equations (6.3-laJ) to (6.3-lb3) for the different failure modes should be inserted in Equation (6.3-1).

6.4

Verification for load combinations including seismic actions

The proper design of anchorages for seismic conditions involves many considerations apart from the specific resistances assigned to the anchors. These may include the effects of large displacements, degradation of the supporting member, secondary forces associated with eccentricities and requirements for ductile behaviour.

This section provides additional requirements for anchorages used to resist seismic actions. It is applicable to connections between structural elements or between non-structural attachments and structural elements.

The simulation of seismic loading in prequalification tests should properly include consideration of crack width, number and amplitude of load cycles on the anchorage and the member resulting in opening and closing of cracks, strain rate and loading direction. Other factors may be relevant for specific cases.

Anchors used to resist seismic actions should be prequalified for cracked concrete, In addition, they should be prequalified by suitable tests simulating seismic conditions. When performing anchorage design for seismic applications, the concrete in the region of the anchorage should always be assumed to be cracked.

Critical regions include, but are not limited to zones where plastic hinges in a beam or column may form and regions in shear walls or coupling beams where large diagonal cracks may occur.

The provisions in this section do not apply to the design of anchorages in critical regions of concrete elements where concrete spalling or excessive cracking may occur.

The question of anchor displacements in the case of seismic loading should be considered from two perspectives:

Anchor displacements in the case of seismic loading should be assessed using engineering judgement.

the anchor displacements in response to the imposed loading may be large and may have negative consequences for the performance of the attachment; the displacements imposed by the response of the structure on the anchorage may be large and may exceed the anchor displacement capacity. Each of these considerations requires careful assessment of the anchorage detailing and the expectations for the anchorage performance.


111

Part I: 6 Verffication of limit states

112 When distributing forces to the individual anchors of a group, the designer should take into account the stiffness of the fixture and its ability to redistribute loads to other anchors in the group beyond yield of the fixture. Yielding of the fixture is not excluded by the design.

Annular gaps should be avoided to prevent movement of the fixture relative to the anchor during cyclic shear. Such movement may result in an increase of the shear load on the anchorage due to impact (Rieder, Bergrneister, 2010). Furthermore, under cyclic shear, gaps will lead to unequal distribution of shear loads to the anchors of a group, thus resulting in a reduced group resistance. Engineering judgement is necessary to determine whether the restriction on annular gaps applies in every case.

In general, annular gaps between an anchor and its fixture should be avoided for anchorages to be subjected to seismic actions. Loosening of the nut or screw should be prevented by appropriate measures. For less critical applications, a small annular gap (dJ~ df,l with df,l as defined in Table 4.3-1) may be allowed if the effect of this gap on the magnitude of the shear load acting on the anchorage, on the distribution of the shear load to the anchors of a group and on their resistance is taken into account. Design values of the effect of seismic actions on the fixture should be determined according to structural design codes using the partial factors given in Section 3.4.1. Vertical seismic actions acting on elements should also be considered where appropriate.

In general, the loads acting on the fixture should be distributed to the anchors of a group according to Section 4.3.1 (see also Section 4.5). For steel and pullout failure under tension and shear load of single anchors, the characteristic resistances to seismic actions, Rk.,q (NR'.,.,q; VRk.,.,q; MR,.,.,q; NRk.p.,q), should be detennined on the basis of the results of appropriate qualification tests. For the calculation of concrete cone, blowout or splitting failure under tension loading and pryout or concrete edge failure under shear loading, the characteristic resistance to seismic actions is assumed to be equal to the resistance under static loading multiplied with the seismic reduction factor a,q. Uncertainty exists on both the resistance and actions side with respect to the design of anchorages to resist seismic forces.

In Equation (6.4-1 b,c), the term a,q is primarily intended to address uncertainty associated with anchorage resistance. In Equation (6.4-1 b) it accounts for the potential non-uniform loading of anchors in a group arising from differences in anchor stiffness (compare factors If/RN and If/RV in Section 6.3). A value a,q = 0.75 is proposed in CEN-TS (CEN, 2009) and a,q = 1.0 in ACI 31S-0S App. D (ACI 31S, 200S). These values are valid for the anchor

configurations covered in this Design Guide. For larger anchor configurations (e.g., collector elements) a more detailed analysis to account for the load distribution to the anchors should be performed. In Equation (6.4-1 c) the value a,q accounts for crack widths under seismic conditions that may be larger than those in non-seismic conditions and the general damage state of the concrete. A value of a,q = 0.75 is suggested based on current experience (ACI 31S-0S App. D (ACI 31S, 200S), CEN-TS (CEN, 2009)). Further research is needed to determine the value a'q for the different failure modes.

The principle objective of the seismic design of anchorages is to prevent brittle failure. In the case of structural connections (e.g., beam to column) the connection should not fail (i.e., suffer loss of load-carrying capacity) prior to the development of the yield capacity of the connected members (see Figure 6.4-la). It may also be permissible to develop the yield capacity of the fixture or baseplate (Silva, 2002), thus affording sufficient displacement capacity to avoid brittle failure (Figure 6.4-1 b). Of course, these two options are not mutually exclusive and a connection may permit the development of several points of yielding. Where the attached member has a specific ultimate capacity that can be reliably predicted, it is acceptable to proportion the connection for this strength (Figure 6.4-1 c). Mp

so,cq

.... ,'I '~

a) Figure 6.4-1:

Mp

• j

Vult

Sd,C
j

r'

___________I

b)

II

The design resistance of an anchorage to seismic actions for tension and shear loads Rd.,q should be calculated as follows: characteristic resistance determined in appropriate prequalification tests (steel failure under tension and shear load and pullout failure under tension load):

Rd .'q = R'.,q (single anchors)

(6.4-1 a)

Rd." = a,q . R'.,q (anchor groups)

(6.4-lb)

YM

YM characteristic resistance not determined in appropriate prequalification tests (concrete cone, blowout or splitting failure under tension loading and pryout or concrete edge failure under shear loading):

R, -aeq .YM -

Rd,eq -

(6.4-lc)

with:

R'"q =

characteristic seismic resistance for a given failure mode determined in appropriate prequalification tests

R,

characteristic resistance for a given failure mode under static loading

a,q

seismic reduction factor

YM

partial factor for resistance according to Section 3.4.2.4.

The design of anchorages to resist seismic actions should be based on at least one of the following approaches: (I) The anchorage is designed for the minimum of the following: the force corresponding to yielding of the attached ductile steel element taking into account over-strength; -

the maximum force that can be transferred to the connection by the attached clement or structural system.

Sd.eq

I

,1--...........,

r--

c)

Seismic design for protection of the anchorage: a) yielding of the attached element; b) yielding of the fixture; c) design for capacity of the attached element


113


114

Equation (6.4-2) should be required for tension (shear) only, if only tension (shear) loads act on the anchorage, or the Equation (6.4-2) should be observed for tension and shear, if combined loading acts on the anchorage.

(2) The strength of the anchorage is governed by the strength of ductile steel anchor. To ensure ductile steel failure of the anchorage, the following relation should be satisfied:

Under specific circumstances it may be desirable to design for yielding of the anchors (Figure 6.4-2). A requirement for ductile anchor yielding in tension requires consideration of the gauge length over which yielding can occur in order to provide a meaningful degree of elongation. This may be linked to the performance expectations for the structure.

R

< 0 6. Rk,other,eq

k,s,eq -

(6.4-2)

.

Yinst

with:

Fy

Rk.",q

characteristic seismic resistance for steel failure

Rk,other,eq

characteristic seismic resistance for all non-steel failure modes

Yin"

partial factor for installation safety according to Section 3.4.2,1

Simultaneously, condition (4) of Section 4,3,2,1 should be observed,

Figure 6.4-2:

Seismic design for ductile anchor yield

Equation (6.4-2) is based on a statistical assessment of various prescribed margins of safety between concrete and steel failure. The factor 0.6 is intended to give a I % probability of concrete failure prior to the intended anchor steel failure for typical anchor and material parameters (Hoehler, 2006). Pseudo-ductile failure modes such as anchor pull-through or pullout may be acceptable. However, sufficient knowledge is not currently available to provide design guidelines for these cases. Note also that the use of anchor yielding or other pseudo-ductile anchor response modes for energy dissipation in system response should be approached with caution. Furthermore, anchor displacements corresponding to yielding, pullout, etc. may result in amplified tension demands as a result of impact. Where ductile behaviour of the anchorage is precluded either due to geometrical limitations (e.g., member thickness, edge distance, anchor spacing) or for strength reasons, brittle failure of the anchorage is avoided by designing for a multiple of the calculated seismic force (Figure 6.4-3).

The value 2,5 corresponds to the usual assumption for the ratio between elastic and inelastic response and it is commonly referred to as response modification factor, The following relationship between the response modification factor, R, and the system ductility, J.l is assumed: R = .J2' f1. -1 , The implied value ofJ.l is approximately 3.5 (Newmark, Hall, 1982), This approach is primarily intended for non-structural elements and should in general be avoided for the connection of primary structural elements, Implicit in this design option are the following assumptions: -

brittle failure is associated with a higher probability of failure because the uncertainties in the earthquake induced actions influence directly the forces on the anchorage;

-

failure of non-structural elements is less likely to result in catastrophic consequences than failure of structural connections, Sd,eq X

For non-structural elements, it may be permissible to satisfY Equation (6.4-3) in lieu of (1) and (2) above,

2.5· Sd,eq

(6.4-3)

5, Rd,eq

with: Rd.eq

according to Equation (6.4-1 a,b,c),

Minimum edge distance and minimum spacing between anchors should be determined as for static design situations,

2.5

I

I

Figure 6.4-3:

Seismic design for a multiple of the calculated seismic force

Different product specific values for seismic design situations may be evaluated from suitable seismic prequalification tests,

The interaction between tension and shear forces should be determined assuming a linear interaction relation as given in Equation (6.4-4), ( NSd"q

l

NRd,eq

J+ ( l

VSd"q

J 1.0 5,

In Equation (6.4-4) the largest ratios NSd"q / different failure modes should be inserted,


(6.4-4)

VRd,eq NRd.,q

and

VSd,eq / VRd.,q,

for the

115


116

For bonded anchors and bonded-expansion anchors the fire resistance associated with bond failure is product dependent, therefore no general rules can be given. Product specific rules may be given in the relevant Approval. However, currently no acceptance criteria for bonded anchors under fire exposure are available. Anchor channels are not covered because sufficient experience is not available. Anchorages close to an edge with fire exposure from two or more sides (see Figure 6.5-1) are not covered due to lack of experience. Some results based on numerical simulations are given in Periski6 (2010).

U'\JV U'\JV

6.5

Fire

6.5.1

General

The design method is valid for cast-in-place headed anchors, expansion anchors, undercut anchors and concrete screws only. The design method covers anchors with fire exposure from one side or from more than one side if the edge distance of the anchor is c 2: 300 mm and c 2: 2he/, The fire resistance is classified according to EN 13501-2 (CEN, 2007) using the Standard ISO time-temperature curve according to ISO 834 (ISO, 1999). The design under fire exposure is carried out according to the design method for ambient temperature given in this Design Guide with the modifications given below. When performing anchorage design under fire exposure, the concrete in the region of the anchorage should always be assumed to be cracked. As a consequence, it is likewise assumed that the concrete is reinforced.

~~~ Figure 6.5-1:

~

Anchorage subjected to fire exposure from multiple directions

It is assumed that fire does not occur concurrently with wind and seismic loading. Therefore, the verification for fire resistance is not required for anchors designed exclusively for wind or seismic loading.

Where anchors resist only wind or seismic forces, verification for fire resistance is not required.

6.5.2 In general, the values for the partial factors are rFJi = 1.0 and rMJi = 1.0.

Partial factors for actions rFJi and for materials rMJi should be taken from CEB (1991) or CEN (2004-2).

6.5.3 The characteristic values given in this Design Guide are superseded by data given in the relevant Approval.

Partial factors

Resistance under fire exposure

In the absence of test data for a specific anchor the following characteristic resistances in the ultimate limit state under fire exposure may be taken. They are valid for anchors installed in concrete strength classes C20 to C50. These values are conservative.

6.5.3.1

Tension load

6.5.3.1.1 Steel failure The characteristic resistance of an anchor associated with steel failure under fire exposure (NRk"Ji) is given by Equation (6.5-1)

N Rk,s,ji

=(J'

Rk,s.fl

·As

(6.5-1)

with: (YRk,s,ji

A,

taken from Table 6.5-1 and Table 6.5-2. These values are also valid for the unprotected steel part of the anchor outside the concrete miniinum cross section along the stressed anchor length

Table 6.5-/: Anchor

Effective

bolt/thread

embed-

diameter, d

ment depth

Characteristic tension strength of a carbon steel anchor under fire exposure Characteristic tension strength aRk.sls of an unprotected anchor made of carbon steel according to ISO 898 (ISO, 2009-1) in case of fire exposure in the time up to: (lh,s,fi [MPa]

her


30 min

60 min

90 min

120 min

(R 15 to R30)

(R45 and R60)

(R90)

(RI20)

~30

10

9

7

5

8

;:: 30

10

9

7

5

10

;::40

15

13

10

8

::: 12

;:: 50

20

15

13

10

[mm]

[mm]

6

117

118


Table 6.5-2:

Characteristic tension strength of a stainless steel anchor (steel according to Table 7-1, lines 8 to 11) under fire exposure

Anchor Effective Characteristic tension strength CJ'Rk..ji of an unprotected anchor of stainless bolt/thread embedment steel according to ISO 3506 (ISO, 2009-2) in case aftire exposure in the diameter, d depth time up to: h'f

aRk.s/<

[mm]

[mm]

[MPa]

30 min

60 min

90 min

(R 15 to RJO)

(R45 and R60)

(R90)

120 min (~

R120)

6

~

30

10

9

7

5

8

~

30

20

16

12

10

10

;;:::40

25

20

16

14

:::: 12

;;::: 50

30

25

20

16

---

6.5.3.1.2 Pullout failure The characteristic resistance of anchors associated with pullout failure under fire exposure (NRk•pji) may be obtained from Equation (6.5-2).

N Rk,p,fi

=ap,N,ji

·NRk,p

(6.5-2)

with: Based on limited test experience (Reick, 200 I) the following values of ap.Nji may conservatively be used:

= 0.25 for fire exposure up to 90 minutes ap.Nji = 0.20 for fire exposure exceeding 90

reduction factor

ap,Nji

=

NRk•p

ap.Nji

characteristic resistance in cracked concrete C20 under ambient temperature given in the relevant Approval

minutes and up to 120

minutes 6.5.3.1.3 Concrete cone failure The characteristic resistance of an anchorage associated with concrete cone failure under fire -exposure (NRk.cJ;) may be calculated according to the relevant parts of this Design Guide valid for ambient temperature with the following modifications: Based on studies in Reick (200 I) and Periski6 (20 I 0) the following values of ac.N.fi may conservatively be used:

a a

c.N.fl c.N.fl

~ 1.0 200

= h",

(6.5-3)

N°Rk,r:.ji =ac,N,ji ·N°Rk,c

for fire exposure up to 90 minutes

~ 1.0 200

= 0.8· hej

replace N~k.c by N'!u..c.fl according to Equation (6.5-3).

-

with: for fire exposure exceeding 90 minutes and up to

ac,N,fl

°

120 minutes h'j= effective embedment depth in mm

NRk,c

Note that according to Reick (2001) and EOTA TR 020 (EOTA, 2004-2) the value N~k.c is limited to C20. However, based on the Periski6 (2010) this

reduction factor characteristic resistance of a single anchor in cracked concrete under ambient temperature according to the relevant product specific part of this Design Guide

limitation has been neglected here. A limited number of test results indicate that the critical spacing should be increased to account for the reduction in concrete strength associated with fire exposure (Reick, 200 I).

replace S,,·.N = 2C,,·.N = 3h'f (6.5-4): s".N.fl = 2C".N.fl = 4h",

by

S".Nji

according

to

Equation (6.5-4)

6.5.3.1.4 Splitting failure The assessment for splitting is predicated on the assumption that the concrete member in which the anchor is located is reinforced.

The assessment of splitting failure due to loading under fire exposure is not required because the splitting forces are assumed to be taken up by the reinforcement.

6.5.3.2

Shear load

6.5.3.2.1

Steel failure

6.5.3.2.1.1 Shear load without lever arm The characteristic resistance of an anchor associated with steel failure under fire exposure (VRk.,ji) is given by Equation (6.5-5): VRk.,.fi

= k, . 0"Rk",fi 'A,

(6.5-5)

with: Under normal temperature the ratio between the characteristic shear and tensile strength is assumed as 0.5 (see Equation 10.2-1). A limited number of tests indicate that this ratio increases under fire conditions. It is assumed here as k, = 1.0.


k, (JRk,s,fi

A,

ratio between shear and tensile strength 1.0 taken from Table 6.5-1 or Table 6.5-2 stressed cross section of the anchor in the shear plane

119

Part 1: 6 Verification of limit states

120

6.5.3.2.1.2 Shear load with lever arm The approach for anchors loaded in shear with a lever ann is based on theoretical considerations only.

The characteristic resistance of an anchor associated with steel failure loaded in shear with a lever ann under fire exposure (VRk.,mji) is given by Equation (6.5-6):

a ·Mo M Rk".ft < V I Rk,s,fi

V

Rk,SIII,/i

(6.5-6)

with: aM

=

factor discussed in Section 4.3.1.5

I

length of the lever ann according to Equation (4.3-2)

MORk,s,ji

characteristic bending resistance of an individual anchor

Equation (6.5-6a) is taken from EOTA Technical Report TR 020 (EOTA, 2004-2).

1.2·

w,/ .

(YRk.'.ft

[Nm]

(6.5-6a)

Wei

elastic section modulus of an individual anchor at the sheared cross-section

O'Rk.,ji

according to Table 6.5-1 or Table 6.5-2

VRk"ji

characteristic shear resistance for a lever ann equal to zero calculated according to Equation (6.5-5)

6.5.3.2.2 Concrete pryout failure The characteristic resistance of an anchor associated with pryout failure under fire exposure (VRk.,pji) may be obtained using Equation (6.5-7):

VRk.'P.ft

=k• . N Rk".ft

(6.5-7)

with: According to current experience:

k. = 1.0

hej < 60 mm

k. = 2.0

he/? 60 mm

k4

factor valid· for ambient temperature. It is given in the Approval.

NRk,cji

calculated according to Section 6.5.3.1.3

6.5.3.2.3 Concrete edge failure The characteristic resistance of an anchorage associated with concrete edge failure under fire exposure (VRk.,ji) may be calculated according to the relevant product specific part of this Design Guide valid for ambient temperature by replacing

V:

k., with V;k.,.fi according to Equation (6.5-8):

VORk,c.fi =ac,V,ji ·Vo Rk,c

(6.5-8)

with: The concrete edge resistance under fire exposure is influenced by several parameters including member thickness, edge distance, etc. The following values for ae.vji , taken from EOTA Technical Report TR 020 (EOTA, 2004-2), are believed to be conservative: a,.vji =

0.25 for fire exposure up to 90 minutes

a,.vji =

0.20 for fire exposure exceeding 90 minutes and up to 120 minutes

aeYji

reduction factor

VRk°.,

characteristic concrete edge resistance of a single anchor in cracked concrete under ambient temperature according to the relevant product specific part of this Design Guide

Note, that according to Reick (2001) and EOTA TR 020 (EOTA, 2004-2) the value V;k., is limited to C20. However, based on the Periski6 (2010) this limitation has been neglected here.

6.5.3.3 Due to a lack of available data for combined loading under fire exposure conditions, the combined loading condition is evaluated based on experience with ambient temperature conditions.


Combined tension and shear load

The interaction equations given for ambient temperature are assumed to be valid for fire loading; however, the resistances for ambient temperature should be replaced with those for fire.

121

122

Part I: 7 Durability

7 This section provides general guidance on corrosion protection. The required method of corrosion protection should be evaluated by the design professional on a case by case basis. The following considerations are relevant: In general, moisture is necessary for corrosion to occur. Therefore, for anchorages for use in structures subject to dry conditions no special corrosion protection is necessary for steel parts. However, care should be taken that anchors in interior conditions will not be exposed to moisture resulting from, e.g., condensation or the application of wet finish materials such as plaster, over the life of the anchorage. The coatings on post-installed anchors and anchor channels, e.g., a zinc coating with a minimum thickness of 5 !lm, are provided only to prevent corrosion during storage and shipping prior to use. For anchorages for use in structures subject to normal atmospheric exposure or exposure in damp internal conditions, the metal parts should be protected in an appropriate manner. One such type of protection is the use of an appropriate type of corrosion resistant steel. The type of corrosion resistant steel used for the various service environments should be in accordance with Standard Codes of Practice. In general, austenitic steels meeting the requirements of corrosion protection Class III as given in Table 7-1 have shown good performance in exterior environmental conditions. The use of other corrosion protection methods such as hot-dip galvanizing, sheradizing, etc. may also be appropriate in some cases. In particularly aggressive environments such as permanently alternating immersion in seawater or the splash zone of seawater, chloride atmosphere of indoor swimming pools or atmosphere with extreme chemical pollution, e.g., in desulphurisation plants or road tunnels especially when de-icing materials are used, special consideration should be given to corrosion resistance. The metal parts of the anchor (bolt, screw, nut and washer) should be made of corrosion resistant steel suitable for the high corrosion exposure. In general, steel types according to corrosion Class N in Table 7-1 have shown good performance. Another alternative to ensure corrosion resistance is to provide non-alloyed steel with double corrosion protection (e.g., hot-dip galvanizing with a coating thickness of 70 !lm to 100 !lm plus a plastic coating).

Table 7-1: European Material I 2 3 4 5 6 7 8 9 10

II 12 13 14 15 16 17 18

Number 1.4003 1.4016 1.4301 1.4307 1.4567 1.4541 1.4318 1.4401 1.4404 1.4578 1.4571 1.4439 1.4362

Durability

The durability of an anchorage should not be less than the intended period of use of the part of the structure for which the anchorage is required. For this period of use, the mechanical properties as well as the load bearing behaviour of the anchorage should not be adversely affected by environmental influences such as corrosion, oxidation, aging or alkalinity of the concrete. The anchorage and its protection should be selected in accordance with the environmental conditions at the location of the anchorage. It should be borne in mind that there may be an adverse change in the environmental conditions over the period of use, e.g., corrosion as a result of increased industrialization and that in general, anchorages cannot be inspected and maintained. The use of anchors in the context of durability requirements is regulated by the Approval. In general, the requirements correspond to an assumed intended working life of the anchorage of 50 years.

Examples of corrosion resistant steels and their applications (DIEt, 2009) Corrosion Common abbreviation protection class 11 Low A2 A2L A2L A3 A2 A4 A4L A4L A5

Typical applications

Interiors

III Moderate

Accessible constructions without significant chloride or sulphur dioxide loads

III I Medium

Inaccessible constructions \) with moderate chloride or sulphur dioxide loads

')

'J

1.4462

')

1.4539 1.4565 1.4529 1.4547

4) 4)

IV I Severe

4) 4)

Installations with high corrosion potential due to exposure to chlorides or sulphur dioxide (or due to chemical concentrations, e.g., as found in seawater and road tunnel

atmosphere); for indoor pools see footnotes 2)3)

I) Inaccessible means constructions whose condition cannot be inspected or can only inspected with difficulty and can only be repaired, if necessary, at very great expense 2) Steel with material No. 1.4539 for components in indoor pool atmospheres without regular cleaning of the steel and water complying with German's Drinking Water Statute 3) Steel with material Nos. 1.4565, 1.4529 and 1.4547 for components in indoor pool atmospheres without regular cleaning of the steel and water rich in chloride salt (e.g., brine

water) 4)

No common abbreviation has been decided yet

Electrolytic corrosion may occur between dissimilar metals, e.g. carbon steel in contact with corrosion resistant steel. Other forms of corrosion may occur, e.g. pitting corrosion, crevice corrosion and stress corrosion. These may be particularly relevant for corrosion resistant steels or high strength steel. If an anchor is coated to ensure its proper functioning, e.g. the expansion cone of a torque-controlled expansion anchor, the durability of the coating should be checked in the prequalification tests for the intended conditions of use. fib Bulletin 58: Design of anchorages in concrete

123

Part I: 8 Provisions for ensuring the characteristic resistance ofthe concrete member

Forces originating from anchored components should be accommodated in the design of the structure as required to prevent local overstress of the immediate structural elements. One approach is to check the capacity of the first structural element in the load path (for example, the floor beam directly under an anchored component) for all loads, including the anchorage load. This procedure is repeated for each successive structural element or connection in the load path until the load case including the anchorage loads no longer governs the design of the element. This will occur when the anchorage loads become small relative to the other actions on the structural element.

124

8

Provisions for ensuring the characteristic resistance of the concrete member

8.1

General

The local transmission of the anchor loads to the concrete is checked according to Equation (3.3-1). The characteristic resistance of the anchorage for various types of anchors and for various possible failure modes is given in the following Parts of this Design Guide. The transmission of the anchor loads to the remainder of the structure should be checked for the ultimate limit state and the serviceability limit state according to the usual verifications with due consideration of the anchor loads. For these verifications the additional provisions given in Sections 8.2 and 8.3 should be taken into account.

8.2 The reasoning for the provisions according to Section 8.2 are given in Lieberum et al. (1987) and Reuter, Eligehausen (1992). Where a strut and tie model is used for the determination of shear resistance (Figure 8.2-1), the influence of the anchor-induced stresses on the design shear resistance associated with concrete struts, VRd,c, and tension ties (shear reinforcement), VRd,,, may be taken into account in lieu of using Equation (8.2-1 b).

Shear resistance of concrete member

(1) In general, the shear forces VSd,a induced in the concrete member at the support by anchor loads should not exceed the value VSd•a

=0.4· VRd•1

(8.2-la)

(member without shear reinforcement) VSd,a =O.4·min(VRd ,,;VRd ,c)

(8.2-lb)

(member with shear reinforcement) with:

design shear resistance of member with shear reinforcement as governed by strength of web reinforcement according to CEB-FIB Model Code

VRd"

I~ I

I//I/\~ I

Tension tie V Rd =

min (VRd,c' V Rd"

\

1/

tI I, V

1990 (CEB, 1993), Equations (6.3-12) and (6.3-13) VSd

design shear resistance of member with shear reinforcement as governed by strength of concrete compression strut according to CEB-FIB Model Code 1990 (CEB, 1993), Equations (6.3-10) and (6.3-11)

VRd,c

Rd

concrete strut

)

VRd.c = design shear resistance of concrete compression strut of member with shear reinforcement VRd" =

d~sign shear resistance of member without shear reinforcement according to CEB-FIB Model Code 1990 (CEB, 1993), Equation (6.4-8)

=

VRd, I

When calculating VSd.a the anchor loads should be assumed as point loads with a width of load application tl = S" + 2h'J and t, = Sa + 2h'f where S,I and Sa are the distances between the outermost anchors of a group in direction 1 and direction 2, respectively.

design shear resistance of web reinforcement of member with shear reinforcement

Figure 8.2-1:

Strut and tie modelfor the determination ofshear resistance of a reinforced concrete member

Aids for calculating the active width are given in textbooks, e.g., in DAfStb (1991).

The width over which the shear force is transmitted should be calculated according to the theory of elasticity. (2) Equation (8.2-1) may be neglected if one of the following conditions a) to d) is rifet. a) The embedment depth of the anchor is h'f~0.8·h

(8.2-2)

b) The shear force VSd,a at the support of the concrete member caused by the design actions including the anchor loads is VSd,a "

(8.2-3a)

0.8· VRd,1

(member without shear reinforcement) VSd,a ,,0.8· min (VRd ,,: VRd,C)

(8.2-3b)

(member with shear reinforcement) with VRd. Io

V Rd.,

and

VRd,c

as defined in Equation (8.2-1).

c) Under the characteristic actions, the tension force NSk of a single anchor or the resultant tension force Nt, of the tensioned anchors of an anchor group is :::: 30 kN and the spacing, a, between the fib Bulletin 58: Design ofanchorages in concrete

125

Part I: 8 Provisions for ensuring the characteristic resistance of the concrete member

126 outer anchors of adjacent groups or between the outer anchors of a group and single anchors or between single anchors satisfies Equation (S.2-4).

In Equation (S.2-4a) and Equation (S.2-4.b) the constant carries the dimension [mm I kN°.5]

a ~ 200· ~NSk for single anchors

(S.2-4a)

a ~ 200· ~ NIk for anchor groups

(S.2-4b)

with a in [mm] and NSk in [kN]. Shear stirrups may be provided in order to accommodate transmission of the anchorage loads to the compression zone of the concrete member. Provision of appropriate stirrups is assumed to prevent any negative influence of the anchorage on the shear capacity of the concrete member. The stirrups may also be used to increase the capacity of the anchorage (see Part Nand Part V).

d) The anchor loads are taken up by stirrups that enclose the tension reinforcement of the concrete member and are anchored at the opposite side of the concrete member. The distance from any anchor to the stirrups should not be larger than h,! (see Figure S.2-2). At least two stirrups should be provided.

Supplementary stirrups

= Figure 8.2-2:

t

Stirrups to transfer the loads to the compression zone of the concrete member

(3) If under the characteristic actions, the tension force NSk of a single anchor or the resultant tension force NIk of the tensioned anchors of an anchor group is larger than 60 kN, then either the embedment depth of the anchors should be h,/? O.Sh or supplementary stirrups according to paragraph (2)d) above should be provided.

~

The shear resistance of slabs and beams made of prefabricated concrete and added cast-in-place concrete depends on the amount of shear reinforcement crossing the joint area. If the shear reinforcement takes up all the shear forces (Figure S.2-3a), then the anchor loads may be transmitted into the precast concrete. However, if the shear reinforcement takes up only a part of the shear forces or if precast and cast-in-place concrete are not connected by a shear reinforcement (Figure S.2-3b,c), then the shear capacity of the structural member may be significantly reduced by anchor loads transmitted into the precast concrete, because they increase the tensile stresses in the joint area. In these applications, the anchor loads should be transmitted into the cast-in-place concrete only (Figure S.2-3c). Therefore, only the embedment depth of the anchor in the cast-in-place concrete should be assumed as effective. An exception is the anchorage of suspended ceilings or similar construction with a weight up to 1.0 kN/m' (Figure S.2-3b), because the tensile stresses in the j oint area caused by this load are insignificant.

(4) The above conditions also apply to slabs and beams made of prefabricated units and added cast-in-place concrete. However, anchor loads may be transmitted into the prefabricated concrete only if the safe transmission of the loads into the cast-in-place concrete can be shown. This condition may be assumed as satisfied, if the precast concrete is connected with the cast-in-place concrete by shear reinforcement (e.g., stirrups) according to CEB-FIP Model Code 1990 (CEB, 1993), Equation (6.10-1) with fJ = 0.0 (Figure S.2-3a). If this shear reinforcement between precast and cast-in-place concrete is not present, only the loads of suspended ceilings or similar construction with a weight up to 1.0 kN/m' may be anchored in the precast concrete (Figure S.2-3b). Alternatively, the anchor should extend into the cast-in-place concrete and the embedment depth in the precast concrete is disregarded, when calculating the anchor resistance (Figure S.2-3c).

Shear reinforcement according to CEB-FIP Model Code 1990 (CEB.1993) Equalion (6.10-1) wilh p= 0.0

II

Casl-in-place

concrete

-+-+----her

~ a) Figure 8.2-3:

Precast concrete

g:51 kN/m 2

b)

~ c)

Anchorages in beams and slabs made ofprefabricated concrete and added cast-in-place concrete


127

Part I: 8 Provisions for ensuring the characteristic resistance of the concrete member

128

8.3 Anchor splitting forces are induced in a concrete member by two actions: (1) transfer of a concentrated load into the concrete member (compare Figure 8.3-la with Figure 8.3-lb);

Resistance to splitting forces

In general, the splitting forces caused by anchors should be considered in the design of the concrete member.

(2) the wedging action of undercut anchors (a wedging action will occur also for headed anchors after the formation of a concrete wedge under the head at a high bearing pressure), by bond stresses caused by bonded anchors or by expanding torque-controlled or deformationcontrolled anchors.

r

r

Fsp= O.3F

I-I

I J

Fsp

,

Tc

-~Fsp ~

tCc

tcc a)

Figure 8.3-1:

'Tc

b)

Splitting forces due to concentrated loads and simplified strut-and-tie models: a) Load applied at the concrete surface (compression); b) load transmitted by anchor (tension)

The splitting forces may be taken up by reinforcement or by compression forces if the load transfer area is located in the compression zone of the concrete member. The splitting forces may be neglected if one of the following conditions is met: (I) The load transfer area is in the compression zone of the concrete member. For anchorage in slabs, walls and shells the compression zone should be present in both directions.

For normal reinforced slabs of typical thickness the splitting forces induced by the anchor may be neglected for anchor loads less than 10 kN.

(2) Under the characteristic actions, the tension force N s• of single anchors, or the resultant tension force Nf. of the tensioned anchors of

If anchors are located in the tension zone of a concrete member, in general the splitting forces will increase the tension force in the reinforcement (see Figure 8.3-2). This should be taken into account in the design, if the conditions (2) or (3) of Section 8.3 are not observed. The ratio between splitting force Fsp and anchor tension force N should be given in the relevant Approval or should be evaluated in the prequalification procedure (see Section 1.3). If not, the following values should be considered as a first indication:

an anchor group, is small in respect to the tension resistance of the member longitudinal reinforcement.

Fsp

=

O.SNSd for bonded anchors, headed anchors and anchor channels 1.ONsd for undercut anchors

(3) Under the characteristic actions, the tension force NSk of a single anchor, or the resultant tension force Nfk of the tensioned anchors of an anchor group is not larger than 30 kN. In addition, for anchorages in slabs and walls an appropriate reinforcement for concentrated loads is provided in both directions in the region of the anchorage. The area of the transverse reinforcement should be at least 60% of the longitudinal reinforcement required for the actions due to anchor loads.

1.SNsd for torque-controlled expansion anchors 2.0NRd for deformation-controlled expansion anchors

I

I

b

.,,1-

I_ T=..M + F ~1 Z

Figure 8.3-2:

sp

z

Increase of tension force in reinforcement due to anchor splittingforces

The limiting value of 30 kN in condition (3) is valid for a reinforcement ratio fl = A, / (b'h) '" 0.5%. For a larger reinforcement ratio this value may be increased.


129

Part II: 9 Scope

l30

PART II: CHARACTERISTIC RESISTANCE OF ANCHORAGES WITH POSTINSTALLED EXPANSION ANCHORS, UNDERCUT ANCHORS, SCREW ANCHORS AND TORQUE-CONTROLLED BONDED EXPANSION ANCHORS

9

Scope

Structural concrete is defined as all concrete used for structural purposes including plain, reinforced and prestressed concrete. In general, the strength classes, for which the design method is valid, is C20 to C50 according to CEB-FIP Model Code 1990 (CEB, 1993).

Part I applies unless otherwise noted. Part II applies to anchorages with post-installed expansion anchors, undercut anchors, screw anchors, and torque-controlled bonded expansion anchors (see Figure 1.2-1 to Figure 1.2-4 and Figure 1.2-5b) loaded by tension, shear, combined tension and shear forces as well as bending and torsional moments. It applies to members made of structural concrete with normal weight aggregates. The range of concrete strength classes, for which the design method is valid, is given in the corresponding Approval.

In general, for screw anchors having an embedment depth up to approximately h'J= !OdD, the pullout resistance exceeds 85% of the concrete cone resistance. The value of 85% is derived from theoretical considerations, which indicate that screw anchors with a characteristic pullout resistance less than 85% of the characteristic concrete cone resistance will exhibit combined pullout and concrete cone failure similar to bonded anchors. This failure mode has not been studied in detail to date.

For screw anchors the design method given in this Part is valid only if the characteristic resistance for pullout failure, N Rk.p , given in the Approval is larger than 85% of the characteristic concrete cone resistance of a single screw anchor, N~k.c' according to Equation (l0.1-2a). To ensure suitability and durability of these anchors for use in structural concrete, prequalification testing should be performed (see Section 1.3).

Additional rules for anchors with larger embedment depths may be given in the relevant Approval. In general, this Part is valid for concrete members and anchorages subjected to predominantly static loading. Exceptions to this rule are addressed in Sections 13 arid 14.

According to the safety concept of partial factors (see Equation (3.3-1)), it should be shown that the design value of the actions does not exceed the design value of the resistance. Equation (3.3-1) should be applied for all types of actions on the anchors (tension, shear, combined tension and shear), as well as for all possible failure modes (steel failure, pullout failure, concrete

cone failure and splitting failure under tension loading and steel failure, pullout failure, pryout failure and concrete edge failure under shear loading). Flowcharts for the calculation of the characteristic resistances for the elastic and plastic design approach are given in Figure 9-1 and Figure 9-2, respectively.

In the following sections, equations for calculating the characteristic resistance of anchorages without anchorage reinforcement for the elastic design approach (Section 10) and plastic design approach (Section 11) are given for all types of actions and for all failure modes. Requirements for the serviceability and fatigue limit states and for seismic actions are given in Sections 12 to 14. The provisions are valid, when the spacing between the outer anchor of adjoining anchor groups or to single anchors or the distance between single anchors are a > Sc"N (concrete failure in tension or pryout failure in shear), a> sa.,p (splitting failure) and a> 3c[ (concrete edge failure in shear) (see Figure 1.2-8 to Figure 1.2-10).

The effect of abandoned drilled holes can be neglected in the design, provided that those holes are filled with high strength non-shrink mortar. In general, for the majority of structures the poslttoning and size of existing reinforcement in the concrete member in which post-installed anchors are placed is not known. However, in the following situations detailed information may be available:

during design of new construction, anchor reinforcement for postinstalled anchorages is specified;

Where the existence of anchor reinforcement can be verified with respect to size and positioning, this reinforcement may be taken into account for the calculation of the characteristic resistance of the anchorage following the approach for headed anchors given in Section 19.2. Tolerances on the position of the post-installed anchors in respect to the location of the anchor reinforcement should be taken into account in an unfavourable way such to reduce the calculated resistance.

drawings and construction protocols of existing structures are available; detection tools based on scanning techniques are used to provide infonnation on existing reinforcement. Provided the location as well as the size of the existing reinforcement is known and the existing reinforcement fulfils the requirements to act as anchor reinforcement, then this reinforcement may be taken into account in the design of post-installed anchorages. The design should be carried out following the approach for headed anchors given in Section 19.2 for the verification of failure modes affected by anchor reinforcement (concrete cone failure under tension loading and concrete edge failure under shear loading).


l31

132

Part II: 9 Scope

Note that for the typical range of embedment depth of post-installed mechanical anchors the consideration of anchor reinforcement may rather be applicable for the calculation of the resistance to shear loading than for the resistance to tension loads. Because the exact location of the anchors with respect to the position of anchor reinforcement may not be known, the corresponding tolerances need to be taken into account in an unfavourable way, when designing postinstalled anchors including anchor reinforcement. For anchorages close to an edge with an anchor reinforcement to take up shear loads, cracks caused by the shear load will occur in the concrete well before reaching the ultimate load. The width of these cracks is limited to about 0.3 mm in the serviceability limit state. To avoid failure of the tensioned anchors, the design should be performed using anchors suitable for cracked concrete. Design for cracked concrete is not necessarily required where the exponent a in the interaction Equation (10.3-ld) (simplified approach) or Equation (10.3-3) (alternative approach) is conservatively taken as a= 2/3 (see Section 19.2.3).

In case of combined tension and shear loads where the shear load is taken up by anchor reinforcement, premature failure of the tension loaded anchors due to excessive cracking caused by the shear load should be avoided. It is therefore mandatory in such cases to use anchors suitable for cracked concrete.

To use this Design Guide the following values should be available either from an Approval or they should be evaluated from the results of prequalification tests (see Section 1.3). - N Rk., (or A,,j,,k)

See Section 10.1.2

-NRk,p

See Section 10.1.3

- k", k"""

See Section 10.1.4

- h'J

See Section 10.1.4 and Figure 2.5-1

-S",N, C",N

See Section 10.1.4

- c""p' s""p

See Section 10.1.5

- Cmim Smim

hmin

See Section 10.1.5

- VRk" (or A,,j,,k and k2)

See Section 10.2.2.1

- M~k,'


- VRk,p (or k3)

See Section 10.2.3

- k4

See Section 10.2.4

- d, d"om,

See Section 10.2.5.1 and Figure 2.5-1

-IJ


- Type of steel (ductile, brittle)

See Sections 10.2.2.1, 11.1 and 4.3.2.1(4)

- rM;

for different failure modes

See Section 3.4.2

- Ratio between splitting force and anchor tension force

See Section 8.3

- Limitation on concrete strength classes of base material The minimum values for member thickness and reinforcement as well as for edge distance and spacing of anchors given in the relevant Approval should be respected.


133

Part II: 9 Scope

134

Durability (Section 7)

Application criteria

(Sections 4.3.1 and 9)

Sleel resistance

Concrete resistance

Sleel resistance

Find approprfate partial factors (Section 3.4.2)

Concrete resistance

Find appropriate partial factors (Section 3.4.2)

I Find sm"" ..,,\!

Find smallest

design resistance NRd

design reisstance

VR~

If combined lenslon and shear (Section 10.3)

NSd S NRd

VSd ,.VRd

Serviceability limit state (Section 12)

Fatigue (Section 13)

Seismic (Section 14)

Fire (Section 6.5) Ensuring characteristic

resistance of concrete member (Section 6)

Figure 9-1:

Flowchart B for the calculation of the resistance of anchorages with post-installed expansion anchors, undercut anchors, concrete screws or torquecontrolled bonded expansion anchors (elastic design approach)

I~ I j

Durability

(Section 7)

I

ApplicatIon cnteria (Sections 4.3.2.1 and 11.1)

I

j Shear

(Section 11.3)

l I Steel resistance

Steel resistance

------r

I

Concrete resistance

I

Concrete pryout (Sect. 11.3.3)

I

I V~
--'-

I~ Figure 9-2:

Flowchart C for the calculation of the resistance of post-installed expansion anchors, undercut anchors, concrete screws or torque-controlled bonded expansion anchors (plastic design approach)


135

Part II: 10 Ultimate limit state - elastic design approach

l36

10

Ultimate limit state - elastic design approach

According to the elastic design approach, loads are distributed to the anchors of an anchor group following the theory of elasticity (see Section 4.3.1). The field of application is given in Section 4.3.1.1. For screw anchors see also Section 9.

The most loaded anchor of a group is the anchor with the highest design tension load (N;d)'

10.1

Resistance to tension load

10.1.1


The required verifications are summarized in Table 10.1-1.

Table JO.1-1:

Required verifications Jor tension loading (elastic design approach)

Failure mode Steel failure

Most loaded anchor NM,s

NSd 'SNRcI,s

=--

hn

Pullout 2 failure

Anchor group ,)

Single Anchor

NSd :S;NRd,p

Concrete 3 cone failure

N

Splitting 4 failure

NSJ :s; NRd"P

Sd -

Rd,c

::: NRk,p

r"tp

N"Sd
Anchor group ,)

,$

Y'n N

N"Sd -
::: NRk,c:

y,.

Ng
Rd,c

rAte

=

N Rk,sp YAhp

= NRk,c r,lfe

Ngso p::: N Rk,sp Y"frp

,) Verification is performed for those anchors ofa group loaded in tension.

10.1.2 The characteristic resistance N Rk., of an anchor in the case of steel failure given in the Approval is obtained from Equation (10.1-1). N Rk.'

Steel failure

The characteristic resistance N Rk., of an anchor in case of steel failure should be taken from the relevant Approval.

(10.1-1)

= A, . Juk

For anchors having a variable cross section over the anchor length, Equation (10.1-1) should be verified for the various cross sectional areas and corresponding steel strengths.

10.1.3 Reliable design models for calculation of the characteristic resistance for pullout failure modes are not available. Therefore, the resistance for pullout failure is evaluated from the result of Approval tests (see Section 1.3).

Pullout failure

The characteristic resistance NRk.p of an anchor in case of pullout failure should be taken from the relevant Approval.

10.1.4 The characteristic resistance against the formation of a concrete cone may be increased by a compressive force acting on the concrete surface close to the tensioned anchors, e.g., when a bending moment is acting on the fixture and the anchor spacing is s::; 1.5h'f (see Figure 10.1-1). This influence is neglected in Equation (10.1-2), since no generally accepted design model is yet available. Design equations are discussed in Bruckner et al. (2001) and Fichtner, Eligehausen (2007). ('><.

Concrete cone failure

The characteristic resistance N Rk•c of an anchor or an anchor group in the case of concrete cone failure is obtained from Equation (10.1-2): N M,e =NoRk,c 'If/A,N 'If/s,N 'If/eC,N 'If/rC,N

with:

NOM,e -

~!lflll~~~('-,JJr~lJ".'L""'~

c

Figure 10.1-1: Example oj an anchorage where the compression Jorce caused by a bending moment acting on the fixture may increase the concrete cone capacity oj the tensioned anchor fib Bulletin 58: Design ofanchorages in concrete

If/,.N

=

If/ec,N

=

If/re,N

characteristic resistance of a single anchor without edge and spacing effects

Ac.N/~.N

If/A.N

M

tl T

(10.1-2)

factor accounting for the geometric effects of spacing and edge distance factor accounting for the influence of edges of the concrete member on the distribution of stresses in the concrete factor accounting for the group effect when different tension loads are imposed to the individual anchors of a group (e.g., eccentric loading) factor accounting for the negative effect of closely spaced reinforcement in the concrete member on the strength of anchors with an embedment depth h'f< 100 mm

l37


138 The definition of the embedment depth hej as used in the following equations is shown in Fig. 2.5-1 and Fig. 2.5-2 for the various anchor types. The different quantities in Equation (10.1-2) are explained below.

The reduced concrete cone capacity in cracked concrete relative to the value in uncracked concrete is due to the disturbance of the distribution of stresses in the concrete. Certain types of torque-controlled expansion anchors (see Figure 1.2-1) and deformation controlled expansion anchors (see Figure 1.2-2) may not be suitable for transferring tension loads into cracked concrete. Therefore, these anchors may only be used in concrete that remains uncracked in the proximity of the anchor during the service life of the anchorage.

a) The characteristic resistance of a single anchor without edge and spacing effects, N~k.e' is obtained from Equation (l0.1-2a):

N....e = k

J •

.g:;. h;)

(1O.1-2a)

k J = k" = 7.7 [NO.5 / mmO. 5] cracked concrete k

J

=k""" =11. 0

[NO.5 / mm0.5] uncracked concrete

According to Equation (1O.1-2a), the concrete cone resistance increases with h;) . This is in conformity with experimental and analytical results based on fracture mechanics (Eligehausen et aI., 2006-2). On the basis of a large experimental database the mean concrete cone failure load (mean resistance) ofa single anchor in uncracked concrete can be approximated by (Eligehausen et aI., 2006-2):

N~II'c :::: k· ~fcC,200 . h~/

(10.1-3a)

where /ce.200 represents the concrete strength measured on cubes with a side length of 200 mm, and k has been identified as 13.5 for mechanical anchors. The values of kJ used in Equation (l0.1-2a) are derived based on the Equations (l0.1-3a,b,c):

;;k

= 0.84;;k.200

(10.1-3b)

Note that Equation (1O.1-3b) is valid for concrete C20. However, this factor may be conservatively taken as constant for all concrete strength classes.

N Rk.e

=0.75NRm •e

assuming a COY = 15%

(l0.1-3c)

Comparison of experimental data has shown that the mean concrete cone capacity of cracked concrete may reasonably be assumed as about 70% of the capacity in uncracked concrete (Eligehausen et aI., 2006-2). kJ-values depend on anchor type and dimensions. kJ-values other than given in Equation (10.1-2a) but not larger than the values valid for headed bolts (see Section 19.1.1.4) k,,= 8.9 and k""" = 12.7 may be taken if proven by suitable prequalification tests. For undercut anchors with a bearing area fulfilling the requirements given in Section 19.1.1.3, values k,,= 8.9 and k""" = 12.7 may be assumed. b) The factor If/A.N = Ae.N / A~.N takes into account the geometric effects of spacing and edge distance, where:

A~N

A~,N =Sc.r.N° Scr.N

2

Figure 10.1-2: Idealised concrete cone and area A~.N of an individual anchor loaded in tension


(l0.1-2b)

Scr,N

.A

L~j]

reference area of the concrete cone of an individual anchor with large spacing and edge distance projected on the concrete surface; the concrete cone is idealised as a pyramid with a height equal to hejand a base length equal to S".N (see Figure 10.1-2)

Ae.N

actual projected area of concrete cone of the anchorage at the concrete surface, limited by overlapping concrete cones of adjacent anchors (s < S",.N), as well as by edges of the concrete member (c < C".N). It may be deduced from the idealised failure cones of single anchors. Examples for the calculation of Ae.N are given in Figure 10.1-3 and Figure 10.1-4. In general the values S".N and C".N may be taken according to Equation (l0.1-2bd Scr,N ::::

3hef

Ccr,N ::::

O.5scr ,N

(l0.1-2b J)

= I.5he!

(10.1-2b2)

139

140


O5

5,

,I' o

Sq.>!,

1~

I

Ic

0.55<","

JS(

. AC.N=(O.5s a ,N+ C

Ae,N= (Sct,N+Sl)'(S",N+S2)

"'

",a_~,

05' • 1

a)C[ 'l~ ""

b)

~

" l ,

?5SO',N 0.5s"'JI

I

'

.0.55",>11 O.5Set.~

'A<;:.N = (scr,NHscr,N+S2)

c)

r!: . ~

Figure 10,1-3: Examples of idealised concrete cones and areas A"Nin the case of tension loading: a) anchor group (s, < S",N, S2 < s",,,) far from edges; b) single anchor at an edge (c, < C",N); c) anchorage with s, > S",N, S2 < S",N far from edges

For anchorages with s, > S"',N (example see Figure 10.l-3c) a common failure cone of all anchors is not expected to occur. Therefore, the characteristic concrete cone resistance should be calculated taking into account the subgroups,

~

~

.1lo

.1l

d

~

N

'"

•

~

d

N

o

k C, I, 5,

C,

Ae,N=-

if

a)

(c 1+

Cer,N

:5:

Scr,N

51

Ae.N= (C 1+ 5 1+ O.5s cr.N )' (C 2+ 5 2+

+ O.5S cr,N)'Scr,N

51

c 1 ::;;:

~,5S0'"1 >I'

4

if (c

and

b)

c,):5: C",N (5," ,5,):5: 5",N

Q.5S cr,N)

and

Figure 10,1-4: Examples of areas A"N in the case of tension load: a) group of two anchors at the edge of a concrete member; b) group offour anchors at the corner of a concrete member

Anchorages with a large edge distance show a rotationally symmetric distribution of stresses in the concrete, This distribution is disturbed if the anchor is located close to an edge, which causes a reduction of the concrete cone failure load,

c) The factor 'f/"N accounts for the disturbance of the distribution of stresses in the concrete by edges of the concrete member. For anchorages affected by more than one edge, e,g" anchorages in the comer of a concrete member or in a narrow member, the smallest edge distance, c, should be inserted in Equation (10.l-2c), c '!-',N =0,7+0,3·-,,1.0 (10.1-2c) ,

For reason of simplicity, the eccentricity factor may be taken as ,!-,,,,N = 1.0 if the most stressed anchor is verified ( N;d " N:u." / r Me) and the characteristic resistance of this anchor is taken as N:u..,,, NRk" / n with NRk" according to Equation (10.1-2) with ,!-,,,,N = 1.0 and n = number of anchors loaded in tension.


cer,N

d) The factor ,!-,,,,N accounts for the reduction of the group capacity when the tension loads acting on the individual anchors of a group are not uniform. If/ec,N

1

,,1.0

(l0,1-2d)

1+2eN /s cr ,N

141


142 with:

For the example shown in Figure 4.3-4c, (10,1-2) is:

'f/ec,N

to be inserted in Equation

eccentricity of the resulting tensile force acting on the tensioned anchors with respect to the centre of gravity of the tensioned anchors (see Section 4.3,1.2), Where there is an eccentricity in two directions (see Figure 4.3-4c), 'f/ec,N should be determined separately for each direction according to Equation (10, 1-2d) and the product of both factors should be inserted in Equation (10,1-2),

eN

I If/cc,N

1+2eN"/s,,,N 1+2eN,2/s",N

For anchorages in the vicinity of reinforcement, the tensile stresses in concrete induced by the anchorage and by the bond action of reinforcement are superimposed, This effect is especially pronounced for small bar spacing and large bar diameters, Furthermore, the concrete strength in the region of closely spaced reinforcement may be smaller than in the core of the member, Both effects are taken into account by the factor 'f/,.,N' For anchorages with an embedment depth h'/::: 100 nun surface reinforcement may have positive effects, The concrete cone capacity may increase due to confinement of the concrete and the ductility may increase due to dowel action of the reinforcement (Nilsson, Elfgren, 2009), Further investigations are needed in order to clarifY and quantifY these effects,

e) The factor 'f/,.,N accounts for the reduced strength of anchors with an embedment depth h,/< 100 mm, inserted in a concrete element with closely spaced reinforcement.

hi =0,5+-'", 200

'f/

N

'f/",N=

for s < 150 mm (for any diameter d,) or s < 100 mm (for d,::; 10 mm) fors::: 150 mm (for any diameter d,)

1.0

(IO,I-2e l) (10,1-2e2)

or s::: 100 mm (for d,::; 10 mm) where s denotes the spacing of reinforcement within the concrete element. f) Special cases

IC 2,2

C 2,2

0 •

(

I' a)

5,

~2

•

C 2,1

•

,,

,r C, ,f

(c, : C2,,; C2,2):;S; Cer,N

0

1

•

52

lC

2 ,1

C,,' j' 5, " C,,2 ,f

b) (c",; C,,2; C2,,;C 2,2)

:;s; Cer,N

Figure 10,1-5: Examples of anchorages in concrete members where h;I' S;"N and C;',N may be used: a) anchorage with three edges; b) anchorage with four edges

~

I

.-----'

\

v

I

u

-1+---+1

-' 1.

C,

C2

S,

"

1.

'--'

"" I!I />><'"

//l":~

' hef

200

..

0

hef and h'ef =s=, - - , h'I

cer,N

(10,1-2f2)

scr,N

with:

maximum centre to centre spacing of anchors::; Sa,N

10,1-4 and in Equations (IO.l-2c) and (lO.l-2d) the values S",N and C"',N are replaced by S;"N and C;, .. N' determined according to Equation (10, 1-2f3), respectively:

c, ~ 110 mm

.c

cm~ = __

The value h;1 is inserted in Equation (10, 1-2a) for he; Furthermore, for

Example: 1:1

For groups of anchors h'l should be substituted by the larger of the following values:

the determination of A~,N and Ae,N according to Figure 10,1-2 to Figure

"

t

(l0,1-2fl )

cer,N

Sma, =

/ /

u

h he/' =crn~ - - , 'I

cm., = maximum distance from the centre of an anchor to the edge of concrete member::; C",N

\

0 0

N

~

In applications where three or more edge distances are smaller than C",N (see Figure 10,1-5), Equation (10,1-2) leads to conservative results, In case of a single anchor, more precise results are obtained if the value he/is substituted by:

c,= 100 mm C3 = 120 mm =C rn" c,= 80 mm S, = 210 mm h,,= 200 mm h;r= max(120/1 ,5; 210/3) =80mm

, scr,N

, =2ccr ,N

h~ =y;-"Scr,N

(10,1-2f3)

'I

An example for the calculation of h;1 is illustrated in Figure 10.1-6,

Figure 10,1-6: Illustration of the calculation of h;1 for an anchorage with two anchors influenced by four edges, When calculating h;I'

S",N = 2C",N =

3h,/is assumed

10.1.5 Splitting failure may occur either during installation of anchors or due to loading, In any case, splitting failure should be avoided, The design model for splitting failure in uncracked concrete does not take into account the influence of edge reinforcement. Because at edges the concrete tensile strength may be partly used up by tensile stresses due to shrinkage, edge reinforcement should be provided to compensate for this effect.

Splitting failure

If the edge distance of an anchor is smaller than the value c""P (ca"p see Section 10,1.5.2), then adequate reinforcement should be provided parallel to the edge of the member.

A general design model allowing for the calculation of the characteristic splitting resistance is not yet available, In absence of more accurate information, adequate conservative rules should be adopted,


143

Part 11: 10 Ultimate limit state - elastic design approach

144

10.1.5.1

Splitting failure due to anchor installation

Splitting failure is avoided during anchor installation provided that sufficient edge distance, spacing of anchors, member thickness and reinforcement are ensured, Minimum values for those parameters are included in the relevant Approval or, alternatively, they should be evaluated on the basis of results obtained from appropriate tests in the prequalification procedure (see Section 1.3),

10.1.5.2 a) The characteristic edge distance, ca"p, (= 0,5s""p) is normally evaluated by testing single anchors at the comer. Since higher splitting forces are generated in the concrete by a group of anchors, larger edge distances (c ::: l.2c"",p) are required for anchor groups to preclude a splitting failure,

2h'f for undercut anchors, screw anchors and torque-controlled bonded expansion anchors

(10, 1-4a)

3h'ffor expansion anchors

(1O.I-4b)

The splitting forces generated by the anchor may cause splitting cracks in the concrete, However, if the concrete member is adequately reinforced and the crack width due to quasi-permanent actions including the splitting forces induced by the anchors is limited to Wk - 0,3 mm, it may be assumed that the concrete cone resistance and the pullout resistance valid for anchors in cracked concrete will be reached, Naturally, the anchor should be qualified for application in cracked concrete, Equation (10,1-5) is an approximation, because the splitting failure load depends partly on other parameters than the concrete cone failure load, However, it is believed that Equation (10,1-5) is conservative for anchors exhibiting concrete cone failure, Adequate values for ce",p and s""p should be given in the relevant Approval or be evaluated from the results of appropriate tests during the pre qualification procedure (see Section 1.3), The

Verification of splitting failure is not required provided that one of the following conditions is fulfilled: (I) The depth of the concrete member is h::: hm;" and the edge distance in any direction is C::: 1.0c""p for single anchors and c::: 1.2ca"p for anchor groups, The characteristic edge distance c""p and the characteristic spacing sa"p should be taken from the relevant Approval.

As a first indication the following values may be taken, which are valid for a member thickness h = 2h'f:

c""p

Splitting failure due to anchor loading

(2) Anchors suitable for application in cracked concrete are used. The characteristic resistance for pullout failure and concrete cone failure is calculated for cracked concrete and adequate reinforcement is arranged in the concrete element able to resist the splitting forces and to limit the crack width,

b)

If condition a) above is not fulfilled, then the characteristic resistance of a single anchor or an anchor group for splitting failure should be calculated according to Equation (10,1-5):

N Rk,sp

::::::;

~,c ''1/A,N 'If/s,N 'lj/ec,N 'Ij/re,N ''f/fI,sp

(10.1-5)

,

characteristic edge distance, c""p, ensures that single anchors with c::: ca"p will reach the concrete cone failure load according to Equation (10, 1-2a), For anchors that exhibit pullout failure in single anchor tests at large edge distance, the value c""p is evaluated for the characteristic pullout resistance NRk,p' Hence, Equation (10.1-5) yields unconservative results because the outset value is taken as concrete cone resistance for a single anchor instead of the pullout resistance, Io this case, the value of NRk,P should be substituted for N~k,e in Equation (10,1-5), This adjustment is unnecessary if the pullout and

and

(1O.I-2a) to (l0,1-2f) and

If/A,N

"",N,

'I'",N

according

to

Equations

= Ae,N / A~,N as defined in Section

1O.I.4b. When applying the relevant equations, the values S""N and C""N should be replaced by the values s""'P and c""'P' defined on the basis of a member thickness equal to hm;,,, respectively, If/iI,SP

concrete cone resistances are nearly equal. The special case of anchorages with three or more edge distances c < c""P is addressed by including Equation (lO.l-2f) in Equation (10,1-5),

'I'""p

factor to account for the influence of the actual member thickness on the characteristic splitting resistance

1

=(h h J213j::;; (he! + 1.5c J213 : ; 2 hm,.

mm

,0

(lO.l-5a)

~1.0

If c""P as determined in the prequalification tests is not larger than C",N, then splitting failure is assumed not to occur and Equation (10.1-5) may be neglected for all applications,

For anchorages affected by more than one edge, e,g" anchorages in the comer of a concrete member or in a narrow member, the smallest edge distance should be inserted for CI in Equation (lO.l-5a),

The member thickness influences the splitting failure load up to a limiting value, The value h'f+ 1.5cI is based on experimental investigations by Asmus (2007), The factor 'I'h"p is limited to 2,0 because in tests a larger increase of the splitting failure load due to an increase of the member depth has not been observed,

10.2 For consideration of friction forces in the desigo, see Section 4.2,

N~k,e ,

'I'",N

with

Resistance to shear load

Io general, the contribution of friction between fixture and concrete surface to the shear resistance of anchorages is neglected,

The shear resistance of an anchorage should be calculated for all possible failure modes.

10.2.1 The most loaded anchor of a group is the anchor with the highest desigo shear load ( V;~

)



The required verifications are summarised in Table 10.2-1.

145


146

Table 10.2-1:

Required verifications for shear loading (elastic design approach)

Failure mode

Single Anchor

Steel failure without

VSd :$; VRd,s :::: VRk,s

Anchor group') Most loaded anchor V," Sd < _ VRd,s =

y""

lever arm

Steel failure 2 with

VScI ::;V ." = VRk,sm -Rd

Y..

Anchor group

v:Rk,s hE

v~::; VRd ,S'" = VRk,sm -y..

lever arm

3

Pullout failure

V
Rd ,p

VRk,p

=-

r,lfp

V II
Rd,p

=VRk,p Y!.fp

Concrete VRJ;.,cp v~ ::; v. _VRk,cp a)
In general the value VRk.' given in the Approval is obtained from Equation (10.2-1):

VRk ., =k2 ·A, '/',k

10.2.2

Steel failure

10.2.2.1

Shear load without lever arm

The characteristic resistance VRk., of an anchor in the case of steel failure should be taken from the relevant Approval.

(10.2-1)

with:

k2 = 0.5

For anchors with a reduced section along the length of the bolt, e.g., bolt type expansion anchors, the characteristic resistance for steel failure VRk., may be smaller than the value given by Equation (10.2-1) if failure is caused by shear in the reduced section. In a case where the sleeve of a sleeve-type anchor extends through the fixture, the shear resistance VRk., of the anchor is increased beyond the capacity of the bolt, depending on the ductility and relative stiffness of the anchor sleeve and bolt. The degree to which the shear resistance is increased is highly dependent on the anchor design.

In both cases, the characteristic resistance should be taken from the relevant Approval or evaluated from the results of appropriate prequalification tests (see Section 1.3). When the shear load is acting in the direction of a row of anchors with hole clearance (ael:s. ael.! according to Table 4.3-1) and all anchors are assumed to resist the imposed shear load, the strength of the anchors made of brittle steel (rupture elongation measured over a length of five bolt diameter < 8%) is negatively affected by the limited anchor deformability. To account for this effect, an adequate reduction factor (- 0.8) should be used (Fuchs, 1992). This effect can be neglected if the anchor steel is ductile (rupture elongation measured over a length of five bolt diameter ~ 8%). For anchorages with ael> ael.!, the influence of the hole clearance with respect to the anchor diameter on the anchorage behaviour is taken into account by assuming that only some of the anchors resist the imposed shear load (examples see Figure 4.3-18 and Figure 4.3-19).

A reduction factor equal to 0.8 should be applied to the shear resistance of the most loaded anchor of a group of anchors, calculated according to Equation (10.2-1), when the hole clearance is ael:s. ael.! (ael.! see Table 4.3-1), the anchors are made of steel with low ductility, the shear load is acting in the direction of the row of anchors and all anchors are assumed to resist the applied shear load(for examples see Figure 4.3-5). When shear loads of alternating sign are imposed to the anchorage, appropriate measures should be taken to avoid a fatigue failure of the anchor steel (see Section 6.3).

10.2.2.2 For anchors with a significantly reduced section along the anchor length, the characteristic bending resistance should be calculated for the reduced section or evaluated by appropriate tests.

Shear load with lever arm

The characteristic resistance of an anchor is obtained from Equation (10.2-2). VRk,SII/

aM .

MO Rk,s::;; VRk,s

(10.2-2)

I

where:


aM

a factor discussed in Section 4.3.1.5

I

length of the lever arm according to Equation (4.3-2) 147


148

In general the characteristic bending resistance of an anchor is calculated according to Equation (l0.2-2a):

M~k"

=1.5 . w", .!"k

(1O.2-2a)

M~.

=

We'

Equation (10.2-2a) is based on Scheer et al. (1987).

VRk.,

section modulus of an individual anchor at the sheared crosssection

=

10.2.3 Anchors with a low pullout resistance, NRk,p, compared to concrete cone resistance, N~k,e' may fail by pullout failure under shear load. The corresponding characteristic resistance should be evaluated from test results.

characteristic bending resistance of an individual anchor taken from the relevant Approval

characteristic shear resistance for lever arm equal to zero taken from the relevant Approval (see Section 10.2.2.1)

Pullout failure

The characteristic resistance VRk•p of an anchor in case of pullout failure should be taken from the relevant Approval.

As a first indication Equation (10.2-3) can be used (compare Section 3.2 and Equation (10.2-4)): VRk,p

= k, . NRk,p

(10.2-3)

with:

k,

2.0

NRk,p

characteristic resistance according to Section 10.1.3

The factor k, in Equation (10.2-3) should be considered as approximation. More exact values of k, should be given in the Approval or may be evaluated from the results of pre qualification tests (see Section 1.3).

10.2.4


The characteristic resistance VRk,ep of an anchorage in case of pryout failure is obtained from Equation (10.2-4): The effect of the eccentricity in creating an uneven shear load distribution needs to be accounted for. A reasonable assumption is to set eN = ev.

VRk,ep

=k .. N Rk •e

with

As a first indication the following values may be taken for k4 :

NRk,e =

1.0 for h eJ < 60 mm

k4

(10.2-4)

k4

=

characteristic resistance according to Section 10.1.4, determined for the anchors loaded in shear assuming eN = ev factor to be taken from the relevant Approval.

2.0 for heJ?:. 60 mm

~"T « ~7~ / Z

Ae.N

1

ii

w

~Nt~..Ii'"]52 ....

TSd

',r

fB."r;;

~I 0.55,

1.§h(!f

5

-

Ae.N

Ii ~ .l'l

v'"

o

For anchor groups with shear forces (or components thereof) on the individual anchors in opposing directions (e.g., anchorages loaded predominantly by a torsion moment), the most unfavourable anchor should be verified. When calculating the area Ae,N it should conservatively be assumed that there is a virtual edge (c = O.5s) in the direction of the neighbouring anchor(s) (see Figure 10.2-1) .

UN

k5 , ,f

~

~

f05~f

'

)

s, :S Scr.N and S2:S Scr.N

(Cl;C2):'Ocer.Nands l :'OS,,·.N

a)

b)

Figure 10.2-1: Calculation of area Ae,N for pryout failure for group anchorages with shear load (or components thereof) on anchors acting in opposing directions: a) group of four anchors away from edges; b) group of two anchors located in a corner.

10.2.5 In general, for anchor groups with 4 or less anchors and an edge distance c ?:. max( 60d"o"" IOh eJ) in all directions, it may be assumed that no concrete edge failure will occur. For anchor groups with more than 4 anchors the verification of concrete edge failure should be performed.


In Section 4.3.1.3 a general method and an alternative approach are presented to calculate the shear loads on anchors. The corresponding concrete edge resistance should be calculated according to Section 10.2.5.1.1 or 10.2.5.1.2, respectively.

According to Section 4.3.1.3, in case of anchors close to an edge loaded by shear forces or torsional moments, it may be assumed that the failure crack originates either from the front or from the back anchor(s). If it is assumed that the failure crack originates from the front anchors and the required verifications for tension, shear as well as combined tension and shear loads are satisfied, no serviceability check is necessary. If it is assumed that the failure crack does not originate from the front anchors, then an additional check at the serviceability limit state is required (see Section 6.2).


149

150

Part II: 10 Ultimate limit state- elastic design approach

10.2.5.1

General method

10.2.5.1.1 Failure crack originating from the front anchors The characteristic resistance VRk•c of a single anchor or the front anchors of an anchor group without or with hole clearance close to an edge is obtained from Equation (10.2-5):

v:Rk,e =V'Rk,e . u,A,V . u, . u,s,V . '"ec,V . '"a,V .'f're,V 'IF ." h,V 'r

'r

'f"

(10.2-5)

'f"

where:

v, -

characteristic resistance of an anchor loaded perpendicular to the edge, where effects of spacing, further edges and member thickness are not applicable

Rk,c

If/A.V =

factor to take into account the geometric effects of spacing, member thickness and further edges

=

Ac.v / A~.v

If/iI,V =

correction factor to take into account that the resistance does not decrease linearly with the member thickness as assumed by the ratio Ac v / A~ v

If/,.v

=

factor to take into account the influence of further edges on the distribution of stresses in the concrete

'f/ec.v=

factor to take into account a group effect when different shear loads are acting on the individual anchors of a group (e.g., eccentric shear loading)

If/a,v =

factor to take into account the angle between the shear load applied and the direction perpendicular to the free edge of the concrete member under consideration

Ij/re, V=

factor to take into account the type of edge reinforcement

"

~ 2

a'

• •

-

• •

VSd

•

o Unloaded anchor

V,

The different factors in Equation (10.2-5) are explained below. V, = VSd 'cosa' V2 = VSd 'sina'

Vs9,

V2

s] c1 V

s1

c1

J c,

,1·

s,

t

IV

Loaded anchor

a) O.5V2

For anchorages placed at a comer, the characteristic resistance should be checked for both edges, the smallest ratio V!J Rd •c is decisive (for an example see Figure 10.2-2).

'"

b)

0

- VO flO CJ. v /

.,~

1/

C2

Sd

1

I

O);~

j

S2

j.

c)

Figure 10.2-2: a) Example of a group of anchors with normal hole clearance (ael:::: ael.J at a corner under shear loading; b) resistance verified for the left edge; c) resistance verified for the bollom edge

Care should be exercised in applying the correct angle of load direction, edge distance and spacing for the calculation of the characteristic resistance according to Equation (10.2-5). Because c, is always defined as edge distance in direction perpendicular to the edge for which the resistance is verified, the indices of the spacing and edge distance in Figure 1O.2-2c have been changed compared to Figure 1O.2-2b. According to Equation (10.2-5a) the concrete resistance increases with c1.5. This agrees with test results and can be explained by fracture mechanics. The influence of the anchor stiffness on the concrete resistance is taken into account by means of doom and 1j (see Equation (10.2-5a)), This effect decreases with increasing edge distance.

a) The characteristic resistance of a single anchor with large values for edge distance in direction 2 (see Figure 10.2-3) and member thickness loaded in shear perpendicular to the edge corresponds to:

v' - k Rk,e -

v'

da

1/011/'

IP rr 'Cj1.5 f 'VJck

(10.2-5a)

with:


151


152

Note that the given values for the parameter k, are determined based on SI units. The basic approach for calculating the characteristic concrete edge breakout resistance as represented by Equation (10.2-5a) is based on numerical simulations and numerous test results (Hofinann, 2005). The concrete capacity design (CCD) approach for edge breakout (Fuchs et aI., 1995) as given in Equation (lO.2-6a) is based on tests with anchors having dnom:O: 40 mm and 1j:O: 8dnom , the majority of tests having been conducted with d"om :0: 30 mm.

V%m.c

=1.o.(lLJO., .~dnom '~fcc,'oo ·ci· d

5

(10.2-6a)

where V;'n,c is the mean concrete edge breakout resistance and icc"oo represents the concrete strength measured with 200 mm cubes. Hofmann (2005) proposed Equation (lO.2-6b) and extended the ranges of £:410111 and lj.

V;'",c =3.0,d:a", .If '~fcc,'oo where a and respectively.

fJ

·ci

=

k,." = 1.7

kv

= kv,uner = 2.4

anchorages in cracked concrete

a=o.I{~r

anchorages in uncracked concrete

[-]

(1O.2-5aJ)

[ -]

(lO.2-5a,)

O

fJ --0.1·

(d J ~:II/

"

dl/omS 60 mm

nom

5

k,

(10.2-6b)

For anchors having dnom > 60 mm the limiting value of dna", = 60 mm should be inserted in Equations (10.2-5a) and (lO.2-5a,).

1j= influence length =

hel for anchors with constant diameter over the embedment depth (e.g., threaded rods)

=

for other cases, as given in the relevant Approval or as determined from the results of prequalification tests (see Section 1.3)

The following limits on the influence length apply: are given by Equations (lO.2-5aa and (lO.2-5a,),

The majority of tests in the underlying database were carried out in the range dnom:O: 40 mm and 1j:o: 12.5dnom . In the associated numerical studies, d,wm was extended to 190 mm and 1j to 16d"om' Hofmann (2005) noted that the modified expression may be used for d,wm:O: 65 mm with a limit on 1j of 16dnolll o

Testing by Lee et al. (2010) with headed anchors of dbetween 60 mm and 90 mm indicates that Equation (10.2-6b) is unconservative for large diameters, when 1j is taken as equal to hel and the influence of 1j on the concrete edge breakout resistance is very limited for large diameters.

In Grosser (2011) bonded anchors with dnom:O: 24 mm and 1j:O: 20d"om were tested and the results were compared with Equation (10.2-6b). The comparison indicates that for the tested anchors an upper limit for 1jof 12dnom yields reasonable results.

11 :0: 12dnom for d,w", :0: 24 mm

:s 8dl/om for dl/olll > 24 nun For anchors with constant diameter over the embedment depth (e.g., threaded rods) having an embedment depth hel larger than the limiting values for &; the limiting values are inserted in Equations (lO.2-5a) and (lO.2-5aJ). Where the diameter is not constant over the embedment depth or where the anchor is provided with a shear sleeve that does not extend continuously o"er the entire embedment depth, the value of dnom and 1j are given in the relevant Approval or should be evaluated from the results of pre qualification tests (see Section 1.3). For anchors without sleeves the term d,w", is replaced by d in Equations (l0.2-5a) and (lO.2-5a,).

Based on the sum of the previously discussed investigations, the following limits on Equation (lO.2-5a) have been developed: dllom :560mm IfS 12d,1011I for d,lOm:5 24 Inm

:5 8dl/om for C£'OI1l > 24 mm For anchors having d,wm> 60 mm the limiting value of d,w", = 60 mm should be inserted in Equations (lO.2-5a) and (l0.2-5a,). For anchors with constant diameter over the embedment depth, such as e.g., bonded anchors using threaded rods, the influence length II is equal to the embedment depth hef- For this type of anchor with embedment depth hel larger than the above given limiting values for &; the limiting values are inserted in Equations (lO.2-5a) and (l0.2-5aJ). For anchors having dnom:O: 24 mm and h4 > 12d"o"" the limiting value of 11 = 12dnom should be inserted in Equations (lO.2-5a) and (10.2-5aJ). For anchors having dnom > 24 mm and h4 > 8d"on" the limiting value 11 = 8d,wm should be inserted in Equations (10.2-5a) and (10.2-5aa. Note that the investigations regarding the extension of the range for 1jhave been carried out using bonded and headed anchors with a constant diameter over the embedment depth. Where the diameter is not constant or where the anchor is provided with a shear sleeve that does not extend continuously over the entire embedment depth, the appropriate values for the diameter and influence length should be taken from the relevant Approval or should be determined from the results of prequalification tests, however, the limiting values for dnom and 1j given above should be respected. The values of k, used in Equation ((lO.2-5a) are derived using the relationships given in Equations (lO.l-3b,c).


153


154

h

A~.v= 1.SC1 . 3c, = 4.5cf

Figure 10.2-3: Idealised concrete body and area A:'v for a single anchor loaded in shear

1.5ct~

/

T/

11

~t , ,r1,5C\L1.5C \L

A,.v= 1.5c, . (1.5c, + c,) C2::; 1.5c,

Ac.v

AD'.V = area of concrete breakout body of a single

anchor at the lateral concrete surface not affected by edges in direction 2, member thickness or adjacent anchors, idealising the shape of the fracture cone as a half-pyramid with a height equal to c, and base lengths of l.5c, and 3c, (Figure 10.2-3)

b)

hI)/~ ~-=t

h!~

Ac,v

A,.v= (2 ·1.5c, +s')'h h51.5c, 52:S

'1/A.V = A,.v / A;'v where:

A,.v= 2 ·1.5c,·h h 51.5c,

a)

,(SC:f S"ll.SC,,f

b) The geometric effects of spacing, edge distances parallel to the direction of load and thickness of the concrete member on the characteristic resistance are taken into account by the factor:

3c, c)

4.5c~

tsc~S'R

Ac,v

A,.v= ( 1.5c, + 5,+ c, )'h

h 51.5c, sz::5 3e 1 C2:::S 1.5c 1

d) Figure J 0.2-4: Examples of actual areas A,.v for different anchor arrangements under shear load: a) single anchor at a comer; b) single anchor in a thin concrete member; c) group of anchors in a thin concrete member; d) group of anchors at a comer ofa thin concrete member

The anchor resistance decreases with decreasing member thickness. However, according to tests (Zhao et al., 1989; Eligehausen, Grosser, 2007) and numerical simulations (Hofmann, 2005), the reduction of anchor resistance is less pronounced than assumed by the factor A"v / A;'v . This is taken into account by the factor \Vi,yaccording to Equation (lO.2-5c).

(10.2-5b)

A,.v = actual area of concrete breakout body of the anchorage at the lateral concrete surface. It is limited by overlapping concrete cones of adjacent anchors (s < 3c,), by edges in direction 2 (C2::S 1.5c,) and by member thickness (h 5 l.5c,). It may be deduced from the idealised half-pyramid of the individual anchors. Examples for the calculation of A,.v are given in Figure 10.2-4

For the calculation of A~.v and A,.v it is assumed that the shear loads are applied perpendicular to the edge ofthe concrete member.

c) The factor \Vi,.v takes into account that the resistance does not decrease linearly with the member thickness as assumed by the ratio A"v / A~.v . 'I/",v

=~1.5C' h

>10 .

(l0.2-5c)

Further experimental and numerical investigations (Eligehausen, Grosser, 2007) indicate that the adjustment for larger edge distances in thin members (Le., for values of c, / h ~ 1.5) should take the form:

5 'I/".v = (1-h• C,

I/3

J

~ 1.0

(10.2-5cd

Note, however, that in such cases the presence of typical slab reinforcing will serve to increase the shear resistance and the use of Equation (I 0.2-5c) is still acceptable. Where larger shear forces must be resisted in thin members, provision of dedicated anchor reinforcement is advisable.

d) The factor If/,.v takes account of the disturbance of the distribution of stresses in the concrete due to further edges of the concrete member on the concrete edge resistance. For anchorages with two edges in direction i(e.g., in a narrow concrete member) the smaller edge distance c, should be inserted in Equation (l0.2-5d). 'I/,v ,

For reasons of simplicity the eccentricity factor may be taken as 'I/",v= 1.0 if the most loaded anchor is verified (V;~ 5V/;,,/YM,) and the characteristic resistance of this anchor is taken as V;~" = VRk,' / n with VRk" according to Equation (10.2-5) with 'I/",v= 1.0 and n = number of anchors loaded in shear.

(l0.2-5d)

e) The factor 'I/"y takes into account a group effect when different shear loads are acting on the individual anchors of a group. 1 (10.2-5e) --.,-;;;-, < 1.0 'I/",v

= 1+2ev /(3c,)

where: ev


=0.7+0.3·~<1 1.5c, - .0

eccentricity of the resulting shear load acting on the anchors relative to the centre of gravity of the anchors loaded in shear (see Figure 4.3-21)

155


156

Where anchors are loaded in shear parallel to the concrete edge, failure is initiated by splitting forces perpendicular to the edge. They are a fraction of the applied shear load. In order to account for the fact that a higher shear load acting parallel to the edge is required to cause edge failure as compared to a shear load acting perpendicular to the edge, the factor \1'90', v is introduced. The ratio of the splitting force to the shear force applied parallel to the edge depends on the pressure in front of the anchors in the direction of loading compared to the concrete compression strength. This relation is assumed to be a linear function. The pressure increases as a function of the concrete resistance perpendicular to the edge, which is approximately proportional to VRk •o ,"' and decreases with the number of anchors in a group.

f) The factor \l'a. v takes into account the angle av between the load applied V~ and the direction perpendicular to the edge for which the resistance is verified (see Figure 10.2-2b,c). I

\l'a,v

= I

(cosa v )

1fI90oy ::; 4.0. k . 4 (

n2 . (d)' nom

v:

J

, ;:: 1.0

(10.2-5f)

l \l'90',V

with: av

=

angle between design shear load V~ and a line perpendicular to the edge for which the resistance is verified (see Figure 1O.2-2b,c)

\l'90',v

=

1.5 for n, = I

Therefore, the factor \1'90', v increases with decreasing edge distance and with increasing number of anchors (Hofmann, 2005; Grosser, Eligehausen, 2008). The values \l'90'Y given in Equation (l0.2-5f) are a simplification and are valid for larger edge distances where the concrete edge resistance is equal to the anchor steel resistance. At smaller edge distances the values \l'90'Y increase. In such cases, the value \1'90', V may be evaluated in accordance with Equation (1O.2-5fD. In ACI 318 Appendix D (ACI 318, 2008), the value of 2.0 is taken. In the CEN Technical Specification (CEN, 2009), a value of 2.5 is used.

'+( sina'J

2.0 for n2 = 2 2.5 for n, = 3 n2

=

number of anchors for which concrete edge failure verified (see Figure 10.2-5)

O ,5

. ick

:<; 4,0

(1O.2-5f1)

Rk,c,.l

with: k4

1.0 [-] anchorages without hole clearance and single anchors with hole clearance =

0,8 [-] anchorages with normal hole clearance (ad:::; ad. I)

n,

number of anchors for which concrete edge failure is verified (see Figure 10.2-5)

VRk,d =

concrete breakout resistance for loading perpendicular to an edge according to Equation (10.2-5) without factor \l'aY

For a row of anchors arranged and loaded parallel to the edge it is assumed that the shear load is distributed uniformly to all anchors of the group (see Section 4.3.1.3). However, in the case of anchors with normal hole clearance (ad:::; ad,D in the fixture and a small edge distance, the load may not be distributed equally to the anchors. This is accounted for by the factor k4 = 0.8 in Equation (l0,2-5fD (Hofmann, 2005). The values \l'90',V given in Equation (l0.2-5f) are valid for anchorages with larger edge distances which fail at displacements much larger than the hole clearance. Because of this, it may be assumed that the shear force is equally distributed to all anchors. ./

VSdJ

~...

5 2 .2

•+ I

n,=3

5 2. 1

1-.1 " 5,

VSdl

ill,

~

•• 1--

VSd

/

• • I-I-, -----I I

5 1,2

r-

-

VSd 51.1

C l ,l

•

~ /

/

./

5,

,c,

5,

n,=2

,

~

c,

5,

n,=2

n,=1

Figure 10.2-5: Determination of n, for the evaluation of \1'90', v in Equation (10.2-5f) based on the number of anchors for which concrete edge failure is verified


157

IS

a Ultimate limit state -

Part 11: J

elastic design approach

158

Equation (10.2-5f) assumes a quadratic interaction between the shear resistances for loading perpendicular and parallel to the edge. It is derived from Equation (l0.2-5f,).

.' cosav

VRk .' (

J' +(V.

Rk , . sinav )'

VRk•d

= 1.0

(1O.2-5f,)

VR/;c.11

with: VR/-.,

= characteristic concrete edge

resistance for a shear load acting

with an angle av to the edge VRk",.l

= characteristic concrete edge resistance for a shear load acting

VRk.,.11

= characteristic concrete edge resistance for a shear load acting

perpendicular to the edge calculated according to Equation (10.2-5) with VI~,' = 1.0 parallel to the edge

= '1/90".v . VRk.c.l . av

=

angle as defined in Figure 10.2-2b,c

The value of VI",v is based on experimental investigations by Fuchs and Eligehausen (1989).

g) The factor VI,·,.vtakes into account the type of edge reinforcement used. VI,-,.v

=

1.0, for anchorages without supplementary reinforcement as defined in Figure 10.2-6

(10.2-5g l )

VI,-,.v

=

lA, for anchorages with edge reinforcement (d,2: 12 nun) and closely spaced stimlps (d,2: 12 nun, spacing ~ 100 nun) and edge

(1O.2-5g,)

distance 2: 100 mm (see Figure 10.2-6)

VSd

dsi:::12 mm

A

d,.12mm

~

V

~

1:5100 mm

\

IS100

mm

Figure 10.2-6: Anchorage at an edge loaded in shear with edge reinforcement and closely spaced stirrups

I

"'---8

i:

I

}-S-+

! ~!J}

if (c,.,:c,.,)<1.5c,

and

h) Special cases For anchorages in a narrow, thin member with C2,m" < 1.5cI and h < l.5CI (see Figure 10.2-7) the calculation according to Equation (10.2-5) leads to conservative results. More precise results are achieved if CI is limited in case of single anchors to the value of:

c; = max (c,.mru< ;~) 1.5

h < 1.5c,

or in the case of groups, CI is limited to the value of:

=max(c"m~ .~. S',m~)

Figure 10.2-7: Example for an anchorage in a thin, narrow member where the value c; may be used

c'

An example for the calculation of c; is illustrated in Figure 10.2-8.

with:

I

CZ,max SZ,max


(10.2-5h l )

1.5

1.5 '1.5'

(10.2-5h,)

3

largest of the two edge distances in direction 2 maximum spacing between anchors within the group direction 2 (~3cIl

III

159


160

c;

The value is inserted in Equations (10.2-5a) to (10.2-5e) and it is used to determine the areas AO,y and A,y according to Figure 10.2-3 and Figure 10.2-4 instead of CI. c,

r------,

1.---.1 /t.' ______"::::i, ~ ./'

/

//

'-

I

Cv

c·

I',' 5,

C2.2

j.

,I'

h

c,= 200 mm 5,= 100 mm h = 120 <1.5,200 mm

c,.,= 150 mm < 1.5,200 mm c,.,= 100 mm < 1.5'200 mm c; = 150f1.5= 100mm

Figure 10.2-8: Examplefor the calculation of the value

c;

For anchorages without hole clearance arrayed perpendicular to the edge and having a small ratio SI / CI, the verification assuming that only the part VSd / nl of the total load on the group is resisted by the front anchors may be unconservative. This is explained in Figure 10.2-9 for a group of four anchors without hole clearance loaded by a shear load oriented perpendicular to the edge. It is assumed that a centric shear load acting toward the edge is distributed equally to all anchors (see Section 4.3.1.3.1; subsection (2)). Tests have shown, that the maximum concrete edge failure load of the group is reached when the failure crack originates from the back anchors. This failure load is not influenced significantly by the front anchors. In the case of a large anchor spacing perpendicular to the edge, the resistance of the group is greater than or equal to two times the resistance of the near edge (front) anchors (Figure 10.2-9a). Therefore, the verification of the near edge anchors according to Equation (3.3-1) is conservative. In the case of a very small anchor spacing perpendicular to the edge (SI «CI,I) (Figure 10.2-9b), the resistance of the group is approximately equal to the resistance of the front anchors. In this case the verification of only the front anchors - assuming an equal distribution of the shear load to all anchors - is unconservative.

For anchor groups without hole clearance loaded by a shear load perpendicular to the edge the characteristic concrete edge resistance should be limited by Equation (10.2-6): VRk"

= VRk., ( c""

)jn,

(10.2-6)

with: VRk., ( c"" )

characteristic edge resistance calculated for the back anchor(s) according to Equation (10.2-5) inserting c] =c],nl

nl

number of anchors rows in the direction 1 perpendicular to the edge

Therefore, since it has been assumed that the shear load is equally distributed to all anchors, the concrete edge resistance of the front anchors is limited by Equation (10.2-6). This equation gives the concrete edge resistance as the concrete breakout calculated for the back anchors divided by the number, nl, of anchor rows in the direction perpendicular to the edge (nl = 2 in Figure 10.2-9). This limitation should assure that the whole group does not fail before the assumed failure crack occurs at the front anchors.

~

, ili

V5d

I

c,,T";t=-; ill

c"

C1.1

V Rd (group);' 2VRd (front anchors)

a)

•

•

V Rd (group) - VRd (front anchors)

b)

Figure 10.2-9: Example of a group of anchors without hole clearance loaded in shear toward the edge: a) SI large ;b) SI small

For anchor groups with hole clearance loaded by a shear load perpendicular to the edge it is assumed that the shear load is taken up by the front anchors only (see Section 4.3.1.3.1, subsections (3) and (4)). Therefore, the verification according to Equation (3.3-1) is conservative. For anchor groups with no or nonnal hole clearance (a,,::; a". I) loaded in shear parallel to the edge it is assumed that all anchors take up shear loads (see Section 4.3.1.3.1, subsection (3)). Tests with anchor groups with torsional restraint (compare Figure 4.3-16b) have shown that the failure load of the group may be larger than twice the failure load calculated with the edge distance of the front anchors. Tests with anchor groups with a small spacing and small edge distance without torsional restraint loaded in shear parallel to the edge have not been performed. For these applications the characteristic concrete edge resistance


161

Part II: J 0 Ultimate limit state - elastic design approach

162

calculated for the front anchors according to Equation (10.2-5) should be used with caution. Equation (10.2-7) is conservative.

Where the resistance VRk c.L for anchor groups without hole clearance is limited by Equation (10.2-6), the characteristic concrete edge resistance for an inclined shear load should be calculated as:

v

=VRk,C,J.. .~a,V

Rk,c

(10.2-7)

with: VRk,c,J.

according to Equation (10.2-6)

'l/a. v

according to Equation (10.2-5f)

10.2.5.1.2 Cases where the failure crack originates from anchors beyond the front anchor or front anchor row The ultimate concrete edge failure load of anchor groups without or with hole clearance arrayed perpendicular to the edge is reached, when a crack originates from the back anchor or back anchor row. It is equal to the value calculated using the edge distance corresponding to the back anchors or anchor row. It is assumed that in this case the front anchor or front anchor row do not significantly influence the concrete edge resistance of the group. However, according to results of tests described in Grosser, Cook (2009) for anchorages with normal hole clearance, a small edge distance and a ratio :S 1.0 the concrete edge failure load of the back anchor(s) may be negatively influenced (up to 20%) by the crack generated at the front anchor(s).

For anchorages with multiple anchors or anchors rows arrayed perpendicular to the edge, the characteristic resistance corresponding to concrete edge failure originating from the back anchor or anchor row corresponds to:

VRk.e = V:k•c ·If/A.V ·If/".v ·If/,.v ·If/".v 'If/a.V ·If/re.V

(10.2-8)

V:

s, /c,.,

where k•e , 'l/A. v, If/I,,V, If/,,V, 'I/",V, 'l/a. v and '1/". v are calculated in accordance with Section 10.2.5.1.1 using the edge distance of the back anchor or anchor row. The limitation given by Equation (10.2-6) does not apply.

Note that for the verification of steel and pryout failure, it is assumed that only those anchors located in the line of the considered failure plane and further away from the edge resist shear forces (examples see Tables 4.3-2 to 4.3-4). Furthermore, serviceability limit state check according to Section 6.2 is required.

For anchorages without hole clearance, up to three anchors or anchor rows are permitted perpendicular to the edge. In this case, the characteristic concrete edge resistance corresponding to the middle anchor or anchor row should be calculated in accordance with Equation (10.2-8) whereby the edge distance of the middle anchor or anchor row is used. The limitation given by Equation (10.2-6) applies in this case. For combined tension and shear loading, additional restrictions apply; see Section 10.3.2.

10.2.5.2

Alternative approach

In the alternative approach, a shear force acting parallel to the edge is substituted by a virtual shear force acting perpendicular to the edge (see Section 4.3.1.3.3). When using this approach the characteristic resistance for concrete edge failure should be calculated according to Equation (10.2-5) and Equation (10.2-6) (failure crack is assumed to occur at the front anchors) or Equation (10.2-8) (failure crack is assumed to occur at the back anchors), however neglecting the factor 'l/a.v.

10.3

Resistance to combined tension and shear load

10.3.1

Anchorages far from edges, anchorages close to edges with shear resisted by front anchors

For the verification of anchorages under combined tension and shear loads a simplified and an alternative, more accurate approach are distinguished: NSd/NRd

10.3.1.1

I

,

1.0C:"""",,-~~

-::::.V( ""V

"""""X

0.6

\

.

004 0.2

0.0

For combined tension and shear loads the following conditions should be satisfied:

Eqn. (10.3-1a,b.c) /Eqn. (10.3-2) with a = 2.0

0.8

!

!

I

0.0

0.2

0.4

\

0.8

NSd

\ N \\

(IO.3-la)

VSd

:<;; 1.0

(1O.3-lb)

VRd NSd

+ VSd

N Rd

VRd

:<;; 1.2

(lO.3-lc)

•

1.0

VSdNRd

Figure 10.3-1: interaction diagram for combined tension and shear loads


:<;; 1.0

N Rd

Eqn. (10.3-1d) and Eqn. (10.3-3) withu=1.5

!!

0.6

Simplified approach

For the ratios NSd / N Rd and VSd / V Rd the largest value for the different failure modes (see Table 10.1-1 and Table 10.2-1) should be inserted in Equation (10.3-la,b,c).

163

Part II: Ja Ultimate limit state - elastic design approach

164 Equation (1O.3-la,b,c) may be replaced by Equation (1O.3-ld):

NSd (N Rd

Ja +( VVSd Ja $1.0 Rd

(1O.3-ld)

where a= 1.5 and NSdl NRd and VSdl VRd as given by Equation (l0.3-la,b,c). a = 1.0 may be taken as a conservative simplification.

10.3.1.2 An example for the interaction distinguishing between steel and concrete failure modes is given in Figure 10.3-2, where the design resistance N Rd under tension load is plotted as a function of the design resistance VRd under shear load. For comparison the interaction according to the Equation (lO.3-ld) is plotted as well.

100

N" N L Rd,s

80 NRd,c

,$

20

l

140 kN

Eqn. (10.3-3) with a;; 1.5

Eqn. (10.3-1d) with CI. = 1.5

VRd.S

o

(10.3-2)

Rds ,

where a= 2.0 and NRd., and VRd., are the characteristic steel resistances for tension and shear loading, respectively. For anchor groups NSd and VSd are replaced by N~d and V;, respectively. If N~d and V; are associated with different anchors in a group, the interaction should be verified for all anchors.

60

40

For steel failure modes the interaction is verified according to Equation (10.3-2):

.

NRd = 100 kN NRd,e= 70 kN V Rd ,& = 50 kN VRd,c=

Equations (lO.3-la,b,c) and (l0.3-ld) may yield conservative results. More accurate results are obtained by the following approach, which distinguishes between steel and concrete failure modes.

NSd )a + (3....)a $1.0 ( NRds V

Example with: Eqn. (10.3-2) witha=2.0


For concrete failure modes the interaction is verified according to Equation (10.3-3): VRd,c\

vRd

o 20 60 40 60 100 120 140 Figure 10.3-2: Comparison of interaction approach according to Equations (10.3-2), (10.3-3) and (lO.3-ld)

NSdJa +(VSdJa $1.0 ( N Rd V

(10.3-3)

Rd

where a = 1.5 and NSd I NRd and VSd I VRd are taken as the maximum value for applicable concrete. failure modes under tension and shear loading, respectively. Equations (10.3-2) and (10.3-3) should both be satisfied.

10.3.2

Anchorages close to edges with shear resisted by the back anchors

In cases where concrete failure governs, the initial concrete edge failure of the front anchors will negatively influence the tension capacity of the group. This case is handled in Eligehausen et al. (2006-2), Section 4.1.3.2. For this reason, a is taken as 1.0 for the verification of concrete failure modes.

In the simplified approach Equation (IO.3-ld) should be satisfied, however, the exponent should be taken as a= 1.0.

Equation (IO.3-ld) with a= 1.0 may yield conservative results. More accurate results are obtained by the alternative approach

In the alternative approach Equations (10.3-2) and (10.3-3) should be satisfied; however, a= 1.0 should be used in Equation (10.3-3).

Where the shear resistance is assumed to be provided entirely by the back anchor(s), premature failure of the front anchors loaded in tension due to excessive cracking associated with shear edge breakout should be avoided. It is therefore necessary in such cases to provide reinforcement of appropriate size and orientation to limit the crack width at the front anchors and perfonn the design for cracked concrete using anchors suitable for this condition. Regarding the optimal size and orientation of the reinforcement further research is required.

For both, simplified and alternative, approaches the design (addressing the ultimate as well as the serviceability limit state) should be perfonned for cracked concrete using anchors suitable for this condition and reinforcement of appropriate size and orientation should be provided to limit the crack width at the front anchors.

If no suitable reinforcement is provided to limit the crack width, the front anchor(s), i.e., anchor(s) located in the crack (see Figure 10.3-3b), do not significantly and reliably contribute anymore to the transfer of the applied tension and shear loads into the base material. Consequently, only the remaining anchors (see Figure 10.3-3b,c) should be considered to resist tension and shear forces in this case. It is assumed that the failure plane at the front anchor(s) does not significantly influence the concrete resistance of the remaining anchors subjected to shear loads acting towards the edge (see Section 10.2.5.1.2). Therefore, the verification of shear resistance may be perfonned for the subsystem shown in Figure 1O.3-3b. On the other hand it may be assumed that the failure plane at the front anchor(s) affect their tension resistance associated with concrete failure. Therefore, it is reasonable to conservatively assume a fictitious edge at the location of the front (failed) anchor(s) for the verification of tension resistance of the remaining anchors as shown in Figure 10.3-3c. In this case the exponent a of the interaction equation for the simplified approach (Equation (I 0.3-1 d)) and the alternative

If the crack width at the front anchors is not limited, the anchors located in the crack do not contribute to the tension resistance. Hence, the remaining anchors must be able to transmit the tension load acting on the fastening to the concrete base material, assuming a fictitious edge at the location of the front anchors. In this case the exponent a of the interaction equation for the simplified approach (Equation (10.3-ld)) and the alternative approach (Equation (10.3-3)) should not be taken greater than 1.5.


165


164 Equation (IO.3-la,b,c) may be replaced by Equation (1O.3-ld): ';:;1.0 ( NNSdJ" +(VSdJ" V Rd

(1O.3-ld)

Rd

where a = 1.5 and NSd / NRd and VSd / VRd as given by Equation (IO.3-la,b,c). a= 1.0 may be taken as a conservative simplification.

10.3.1.2 An example for the interaction distinguishing between steel and concrete failure modes is given in Figure 10.3-2, where the design resistance N Rd under tension load is plotted as a function of the design resistance VRd under shear load. For comparison the interaction according to the Equation (lO.3-ld) is plotted as well.


Equations (l0.3-la,b,c) and (10.3-1d) may yield conservative results. More accurate results are obtained by the following approach, which distinguishes between steel and concrete failure modes. For steel failure modes the interaction is verified according to Equation (10.3-2):

N" 100

I

(:Sd )" +(;Sd )" ,;:; 1.0

Example with:

NRd,S

Eqn. (10.3-2) with a.::; 2.0

Rd,s

100 kN NRd •C = 70 kN VRd ,& = 50 kN VRd,c= 140 kN

NRd,S;:

80 NRII,c

where a= 2.0 and NRd., and VRd" are the characteristic steel resistances for tension and shear loading, respectively. For anchor groups NSd and VSd are replaced by N~ and V;~, respectively. If N;d and V;~ are associated with different anchors in a group, the interaction should be verified for all anchors.

60

40

20

l

(10.~)

Eqn. (10.3-3) with a;: 1.5

Eqn. with a = 1.5

For concrete failure modes the interaction is verified according to Equation (10.3-3):

VRd,S

o

VRd,c \

o

20

40

60

80

100

(10.3-2)

Rd,s

120

vRd

140

Figure 10.3-2: Comparison of interaction approach according to Equations (10.3-2), (10.3-3) and (JO.3-ld)

J" ,;:; 1.0 ( NNSd J" +(VSd V Rd

(10.3-3)

Rd

where a = 1.5 and NSd / NRd and VSd / VRd are taken as the maximum value for applicable concrete failure modes under tension and shear loading, respectively. Equations (10.3-2) and (10.3-3) should both be satisfied.

10.3.2 In cases where concrete failure governs, the initial concrete edge failure of

Anchorages close to edges with shear resisted by the back anchors

In the simplified approach Equation (lO.3-ld) should be satisfied,

the front anchors will negatively influence the tension capacity of the group. This case is handled in Eligehausen et al. (2006-2), Section 4.1.3.2. For this reason, a is taken as 1.0 for the verification of concrete failure modes.

however, the exponent should be taken as a = 1.0.

Equation (l0.3-1d) with a= 1.0 may yield conservative results. More accurate results are obtained by the alternative approach

In the alternative approach Equations (10.3-2) and (10.3-3) should be satisfied; however, a= 1.0 should be used in Equation (10.3-3).

Where the shear resistance is assumed to be provided entirely by the back anchor(s), premature failure of the front anchors loaded in tension due to excessive cracking associated with shear edge breakout should be avoided. It is therefore necessary in such cases to provide reinforcement of appropriate size and orientation to limit the crack width at the front anchors and perfonn the design for cracked concrete using anchors suitable for this condition. Regarding the optimal size and orientation of the reinforcement further research is required.

For both, simplified and alternative, approaches the design (addressing the ultimate as well as the serviceability limit state) should be perfonned for cracked concrete using anchors suitable for this condition and reinforcement of appropriate size and orientation should be provided to limit the crack width at the front anchors.

If no suitable reinforcement is provided to limit the crack width, the front anchor(s), i.e., anchor(s) located in the crack (see Figure 10.3-3b), do not significantly and reliably contribute anymore to the transfer of the applied tension and shear loads into the base material. Consequently, only the remaining anchors (see Figure 1O.3-3b,c) should be considered to resist tension and shear forces in this case. It is assumed that the failure plane at the front anchor(s) does not significantly influence the concrete resistance of the remaining anchors subjected to shear loads acting towards the edge (see Section 10.2.5.1.2). Therefore, the verification of shear resistance may be perfonned for the subsystem shown in Figure 10.3-3b. On the other hand it may be assumed that the failure plane at the front anchor(s) affect their tension resistance associated with concrete failure. Therefore, it is reasonable to conservatively assume a fictitious edge at the location of the front (failed) anchor(s) for the verification of tension resistance of the remaining anchors as shown in Figure 10.3-3c. In this case the exponent a of the interaction equation for the simplified approach (Equation (IO.3-ld)) and the alternative

If the crack width at the front anchors is not limited, the anchors located in the crack do not contribute to the tension resistance. Hence, the remaining anchors must be able to transmit the tension load acting on the fastening to the concrete base material, assuming a fictitious edge at the location of the front anchors. In this case the exponent a of the interaction equation for the simplified approach (Equation (l0.3-1d)) and the alternative approach (Equation (10.3-3)) should not be taken greater than 1.5.


165


166

approach (Equation (10.3-3)) should not be taken greater than a= 1.5. Note that in the case of a group of two anchors perpendicular to the edge or a group of four anchors subjected to combined tension and shear loading, failure of the front anchors will likely lead to failure of the group due to the resulting tension eccentricity (see Figure 10.3-4) .

II

N",

Assumed failure plane

vsollY , adgo a)

- - -

• loaded anchor

o unloaded anchor

-

I-

----hi!,,!ti~"~

e---<>

~e

/'

edge

b)

c)

Figure 10.3-3 Example of a group of anchors loaded in tension and shear toward the edge: a) side view; b) subsystem for verification of shear resistance; c) subsystem for verification of tension resistance N~

1

Jill

V~

&&, 2

!LIl1

rfl1

~v~

IV~

2

N~

2

a)

"2

~ IIIfll

W~ nlnv~ N~

W~ b)

c)

Figure 10.3-4 Example of a group offour anchors loaded in tension and shear toward the edge where reinforcement to limit crack width has not been provided: a) action and resistance on group; b) failure of front anchors in shear leading to loss of tension resistance; c) premature failure of group due to unbalanced tension

10.3.3 The interaction Equation (10.3-4) is based on Scheer et al. (1987).

Anchorages loaded by a tension load and a shear load with lever arm

For anchorages loaded by a tension load and a shear load with lever arm, the following additional verification is required: NSd NRd,s

+

~ 1.0

VSd

(10.3-4)

VRd,sm

with: NSd

design tension force on anchor

NRd.,

design tension steel resistance

VSd

design shear force on anchor

VRd.""

design shear steel resistance for an anchor loaded by a shear force with lever arm (see Section 10.2.2.2)

11

Ultimate limit state - plastic design approach

In the plastic design approach the distribution ofloads on the fixture to the anchors of a group is performed according to the theory of plasticity (see Section 4.3.2). In general, the complete anchorage is checked according to Equation (3.3-1). Therefore, in general the required verifications are written for the group.

11.1

Field of application

The plastic design approach is allowed only if the conditions given in Section 4.3.2.1 are satisfied.


167

Part II: II Ultimate limit state - plastic design approach

168

11.2


The required verifications are summarized in Table 11.2-1. Table 11.2-1:

Required verifications for tension loading (plastic design approach)

Failure mode

Anchor groups

Steel failure

Nff-

:5, Nf,."

/ YAI;

Pullout failure

Equation (11.2-2)


Equation (11.2-3)

Splitting failure

See Section 11,2.4

Only those anchors that satisfy Equation (4.3-8) of Section 4.3,2.2 should be assumed to transfer a tension force,

11.2.1 In Equation (11.2-1) the same diameter and steel strength are assumed for all tensioned anchors of a group.

Steel failure

The characteristic resistance of a group of tensioned anchors Nf,." may be taken as equal to the sum of the characteristic resistances of the anchors loaded in tension (Equation (11.2-1)), Nf,."

= n ' N Rk.,

(11.2-1)

with N Rk" obtained according to Section 10,1.2 and n = number of tensioned anchors,

11.2.2 The factor 0.6 in Equation (11.2-2) is intended to give a I % probability of pullout failure prior to the intended anchor steel failure for typical anchor and material parameters (Hoehler, 2006).

Pullout failure

For the characteristic resistance NRk,p of one anchor in the case of pUllout or pull-through failure see Section 10,1.3, To satisfy Equation (4.3-4) of Section 4,3,2.1, the pullout resistance of the most loaded tensioned anchor should meet Equation (11.2-2):

(11.2-2)

NRk,p ;;::: NRk,s . Yillsr/ O.6

with NRk,p according to Section 10,1.3, N Rk" according to Section 10,1.2, and y;"" according to Section 3.4,2,1.2,

11.2.3 If in the design a constant tension force is assumed for all tensioned anchors, then the eccentricity factor is 'f/",N = 1.0, In Equation (11.2-3) the same diameter, steel strength and embedment depths are assumed for all anchors of a group,

The factor 0,6 in Equation (11.2-3) is intended to give a 1% probability of concrete failure prior to the intended anchor steel failure for typical anchor and material parameters (Hoehler, 2006),


For the calculation of the concrete cone resistance Section 10,1.4 applies, To satisfy Equation (4.3-4) of Section 4,3,2.1, the anchorage depth should be large enough for Equation (11.2-3) to be met: (11.2-3)

NRk,e ;;:: Nfu.,$ . Yillst /0.6

with N Rk" according to Equation (10,1-2) and Nf,." according to Equation (11.2-1) and y;"" according to Section 3.4,2,1.2,

11.2.4

Splitting failure

A splitting failure is avoided by complying with Equation (11.2-3), where N Rk" is replaced by NRk"p according to Equation (10.1-5), The verification of the splitting resistance may be omitted if one of the conditions in Section 10.1.5.2, subsection a) is met.

The verification for pullout failure is not required, because anchorages that meet Equation (11.2-2) will not fail due to pullout under shear loading, Anchorages loaded in shear with lever arm (see Section 4.3,1.5) have not been investigated and are not covered by this Design Guide,

11.3


11.3.1



Required verifications for shear loading (plastic design approach)

Failure mode


Anchor groups

Steel failure, shear load without lever arm

VlI:5, V:', /Y..


Equation (11.3-2)


Equation (11.3-3)

169

Part II: 11 Ultimate limit state - plastic design approach

170

11.3.2 Because a plastic design approach is allowed only for ductile steel, the factor 0.8 to account for the influence of hole clearance on the steel shear resistance (see Section 10.2.2.1) may be increased up to 1.0. In Equation (11.3-1) the same diameter and steel strength are assumed for all anchors of the group loaded in shear.

Steel failure

The characteristic resistance of a group of anchors loaded in shear V:'., may be taken as equal to the sum of the characteristic resistances of the individual anchors loaded in shear (Equation (11.3-1)).

.

.

v~s =n'VRks

(11.3-1)

with VRk., obtained according to Section 10.2.2.1, and n = number of anchors loaded in shear.

11.3.3 Equation (11.3-2) is satisfied if all anchors have an embedment depth that meets Equation (11.2-3). The factor 0.6 in Equation (11.3-2) is intended to give a 1% probability of concrete pryout failure prior to the intended anchor steel failure for typical anchor and material parameters (Hoehler, 2006).


To calculate the concrete pryout resistance Section 10.2.4 applies. To satisfy Equation (4.3-4) of Section 4.3.2.1, Equation (11.3-2) should be met: VRk .cP <: V:')0.6

with VRk.cp according to Section 10.2.4 and (11.3-1).

11.3.4 If in the design a constant shear force is assumed for all anchors loaded in shear, then the eccentricity factor is If/,c.v= 1.0. If in the design the friction resistance is neglected, then VRkJ may be omitted in Equation (11.3-3). The factor 0.6 in Equation (11.3-3) is intended to give a 1% probability of concrete edge failure prior to the intended anchor steel failure for typical anchor and material parameters (Hoehler, 2006).

In general the value L11VfRk" is calculated according to the Equation (13-1):

.

/).MRk " :::; C!aRk flat . ~I


(13-1)


VRk.c <: V:')0.6 + VRk .f

(11.3-3)

with: VRk,c = characteristic edge resistance according to Equation (10.2-5) and Equation (10.2-6) for the anchor(s) closest to the . edge

V:'.,

=

see equation (11.3-1)

VRk •f

=

see Equation (4.2-1)


Section 10.3 applies.


For the required verifications see Section 6.2. The characteristic displacement of the anchor under given tension and shear loads may be taken from the relevant Approval or from the results of prequalification tests (see Section 1.3).

13 Due to temperature variations, anchorages of fayade elements experience alternating shear loads. Therefore, either the fayade elements are anchored so that no significant shear forces due to the restraint of defonnations imposed on the fayade element will occur in the anchorage, or, in a stand-off installation, the bending stresses Lto; = o;,,,,ax - 0;.",;" in the most stressed anchor, caused by temperature variations, should be limited to avoid a steel fatigue failure. The characteristic fatigue bending resistance of anchors in a stand-off installation to fasten fayade elements may be taken as 4 LtaRkJa' = 100 MPa (Utescher, 1978). This value is valid for about 10 cycles of temperature variations.

according to Equation

To satisfy Equation (4.3-4) of Section 4.3.2.1, Equation (11.3-3) should be met:

12 In some Approvals the given characteristic displacements are valid for short-duration loading only. They may increase because of sustained loads or cracks with varying width caused by variable loads on the concrete structure. The increase depends on the type of loading and the type of anchor and may reach a factor of 1.5 to 2.0 for tension loading and 1.2 to 1.5 for shear loading. Furthermore, the shear displacements may increase due to a gap between fixture and anchor if the diameter of the clearance hole is larger than the diameter of the anchor.

V:'.,

To calculate the concrete edge resistance Section 10.2.5 applies.

11.4 Because in the plastic design approach the concrete design resistance is required to be much higher than the steel design resistance, the interaction Equations (10.3-2) should be applied for the most loaded anchor. Then NRd and VRd are the design steel resistance in tension and shear, respectively, of that anchor.

(11.3-2)

Fatigue loading

Fatigue loading on the member serving as the base material or on the anchorage may be allowed, if this is stated in the relevant Approval or if it has been shown in the prequalification procedure that the anchors are suitable for these applications. In both cases the corresponding conditions (e.g., permanent prestressing force of sufficient magnitude) should be met.

The verification for fatigue loading on the anchorage should be perfonned according to Section 6.3. The values LlNRk." LlNRk,p, LtVRk,,, LtV...",,, If/PN and If/RV should be taken from the relevant Approval or should be determined 171

Part II: 14 Seismic loading

where LtO"RkJat is the characteristic tension resistance nnder fatigue loading given in the relevant Approval or determined from the results of suitable prequalification tests.

172 from the results of suitable prequalification tests (see Section 1.3). The value should be calculated according to Equation (10.2-2) replacing M'R'.' by LlMRk., and V Rk., by LtVRk.,. The value for LlMRk., should be taken from the relevant Approval. LtVRk.,m

14

Seismic loading

Seismic loading on anchors may be allowed if this is stated in the relevant Approval or it has been shown in the prequalification procedure (see Section 1.3) that the anchors are suitable to take up seismic loads. The verification for seismic loading on the anchorage should be performed according to Section 6.4.

PART III: CHARACTERISTIC RESISTANCE OF ANCHORAGES WITH BONDED ANCHORS AND CONNECTIONS WITH POST -INSTALLED REINFORCING BARS

15 It is necessary to distinguish between two types of connections: (see Figure IS-I): a) Connections with bonded anchors: The installed steel elements (e.g., threaded rods) behave essentially like anchor bolts. They may be stressed by tension, shear or combined tension and shear loads. Anchor tension loads are introduced into the concrete by bond and they cause tension stresses in the concrete in the region of the anchorage (Figure IS-Ia). The design of the connection is performed in principle as for other types of anchors, however, with some modifications to take account of the characteristics of bonded anchors (see Section 16). The conditions of use of bonded anchors are deduced under the assumption that the concrete structure which takes up the load on the anchorage is essentially at the serviceability limit state when the anchorage reaches its failure load (see Section 6.1).

General

Part I applies unless otherwise noted. In general, Part III is applicable to anchorages with bonded anchors (see Figure 1.2-Sa) and post-installed reinforcing bars. Anchorages with bonded anchors are addressed in Section 16. Connections with post-installed reinforcing bars are dealt with in Section 17.

b) Connections with post-installed reinforcing bars: The bars are essentially stressed by tension forces. These forces are introduced into the concrete by bond and either transferred by compression struts to the existing cast-in-place reinforcement (Figure IS-Ib) or they are balanced by a compression strut (e.g., at an end anchorage, see Figure IS-Ie). In both applications the behaviour is mainly controlled by the splitting tensile resistance of the concrete and the amonnt and detailing of transverse reinforcement present. In cases with large confinement by concrete and/or transverse reinforcement the behaviour is controlled by the pullout strength of the post-installed or cast-in-place reinforcing bars. Concrete cone failure or combined pullout and concrete cone failure is prevented by the existing reinforcement (Figure IS-1 b) or by a compression strut (Figure IS-Ic). The design of the


173

Part III: 15 General

174

connection is performed according to provisions for reinforced concrete (see Section 17). They should ensure that yielding of the reinforcement is reached before a bond failure occurs to reduce the risk of brittle failure. The conditions of use are deduced under the assumption that failure of the connection may cause failure of the reinforced concrete structure. While the force path shown in Figure 15-1 b or Figure IS-Ie is straight forward and can be idealised in terms of bond stresses that develop in the concrete surrounding the lap splice or the anchored bar, respectively, in many cases the manner of force transfer is less obvious and may require a more detailed analysis using strut and tie modelling. It should be noted that with bonded anchors and post-installed reinforcing bars, as with other types of anchors, the force path involves utilisation of the tensile strength of the concrete.

t

t

"

"

t "t "t

,.,

r

d--~

~~ tJ ~ )-.J I /!I!~-= •.....•. c

.=

7 " . ." . 7

(v.-.....:--.I:7~::rL /\!t7TL!.17;

!/!,?z

,

r;;;;. ;· a)

Figure 15-1:

b)

,

f)??

2 ?

2 2

2 2 ?

?

? J

_______

t c)

Application types: a) anchor application - bond/concrete breakout may control tension resistance; b), c) applications with reinforcing bars where embedment is determined with development length theory - splitting / pullout may control tension resistance

Additional characteristics for distinguishing between anchorages with bonded anchors and connections with post-installed reinforcing bars are given in Table IS-I.

Table 15-1:

Comparison

Characteristics for distinguishing between anchorages with bonded anchors and connections with postinstalled reinforcing bars Anchor applications

Reinforcing bar applications

Forces in the bar

Tension, shear, combined tension and shear

Tension only

Load transfer

Tension stresses in concrete

Splice with cast-in-place rebar, anchoring in compression strut

Tension: steel, combined pullout and concrete cone, concrete cone, splitting.

Steel, bond (pullout, splitting)

mechanism

Failure modes

considered

Shear: steel, pullout, pryout, concrete edge Supplemental reinforcement

May be used to tie back the concrete breakout body and to take up splitting forces - In general not considered in design concept

Generally used to take up splitting forces considered in design concept

Cracked concrete

Different design resistances assigned for:

Implicit in the design

- uncracked concrete - cracked concrete Ultimate limit state

Limited by a variety of possible failure modes including steel failure; shallow embedment as governed by concrete failure accepted

Design for steel yield or bond (pullout, splitting)

Design method

fib Design Guide, CEN T echoical Specifications (CEN, 2009), EOTA Techoical Report 029 (EOTA, 2007), ETAG 00 I Annex C (EOTA, 1997), AC! 318 Appendix D (AC! 318, 2008), AC 308 (ICCES,2009)

e.g., CEB-FIP Model Code 1990 (CEB, 1993), Eurocode 2 (CEN, 20041), AC! 318, Section 12 (AC! 318, 2008)


175

Part III: 16 Anchorages with bonded anchors

176

Structural concrete is defined as all concrete used for structural purposes including plain, reinforced and prestressed concrete. In general, the strength classes, for which the design method is valid, are C20 to CSO according to CEB-FIP Model Code 1990 (CEB, 1993).

16

Anchorages with bonded anchors

16.1

Scope

This section is applicable to bonded anchors installed in members made of structural concrete with normal weight aggregates. The range of concrete strength for which the design method is valid is given in the corresponding Approval. The anchorages may be subjected to tension, shear, combined tension and shear forces, as well as bending and torsion moments. To ensure suitability and durability of bonded auchors for use in structural concrete, prequalification testing should be performed (see Section 1.3). In general, this Part is valid for concrete members and anchorages subjected to predominantly static loading; for exceptions to this rule, see Sections 16.S and 16.6.

Discussion on the mmnnum embedment to avoid anchorage in substandard cover concrete may include several considerations such as, concrete type, compaction, reinforcing type, position, etc. Traditionally, a limit of 40 mm has been used. However, larger values may be valid for specific cases. It may also be desirable to avoid shallow anchorages, where load redistribution and ductility are required. A proposal for the minimum effective embedment depth as a function of the anchor diameter that reflects the above considerations is given in Table 16.1-1. Table 16.1-1:

In the following sections, equations for calculating the characteristic resistance for the elastic and plastic design approach are given for all loading directions and all failure modes.

Recommended minimum embedment depths of bonded anchors

Anchor diameter d [mm] Minh,[[mm]

The provisions are applicable to anchorages over a limited embedment depth range. As a practical matter some limit on the minimum embedment is necessary to avoid anchorage in cover concrete of lesser integrity. A conservative minimum embedment that is consistent with the design models in this Design Guide is given in Table 16.1-1. The limit on the maximum embedment is given by h'J= 20d. This reflects the limits of the existing database.

$10

12

16

20

~25

70 80 90 4d Note: smaller minimum embedment depths may be valid for certain types of bonded anchors if stated in the relevant Approval 60

Tension failure of bonded anchors may result from bond failure between the bonding material and the concrete or between the anchor element aud the bonding material. Current research indicates that these two failure modes are

The upper limit on the drilled hole diameter is given by d o:5 LSd.

indistinguishable from the standpoint of resistance provided that the bond line is kept relatively thin. This is accomplished with the limit of do :5 I.Sd (Cook et aI., 1998). According to the safety concept of partial factors (see Equation (3.3-1)), it should be shown that the design value of the actions does not exceed the design value of the resistance. Equation (3.3-1) should be applied for all types of actions on the anchors (tension, shear, combined tension and shear), as well as for all possible failure modes (steel failure, combined pullout and concrete cone failure, concrete cone failure and splitting failure under tension loading and steel failure, pryout failure and concrete edge failure under shear loading). Flowcharts for calculating the resistance for the elastic and plastic design approach are given in Figure 16.1-1 and Figure 16.1-2.

In the following, equations for calculating the characteristic resistance for the elastic design approach (Section 16.2) and plastic design approach (Section 16.3) are given for all types of actions and all failure modes. Requirements for the serviceability limit state, for fatigue and for seismic actions are given in Sections 16.4 to 16.6. The provisions are valid when the spacing between auchors of adjoining anchor groups or adjoining single anchors or the distance between single anchors are a > S".Np (S",.Np see Equation (16.2-1b) (combined pullout and concrete cone failure), a> S",.N (concrete cone failure in tension or pryout failure in shear), a> se,'"p (splitting failure) and a> 3Cl (concrete edge failure in shear) (see Figure 1.2-8 to Figure 1.2-10), Abandoned drilled holes filled with high strength non-shrink mortar do not have to be considered in the design of the anchorages.

In general, for the majority of structures the positioning and size of existing reinforcement in the concrete member in which post-installed anchors are placed is not known. However, in the following situations detailed information may be available:

during design of new construction anchor reinforcement for postinstalled anchorages is specified;

Where the existence of anchor reinforcement can be verified with respect to size and positioning, this reinforcement may be taken into account for the calculation of the characteristic resistance of the anchorage following the approach for headed anchors given in Section 19.2, Tolerances on the position of the post-installed anchors in respect to the location of the anchor reinforcement should be taken into account in an unfavourable way such to reduce the calculated resistance,

drawings and construction protocols of existing structures are available; detection tools based on scanning techniques are used to provide information on existing reinforcement. fib Bulletin 58: Design ofanchorages in concrete

177


178 Provided the location as well as the size of the existing reinforcement is known and the existing reinforcement fulfils the requirements to act as anchor reinforcement, then this reinforcement may be taken into account in the design of post-installed anchorages. The design should be carried out following the approach for headed anchors given in Section 19.2 for the verification of failure modes affected by anchor reinforcement (concrete cone failure under tension loading and concrete edge failure under shear loading). In the context of connections with bonded anchors no specific investigations have so far been carried out to study the influence of anchorage reinforcement on the combined pullout and concrete cone failure load. Hence a verification of this failure mode is still required. Note that for the typical range of embedment depth of post-installed bonded anchors the consideration of anchor reinforcement may rather be applicable for the calculation of the resistance to shear loading than for the resistance to tension loads. Because the exact location of the anchors with respect to the position of anchor reinforcement may not be known, the corresponding tolerances need to be taken into account in an unfavourable way, when designing postinstalled anchors including anchor reinforcement. For anchorages close to an edge with an anchor reinforcement to take up shear loads, cracks caused by the shear load will occur in the concrete well before reaching the ultimate load. The width of these cracks is limited to about 0.3 mm in the serviceability limit state. To avoid failure of the tensioned anchors, the design should be performed using anchors suitable for cracked concrete. Design for cracked concrete is not necessarily required where the exponent a in the interaction Equation (1O.3-ld) (simplified approach) or Equation (10.3-3) (alternative approach) is conservatively taken as a= 2/3 (see Section 19.2.3).

In case of combined tension and shear loads where the shear load is taken up by anchor reinforcement, premature failure of the tension loaded anchors due to excessive cracking caused by the shear load should be avoided. It is therefore mandatory in such cases to use anchors suitable for cracked concrete.

To use this Design Guide the following values should' be available either from an Approval or they should be evaluated from the results of prequalification tests (see Section 1.3). Durability (Section 7)

Appllca~on criteria 1_____, r-----~I (SecUons4.3.1 and 16.1) ,-

- NRk., (or A"j"k)

See Sections 16.2.1.2 and 10.1.2

- h'f


- 'rRk,cn TRk,lIl1cr


- ken kllner


- Scr,N, Cer,N


- Ccr,sp, Scr,sp


- Glllim Sm;",

hlllill

- VRk., (or A"j"k and k2 ) Find appropriate

partial factors (Section 3.4.2)

Find appropriate partial faelors (Section 3.4.2)

FInd smallest design resistance N""

Find 5m"",,~, deSign resistance VStJ combine,

NSd sNRd

tension and shear

o

See Sections 16.2.2.2 and 10.2.2.2

- k4


-d

See Sections 16.2.2.4 and 10.2.5.1 and Figure 2.5-1

-If

See Sections 16.2.2.4 and 10.2.5.1a)


See Sections 16.2.2.2, 10.2.2.1, 16.3 and 4.3.2.1(4)

Vs. ",VA'

Seismic 16.6)

Fire (Section 6.5) Ensuring characteristic resistance of concrete member (Secllon 6)


- MRk,s

(Section 16.2.3)

(Sec~on


- YM;


See Section 3.4.2


See Section 8.3

- Limitation on concrete strength classes of base material The minimum values for member thickness and reinforcement as well as for edge distance and spacing given in the relevant Approval should be respected.

Figure 16.1-1: Flowchart B for the calculation of the resistance of post-installed bonded anchors (elastic design approach)


179


180

Durability (Section 7) Application criteria (Sections 4.3.2 and 16.3)

Sevlceabllity limit state (Section 16.4) Fatigue (Section 16.5)

Seismic (Section 16.6) Fire

(Sections 6.5) Ensuring characteristic

resistance of concrete member (Section 8)

Figure 16.1-2: Flowchart C for the calculation of the resistance of post-installed bonded anchors (plastic design approach)

16.2


In the elastic design approach the distribution ofloads on the fixture to the anchors of an anchor group is done according to the theory of elasticity (see Section 4.3.1).

The field of application is given in Section 4.3.1.1.

16.2.1


16.2.1.1


The required verifications are given in Table 16.2-1.

The design model for tension loading on bonded anchor groups has been experimentally verified for groups up to 6 anchors and with numerical simulation for groups as large as 9 anchors (Eligehausen et aI., 2006-1; Appl 2009). Experimental verification of larger group sizes is not available; as such, use of the design model given here for larger groups (e.g., 6 x 6) should be approached with caution. In particular, the scatter associated with the resistance of bonded anchors may result in a decrease of the group capacity for larger groups as the anchor spacing approaches the characteristic spacing.

Table 16.2-1: Required verifications for tension loading (elastic design approach) Failure mode

NRk,s

Steel failure

NSd~NRd,s:::--


NSd :S;NRd,C

Combined pullout and 3 concrete cone failure

NSd _NRd,p

2

4 oj

Single anchor

Splitting failure

y,.

NRkc y,.

=--'

Anchor group oj Anchor group 'J Most loaded anchor Nil
Rd,.

=

NRk,s rAt..

NK
Rd,c

N

=~ YM:

=--

N K
NR1;.sp NSd S:NRt/.sp = - -

N Rksp NL::;;NRd,SP=--'-

<

NRk,p

y,.

r.\/sp

YMsp

Verification is performed for those anchors of a group loaded in tension

16.2.1.2

Steel failure

Section 10.1.2 applies.


181


182

16.2.1.3

Combined pullout and concrete cone failure

The characteristic resistance of an anchor and the tensioned anchors of a group in the case of combined pullout and concrete cone failure may be obtained by Equation (16.2-1). NRk,P

=N~,p 'lj/A,Np 'If/s,Np 'If/g,Np 'lj/ec,Np

'If/re,Np

(16.2-1)

The various factors of Equation (16.2-1) are provided below. The bond strength may be dependent on the concrete strength. In general, the influence varies and may conservatively be neglected. The value to be used for the design is given in the Approval.

a) The characteristic resistance of a single bonded anchor N;k.p not influenced by adjacent bonded anchors or edges of the concrete member is: N~.p = T Rk." ·ff· d . he! cracked concrete (16.2-laJ)

N~k,p =

'rRk,llf1cr • J[.

d· he! uncracked concrete

(16.2-la,)

with: TRk." (TRk.""e,) =

The bond strength decreases with time. The ratio bond strength under sustained load to bond strength under short term loading is product dependent. It should be evaluated by suitable prequalification tests. According to ETAG 001, Part 5 (EOTA, 1997) and AC308 (ICC-ES, 2009), bonded anchors are tested with a sustained load corresponding to about 55% of the mean short-time bond strength (as measured in tests with wide supports). If the displacement and residual strength criteria are satisfied at this load level, the actual long term bond strength is higher than 55% of the short-term bond strength due to the conservative criteria used to assess the results of the creep tests (Eligehausen et aI., 2010). In ETAG 001, Part 5 (EOTA, 1997) it is assumed that fulfilment of the creep test criteria is sufficient to assure good performance under sustained loads.

characteristic bond resistance corresponding to a given concrete strength class in cracked (uncracked) concrete given in the Approval or evaluated from the results of suitable prequalification tests (see Section 1.3)

Under sustained load an additional verification according to Equation (3.3-1) should be performed using the characteristic bond strength under sustained load in cracked (uncracked) concrete.

To take the reduced long-term bond strength into account, an additional verification according to Equation (3.3-1) should be performed for combined pullout and concrete cone failure under tension load and combined tension

and shear loading for the quasi permanent tension design load (permanent load and that part of the variable load than can be considered as pennanent) using the characteristic bond strength under sustained tension loading in Equation (16.2-1). The characteristic long-term bond strength used for this check in ACI 318, Appendix D (ACI 318, 2011) or AC308 (ICC-ES, 2009) is 55% or 75%, respectively, of the characteristic bond strength as stated in the Approval. In the Technical Report TR029 of EOTA (EOTA, 2007) no reduction of the short-tenn bond strength as given in the Approval is deemed necessary. A~.N

and

A~,Nand Ae,N

Ap,N

are calculated in the same manner as the reference areas

associated with concrete cone failure (see Figure 10,1-2 to

Figure 10.1-4), whereby the values Scr.Np and Ccr,Np, respectively.

Se"N

and

C",N

are replaced by the values

If the bond strength is shown to vary with concrete strength, then the bond strength corresponding to the minimum concrete strength specified in the Approval (in general concrete strength class C20) should be used in Equation (16.2-lb,), Note that the constant 7,5 in Equation (16.2-lb,) carries the unit MPa, The value of the critical spacing for bonded anchors is determined as a function of the bond strength and the anchor diameter, because the influence zone around a tension-loaded bonded anchor does not grow laterally with increasing embedment depth as for post-installed mechanical and cast-inplace headed anchors, but rather with increasing bond area (anchor diameter) and bond strength (Eligehausen et aI., 2006-1; Appl, 2009), For higher bond strengths and shallow embedments, this formulation can lead to the calculation of critical spacings in excess of 3hejo This agrees with observations of the behaviour of shallow headed anchors (Zhao, 1993), However, for reasons of simplicity the critical spacing of mechanical and cast in place headed anchors is constrained to S",N = 3hej regardless of embedment depth, Therefore, for consistency between the approach to the design of bonded anchors and mechanicaVheaded anchors, an upper limit on S",Np of 3hej is proposed in Part 5 of CENITS 1992-4:2009 (CEN, 2009), There are two observations associated with this proposal:


b) The factor

lj/A,Np

= Ap,N / A~,N takes into account the geometric effects of

axial spacing and edge distance on the characteristic resistance, where: A;,N

=

reference bond influence area

(S",NS Ap,N

Scr,Np

=

actual bond influence area, limited by overlapping areas of adjacent anchors (s:5 S",Np) as well as by edges of the concrete member (c :5 C",Np) 20d. • ,TRk ,lIIlcr <3h ef 7.5

with Ccr,Np

(16,2-lba

TRk,,,,,,,

O.5Sc'~Np

(16.2-1 b,)

corresponding to concrete C20 (16.2-lb3)

183


184

(I) For shallow embedment depths, where TRk is close to the value ofbond stress corresponding to concrete breakout (max TRIo see Equations (16.2-ld.) and (16.2-ld5)), the imposition of a 3hej limit on S".Np results in prediction of higher failure loads for groups as compared to predictions without this limitation. There are currently no test results available for these cases. In order to reduce the effect of this difference in the predicted resistances, a limit on the minimum effective embedment as given in Table 16.1-1 is implemented. (2) For the case where the limit on S,,·.Np is imposed, calculation of the tension resistance for certain cases, e.g., anchors in a comer condition, may result in declining predicted values for N Rk.p with increasing embedment, an anomalous artefact that has no theoretical or observational explanation. Where the limit is not imposed, however, changes in the predicted governing failure mode may occur, e.g., with comer anchorages where the edge distance is progressively increased for constant embedment. Note that the limit of 3hej on (2006-1) or Appl (2009).

S".Np

is not addressed in Eligehausen et al.

As a simplification, the same characteristic spacing and edge distance is used for calculations associated with cracked and uncracked concrete conditions. This approach is used for other types of anchors as well and is generally conservative. c) The factor %.Np takes account of the distribution of stresses in the concrete due to edges of the concrete member. For anchorages with several edges, e.g., anchorages in a comer the smallest edge distance should be inserted in Equation (16.2-lc) 'f/,.Np

C = 0.7 + 0.3 ._-:;:; 1.0

(16.2-lc)

ccr,Np

In many applications the factor 'f/g.Np is relatively small « 1.3). It may be neglected for reason of simplification.

d) The factor 'f/g.Np takes account of the effect of the failure surface of anchor groups. 'f/g,Np

=

'f/~,NP

-

J( J' ('f/~,NP -I) ~ S

(16.2-ld,)

1.0

scr,Np

.~

with: The value ofn is limited in Equation (16.2-ld,) and (16.2-ld3) due to the lack of test data for larger groups.

o

Iffg,Np

-.In-(-.In- I )(

T

Rk

."

max'Rk,cr

J1.5 ~1.0

(16.2-ld,)

(cracked concrete)

-.In -( -.In -I)

L5 Rk

(max r T

,,,,,,,

Rk,ullcr

J

~ 1.0

(16.2-ld3)

(uncracked concrete) n

The value max'Rk represents the bond stress corresponding to a concrete cone failure originating from the embedded end of the anchor. It is derived by equating the expression for combined pullout and concrete cone failure with that for concrete cone breakout, which is assumed to define the maximum carrying capacity of the concrete. The value 7.7 in Equation (16.2-1 ct.) (applications in cracked concrete) may be increased to 8.9 and the value 11.0 in Equation (16.2-ld5) (applications in uncracked concrete) to 12.7 if stated in the relevant Approval. See Section 10.1.4 for the derivation of the coefficients in Equations (16.2-1 ct.) and (16.2-1 d5).

• ••

D3'" l-l ••

• • •

5 21

• ••

•

5

(5, + 5 2.1+5 2.2)

•

5 2,1

(5 ,+ 5 , .2+5 2.1+ 5 2.2) "

•

• ••

11.0 ./h _.-' Jr.d ,j'hk

(16.2-1ct.) (16.2-ld5)

Where anchors in a group are not spaced equally the average value of the anchor spacing may be inserted as s in Equation (16.2-ld,). Examples are shown in Figure 16.2-1.

5 2,2

5 2. 1

l-U

5 1,1 5 1,2

$1,1 $1,2

5

max TRk,//l/cr

7.7 · ~hej' hk d

Jr.

03

22 j5

l-U

5,

maXTRk,cr

number of tensioned bonded anchors in a group (::; 9)

5

(5 ,., + 5 , .2+ 5 2.1+ 5 2.2 )

4 4 Figure 16.2-1: Determination of average spacingfor typical cases 3


185


186

For reason of simplification, the eccentnclty factor may be taken as /f".Np = 1.0 if the most stressed anchor is verified (N;d::; N;d) and the characteristic resistance of this anchor is taken as N':u,.p

=N Rk.P / n

with NRk•p according to Equation (16.2-1) with /f,e.Np = 1.0 and n = number of anchors loaded in tension.

e) The factor /f,e.Np accounts for the reduction of the group capacity when the tension loads acting on the individual anchors of a group are not uniform. I ' 1+ 2eN /

'f/ec,Np

<1.0

(16.2-le)

scr,Np

with: eccentricity of the resulting tensile load acting on the tensioned anchors (see Section 4.3.1.2). Where there is an eccentricity in two directions, /f".Np should be determined separately for each direction and the product of both factors should be inserted in Equation (16.2-1)

eN

f) The factor /f".Np accounts for the reduced strength of anchors with an embedment depth hcJ< 100 mm, inserted in a concrete element with closely spaced reinforcement.

hi

for s < 150 mm (for any diameter d,)

200

ors< 100 mm (ford,::S IOmm)

/f~N. =0.5+-'• P

for s 2: 150 mm (for any diameter d,)

= 1.0

/f".Np

(16.2-1fJ) (I 6.2-1 f2)

or s 2: 100 mm (for d,::S 10 mm) where s denotes the spacing of reinforcement within the concrete element.

16.2.1.4 In general, the maximum concrete capacity of anchorages with bonded


Section I 0.1.4 applies.

anchors is limited by the concrete cone resistance according to Equation (10.1-2) with N~., as follows: N°Rk,c =k1 'Jcko., ·hJ.' ej

kJ =k" =7.7 [../N/mm ] cracked concrete kJ = k""" = 11.0

[../N I mm ]

uncracked concrete

Larger kJ-values (k,,::S 8.9; k"",,::S 12.7) may be taken if stated in the relevant Approval.

16.2.1.5

Splitting failure

Section I 0.1.5 applies.

16.2.2


16.2.2.1


The required verifications are given in Table 16.2-2. Table 16.2-2: Failure mode Steel failure without lever arm

Required verifications for shear loading (elastic design approach) Anchor group 'J

Single Anchor

Most loaded anchor VSd

:::;VRds = VRk,s Ylill

Steel 2 failure with lever arm

v:sa <- v:Rd,SIt/ -_-VRk-•sm-

Concrete 3 pryout failure

VS<} -
y,\/:;

VRk,cp

Anchor group

v."Sd :::;; VRd,s = V,Rk,s Y~"

"

J~

VSd:::;rRd,sm

= VRk,sm __ YM.>

Sd < _ v:Rd,cp = V:'

v:Rk,cp

a)

YAte

Concrete v Vi:J 5VRd.c=VRk ,c b) VSJ:::; VRd,c = Rk,c 4 edge rAlc r," failure 'J Veriflcation is performed for those anchors of a group loaded in shear b) Verification is performed for the anchors assumed to generate concrete edge failure; see Section 4.3.1.3

16.2.2.2

Steel failure



187


188

16.2.2.3 Because pryout and combined pullout and concrete cone failure under shear load are generated by the same mechanism (see Section 3.2), for reason of simplification both failure modes are covered by Equation (16.2-2).


Anchorage capacity may be limited by a concrete pryout failure at the side opposite to the load direction. The corresponding characteristic resistance VRk.ep may be calculated from Equation (16.2-2). (16.2-2)

VRK •ep =k4 .rnin(NRK.e;NRK •p )

with: As a first indication the factor k4 may be taken as 1.0 for h'f~ 60 mm and 2.0 for h,f> 60 mm.

k,

factor, which may be taken from the relevant Approval or evaluated from the results of prequalification tests (see Section 1.3)

NRk.p

value according to Section 16.2.1.3

NRk.e

=

value according to Section 16.2.1.4

For group anchorages with shear forces (or components thereof) on the individual anchors in opposing directions (e.g., anchorages loaded predominantly by a torsion moment), the most unfavourable anchor should be verified. When calculating the area Ae.N or Ap•N, it should be assumed that there is a virtual edge (c = O.5s) in the direction of the neighbouring anchor(s) (see Figure 10.2-1).

16.2.2.4


Section 10.2.5 applies. In Equations (10.2-5a) and (l0.2-5a2) danm should be replaced by d.

16.2.3



16.3 The use of bonded anchors in cases where plastic design is to be used presents special problems. It is necessary to ensure that the unbonded length is adequate to guarantee the necessary elongation associated with plastic design. This may be accomplished by de-bonding a length of the anchor, or


Section 11 applies. However, in Equation (11.2-2) the value NRk.P should be calculated according to Section 16.2.1.3 and in Equation (11.3-2) the value VRk.ep should be calculated according to Section 16.2.2.3.

"

by providing sufficient rod length between the surface of the concrete and the fixture (e.g., as in an anchor chair).

16.4


Section 12 applies.

16.5

Fatigue

Section 13 applies. As a first approximation LlrRk!nl may be taken as 0.5 rRk (Spieth, 2002).

The resistance LlNRk•p should be calculated (16.2-1) replacing the value rRk in Equation (16.2-1a) by

using t;.rRK,Ja"

Equation The value

should be taken from the relevant Approval or should be determined from prequalification tests (see Section 1.3).

LlrRk!at

16.6

Seismic loading

The verification for seismic loading on the anchorage should be performed according to Section 6.4. The resistance- NRk.p should be calculated using Equation (16.2-1) replacing the value rRk in Equation (l6.2-1a) by rRk.'q' The value rRk.'q should be taken from the relevant Approval or should be determined from suitable prequalification tests in cracked concrete where crack width and cycling is representative of seismic loading.

The use of bonding material to embed reinforcing bars in hardened concrete is a common construction practice, particularly in the strengthening and renovation as well as the extension of existing structures. In order to provide a monolithic connection between the new and the existing concrete element post-installed reinforcing bar connections are established e.g., by overlapping joints with existing reinforcement in a building component (see


17

Connections with post-installed reinforcing bars

17.1

Scope

This section addresses the prequalification, design and installation of connections made with deformed reinforcing bars (/'yk ~ 500 MPa) and polymer (epoxies, vinyl esters, etc.) or cementitious bonding systems in existing structures made of nonnal weight concrete of strength class C12 to C60 to resist predominantly static loads. Applications involving fatigue and/or seismic loading are permitted provided that such applications are

189


190 Figure 17.1-la) or by anchoring the reinforcement at a slab or beam support (see Figure 17.l-lb). This type of structural connection is addressed in this section ofthe Design Guide. 11111111111111111 ////rexlstlno_/ / / / '; . m! // F';"""~ "u",,",",', ~-:,:/; nAw1/~/,

encompassed in the Approval or have been addressed in suitable prequalification tests. All configurations permitted in Model Code 1990 (CEB, 1993) for cast-in straight deformed reinforcing bars are permissible for post-installed reinforcing bars as well.

a)

III IIIII IIIII IIIIII IIII

b)

Figure 17.1-1: Example of connections with post-installed reinforcing bars: a) overlap joint in slabs and beams; b) end anchoring ofslabs or beams In this Design Guide, it is proposed that the design of post-installed reinforcing bars follows the design rules given in Model Code 1990 (CEB, 1993) for cast-in reinforcing bars taking into account the rules for the design of shear joints. The limit on the nominal yield strengih of reinforcing is given in Model Code 1990 as 500 MPa. When other design codes for reinforced concrete are used for the design of post-installed reinforcing, the corresponding limits on steel strength, spacing, etc. should be applied.

17.2 The basic requirements to be verified in the prequalification testing are as follows:

- ability of the drilling method to achieve straight and accurate holes over the maximum embedment lengths anticipated for the system; - ability of the injection system to place bonding material over the full length of the maximum hole depth without the introduction of air pockets;

Prequalification testing

Prequalification testing of systems for the installation of post-installed reinforcing bars is necessary to both ensure suitability and durability of the

bonding material for use in structural concrete as well as to verifY the effectiveness of the system for achieving an accurate installation and a consistent strength.

- ability of the post-installed reinforcing bars to exhibit corrosion resistance equivalent to or greater than cast-in reinforcing for the applicable exposure class; and - ability of the post-installed reinforcing bars to develop tension capacities equivalent to or greater than cast-in reinforcing when installed with normal concrete cover dimensions taking into account all relevant influencing factors such as type of loading (short term, long term, fatigue or seismic), temperature range and concrete cracking. As a rule, reinforcing bars embedded with bonding material (polymer and/or cementitious) should exhibit equal or superior strength and comparable stiffness when tested side by side with cast-in-place defonned reinforcing bars of equivalent diameter, embedment length, edge distance, spacing, etc. Such tests should be conducted in the manner used to determine permissible bond stress for cast-in bars; that is, in configurations where splitting and pullout will control the behaviour. Testing regimes involving testing close to edges have shown that the splitting forces are roughly equivalent to cast-in-place bars (Spieth, 2002). A primary factor is the ability of the bonding material to develop a relatively uniform state of stress along the length of the bar. Overly stiff bonding materials may result in zipper-type failures. Additional considerations include the effect of concrete cracking along the bar caused by tension stresses perpendicular to the bar direction on the bond behaviour and the response to elevated in-service concrete temperatures. The ability of the bonding material to provide a durable load transfer over the anticipated service life under sustained load and a variety of environmental exposure conditions should also be investigated. Since the bonding material will prevent direct contact of the reinforcing steel with the concrete, the normal passivation of the steel surface induced by the alkaline concrete environment may not occur. It is therefore necessary to ensure that the bonding material provides a similar level of corrosion protection for the reinforcement. The fib Bulletin 58: Design of anchorages in concrete

191


192

perfonnance of the system should be checked for the entire range of applicable bar diameters, embedment lengths, concrete grades and in-situ temperatures. The prequalification tests should be perfonned on reinforcing bars installed using the manufacturer's printed installation instructions and in conditions most similar to those that will be experienced on the job site. The installation instructions should be of sufficient specificity to anticipate all aspects of the installation process so as to provide for a low degree of job-site improvisation and attendant installation error (see Section 3.5.2). The maximal pennissible anchorage depth in relation to the installation tools used should be specified in the installation instructions and should be verified at the specified extremes by means of handling tests during the product evaluation. The ability of the drilling system to provide straight and accurate holes of the required diameter and length, particularly in near-edge conditions, should be verified.

The design of the connection should take into account the condition of the existing structure. The selection of the materials (bonding material, reinforcing steel) for the joint should consider the applicable exposure class.

17.3

Design

17.3.1

General

Post-installed reinforcing bar connections should be designed in accordance with good engineering practice. The detennination of internal section forces to be transferred across the construction joint should conform to the CEB-FIP Model Code 1990 (CEB, 1993). When ascertaining the tensile force in the post-installed reinforcing bars, allowances should be made for the in-situ effective position of the post-installed reinforcement taking into account the expected variances from the nominal position due to imperfect drilling. At a minimum, the following infonnation should be provided in the design documents: - strength of existing concrete and grade of post-installed reinforcing bars; - diameter, spacing, concrete cover and hole depth for the post-installed reinforcing bars;

Only the drilling system(s) specified in the Approval should be used on site.

drilling system including drilling aid as necessary, e.g., for drilling long holes close to edges and to other bars as required;

Jomt preparation requirements, including the degree of surface roughness; thickness of concrete cover or type, position and anchorage of insulating material etc. as required for fire protection.

17.3.2 The bond resistance of post-installed reinforcing bars may not increase with increasing concrete strength in the same manner as for cast-in reinforcing bars. In these cases, the bond strength corresponding to a limiting' concrete strength class may be mandated for applications in concrete with a higher strength class (see Figure 17.3-1). design bond strength for reinforcing bars as a function of concrete strength according to CEB-FIP Model Code 1990 (CES.1993)

tbd

"

design bond strength for post-installed

~ reinforcing bars according to Approval

-

No increase in design bond strength for increasing concrete strength

t'k Figure 17.3-1: Example for determination of governing design bond strength as a function of concrete strength class

Dimensioning of the connection

The dimensioning of the connection should be performed according to the CEB-FIP Model Code 1990 (CEB, 1993) assuming a bond resistance Ji,d as given in the Approval. The bond resistance should not exceed that given for defonned cast-in reinforcing bars in the code. Requirements for transverse reinforcement should confonn to those applicable to cast-in bars. The following additional restrictions and requirements may apply: - restrictions on the minimum concrete cover; - restrictions on the minimum bar spacing; requirements for the minimum bond length; restrictions on concrete strength used in design. For the transfeYof shear forces across the joint, the design should consider appropriate measures for the preparation of the concrete surface, e.g., roughening, keying, etc. in accordance with the assumptions made for the design. The design should be in accordance with CEB-FIP Model Code 1990 Chapters 3.9, 3.10, 6.10 and 14.3 (CEB, 1993).

The minimum concrete cover and bar spacing to avoid splitting of the concrete during drilling are dependent on the method of drilling (hammer drill, core drill, etc.). For hammer drilling a minimum spacing for postinstalled reinforcing bars of 4d, > 40 mm is advisable. In addition, inaccuracies in the drilling trajectory associated with the drilling system used should be accommodated in the minimum cover and spacing requirements. As a result, the minimum cover and bar spacing may exceed those required for cast-in bars. An example for minimum cover requirements as a function of drilling method is given in Table 17.3-1. These values are valid for freehand drilling. They may be reduced if a suitable drilling aid is used. The efficiency of such aids should be checked by tests.


193


Table 17.3-1:

194

Example a/increased minimum cover requirements/or post-installed rein/arcing bars

Drilling method Rotary hammer drilling Compressed air drilling

Bar diameter d,

required concrete cover (mm)

:5 20 mm

30 mm + 0.06')/, 2: 2d,

25mm

40 mm + 0.06')/,2: 2d,

:520 mm

50 mm + 0.08')/,2: 3d,

25mm

60 mm + 0.08')/,2: 2d, " This term may be significantly reduced if a drilling aid is used Care should be taken in the preparation of the joint to remove any unsound concrete and loose material, and clean the exposed existing reinforcement as required. Carbonated concrete in the location of the postinstalled reinforcing bars should be removed in order to reduce the potential for corrosion. Revision of the design to acconunodate the extent of removal of existing concrete and the rehabilitation of the existing reinforcing bars may be necessary.

17.4 Where structural fire design requirements control the design, possible methods to improve the fire resistance of the joint are as follows: - increase the concrete cover over the post-installed reinforcement to reduce the internal concrete/bonding material temperature; increase the bond length of the post-installed reinforcing bars to compensate for reduced bond resistance associated with increased temperature;

Design for fire

Where structural fire design requirements are in force, the joint should be assessed accordingly taking into account the response of the bonding material to increased temperature under fire exposure.

provide insulating material on the concrete surface to reduce the internal concrete temperature. The method employed should take into account the temperature response of the bonding material as described in the Approval. The organic materials in bonded anchor systems may be permanently damaged through carbonisation during a fire. Verification of the competency of the bonding material after a fire may be undertaken through local investigation. Alternatively, if sufficient cover is provided, it may be possible

to establish that the bonding material has not been compromised, e.g., if an assessment of the internal temperature in the concrete during the fire event has not exceeded the critical carbonization temperature. No information in respect to this topic is currently available in the literature.

17.5 The installation of post-installed reinforcing bars may place particular demands on the training of the installation personnel. Accurate drilling of long holes with close edge distances, cleaning of deep holes and installation of large quantities of bonding material without voids in general requires special training and equipment. Measures for the verification of the proper installation on site may vary by country; e.g., emphasis may be placed on precertification and training of installers as opposed to job-site inspection.


Installation and job site quality control

The installation of post-installed reinforcing bars should be carried out in accordance with the manufacturer's installation instructions. The drilling and cleaning of the holes and the installation of the bonding material and reinforcing bars should be performed with the equipment specified by the manufacturer. The work should be performed by suitably qualified personnel under adequate supervision. Job site quality control measures should be provided and should verifY the design conditions as specified in the construction documents.

195

Part IV: I8 Scope

196

PART IV: CHARACTERISTIC RESISTANCE OF ANCHORAGES WITH CAST-IN HEADED ANCHORS

18

I

a)

b)

Scope

Part I applies unless otherwise noted. Part IV applies to anchorages accomplished with cast-in headed anchors (Figure IS-I) loaded by tension, shear, combined tension and shear forces, as well as bending and torsional moments. A variety of attachment options are addressed. Most commonly, the anchors either pass through a hole in the fixture and are secured with a nut and washer (Figure IS-la) or, in the case of stud anchors, are welded directly to the fixture (Figure IS-I b,c). One of the primary differentiating characteristics between these two configurations from the standpoint of resistance is that through-bolted cast-in anchors (Figure IS-Ia) most often feature an annular clearance between the anchor and the fixture whereas welded anchorages do not. Anchors may also be threaded directly into the fixture, in which case they may be assumed to share some of the characteristics of welded anchorages. This Part addresses both prestressed and non-prestressed anchors. Note that welded anchorages as shown in Figure IS-1 b,c cannot be prestressed. Specialty inserts, strap-type anchors, L- and I-bolts are not covered in this Design Guide. This Part applies to members made of normal weight concretes ranging between strength classes C20 and C90 as defined by CEB-FIP Model Code 1990 (CEB, 1993).

Stud welding or metal-arc welding

c)

Figure 18-1:

Examples of headed anchors covered by this Design Guide: a) headed bolt; b) headed stud welded to an embed plate; c) group of headed studs welded to an embedplate

The wide variety of shapes and configurations of speciality inserts makes it difficult to prescribe generalized tests and design equations for many insert types. Hence, they have been excluded from the scope of this Design Guide. While L- and I -bolts share some of the characteristics of headed cast-in anchors covered by this Guide, their behaviour in groups and with respect to concrete breakout, splitting, etc. has not been sufficiently investigated to permit their inclusion in the design model used in this Design Guide. The design model contains limits on the bearing stress in the concrete under the head which relate to the relationship between splitting forces and tension forces and controls the displacement of the anchor. This in tum affects the concrete breakout behaviour. These limits are given in Section 19.1.1.3 (ultimate limit state) and Section 21 (serviceability limit state) and will effectively dictate the size of the head. The tests used to determine these limits did not involve fatigue or seismic loading of the concrete member. The plate dimensions, anchor spacing, edge distance and member thickness provided for embed plates should ensure that full consolidation of the concrete around the anchors and under the plate is facilitated.

The following conditions should be fulfilled in order to ensure that the behaviour of cast-in headed anchors conforms with the design model used in this Design Guide: I. the angle of inclination of the bearing surfaces of the head as measured from the anchor longitudinal axis is greater than or equal to 45°, the thickness of the head is not less than OAd and the bearing surface projection as given by 0.5(d}, - d) is not less than the maximum of 0.25d and 4 mm.

2. in the case of anchors threaded directly into the fixture, the engaged thread length is not less than the nominal anchor diameter. 3. the loading of the concrete member is limited to predominantly static loading. Suitability tests may be omitted if these conditions are met. Where these requirements are not met, prequalification testing may be necessary analogous to the tests specified in Section 1.3. Prequalification testing may be necessary to evaluate the values c".,P' the characteristic displacements under given loads and the characteristic fatigue and seismic resistance. As a minimum, the manufacturer and the grade and type of steel should be marked on the anchor. Positioning and securing of anchors and embed plates in the formwork, prior to placement of the concrete, should be carefully executed taking into account the provisions in Section 3.5. Care should be taken during concrete placement to ensure proper consolidation of concrete around the anchors and under the fixture .. In general, the loading of the anchorage and the concrete member, in which the anchorage is located, should be limited to predominantly static loading. Anchors welded to or threaded into the fixture may be suitable for fatigue loading if the conditions in Section 22 are met. Seismic loading may be permissible if proper consideration is given to the effects of seismic actions on the member and the anchorage. The requirements for the anchorage are addressed in Section 23. According to the safety concept of partial factors (see Equation (3.3-1)), it should be shown that the design value of the actions does not exceed the design value of the resistance. Equation (3.3-1) should be observed for all loading directions on the anchors (tension, shear, combined tension and shear) as well as all failure modes (steel failure, pullout failure, concrete cone failure, splitting failure, side-face blowout failure under tension loading and steel failure, pryout failure, concrete edge and pullout failure under shear loading). Additionally, if anchor reinforcement is present it should be verified for both reinforcement and anchorage failure.


197

Part IV: I8 Scope

198 The distribution of the actions acting on a fixture to the anchor(s) attached to the fixture may always be calculated according to the theory of elasticity (see Section 4.3.1). In certain cases, it may be permissible to calculate this distribution according to the theory of plasticity (see Section 4.3.2).

Flowcharts for calculating the resistance of anchorages with headed anchors according to the elastic and plastic design approaches are given in Figure 18-2 to Figure 18-4.

In the following sections, equations for calculating the characteristic resistance for both design approaches are given for all loading directions and all failure modes. To use this Design Guide the following values should be available either from an Approval or from suitable prequalification testing and evaluation (see Section 1.3). -NRk., (or A"j.,k)


- ka , kuua


- h'l


- Sa.N, C".N


- ce,.,p, s".,p


- emil/> Smill> hmill

See Table 18-1

- VRk., (or A"j.,k and k2)


- M'k.,


- VRk.p (or k3)


- k,


- d, d"

See Sections 19.1.1.3, 19.1.2.3, 10.2.5.1, and Figure 2.5-3

-&



See Sections 19.1.2.2,20,10.2.2.1, and 4.3.2.1(4)

- YMf


See Section 3.4.2


See Section 8.3

- Limitation on concrete strength classes of base material

I

Anchorage resistance can be increased through the provision of suitably dimensioned and detailed reinforcement.

I

Starl

-I

For non-prestressed anchors the minimum values for spacing, edge distance and member thickness given in Table 18-1 should be observed.

Durability

I

{Section 7)

Application Criteria (Sections 4.3.1 and 18)

I (Section TenSion 19.1.1)

I

Steel resistance

Section

Concrete roo. (Section 19.1.1.4)

I

Blowout (Section

19.1.1.6)

I

Find smallest design reslslance NRd

! Ns. s NRO

Table 18-1:

lever arm (Section 19.1.2.2.2)

{Section

19.1.2.2.1)

Concrete resistance

!

1

With

1.IWilhOUI lover arm

I

I

Steel resistance

I

Splitting (Section 19.1.1.5)

I

Pullout (Section

19.1.2.3)

Concrete pryout (Section 19.1.2.4)

Find appropriate partial faclors (Sect. 3.4.2)

I

I Ifcom Ine~ tension and shear (Section 19.1.3)

I I

1

Concrete edge (Secllon 19.1.2.5)

Find smallest design resistance

VK~

\

l

VS
Serviceability limit stale (Section 21) Fatigue (Section 22)

= 5d2: 50 mm

Minimum spacing

Sm;"

Minimum edge distance

Cmfu -

Minimum member thickness oj

h",;" = hef + til + ctfi

3d?:. 50 mm

= thickness of anchor head c. = required concrete cover for reinforcement in conformance with CEB-FIP Model Code 1990 (CEB, 1993)

oj IJ,

I I 1

Minimum values for spacing, edge distance and member thickness for non-prestressed headed anchors -

I

I partialFir1:lfactors appropriate ! (SecL 3.4.2)

I

1

She" (Section 19.1.2)

I

j 19.1.1.2

I

I Concrete resistance

I

Pullout (Section 19.1.1.3)

I

I

Seismic (Section 23)

For prestressed anchors, the values for minimum spacing, edge distance and member thickness should be taken from the relevant Approval or should be evaluated from the results of pre qualification testing (see Section 1.3). The provisions of Sections 19 and 20 are valid when the spacing between the outer anchors of adj oining anchor groups or to single anchors or the distances between single anchors are a> S",N (concrete failure in tension or pryout failure in shear), a> sa.,p (splitting failure) and a> 3Cl (concrete edge failure in shear) (see Figure 1.2-8 to Figure 1.2-10).

Flm (Seellon 6.5)

Ensuring characterlsijc resistance of concrete member (Section 8)

1Figure 18-2:

Eod

I

Flowchart B1 for the calculation of the characteristic resistances of anchorages with headed anchors without anchor reinforcement: elastic design approach


199

Part IV: 18 Scope

200

Durability

(Section 7)

Application criteria (Sections 4.3.1 and 18)

Concrete resistance

reii'll. (Section

119.2.2.7)

Find appropriate partial factors (Sect. 3.4.2)

Find appropriate partial factors (SecL 3.4.2)

Find smallest design resistance NIId

Find smallest design resistance

comDiillli tension and shear (Section 19.2.3)

Ns. "NRd

Vld

VS
SelViceablflty limit state

(Section 21) Fatigue (Section 22) SeIsmic (Section 23)

Fire (Section 6.5) Ensuring characteristic resistance of concrete member (Section 8)

Figure 18-3:

Flowchart B2 for the calculation of the characteristic resistances of anchorages with headed anchors with anchor reinforcement: elastic design approach

I I

I

Durability (Sectlon 7)

(Section 11.2)

j

I

I

I Concrete resistance

I

I Shear (Section 11.3)

ISleel resIstance )

j

!

Section 11.2.1

I

Tension

Steel resistance

T

Application criteria (Sections4.3.2.1, 11.1 and 20)

[

I

I

Start

NS
I

Pullout {Sec1.1122 and 19.1.1.3}

II

Equation (11.2-2)

I

oncrete cone (SecI.112.3 and 19.1.1.4}

II

Splitting (SecI.11.2.4 and 19.1.1.5)

I

Equation (11.2-3)

I

Without lever ann {SeCI.11.3.2 nd 19.1.2.2.1

Blowout SecI.19.1.1.e and 20)

I

I

Concrete resistance

Concrete. pryout {Sect.11.3.3 and 19.1.2.4)

Equation (20-1)

I V~
Equation (11.3-2)

I

I

I

I

oncrele edge (SecI.11.3.4 and 19.1.2.5) Equation (11.3-3)

I

J If combined tension and shear (Sect.19.1.3)

r I I r

Seviceability limit state (Section 21) Fatigue (Section 22) Seismic 23)

(Sec~on

I

Fire (Section 6.5)

I Ensuring characteristic resistance of concrete member (Section 8)

I Figure 18-4:

Eo'

Flowchart C for the calculation of the characteristic resistances of anchorages with headed anchors without anchor reinforcement: plastic design approach


201

Part IV: 19 Ultimate limit state - elastic design approach

When using anchors comprised of multiple headed anchors welded together as shown in Figure 19.1-1, care should be exercised to align the anchors properly during assembly in order to avoid secondary eccentric moments. Consideration should also be given to the potential formation under service loads of a premature concrete failure cone originating from the anchor head closest to the concrete surface. To avoid this possibility, a soft material should be placed around the anchor head, as shown in Figure 19.1-1. The displacement to be accommodated by the soft material may be detennined through appropriate consideration of elastic strain in the anchor shaft and corresponding head displacement under service loads. The soft material should be properly secured to the head to avoid displacement during casting .

202

19


19.1

Anchorages without anchor reinforcement

In the elastic design approach, the distribution of the loads acting on the fixture to the anchors is calculated according to the theory of elasticity (see Section 4.3.1).

The field of application is given in Section 4.3.1.1.

.

•

t

Soft material

h'l

• --"<-

Figure 19.1-1: Example of an anchorage with two anchors welded together

19.1.1


19.1.1.1



Required verifications for tension loading (elastic design approach) Anchor group ,)

Failure mode

2

Single Anchor

anchor

Steel failure

NSd=:;;NRds = - -

Pullout failure

Nsu ~NRd,P = - -

N/lk,S

'

YAfp

NSd

Splitting failure

NSJ

Blowout 5 failure b)

NSd

4

N Rkc -5.NRd ,c =--'Yftk NRk,sp

::;NRd,sp

"

=--

Anchor group ,)

_NRJe,s

NSd =:;;NRd,s-

r,lls NRk,p

Concrete 3 cone failure

Most Loaded

rMs

N h
Rd,p

NRk,p ::::-YMp

NLs.NKdc =N-flk-,., ,

YMc

NRk,sp

Nffd '5.NRd ,sp = - -

Yu,p

N Rkcb

-5.NRd,ch =~

.'"

r.1/Sp

g

_NRJ;,Cb

NSJ::; NIId .cb -

y,"

,) Verification is performed for those anchors of a group loaded in tension b) Verification is not required for anchors with c> O.5hojin members with a thickness of h ~ h,[+ 2cI

The partial factors for YMn YMp, YM,p and YM, are given in Section 3.4.2.1.

19.1.1.2

Steel failure


19.1.1.3 It may be necessary to reduce the pullout resistance according to Equation (19.1-1) to fulfil the requirements in the serviceability limit state (compare


Pullout failure

The characteristic pullout resistance N Rk•p of an anchor is given by Equation (19.1-1).

203


Section 21 and Equation (21-1)).

204

N M.p

=Pk . A"

(19.1-1)

with:

Pk

7.5};k for cracked concrete

(19.1-la)

Pk

10.5};k for uncracked concrete

(19.1-lb)

A"

bearing area of the head 1t (

19.1.1.4 The values of k" and k"n" depend on the concrete pressure under the head. The values given in this Design Guide apply if the characteristic concrete pressure Pk according to Equation (19.1-la,b) is observed. The critical pressure to ensure a concrete cone failure according to Section 19.1.1.4 is discussed in Eligehausen et al. (2006-2) and Furche (1994). On the basis of a large experimental database including tests by Lee et al. (2007) and numerical studies in Ozbolt, Eligehausen (1990), the mean concrete cone failure load (mean resistance) of a single headed anchor in uncracked concrete can be approximated by Eligehausen et al. (2006-2) with Equation (l0.1-3a) with k= 15.5.

d,; - d )/4 (for round head) 2

(l9.1-lc)


Section 10.1.4 applies with the following modifications: a) The characteristic resistance N;'., of a single anchor without edge and spacing effects is calculated according to Equation (10.1-2a) with kJ = k,,= 8.9 [.JN/mm ] (cracked concrete) or kJ = k"ne,'= 12.7 [ .IN I mm ] (uncracked concrete).

b) The definition of embedment depth is given in Section 2.5 (see Figure 2.5-3).

The values of k, used in Section 19.1.1.4a) are derived based on the Equations (1O.1-3a,b,c). However, the factor k= 15.5 has been used for castin headed anchors. The model used in this Design Guide assumes that for a group arranged perpendicular to the edge and loaded by centric tension load, the edge influences the whole group and not only the anchors closest to the edge. This assumption may be unconservative for anchorages with an edge distance c close to the minimum value according to Table 18-1. In such cases, it may be advisable to provide supplementary reinforcement (stirrups and edge reinforcement) in the region of the anchorage as shown in Figure 19.1-2 to offer additional resistance for the near-edge anchors.

t

,

j. c:;; hOI,

d

II

h'l

Edge reinforcement Stirrups

Figure 19.1-2: Example of a near-edge anchorage provided with stirrups and edge reinforcement

19.1.1.5

Splitting failure

Section 10.1.5 applies with the modifications explained in Sections 19.1.1.5.1 and 19.1.1.5.2. 19.1.1.5.1 Splitting failure associated with anchor installation Headed anchors that are not torqued or prestressed (e.g., studs welded to embed plates) do not generate splitting forces prior to application of load.

Splitting failure associated with prestressing or applying a torque moment to headed anchors should be avoided by complying with minimum values for edge distance, spacing, member thickness and reinforcement. These values are given in the relevant Approval or should be evaluated from the results of appropriate prequalification tests (e.g., analogous to Section 1.3). 19.1.1.5.2 Splitting failure due to anchor loading

Headed anchors complying with the provisions I to 3 in Section 18 are generally suitable for applications in which the concrete is cracked. Where cracked concrete conditions are assumed, verification of the splitting failure mode is not necessary (see Section 10.1.5.2). If the characteristic splitting resistance is calculated according to Equation (10.1-5), then the value N;k.e should be calculated according to Section 19.1.1.4 and the values c".,P = 0.5s".,p = 2h'fmay be taken as a first approximation.

Section 10.1.5.2, applies.

19.1.1.6 Blowout failure The model according to Equation (19.1-2) is based on Furche, Eligehausen (1991) and Hofmann, Eligehausen (2009).


Verification of blowout failure is not required, when the edge distance of the anchor in all directions is c> O.5h'f and the member thickness of

205


No tests are available with headed anchors in members with a small thickness (h < h,/+ 2cI) in which blowout failure occurred. In these applications Equation (19.1-2) may yield conservative results. For an anchor group rectangular in shape, the characteristic resistance of the group in the case of blowout failure should be calculated according to Equation (19.1-2) for the row of anchors closest to the edge. This approach is conservative. For anchorages near a comer or in a narrow member with C2 < CI the concrete in the area of the anchor head should be confined by closely spaced reinforcement (stirrup or spiral) with spacing::s 50 nun.

206 h > h,/+ 2cI. If verification is required, the characteristic blowout resistance is given by Equation (19.1-2): NRk,cb =

N~,Cb "Ij/A,Nb 'If/s,Nb 'ljJ'g,Nb 'ljJ'ec.Nb

with:

NORk,cb -

characteristic blowout resistance of a single anchor unaffected by adjacent loaded anchors, proximate comers, or limited member thickness

If/A.Nb

A,.Nb / A;'Nb

factor accounting for the geometric effects of loaded anchor spacing, distance to proximate comers, and member thickness

~

~ \

I I I I I I I I I A~.Nb I IL _ _ _ _ _ _ ...lI

1'8 /

/

--.,

r--

\

4C,j

(19.1-2)

/

1f/,,Nb

factor to take into account the influence of a comer on the stress distribution in the concrete

If/g.Nb =

factor to take into account the influence of the anchor bearing stress on the blowout resistance of an anchor group

If/,,.Nb =

factor to take account of a group effect when different tension loads are acting on the individual anchors of a group

The various factors of Equation (19.1-2) are explained below. a)

b)

Figure 19.1-3: Idealised concrete breakout body and area A~Nb of an individual anchor in the case of blowout failure: a) side view; b) plan view

The average value of k5 has been quantified as 18.5 for headed bolts in uncracked concrete on the basis of a large experimental database in respect to the average blowout resistance of a single anchor for concrete strength measured on cubes with side length of 200 mm (Hofinann, Eligehausen, 2009). The values of k5 used in Equation (19.1-2a) are determined following the procedure given in Equations (10.l-3a,b,c).

1,;

~ \

i-]---tr8 l

iJ:l,(

I

/

IL ________ A~,Nb _

I

J

/

.1 2c, 1

s

JI

8

~ \

\

r=

I

I' c, I

S

(19.1-2a)

see Equation (19.1-1c)

O Ac,Nb

projected area of the idealised concrete blowout failure cone of a single tension-loaded anchor located near the edge of the concrete member, taken as a pyramid with height CI and base length 4cI (see Figure 19.1-3) 16c'I

A~tJb =4c 1'(C2 + 5 + 2c, ) 5::;4c, C.2$2C 1

,1 2c'f

projected area of the idealised concrete blowout failure cone associated with the tension-loaded anchor group located near the edge of the concrete member, as limited by overlapping failure surfaces, proximate comers, or limited member depth. Examples for the detennination ofA,.Nb are given in Figure 19.1-4

c) The factor If/,.Nb takes into account the influence of a proximate comer on the distribution of the stresses in the concrete resulting from anchor loading: If/,Nb

,

rI I

~

f 2c, I.

-1I

~

!

f

I

A~.Nb

s

2C 11

f 2c, I·

A~.Nb =(2c 1+ f )'(4C, + s) sS4c 1 f S 2c 1

c) Figure 19.1-4:

fA. Jck 1'0.75

"nil

b)

r:

~

C1

A"

4C 1

o I AC,Nb ________ ..JI

/ /

/0.75.

ks = k"""

Ae•Nb

--,

=

5

11.1 [N0.25 / mmO. 25] cracked concrete 15.8 [N0.25 / mmO.25 ] uncracked concrete

f 2c, f

I

[

ks = k"

sS4c 1

a)

~

k

°

NRk,cb

b) The ratio If/A.Nb = A,.Nb / A;'Nb accounts for the geometric effects of spacing, distance to a comer and member thickness, where:

A:.~ ;4c,-(4c, + s)

4C1

a) The characteristic resistance of a single anchor near an edge unaffected by adjacent loaded anchors, proximate comers or limited member thickness is given by:

Examples for the determination of A,.Nb for different arrangements of anchors: a) group of two anchors at an edge; b) group of two anchors at a corner; c) group of two anchors in a member with limited thickness relative to the anchor embedment

The eccentricity should be determined for the row of tension-loaded anchors nearest to the edge.


=0.7+0.3. 2 :0;1.0 2cI

(19.1-2b)

For anchorages in a narrow member, the value corresponding to the lesser of the two distances to a comer should be taken for C2 in Equation (19.1-2b). d) The factor If/g.Nb accounts for the bearing areas of the individual anchors ofthe group. If/g.Nb

n

-,In + (1- -,In). ~ ;d.0 4c,

for s::S 4cI

(19.1-2c)

number of tension-loaded anchors in a row parallel to the edge

e) The factor If/,,,Nb accounts for the reduction of the group capacity when the tension loads acting on the individual anchors of a group are not uniform:

207


208 I lfIec,Nb

eN

l+eN /(4cI )

~1.0

(l9.1-2d)

eccentricity of the resulting tension force of the tensionloaded anchors with respect to their centre of gravity

19.1.2


19.1.2.1


Embedded plates loaded in shear derive resistance from the embedded plate as well as the anchors. Since the stiffness associated with the bearing of the embed plate is initially much greater than that of the anchors, spalling of the concrete at the leading edge of the embed plate may occur before the anchors take up significant load. In general, such spalling is unlikely to negatively influence the resistance of the anchorage. It may, however, pose serviceability problems. Shear spalling may be avoided by placing a compressible material around the outside edge of the embed plate. This procedure is particularly recommended for anchorages close to edges.


19.1.2.2

Steel failure

19.1.2.2.1 Shear load without lever arm Section 10.2.2.1 applies with the following modification: The constant k, = 0.6 compared with k, = 0.5 in Equation (10.2-1), takes into account the influence of welding on the shear resistance (Klingner, Mendonca, 1982; Roik, 1982 and Anderson, Meinheit, 2000).

For embed plates with welded studs, the constant k, in Equation (10.2-1) may be increased to k, = 0.6. 19.1.2.2.2 Shear load with lever arm Section 10.2.2.2 applies.

19.1.2.3 In general pullout failure will not occur with headed anchors. However, for headed anchors with small heads and large embedment depths pullout may be decisive.

Pullout failure

Section 10.2.3 applies. However, the value NRk.p used in Equation (10.2-3) should be calculated according to Section 19.1.1.3.

19.1.2.4


Section 10.2.4 applies. However, the value N;k., calculated according to Section 19.1.1.4 should be used when calculating N Rk., in Equation (10.2-4).

19.1.2.5


Section 10.2.5 applies. In Equation (lO.2-Sa) and (lO.2-Sa,) d"o", should be replaced by d.

19.1.3



19.2

Anchorages with anchor reinforcement

19.2.1


Anchor reinforcement to take up tension loads should comply with the following requirements (see also Figure 19.2-1). a) The design tension force Nsd,,, in the anchor reinforcement associated with each anchor should be calculated using the design load on the anchor (see Figure 19.2-lc). The limitation of yield strength and diameter of anchor reinforcement are based on tests by Ramm, Greiner (1991).

b) The anchor reinforcement should consist of deformed bars (fykS 500 MPa) with a diameter not larger than 16 mm. The anchor reinforcement should be detailed in the fonn of stirrups or hoops with bend diameters in accordance with the CEB-FIP Model Code 1990 (CEB, 1993). c) The anchor reinforcement should be placed in close proximity to the headed anchors and preferably tied to the anchors. Ideally, the anchor reinforcement should enclose the surface reinforcement as well.

In the tests by Ramm, Greiner (1991) the anchor reinforcement was placed in close proximity to the headed anchors. The limit on the spacing between anchor reinforcement and headed anchor of O.5h,f is based on theoretical considerations and it is conservative given the limits of utilization of hooked bars according to Section 19.2.1.8.


d) Only those bars with a distance not larger than O.SheJfrom the anchor centreline should be assumed to resist the tension load from that anchor. e) The anchor reinforcement should be tenninated in the assumed failure cone by a bend, hook or loop with a minimum anchorage length of 4d,.

209


210 f)

-:r ,,'

Section A-A

The anchor reinforcement should be anchored outside the assumed failure cone with an anchorage length h.ne' in accordance with CEBFIP Model Code 1990 (CEB, 1993).

g) In general, the anchor reinforcement (number and diameter) determined to resist the force in the most-loaded anchor should be provided for all anchors of the group.

As,!

a)

Orthogonal surface reinforcement should be provided as shown in Figure 19.2-la,b to resist the forces arising from the assumed strut-and-tie model (see Figure 19 .2-1 c) and the splitting forces according to Section 8.3. concrete cone

Section

b)

A

$O.5h .,

,

JJ

,

___it-

J.

I I

I I

~'7T-'

~. ~ /1, A,.I I I r

I I

Idealized/' concrete cone

:=:Ib,net

::.

--h.

Le. A

Ns,t c)

NSd.re = NSd,anchor ",

// ",/

NSd,anChor

Figure 19.2-1: Example of a quadruple anchorage with anchor reiriforcement to take up tension loads: a), b) anchor reiriforcement at a distance:S a.5he! from the anchors; c) strut-and-tie model to calculate forces in the anchor reiriforcement

In practice, anchor reinforcement as shown in Figure 19.2-1 is provided to increase the tension capacity of headed anchors. However, in many applications it may be more effective to increase the embedment depth, thereby providing a more direct load path.

Where such anchor reinforcement is included in the resistance of the anchorage, it should be positioned roughly symmetrical with respect to the anchor group in order to minimise the incompatibility of the resistance mechanisms. The limitation on the diameter of the anchor reinforcement and its distance from the anchors are based on tests (Ramm, Greiner, 1991; Eligehausen et aI., 1992).

19.2.1.1


The required verifications are summarized in Table 19.2-1.

In the model presented below, it is assumed that the anchor reinforcement is fully activated after the formation of a concrete breakout body starting from the anchor head and takes up the total anchor load.

Table 19.2-1:

Required verifications for tension loading anchorages provided with anchor reinforcement Anchor group

Failure Mode

"il 1l r/)

2

Single anchor


N Sd

Pullout failure of

NSd

:::;;

NRJ,s

=

NRk,s

~'-'

" U

Splitting

Nil
Rd,.

=

=

NI/k,p

:::;; NRd,P

N~

::;NRd,p

N Sd :5 NRd,sp

=

oj

NRk,s

= NRJ;,p rup

r,l/p

failure

Anchor group

rM..

YAh

anchor

3

Most loaded anchor

oj

NRJ;,sp

N~

=

NR/;,sp

::;;NRd,sP YlI{;p

YAl
0

4

Blowout failure

5 .., o "" E Steel failure

'"g 8.., Anchorage 6 ~ 'E (bond) .~

oj


< NSJ - NRd,,'b

Ng < N

_NRk,cb -

Sd -

N Rk.roN"
N&l,re

:::;;

N Rd

,(1

Rd,cb

=

NRk,cb

YMc

YJk

N

Rk,rl! = ---

Y!>b,re

N;d,re :::;; N Rd ,(1

failure

Verification is performed for those anchors of a group loaded in tension

211


212 The partial factors for Section 3.4.2.1.

19.2.1.2

rM" rMp, rM,p, rMe

and

rM,."

are given in



19.2.1.3

Pullout failure of anchor

Section 19.1.1.3 applies.

19.2.1.4


Concrete cone failure needs not to be verified when sufficient anchor reinforcement is provided to resist the applied tension load.

19.2.1.5

Splitting failure


19.2.1.6 Blowout failure No tests with headed anchors with anchor reinforcement close to an edge are available in which blowout failure occurred. It is assumed that the model given in Section 19.1.1.6 applies. The model might be conservative.

Section 19.1.1.6 applies. However, a verification for blowout failure should be performed in all applications.

19.2.1.7

Yielding of anchor reinforcement

The characteristic yield resistance N Rk." of the anchor reinforcement provided to one anchor is given by: NRk,re :::; n·

As.re . !;'k,re

(19.2-1)

with: A,.n

cross-section of one bar of the anchor reinforcement

(yk."

nominal yield strength of the anchor reinforcement :s 500 MPa =

n

19.2.1.8 The design resistance N Rd•a according to Equation (19.2-2) is based on the provisions in CEB-FIP Model Code 1990 (CEB, 1993) for the anchorage of tension reinforcement. The factor a" in Equation (19.2-2) takes account of the effect of the bend, hook or loop on the anchorage capacity of the anchor reinforcement in the assumed failure cone.

number of bars of the anchor reinforcement provided to one anchor (see Section 19.2.1)

Anchorage failure of the anchor reinforcement in the concrete cone

The design resistance NRd.a of the anchor reinforcement provided to one anchor associated with anchorage failure in the assumed breakout cone is given by:

N Rd •a =~) 'U'hd/a",

" n

=

11

Table 19.2-2:

1;k

[MPa]

;;~ [MPa]

Design bond stresses ;;~ according to CEB-F1P Model Code 1990 (CEB, 1993) for good bond conditions 20 2.3

30 3.0

40 3.6

50 4.2

60 4.6

70 5.2

(19.2-2)

u

see Equation (19.2-1) length of the anchor reinforcement in the assumed failure cone (see Figure 19.2-1)

>

4d,

=

circumference of one bar

fbd

k6 ·k,·f!

f!

design bond strength according to CEB-FIP Model Code 1990 (CEB, 1993) (see Table 19.2-2)

k6

factor that considers the position of the bar during concreting:

80 5.7

k6 = 1.0 for good bond conditions, as for a) all bars with an inclination of 45° to 90° to the horizontal during concrete placement and b) all bars with an inclination less than 45° to the horizontal which are up to 250 mm from the bottom or at least 300 mm from the top of an individual concrete layer during concrete placement k6 = 0.7 for all other cases and for bars in structural parts constructed with slip forms k,

factor to take into account the effect of concrete confinement on the bond strength 1.0 for concrete cover ofthe anchor reinforcement:s 10d, 1.5 for concrete cover of the anchor reinforcement in all directions> 10d,


213


214 factor taking into account the influence of the bend, hook or loop

are

0.7

19.2.2

Resistance to shear loads

Anchor reinforcement to take up shear loads should be in the form of stirrups or loops (Figure 19.2-3) or in the form of orthogonal surface reinforcement (Figure 19.2-4). It should comply with the following conditions:

In Equation (19.2-3) it is assumed that the total anchor shear force is resisted by the anchor reinforcement.

to one anchor, caused by the design shear force V;~ acting on this anchor is given by Equation (19.2-3).

t---S---t I

I V",

..

e,

z

a) The design tension force N;d.~ in the anchor reinforcement provided

NSd.ro

h"

N"Sd,re =

v."

Sd

(e, + 1)

(19.2-3)

Z

with (see Figure 19.2-2):

..

=

e,

CSd z

Figure 19.2-2: Tensionforce in anchor reiriforcement to take up shear forces

distance between axis of anchor reinforcement and shear force acting on the fixture intemallever arm of the concrete member

d

For single anchors the design tension force in the anchor reinforcement calculated according to Equation (19.2-3) is denoted Nsa;".

'"

0.85d

=

distance between the opposite side of the concrete member and anchor reinforcement

<

min (2h,j, 2Cl)

If the anchor reinforcement is not parallel to the direction of the shear force (see Figure 19.2~3c) then this should be taken into account in the calculation of the design tension force in the anchor reinforcement. The limitation on the diameter of the anchor reinforcement is based on tests by Ramm, Greiner (1991) and Schmid (2010).

b) The

anchor

reinforcement

should

consist

of deformed

bars

(fyk"S 500 MPa) with a diameter not larger than 16 mm. In general, the anchor reinforcement should be detailed in the form of stirrups or loops with a bend diameter, db, in accordance with CEB-FIP Model Code 1990 (CEB, 1993).

c) In general the anchor reinforcement (number and diameter) determined to resist the force in the most-loaded anchor should be provided for all anchors of the group. Anchor reinforcement according to Figure 19.2-3 should be in contact with the anchor to ensure straining of the reinforcing bars with increasing shear load or shear displacement of the anchor. If the anchor reinforcement is not in contact with the anchor, a concrete strut is formed between anchor and bend, which may fail at high pressure thus reducing the efficiency of the anchor reinforcement. The reinforcement should conform to the minimum bend diameter according to CEB-FIP Model Code 1990 (CEB, 1993). When bend diameters larger than these are used, the efficiency of the anchor reinforcement may also be reduced due to the increased flexural stresses in the reinforcing near the bend.

d) If the shear force is taken up by anchor reinforcement according to Figure 19.2-3, it should enclose and contact the anchor shank and should be positioned as close as practical to the concrete surface taking into account minimum concrete cover requirements. Where practical, the anchor reinforcement may also be inclined away from the surface of the concrete thus providing both additional cover and resistance to splitting.

After the formation of the concrete breakout body, the anchor shear load is transferred to the anchor reinforcement by compression struts (see Figure 19.2-4). Anchor reinforcement close to the anchor or between the anchors is effective. Because the shape of the breakout body might vary, the distance of the anchor reinforcement to the anchor should be limited to O.sc,. The anchorage length of the anchor reinforcement in the assumed failure cone should be equal to or larger than the minimum value according to CEBFIP Model Code 1990 (CEB, 1993) to ensure a force transfer according to Equation (19.2-5). For reasons of equilibrium an edge reinforcement should be provided (see Figure 19.2-4).

e) If the shear force is resisted by surface reinforcement as shown in Figure 19.2-4, the following requirements should be met: Only bars with a distance"S 0.5c, from the anchor and bars between anchors with s"S 3c, should be assumed as effective. The minimum anchorage length of the surface reinforcement in the assumed concrete breakout body is:

. I mm 1

10d straight bars with or without welded transverse ' bars

4d,

bars with a hook or bend

Continuous edge reinforcement designed for the forces corresponding to an appropriate strut-and-tie model (see Figure 19.2-4) should be provided. As a simplification, the angle of the compression struts may be taken as 45°. f) The anchor reinforcement should be anchored outside the assumed failure cone with an anchorage length h."" according to CEB-FIP Model Code 1990 (CEB, 1993).


215


e,

a)

~

'-i

1>==

I

!I

Il:

216 VSd

V'i

I~~; db

, Cmln

I

( "'

I 1·1

H

e VSd

, !

b)

j

i 1. emi"

i

is

,

• -

'-'

•

'ir

--

'ir

"'

• -="

v"

6J, h'J c)

Figure 19.2-3: Detailing of the anchor reinforcement in the form of hairpins. Values cm;", h."" and db according to CEBFIP Model Code 1990 (CEB, 1993)

65

~015c,

0

~

I~ 1-

1,t1~

'I

VSd

--

-

INsd

Figure 19.2-4: Surface reinforcement to take up shear forces with simplified strut and tie model to design anchor and edge reinforcement

fib Bulletin 58: Design oj anchorages in concrete

217

218


19.2.2.1



Required verifications for shear loading - anchorages provided with anchor reinforcement

Anchor group .j Failure Mode

" .2 ~ ~

OJ

2

.El

'"

3

*""

Shear force without lever arm Shear force with lever arm

Pullout failure

Single anchor

v.

< v.

_ vRk,s

Rd,.-

Sd -

V. < v:

sa -

VSd

r.llr

VRk,.m

=

Rd,.'"

r,.

VRk,p

::;

VRd,p = - -

r,.

~

Most loaded anchor

Anchor group b)

v."Sd -< v.Rd,. = vRk " y"

v; ~ V~

VRd,.m

= VRk,.m

r,.

= VRk,p ::;;VRd,p rMp

0

U

4

Pryout failure

v:Sdg <- v:Rd,cp = v:Rk,cp

VRk,cp

VSd :::;; VRd,cp

=--

rM,

YMc

5

-"" S

Yielding

N $d,n: -
N~.re

$.

rAls,n!

""

= NRd,re

Nru:,re

r"'s,re

~

<8 .~ ~

6

.j b)

0

""~"

Anchorage failure in the concrete

NSd,re

::;

N M,a

NilSd,re
breakout body b)

Verification is performed for those anchors ofa group loaded in shear Only for anchor reinforcement according to Figure 19.2-4

The partial factors Section 3.4.2.1.

19.2.2.2

for YM"

YMp,

YM" and YM,." are given in



19.2.2.3

Pullout failure


19.2.2.4 In the case of anchorages with anchor reinforcement the anchors may be significantly deformed before failure. This will increase the force causing pryout failure. The reduction of the factor k. is based on tests by Ramm, Greiner (1991).


Section 19.1.2.4 applies. However, the factor k4 given in Section 10.2.4. should be multiplied by 0.75.

19.2.2.5


Concrete edge failure need not be verified when sufficient anchor reinforcement is provided to resist the applied shear load.

19.2.2.6 Tests by Ramm, Greiner (1991) indicate that the efficiency of an anchor reinforcement according to Figure 19.2-3 may be reduced significantly by small deviations in the position of the anchor reinforcement (e.g., not in contact with the anchor shaft, placed not as closely as possible to the fixture) and spalling of the concrete cover in the region of the hairpin bend. The factor kg = 0.5 takes into account usual tolerances. It is valid for anchors with a fixture embedded in the concrete (embed plates) and may be unconservative for surface-mounted fixtures. If the correct position of the anchor reinforcement is ensured (e.g., by welding to the anchor), then the efficiency factor may be increased to kg = 1.

Yielding of anchor reinforcement

The characteristic yield resistance N Rk,n of the anchor reinforcement of one anchor may be calculated according to Equation (19.2-4).

N Rk,rc

=

kg . n· As,re . i;,k,re

(19.2-4)

with:

kg

efficiency factor 0.5 anchor reinforcement according to Figure 19.2-3 1.0 anchor reinforcement according to Figure 19.2-4

n

=

number of bars of the anchor reinforcement of one anchor

19.2.2.7 Anchorage failure ofthe anchor reinforcement in the concrete breakout body The anchor reinforcement according to Figure 19.2-3 is strained by the shear displacement of the anchor. Therefore, no check of the anchorage resistance is required. fib Bulletin 58: Design ofanchorages in concrete

For an anchor reinforcement in the form of hairpins or stirrups as shown in Figure 19.2-3 no check of the anchorage resistance is required.

219


The design resistance NRd.a according to Equation (19.2-5) is based on the provisions in CEB-FIP Model Code 1990 (CBB, 1993) for the anchorage of tension reinforcement.

220 For anchor reinforcement as shown in Figure 19.2-4, the design resistance of the anchor reinforcement provided to one anchor associated with reinforcement anchorage failure in the assumed concrete breakout body is given by:

NRd.~

NM ," =

Straight bars should be used as anchorage reinforcement only if the anchorage length provided is large enough so that the design yield force of the reinforcing bar can be anchored.

LI, ''''f",/a.

(19.2-5)

n


II

length of the anchor reinforcement in the assumed failure cone (see Figure 19.2-4)

II

circumference of one bar

(btl

design bond strength; see Section 19.2.1.8

u.

1.0 for straight bars 0.7 for bars with a hook, bend or loop at the end or welded wire mesh with at least one welded wire within the anchorage length 0.5 for welded wire mesh with at least one welded wire within the anchorage length and a hook or bend at the end

19.2.3

Resistance to combined tension and shear loads

For anchorages close to an edge with an anchor reinforcement to take up shear loads only, failure cracks will occur in the concrete well before reaching the ultimate load (see cracks 1 in Figure 19.2-5). These cracks will reduce the tension capacity of the anchorage. Also, the shear capacity of anchorages with anchor reinforcement to take up tension loads only might be reduced by the early formation of a concrete cone.

Anchorages provided with anchor reinforcement to take up tension and shear loads may be designed in accordance with Section 10.3. Failure of the anchor reinforcement should be treated as concrete failure.

Anchor channels close to an edge with anchor reinforcement to take up the shear load have been tested by Potthoff (2008). The test. results indicate a linear interaction between the tension and shear capacity (Equation (10.3-3) with a= 1.0). No tests have been performed with headed anchors. Because of the higher shear capacity of anchorages with headed anchors, more concrete cracking and thus -a reduced interaction capacity may be anticipated. Therefore, a conservative interaction equation (a = 2/3) is proposed.

For anchorages that are provided with anchor reinforcement to take up tension or shear loads only, Equation (IO.3-ld) (simplified approach) or Equation (10.3-3) (alternative approach) should be used with a= 2/3.

2

-+-

Anchor reinforcement 7

(

Failure crack for shear loading 2 Failure crack for tension loading

Figtlre 19.2-5: Anchorage at the edge with an anchor reinforcement to take tip shear loads tinder combined tension and shear loads

20 No tests have been performed on anchorages with anchor reinforcement designed according to the plastic design approach. However, if the anchor reinforcement is designed to ensure yielding of the headed anchors, a redistribution of anchor forces as assumed in the plastic design approach should occur.


Section 11 applies. However, the modifications for the calculation of the characteristic resistances for the different load directions and failure modes given in Section 19 should be taken into account when applying the provisions given in Section 11. Furthermore, to avoid blowout failure either the edge distance should be CI > 0.5h~f or Equation (20-1) should be satisfied for the anchors closest to the edge. N"",. 2 Nj(", 'Y;,.'/0,6

with N Rk.cb according to Equation (19.1-2),

(20-1) Nfa.5

according to Equation

(11.2-1) and }'i"" according to Section 3.4.2.1.2. For anchorages with anchor reinforcement the following additional modifications apply: a) Anchor reinforcement is provided to take up tension loads. Instead of Equation (11.2-3) verifY Equation (20-2):

mint N"".;Y,' N M,o) 2N"'~ 'Y;,.'/0,6

(20-2)

with:


221

ParI IV: 21 Serviceability limit Slate

222

~

NRk.rc

value according to Equation (19.2-1)

NRd.a


l'

1.5

N Rk•s

characteristic steel resistance of one anchor according to Section 10.1.2 value according to Section 3.4.2.1.2

/'111<1

b) Anchor reinforcement is provided to take up shear loads. Instead of Equation (11.3-3) verifY Equation (20-3):

min(NM,.;Yc -NM,")~VM"IO_6

(20-3)

with: N Rk•re


NRd.a


Y,

1.5

/'111<1

value according to Section 3.4.2.1.2 characteristic steel resistance of one anchor according to Section 19.1.2.2

VRk•s

21


Section 12 applies with the following additions: If the characteristic displacements under tension load have not been evaluated by suitable prequalification tests, then the following information may be taken as a first approximation (Furche, 1994). The short-time displacement under the characteristic tension load may be calculated from Equation (21-2): ON.O =

i:

(21-2)

·Is + Shead

Under long-duration loading the displacements will increase. To limit the displacements under the characteristic tension load to an acceptable value (ON,~ S 2 nun), the concrete bearing pressure p under the head should be smaller than the value padm specified below: P

=NSk

with:

with:

NSk

c,

steel strain of anchor

E,

modulus of elasticity of steel

I,

length of anchor with uniform strain

Shead=

slip of anchor head

k, klO k,

(21-1)

(let )' P

(21-2.)

25ford>10mm 200 for cracked concrete

P

concrete pressure under the head

400 for uncracked concrete

NSk I A"

characteristic tension load on anchor calculated according to Section 4.4

A"

bearing area of the head, as defined in Equation (19.1-lc)

Padm

admissible concrete pressure under the anchor head

2.51ck for cracked concrete

(21-1.)

4.01ck for uncracked concrete

(21-lb)

For an anchor group, NSk in Equation (21-1) should be replaced by

N~.

If anchor reinforcement is present to take up the tension and/or shear loads on the anchorage, the concrete breakout body might form under service load. The width of the corresponding crack should be limited to acceptable values. This is obtained by designing the anchorage capacity of the anchor reinforcement according to CEB-FIP Model Code 1990 (CEB, 1993).

15 ford::: 10 nun

k ..

=

(21-2b)

N.k

characteristic tension load on anchor calculated according Section 4.4

Ah =

bearing area of the head, as defined in Equation (19.1-lc)

A significant increase of displacement will occur when the anchor is located in a crack and the crack width varies due to a variation in the live load on the concrete member, Furthermore, the displacement will increase under sustained load due to creep of the highly compressed concrete under the head. To limit this increase of displacement, the pressure under the head should be limited. The value given in Equation (21-la) has been evaluated from tests on headed anchors that were assessed using the displacement criteria given in EOTA (1997). The value given in Equation (21-1b) is based on current experience. The short-time displacements under the characteristic shear load may be calculated from Equation (21-3) Sv.o=

k

V~ 11'7

(21-3)

with:


223

Part/V: 23 Seismic loading

224

3

kl1

12 [mm /kNl

VSk

characteristic shear load on anchor [kN] calculated according to Section 4.4.

d

anchor diameter [mm]

For an anchor group, VSk in Equation (21-3) should be replaced by V~. The long-time displacement under shear load may be assumed to be av.w"" 1.5av.o. This is an estimate based on limited test data.

22 For embed plates with welded headed studs (insert type of welding) the following values were developed: I1CYkjal = l1'kJar =

100 MPa

(Usami et al., 1988)

35 MPa

(Naithani et aI., 1988)

Fatigue loading

Fatigue loading of the anchorage is allowed when the anchor is welded to the fixture or threaded into the fixture. Section 6.3 applies. Values for /'lOkJat and /'l 'k/at should be taken from the relevant Approval or evaluated from the results of suitable prequalification tests (see Section 1.3).

These values are valid for 2.106 load cycles. For a larger number of load cycles they should be reduced. If the anchor is'threaded into the baseplate, values for I1CYk/at and l1'kjar should be taken from the relevant code of practice for bolts in bearing-type connections.

23 Tests by Hoehler (2006) indicate that the displacement of headed anchors might increase significantly during seismic loading. However, it is believed that this increase in anchor displacement is acceptable if the pressure under the head is limited according to Equation (21-1).

Seismic loading

The verification for seismic loading on the anchorage should be perfonned according to Section 6.4.

PART V: CHARACTERISTIC RESISTANCE OF ANCHORAGES WITH CAST-IN ANCHOR CHANNELS 24 Shear forces applied in the direction of the longitudinal axis of the channel are not covered in this Design Guide due to a lack of a generalized model to describe the slip behaviour of the channel connection and the near edge behaviour under shear loads. In general, product-specific Approvals are required for these applications. Torsional moments causing shear forces perpendicular to the longitudinal channel axis (Figure 24-1) are admissible; however, the provision in this Design Guide should be used with engineeringjudgement.

o

Scope

Part I applies unless otherwise noted. Part V applies to anchorages with cast-in anchor channels, whereby an essentially rigid Connection exists between the channel and the anchor elements (see Figure 1.2-7). The anchor may be welded or forged to the channel. The anchor channel may be loaded by tension, shear perpendicular to the longitudinal axis of the channel, or a combination of tension and shear loads. Shear applied longitudinally along the channel axis is not addressed in this Design Guide. The concrete members in which the channel anchor is embedded should be comprised of concrete containing normal weight aggregate and belonging to a strength class of at least C20 and at most C90 according to CEB-FIP Model Code 1990 (CEB, 1993).

@

Figure 24-1: Example of an anchor channel loaded by a torsional moment

The anchor channels should be placed flush with the concrete surface. A fixture is connected to the channel by channel bolts (hammer head or hooked bolts) with nuts and washers (see Figure 1.2-7).

The design provisions given in this Part of the Design Guide are valid for channels with a height 15 mm ~ hell ~ 50 mm and a corresponding width 25 mm~bell~ 75 mm. At least two anchors should be provided on an anchor channel. The maximum number of anchors is not limited. The spacing between anchors should not be smaller than 5d Or 50 mm and not be larger than the smallest of 5c"'iI' and 400 mm. The distance between the end of the channel and the nearest anchor should be about 25 mm.


225

226

Par! V: 24 Scope The authors are not aware of testing to address the behaviour of anchor channels subjected to seismic loading. This load condition is therefore not addressed in this Design Guide.

In general, within the approach used in this Part of the Design Guide it is assumed that the loading of the anchorage and the concrete member in which the anchorage is located is limited to predominantly static loading. Fatigue and seismic loading are not addressed in this Part of the Design Guide. To ensure suitability of anchor channels in concrete, prequalification testing is necessary (e.g., analogous to the tests specified in Section 1.3). As a minimum, the manufacturer and the size of the channel should be marked on the channel.

w

I

¥

a,)

aJ

Q;J

0

I

aJ

~QJ

-- --

C>f"'", i

I

I

j

a,)

a,)

a~

[ff[[f~tfJ b,)

Figure 24-2: a) Tension:

b,)

b,)

b,)

Failure modes ofanchor channels:

Welding of the anchors to the channel should be done according to the corresponding code of practice. Anchors made of carbon steel may be welded to channels produced from stainless steel. However, in general, anchors made of stainless steel may not be welded to a channel made of carbon steel. Care should be taken during concrete placement to ensure proper consolidation of concrete around the anchors and under the fixture (see Section 3.5). According to the safety concept of partial factors (see Equation (3.3-1», it should be shown that the design value of the actions does not exceed the design value of the resistance. Equation (3.3-1) should be observed for all loading directions (tension, shear, combined tension and shear) as well as all failure modes (see Figure 24-2) (steel failure (failure of channel bolt, local failure by flexure of channel lips, failure by flexure of channel, failure of connection between anchor and channel, failure of anchor), pullout failure, concrete cone failure, splitting failure, blowout failure under tension loading and steel failure (failure of channel bolt, failure by flexure of channel lips, failure of connection between anchor and channel, failure of anchor), pullout failure, pryout failure, and concrete edge failure under shear loading). If anchor reinforcement is present it should be verified for steel and anchorage failure instead of concrete cone failure (tension loading) andlor concrete edge failure (shear loading).

OJ) steel failure of channel bolt; az} flexural failure of

channel lips; a;} flexural failure of channel; a.J failure of connection between channel and anchor; as) steel failure ofanchor; ar;} concrete cone failure. Pullout, splitting and blowoutfailure not shown (compare Figure 3.2-1)

b) Shear:

bJ) steel failure of channel bolt; bz} fle.xural failure of channel /ip; bJ) concrete edge failure; b.J concrete pryout failure. Failure of anchor, failure of connection between anchor and channel and pullout failure not shown.

Flowcharts for calculating the design resistance of anchor channel are shown in Figure 24-3 and Figure 24-4.

The calculation of the distribution of the actions acting on a fixture to the anchors of the channel should be perfonned according to the theory of elasticity (see Section 25). Plastic design of the anchorage is not covered in this Design Guide. In Section 26, equations for calculating the characteristic resistances for the elastic design approach are given for all loading directions covered in this Design Guide and all failure modes. This Design Guide applies only to anchor channels with distance s;?: S~r.N (tension loading) and s;?: Scr.Y (shear loading) to neighbouring anchor channels.

To use this Design Guide the following values should be available either from an Approval or they should be detennined from the results of suitable prequalification tests e.g., according to EOTA (2004-1) or ICC-ES (2010-2).

- bc/~ he/'



-1,

See Section 25.1.2

- NRk.s, N Rk•s.a, N Rk•s.c , NRk.s.l, MRk.sJ/c.t


- h~f


- r1ch.N


- c m/tO, Sm/", hmitO

See Section 26.1.1.5.1

- ccr.sp, scr.sp

See Section 26.1.1.5.2

-d,d"


-A" for I-Anchors


- VRk•s , VRk.s./, VRk,s,c. VRk,s.a


227

228

ParI V: 24 Scope

App(K:atioocritoJia ($9ctlon24) ,~,

Ten,'on

_ M'M.,


- VRk,p(ork3 )


- k,

See Section 10.2.4

- achY



- rAt;



See Sections 26.1.1.2 26.1.2.2, 26.2.1.2,26.2.2.2,26.2.2.6 and 10.2.2.1 See Section 3.4.2 See Section 8.3

- Limitation on concrete strength classes of base material The minimum value for edge distance, member thickness and reinforcement given in the Approval should be observed. The behaviour of anchor channels can be improved by suitably dimensioned and detailed reinforcement crossing the failure surface. The influence of this reinforcement on the strength of anchor channels is taken into account in Section 26.2. rw... ................ IIN... N..,

Figure 24-3:

Flowchart B1 for the calculation of the design resistances of anchor channels without anchor reinforcement: elastic design approach

_'.....,0_0.

,-

ISectlon24)

s ..."

s, ....., ' _

1""'_ .M..,..... I It.., .N...

Figure 24-4:

Flowchart B2 for the calculation of the design resistances of anchor channels with anchor reinforcement: elastic design approach

fib Bulletill 58: Design ofanchorages ill concrete

229

Part V: 25 Determination a/action effects

230

25

Determination of action effects

25.1

Derivation of forces acting on anchors of anchor channels

25.1.1

General

The distribution to the anchors of tension loads acting on the channel may be calculated using a beam on elastic support (anchors) with a partial restraint of the channel ends. The resulting anchor forces depend significantly on the assumed anchor stiffness and degree of restraint For shear loads the load distribution is also influenced by the pressure distribution in the contact zone between channel and concrete. As a simplification for anchor channels with two anchors, the loads on the anchors may be calculated assuming a simply supported beam with a span length equal to the anchor spacing.

As an alternative in the following the triangular load distribution method to calculate the distribution of tension and shear loads to the anchors is introduced.

25.1.2 The rationale for the triangular load distribution method is given in Kraus (2003).

Tension loads

The tension force N;,I in each anchor due to a tension load NSd acting on the channel is calculated according to Equation (25,1-1), which assumes a linear load distribution over the influence length fill and takes into account eqUilibrium. The influence length lin should be calculated according to Equation (25.1-2), An example for the calculation of the forces acting on the anchors is given in Figure 25,1-1.

N'da,i =k.A;,NSd

(25.1-1)

with:

A;

ordinate at the position of the anchor i of a triangle with the unit height at the position of load NSd and the base length /;"

(25.1-la)

k

fA i·1

_ __

•

N~

n

~

11

11

11

11

11

.f--..'-I ' I ' I ' f

number of anchors on the channel within the influence length lin to either side of the applied load NSd(see Figure 25.1-1)

lin = 131~·o5 J; 2!:: S

(25.1-2)

The moment of inertia ly of the channel should be taken from the relevant Approval or should be calculated from the channel cross section. If several tension loads are acting on the channel, a linear superimposition of the anchor forces for all tension loads may be assumed.

(,,=1.55

If the exact position of the load on the channel is not known, the most unfavourable loading position should be assumed for each failure mode (e.g., load acting over an anchor for the case of steel failure of anchor, failure of the connection anchor/channel or pullout failure and load acting between anchors in the case of bending failure of channel).

(,,=1,55

Example:

,_.!.

A,_'~-1.25 ..

,-

I"

N;".I =N;"" =0

- 6

A' _"n-O.25·s_~ j-

lin

A' = ' .. -O.75·s 4

ke

Ii"

-6

N;".2

=~'~'N=iN54

=1.

N"

=~.3.. N =~N54

N"

=L3.· N =.!.N54

2

- ._1__ .

=3.

Al+A)+A,

3

54"639

54"233

Figure 25.1-1.- Examplefor the calculation ofanchor forces according to the triangular load distribution method for an anchor channel with 5 anchors - the influence length is assumed as ~n = 1.5s

The assumption of a simply supported beam to calculate the bending moment is a simplification which neglects the influence of partial end restraints, continuous beam action for channels with more than 2 anchors and catenary action after yielding of the channel. The characteristic values of the moments of the resistance given in the Approval or evaluated from the results of suitable prequalification tests, e.g., EOTA (2004-1) or ICC-ES (2010-2), fib Bulletin 58: Design 0/ anchorages in concrete

The design bending moment in the channel, MSdJle.<> due to design tension loads acting on the channel may be calculated assuming a simply supported beam with a span length equal to the anchor spacing.

231

232

Part V: 26 Ultimate limit state - elastic design approach

should take these effects into account. They may be larger than the plastic moment calculated from the section dimensions of the channel and the nominal yield strength of the channel steel.

25.1.3 In reality, shear loads applied perpendicular to anchor channels are transferred mainly by compression stresses at the interface between channel and concrete. A part of the shear load is transferred by the anchors via bending of the channel. In addition, for reasons of equilibrium the anchors are stressed by tension forces. In the approach presented below it is assumed that shear forces are transferred by bending of the channel to the anchors and by the anchors into the concrete. This simplified approach has been chosen to allow a simple interaction between tension and shear forces acting on the channel.

Shear loads

Shear loads applied to the fixture are transferred to the channel by channel bolts. The provision given in Sections 4.3.1.4 and 4.3.1.5 should be used to determine whether the shear loads act on the channel bolts with or without a lever arm. The shear forces of each anchor due to a shear load acting on the channel perpendicular to its longitudinal axis may be calculated as described in Section 25.1.2.

26


26.1

Anchor channels without anchor reinforcement

26.1.1

Resistance to tension loads

26.1.1.1



The failure modes of anchor channels under tension loading are shown in Figure 24-2a. In addition to failure modes for headed anchors shown in Figure 3.2-1 failure of the connection between anchor and channel, local failure of channel lips due to flexure and flexural failure of channel might occur.

While for group anchorages with post-installed anchors or headed anchors the design resistances for concrete cone failure, splitting failure and blowout failure are calculated for the group of tensioned anchors, for anchor channels these resistances are calculated for a single anchor taking into account the influence of neighbouring loaded anchors. These resistances are compared with the design loads acting on the anchors determined according to Section 25. Instead of verifying all anchors it is sufficient to verify the most unfavourable anchor and the channel bolt with the highest load.

Table 26.1-1: Failure Mode

2

For steel failure and pullout failure the most unfavourable anchor is the highest loaded anchor. For concrete cone failure, splitting failure and blowout failure the most unfavourable anchor is the anchor with the highest ratio N~ / N Rd • Therefore, it might be necessary to verify several anchors.

3

"'" ~

Required verifications for anchor channel without anchor reinforcement under tension loading Channel

Anchor b)

Anchor

N';.,SN""., .•

Channel J anchor

N~:>N"".,.,

Channel lip

Channel bolt")

Design resistance d) N

_NM"", "".,,,---

Y.,.

N"".'$ '" N"".'$ Y..".,

N

N",5N"'$J

_N"".,; ""...,---

Y'h.J

4

Channel bolt

5

Flexure of channel

6

Pullout

N;S:N,.,.p

N&J.p = NRJ..p Y'lp

7

Concrete cone

N;S:NM.<

NM.<=NRJ.o<"

~

N",5N"".,

9

" 0

U

",

",NR>.'

1.. NRJ..,.a",

N",ofo':> N",".A'

N """./1« '"

Y.'~./I"

r.• N"".,p

0

8

N

Splitting

N;'SN",,"p

Blowout 0)

N;'SNlIh•

N/OJ.,p"'r:;

N

/OJ.,"

",NIa .", y., ..

Not required for anchors with c > O.Shej and It > hi + l.5CI Verification required for most unfavourable anchor c) Verification required for channel bolt with highest tension load d) Recommended partial factors see Section 3.4 0)

b)

fib BlIlletin 58: Design of anchorages in concrete

233

Part

v..

26 Ultimate limit state - elastic design approach

234

26.1.1.2 The characteristic resistances N Rk.s.a (failure of anchor) and NRk.s (failure of channel bolt) may be determined according to Equation (10.1-1). The characteristic resistances for failure of the connection between anchor and channel (anchor forged to channel), local failure of channel lips and flexure of channel should be evaluated from the results of suitable prequalification tests, e.g., according to EDTA (2004-1) or ICC-ES (2010-2), because no sufficiently accurate design equations are available.

Steel failure

The characteristic resistances N Rk.•. a (failure of anchor), NRk.s (failure of channel bolt), NRk•s.c (failure of the connection between anchor and channel), N Rk••,1 (local failure by flexure of channel1ips), and MRk,sJle:t (failure by flexure of channel) should be taken from the relevant Approval or determined from the results of suitable prequalification tests, e.g., according to EOTA (2004-1) or ICC-ES (2010-2).

The characteristic resistance NRd.s,JIox is calculated from MRd.s,JI~x taking into account the static system. For a single load in the middle between anchors NRd.s,"e:t == 4MRd.s.",,)s is obtained.

26.1.1.3 For I-anchors welded to the channel the load bearing area A" should be taken from the Approval or calculated from the results of suitable prequalification tests.

Pullout failure


26.1.1.4 The model for calculating the characteristic resistance for concrete cone failure is based on the Concrete Capacity Method (see Section 10.1.4). It has been adapted for anchor channels (Kraus, 2003). Note, that the characteristic resistance of one anchor and not of a group (as for post-installed anchors and headed anchors) is determined by Equation (26.1-1).


The characteristic resistance of one anchor of an anchor channel in the case of concrete cone failure may be calculated according to Equation (26.1-1).

N Rk.c = N~.c . a s.N • ae,N

•a

(26.1-1)

e•N • IjI'",.N

with:

N°~."

characteristic resistance of a single anchor without edge and spacing effects

=

factor to take into account the influence of neighbouring loaded anchors

as.N

,",.N

factor to take into account the influence of edges

,",.N

factor to take into account the influence of a comer factor accounting for the negative effect of closely spaced reinforcement in the concrete member on the strength of anchors with limited embedment depth (hcj < 100 mm),

IjI're.N

The various factors in Equation (26.1-1) are explained below. a) The basic characteristic resistance of one anchor not influenced by adjacent anchors, edges or comers of the concrete member is obtained by:

N~.e = k[ . a~h.N . h~) .

.p;;

[NJ

(26.1-la)

with: The values of kl are calculated as in Section 19.1.1.4.

As a first approximation the factor (26.1-1.,) (Kraus, 2003). a ehN

.

fXch,N

may be estimated from Equation

h )"" 51.0 [-] =....!L

kl = kcr

8.9 [ ../N/mm ] cracked concrete

k,

12.7 [ ../N Irnm ] uncracked concrete

=

k""cr

factor taking into account the influence of the channel on the concrete cone failure load. It should be taken from the relevant Approval or detennined from the results of suitable prequalification tests, e.g., according to EOTA (2004-1) 0' ICC-ES (2010-2).

ac".N

(26.1-la,)

( 180

In Equation (26.1-1al) the constant 180 carries the unit [mm]. Scr.N

b) The influence of neighbouring anchors on the concrete cone resistance is taken into account by the factor as.N according to Equation (26.1-lb).

a s •N

L

1+ "

o

2

1~1

3

[(

1-~ )" seT.N

. N SJ •1

NSJ •o

]

(26.1-lb)

with (see Figure 26.1-1):

I

N"".2

'N S01

'N soo

.

'N SOl

.

.

;' s,

j

s,

I

0= anchor under consideration 1-3 = neighbouring anchors Figure 26.1-1: Example of an anchor channel with different anchor tension forces fib Bulletin 58: Design ofanchorages in concrete

s,

SeT.N

Distance between the anchor under consideration and neighbouring loaded anchors [mm] :S Ser,N

2.(2.8-1.3h.;/180).hef ~3h
NSd.i

design tension force on an influencing anchor

N Sd.O

design tension force on the anchor under consideration

(26.1-lb,)

235

236


n

=

number of anchors within a distance Ser,N to both sides of the anchor under consideration.

c) The influence of an edge of the concrete member on the characteristic resistance is taken into account by the factor ae,N according to Equation (26.1-1c).

~'

ae,N

(26.1-1c)

- - :s; 1.0 ccr,N

bj

aj

Figure 26.1-2: Anchor channel at an edge or in a narrow member

d) The influence of a corner of the concrete member on the characteristic resistance is taken into account by the factor ae,N according to Equation (26.1-1d).

"',ol (J0' ,,
•

2

o 3

0

3

~

ae,N

=

~c

~: ~:~hh:O~~i~:r :~~:~~eration

Figure 26.1-3: Definition of the corner distance of an anchor channel in the corner ofa concrete member

If/rc,N

according to Equation (26.1-1e) is the same as in Section

corner distance of the anchor under consideration (see Figure 26.1-3)

If an anchor is influenced by two corners (example see Figure 26.1-4a), then the factor ae,N should be calculated for the values C2,1 and C2,2 and the product of the factors a",N should be inserted in (26.1-1). e) The factor !fre.N takes into account that the strength of anchors with an embedment depth he!$. 100 mm is reduced by reinforcement with a small bar spacing s. hif

!fre.N=0.5+

200

!fre,N =1

:~::::f I rn: ~

For s < 150 mm (for any diameter ds) ors<100tnm(fords $.10mm)

(26.1-1el)

For s ~ 150 mm (for any diameter d.) or s ~ 100 mm (for ds $. 10 mm)

(26.1-1e2)

f) Special cases - For anchor channels in an application with influence of

~-l;"

~r"

~f

h.l aj

(26.1-1d)

:::;;1.0

with: Cz

The factor 10.1.4(e).

2

ccr,N

•

Anchor under consideration

o

Neighbouring anchor

bj

Figure 26.1-4: a) Anchor channel with influence ofan edge and two corners; b) anchor.channel with influence of two edges and one corner

Equation (26.I-lt) is valid for anchor channels with a constant anchor spacing s.

an edge and two corners (Figure 26,I-4a) or with two edges and one comer (Figure 26.1-4b) with edge distances less than Ccr,N from the anchor under consideration the calculation according to Equation (26.1-1) may lead to conservative results, More precise results are obtained if the value he! is substituted by h;/ according to Equation (26.1-1t) in Equation (26.1-la) and the values S~r,N and

C:r,N

calculated with h;/ according to Equations (26,l-1b J) and (26.1-1cl), respectively are inserted in Equations (26.1-lb), (26.1-lc) and (26.1-1d). h:/

=max(Cmax .he/;-S_.h

e/ )

Ccr,N

(26.1-1f)

scr,N

with: Cma<

=

maximum distance from centre of an anchor to the edge or comer of the concrete member :5 Ccr,N. In the example in Figure 26.1-4a it would bc the maximum value of Cj, C2,1 and C2,2'

26.1.1.5 At the time of writing this document, the characteristic splitting resistance cannot be predicted very accurately, However, it is believed that the foHowing provisions are conservative.

Splitting failure

If the edge distance of an anchor is smaller than the value c cr•sp (see Section 26.1.1.5.2), then a longitudinal reinforcement should be provided along the edge of the member. 26.1.1.5.1 Splitting failure due to tightening of the channel bolt

The minimum values for spacing, edge distance and member thickness shall ensure that full compaction of the concrete in the region of the anchorage is possible and that during the application of a torque moment to the channel bolts no splitting cracks occur in the concrete cover.

fib Blt/letin 58: Design of anchorages in concrete

Splitting failure is avoided during tightening of the channel bolt by complying with minimum values for edge distance cm;'" spacing Sm;", member thickness hmi'" maximum allowed torque moment TillS/ and requirements on reinforcement. These values should be taken from the relevant Approval or detennined from the results of prequalification tests, e.g., according to EOT A (2004-1) or ICC-ES (2010-2).

237

238

Pari V: 26 Ullimale limit slale - elastic design approach

26.1.1.5.2 Splitting failure due to loading Anchor channels with a rigid connection between channel and anchor and a sufficiently large anchor head are suitable for use in cracked concrete. Therefore, in general, splitting failure should be avoided by complying with the condition b) in Section 26.1.1.5.2 (1). Ifin certain cases the characteristic splitting resistance is calculated according to Equation (26.1-2), then the values c~r,.p = 0.5s~r,.p = 2h ef may be used as a first indication,

(1) No verification of splitting failure is required if this is stated in the relevant Approval or if one of the following conditions is fulfilled: a) The edge distance in all directions is c:::: 1.0cer.sp' The characteristic values of edge distance and spacing in the case of splitting under load, ccr,sp and su,sp, as a function of the member thickness should be taken from the relevant Approval or detennined from the results of prequalification tests, e.g., according to EOTA (2004-1) or ICC-ES (2010-2). b) The characteristic resistance for pullout failure, concrete cone failure and blowout failure is calculated for cracked concrete and reinforcement is present to resist the splitting forces and to limit the crack width to W,I;::; 0.3 mm. (2) If the conditions in (1) above are not fulfilled, then the characteristic resistance of one anchor of an anchor channel should be calculated according to Equation (26.1-2).

N Rk,qJ =

ftJRk.c • a.,N • a e•N • a e•N

'11're,N 'IJIII,qJ

(26.1-2)

with N~.c' as,N, ae,N, ae,N, '!fre,N, according to Section 26.1.1.4. However, the values C~r.N and Scr.N should be replaced by c~r.sp and scr.sp in Equations (26.1-1b) to (26.1-1t). The values crr,sp and scr.sp are valid for the member thickness hmjn • The factor If/J,.SP takes into account the influence of the actual member depth h on the splitting resistance. It should be calculated according to Equation (26.1-2a). The member thickness influences the splitting failure load up to a limiting value. The value h ef + l.5cI is based on experimental investigations by Asmus (2007). The factor IfIIl,sp is limited to 2.0 because in tests a larger increase of the splitting failure load due to an increase of the member depth has not been observed.

V/,,~ = (..!!...)' " {< (h
No tests are available with anchor channels in members with a small depth (h < h ef + 2cI) ,in which blowout failure occurred. In these applications Equation (26.1-3) may yield conservative results.

2.0

(26.1-2a)

;::>: 1.0

For anchorages affected by more than one edge, e.g., anchorages in the comer of a concrete member or in a narrow member, the smallest edge distance should be inserted for Cl in Equation (26.1-2a).

26.1.1.6 The model for calculating the characteristic resistance for blowout failure is the same as given in Section 19.1.1.6. However, it has been adopted for anchor channels. For anchor channels oriented perpendicular to the edge, only the most unfavourable anchor with respect to location and loading should be verified.

::;;

min

min

Blowout failure

Verification of blowout failure is not required, when the edge distance of the anchor in all directions is c > 0.5h ef and the member depth is h > hef + 2cI. If verification is required, the characteristic blowout resistance of one anchor is given by Equation (26.1-3): N Rk •cb =

N~k,Cb . a •. Nb ·aC•Nb ·a".Nb ·V'/:.Nb

(26.1-3)

with:

N~k,cb =

characteristic blowout resistance of a single anchor unaffected by adjacent anchors, a comer or the member thickness

as.vb


, ac,Nb

factor to take into account the influence of a corner

a'"Nh

factor to take into account the influence of the member thickness

V'g.Nb

factor to take into accountDthe influence of the anchor bearing area on the behaviour of an anchor group

The various factors in Equation (26.1-3) are explained below. a) The characteristic resistance of a single anchor near an edge unaffected by adjacent loaded anchors, a comer or limited member thickness is given by Equation (26.1-3a). Equation (26.1-3a) is identical with Equation (19.1-2a). For I-anchors the load bearing area A" should be taken from the Approval or evaluated from the results of suitable prequalification tests.

N~.Cb

k . CO.7S

k,

11.1

5

I

•

fA. 1°·75 ck

-V n "

[N0.2S

(26.1-3a)

I mmO. 2S ] cracked concrete

15.8 [NO. 2s l mmO. 2S ] uncracked concrete A"

as defined in Equation (19.1-1c)

b) The influence of neighbouring anchors on the blowout resistance is taken into account by the factor lXs.Nb, which may be calculated according to Equation (26.1-3b).

fib BlIllelin 58: Design ofanchorages in concrele

239

240


as .Nb

1+ t (1- :~l .N::: 1 u

[

)

(26.1-3b)

N

with s, NSd•1 NSd•O as defined in Section 26.1.IAb). c) The influence of a comer of the concrete member on the characteristic blowout resistance is taken into account by the factor a:.Nb according to Equation (26.1-3c).

aCNb --• , -~' 2,c <10

(26.1-3c)

l

with: comer distance of the anchor under consideration (see Figure 26.1-3).

Cz

iJN.

rS;

Ifan anchor is influenced by two corners (example see Figure 26, 1-4a), then the factor a:.Nb should be calculated for the two comer distances CZ,1 and cz,z and the product of the factors a:,Nb should be inserted in Equation (26.1-3), d) The influence of a limited member thickness is taken into account by the factor a",Nb according to Equation (26, I-3d).

h,,+ f

alo Nb =---:0:;1.0

,

with: distance between the anchor head and the lower surface of the concrete member (see Figure 26.1-5)

f

h.

!-

(26.l-3d)

4c1

::; 2Cl

8

f<2c, ' -

L '_ _ _ _ _- - - '

Figure 26.1-5: Anchor channel at the edge ofa thin concrete member

e) The factor If/g,Nb takes account of the bearing areas of the individual anchors of a group . If/g.Nb

.,In+(I-.,Jn) . ..!...- fors::;4cl

(26.1-3e,)

1.0 for s > 4Cl

(26.1-3e,)

4c,

with:

n

number of tensioned anchors in a row parallel to the edge

26.1.2

Resistance to shear loads

26.1.2.1



fib BlIlletin 58: Design of anchorages in concrete

241

242


While for group anchorages with post~instaned anchors or headed anchors the design resistances for concrete pryout failure and concrete edge failure are calculated for the group of anchors loaded in shear, for anchor channels these resistances are calculated for a single anchor taking into account the influence of neighbouring loaded anchors. These resistances are compared with the design loads acting on the anchors determined according to Section 25. Instead of verifying all anchors it is sufficient to verify the most unfavourable anchor and the channel bolt with the highest load. For steel failure and pullout failure the most unfavourable anchor or channel bolt is the highest loaded anchor or channel bolt. For pryout failure and concrete edge failure the most unfavourable anchor is the anchor with the highest ratio V~ /VRd • Therefore, it might be necessary to verify several anchors.

Required verifications for anchor channels without anchor reinforcement under shear loading Design Channel Anchor oj Channel Failure Mode bolt b) resistance oj

Table

26.1~2:

Anchor Anchor I Channel

2

3

"~

Channel lip

V

V~SVRJ""

VRJ.~--_V"'M

r~~

RJ.,'

r.'6"

v

_ V",d

""",---

V"'SVRJ~J

r'bJ

v'" ::;;V"".

Channel bolt

4

VAl" = - ...

V~svRJ.,.

d) .)

V",SV"", ..

v _V

-r:: RI ,.

JoJ.

d)

v _ V..,~ .,--

e)

r"

5

6

~

Pullout

V;' ::;;V"",p

Pryout

V;'

Concrete edge

V;' ::;V,.;,<

s v""""

u"

VRJ,p

V""p ""r:;

VRJ.

v.."" r.I.<'

0

7

V/lJ,c"" V..,<

r"

oJ Verification required for most unfavourable anchor Verification required for channel bolt with highest shear load oj Partial factors see Section 3.4.2 d) Shear loads without lever ann ej Shear loads with lever ann

b)

26.1.2.2 The characteristic resistances of the channel for the failure modes failure of anchor, failure of connection between anchor and channel (anchor forged to channel) and local failure of channel lips due to flexure should be evaluated from the results of suitable prequalification tests, e,g" according to EOTA (2004-1) or ICC-ES (201O~2), because no sufficiently accurate design equations arc available. Bending failure of the channel is prevented by the concrete.

Steel failure

The characteristic shear resistances VRk,s,a (failure of anchor), VRk,s,<, (failure of connection between anchor and channel) and VRk,s,1 (local failure of channel lips) should be taken from the relevant Approval or detennined from the results of suitable pre qualification tests, e.g., according to EDTA (2004-1) or ICC-ES (2010-2).

As a first indication the characteristic shear resistance of the anchor, the connection between anchor and channel, VRk,s,<, and for local failure of channel lips, VRk,s.l may be taken equal to the values valid for tension loading. VRk,s,a,

The characteristic resistance VRk,s (failure of channel bolt in case of shear load without lever ann) may be detennined according to Equation (10.2-1).

The characteristic resistances of the channel bolt (VRk,., and M~k ..) should be taken from the relevant Approval.

The characteristic resistance VRk,sm (failure of channel bolt in case of shear load with lever ann) may be detennined according to Equation (10,2-2). 26.1.2.3 For I-anchors see also Section 26.1.1.3.

Pullout failure

Section 19.1.2.3 applies. 26.1.2.4


The characteristic resistance for concrete pryout failure should be calculated according to Equation (26.1-4).

VlIk,cp =k4 . NlIk,c k4


NlIk,c

characteristic resistance according to Section 26.1.1.4, detennined for the most unfavourable anchor loaded in shear

26.1.2.5 The model for calculating the characteristic resistance for concrete edge failure is based on the Concrete Capacity Method (compare Section 10.2.5). It has been adopted for anchor channels (Potthoff, 2008),

fib Blilletin 58: Design of anchorages in concrete

(26.1-4)


For anchor challlleis with an edge distance in all directions c ;?:max(lOhcfi· 60d) (d = diameter of channel bolt), a check of the characteristic concrete edge resistance may be omitted.

243

244

ParI V: 26 Ultimate limit state - elastic design approach

The characteristic resistance of one anchor loaded perpendicular to the edge corresponds to: = V~,c

VRk,c

'as •V 'aC,V 'ah,V ' a90 o,V '/f/reY

(26,1-5)

with:

v"

characteristic resistance of a part of an anchor channel with one anchor loaded perpendicular to the edge not influenced by neighbouring loaded anchors, member thickness or comer effects

a.,v


~,c

factor to take into account the influence of a comer

a"y

factor to take into account the influence of the member thickness

ah,V

lX90 ,v

factor to take into account the influence of a shear load acting parallel to an edge

\l',...,v

factor to take into account the influence of an edge reinforcement

0

The various factors of Equation (26,1-5) are explained below. As default value Cfch,v=2,5 [.JN/mm ] (cracked concrete) or Cfch,v:=3,5

[ .IN Imm ] (uncracked concrete) may be taken,

a) The basic characteristic resistance of a part of an anchor channel with one anchor loaded perpendicular to the edge not influenced by neighbouring loaded anchors, member thickness or comer effects is: v:O

Rk,c

rr ,c

=ach,v ·"Jck

(26,1-5a)

I.S

1

with:

CfchY

=

factor [.IN I mm

J, It should be taken from the relevant

Approval or determined from the results of suitable prequalification tests, e.g" according to EDTA (2004-1) or ICC-ES (2010-2),

5<,.v

b) The influence of neighbouring loaded anchors on the concrete edge resistance is taken into account by the factor a.,v according to Equation

S ...,V

I

,Iv" Iv", --+.-

0

0

(26,1-5b),

r"'

jv"' ("'

0

0

v"O

•

a sY

0

1+ t,[(I--;-J"', v~,;] ",",v

f" " s~

_

°

distance between the anchor under consideration and the neighbouring anchors

"

:5 Scr,V

4c]

Neighbouring anchor

VSd,l

design shear force of an influencing anchor

VSd,o

design shear force of the anchor under consideration

n

number of anchors within a distance Scr.Y to both sides of the anchor under consideration

~m 2___

30 ....-

Scr,V

S. Anchor under consideration 1

Figure 26, 1-6: Example of an anchor channel with different anchor shear forces

"<'' '1

VSd,o

with (see Figure 26.1-6): Sj

"

"'<' ' '1

cZ,z
~W

(26.l-5b)

+ 2bch

(26,1-5b,)

c) The influence of a corner on the characteristic edge resistance is taken into account by the factor Cfc,v.

2 __

a c •v =

30---

~S1.0

(26,1-5,)

VCcr,v

with:

W

W

a)

b) _

Anchor under consideration

°

Neighbouring anchor

Figure 26,1-7: Example ofan anchor channel with anchors influenced by a) one or b) two comers, anchor 2 is under consideration fib Bulletin 58: Design of anchorages in concrete

ccr•V =0,5scr .v =2c, +bcli

(26,1-5c,)

If an anchor is influenced by two comers (example see Figure 26.1-7b), then the factor Cfc.v according Equation (26.l-5c) should be calculated for each corner and the product of the factors Cfc,v should be inserted in Equation (26.1-5).

245

246


The factor ah,Y as given in Equation (26.1-Sd) has been used, e.g., in Potthoff (2008).

hr1"'c,

Vso

~

h S 2h th +2c,

d) The influence of a member thickness h < he,.,v (example see Figure 26.1-8) is taken into account by the factor allY,

a v = (...!!...-)P <1.0

(26.1-5d)

hcr,v

with:

hlo'y =2c1 +2cc/.

(26.1-Sd J)

/ / / c::

Figure 26.1-8: Example of an anchor channel influenced by the member thickness

An exponent /1=2/3 in Equation (26.1-5d) was established from testing with rectangular channel geometries and is assumed to be conservative for other channel cross section shapes.

The exponent /1 in Equation (26.1-5d) should be taken from the relevant Approval or evaluated from suitable prequalification tests. In the absence of pre qualification tests /1= 2/3 may be used.

When a shear load is applied parallel to the edge, failure is initiated by splitting forces perpendicular to the edge. The ratio of the splitting force to the shear force applied parallel to the edge depends on the pressure in front of the anchors in the direction of loading related to the concrete compressive strength (compare Section 1O.2.S.l.lf). The load transfer area in front of an anchor channel is much larger compared to anchors. Therefore, for a given shear force the splitting forces in front of an anchor channel are much smaller than in front of an anchor. This induces that the factor \f!90".Y= VRk,c,IIIVRk.c,.l. is larger for anchor channels than for anchors.

e) The factor V'90',V takes into account the influence of shear loads acting parallel to the edge (see Figure 26.1-9).

(26.1-5,)

1f/9Q',v =2.S

The results of numerical investigations (Grosser et aI., 2010) and the evaluation of limited test data (Roik, 2009) show that the assumed factor V'90''v= 2.5 for anchor channels arranged and loaded as shown in Figure 26.1-9 with an edge distance close to the value valid for steel failure is conservative. For anchor channels with a smaller edge distance the factor

\f!9O".Y increases. For anchor channels with more than two anchors or with load applied not only on the anchor closest to the edge the factor \f!90',V = 2.5 may be used as well.

L

C,

r---., Vso

~ :

t--j

~

-0

I Figure 26.1-9: Anchor channel loaded by shear loads parallel to the edge

f) The factor V're,V takes into account the influence of an edge reinforcement in cracked and uncracked concrete. If/re,v =1.0

for anchor channels without supplementary reinforcement as defined in Figure 10.2-7.

(26.1-5f)

1f/J"(!,v=IA

for anchor channels with edge reinforcement (ds ~ 12 nun) and closely spaced stirrups (spacing ::5 100 mm and ::5 I.Sc) (see Figure 10.2-6).

(26.1-Sf2)

g) Special cases - For an anchor channel in a narrow, thin member (see Figure 26.1-10) with C2.",,,-,"::5ccr,v (ccrY according to Equation (26.1-5c)) and h < hcr,V (hcr,V according to Equation (26.1-5d)), the calculation according to Equation (26.1-S) leads to conservative results, More precise results are achieved if C[ is substituted by c; according to Equation (26.1-5g) in Equations (26.1-5a), (26,1-5b j ),


247

248

Part V: 26 Ultimate limit slate - elastic design approach

~L_- ___ I Vso

b

I

I ::::;JI~I~

l bCl'l bCl'l

,

" ~ ~ --E',• ---"-, __, _,'"_,"~i,,~ _~!

'-

b.

,

I

_--F·~<=,~jl

c'~ 12h~

2c\

•

Anchor under CO~Sideration

o

Neighbouring anchor

I

I

C 2 .,

I

C2.2

c;

0=

max (c2,m:\X -bch )/2;(h-2hch )/2)

(26.1-5g)

with:

I

I,

I

c,

(26.1-5c,) and (26.1-5d,)

i

c,

largest of the two edge distances parallel to the direction of load

C},max

c',

I

Figure 26.J-JO:Jllustration of an anchor channel influenced by two corners and member thickness. In the example the value C2.2 is decisivefor the determination of c;

26.1.3 For anchor channels the interaction should be verified separately for the channel bolt and the anchor channel since the location of the failure in each case is not coincident.


For the verification of combined tension and shear loads the channel bolts, the channel and the individual anchors of an anchor channel should be checked according to Section 10.3. The interaction should be verified separately for the channel bolt and the anchor channel. The highest loaded channel bolt and the most unfavourable anchor are decisive. For channel bolts Equation (10.3-2) with a"'" 2.0 is valid. For the verification of the anchor channel a simplified and an alternative, more accurate approach are distinguished:

26.1.3.1 In the simplified approach according to Equations (10.3-la) to (l0.3-lc) or

Equation (1O.3-ld) with a"'" 1.5 the following values should be inserted: for Nsa and Vsathe maximum value ofthe design actions valid for the anchor or the channel bolt, for N&/ the minimum value of N Rd.s.a, NRd.s.c> NRd.... t. NRd.sJ/e:" N Rd.p, NRd.c> N Rd.sp and NRd,~b, and for VRd the minimum value of V Rd.s,,,, VRd.s.c, VRd.s.l, VRd.p, V M .cp , and VRd.C' This approach is often conservative, because failure modes are assumed to interact even if the failures occur at different locations.

Simplified approach

Case A: Equations (1O.3-la) to (10.3-1c) or Equation (l0.3-1d) with a"'" 1.5 may be used provided that VRd.s.ch ::; NRd.s.cll

where: VRd.s.cll "'"

design shear resistance of the anchor channel (minimum value of VRd,s.a, VRd.s.c and VRd.s,I); and

N M .s.eI, "'"

design tension resistance (minimum value of

N Rd.s"" NRd.s,c

and

NRd.s.l).

Where the concrete resistance is not much lower than the steel resistance of the channel and the design shear resistance of the anchor channel VRd,s,~h exceeds the design tension resistance NRd.s.du limited testing at the University of Stuttgart with VRd,s,cI/NRd.s.cll ~ 1.8 indicates that this interaction approach may not be conservative. Due to the lack of additional experimental data a conservative linear interaction is proposed for the whole range of VRd.s.cll > N M .s.cI,.

Case B: For used.

26.1.3.2

VRd.s.ch

> N Rd.s•cI, Equation (10.3-1d) with a"'" 1.0 should be


Alternatively, the interaction may be performed separately for steel failure modes and concrete failure modes of the channel, whereby both interactions should be satisfied (see Figure 10.3-2), Separate verifications should be performed for failure of the anchor and the connection between anchor and channel and for the channel (local failure of channel lips and flexural failure of channel) since the locations of the failures are not coincident. Limited testing at the University of Stuttgart indicates that the use of a"'" 2.0 in Equation (10.3-2) for verification of the anchor channel is valid

only if the design shear resistance VRd.s.cIo of the anchor channel is not larger than the design tension resistance N Rd.s.d ,. If the design shear resistance VRd.s.ch of the anchor channel is larger than the design tension resistance NRd.s.ch the power a on the interaction equation (10.3-2) should be evaluated from the results of prequalification tests. A linear interaction is considered to be conservative. The use of the tri-linear interaction equations (10.3-1a) to (l0.3~lc) or Equation (10.3-3) with a"'" 1.5 is considered conservative for concrete failure.


The verification of steel failure modes should be performed as follows:

Case A: For

VRd.s,ch::: NRd,s.cI"

Equation (10.3-2) with a"'" 2.0 is valid.

Case B: For VRd.s.ch > NRd.s.ch, Equation (10.3-2) is valid with a determined from suitable prequalification tests (a::: 2.0). If prequalification tests are omitted then a"'" 1.0 should conservatively be used.

For the verification of concrete failure modes Equation (10.3-3) with a "'" 1.5 is valid independent of the ratio VRd.s.d/NRd.s.d,.

249

250


Anchor channels with anchor reinforcement

26.2

For the field of application Section 24 applies.

26.2.1 SO.51'\,1

".

T~'I ".

surface reinforcement

,a'r"

".

".


For anchors channels with anchor reinforcement to take up tension loads the requirements given in Section 19.2.1 should be met. In addition, for anchor channels parallel to the edge of a concrete member or in a narrow concrete member, the plane of the anchor reinforcement should be located perpendicular to the longitudinal axis of the channel (see Figure 26.2-1).

I N~

0)

b)

Figure26.2-1: Arrangement of anchor reinforcement: a) anchor channel at an edge; b) anchor channel in a narrow member

26.2.1.1 For the most unfavourable anchor see Section 26.1.2.1.



Table 26.2-1:

Verifications for anchor channels wilh anchor reinforcement under tension loading

Failure Mode

2

3

"ell

Channel

Anchor 0)

Anchor

N';., S.NRJ~"

Channel/ anchor

N:.,

Channel lip

y"

NRJ,'~ = N1."",

R .""

N

5

Flexure of channel

6

Pullout

N;"S.NRJ,r

Splitting

N;'5.NRJ~p

Blowout

N';.,S.N,.",.

~

N~d"," = N"", ..

N",S.N"".J

4

~

Design resistance 0)

'5. N RJ~~

Channel bolt

7

Channel bolt b)

N

NsJ'5.NRJ"

NSJ"'~

N

s. NRJ~,"~

= N/Il~.1

RJ.»

1.'~J

0-

= NR1 "

y"

=

RJ",J""

NRJ,p

N

Y!~,fl~

= N/Il,p

1.,,,, =N{;J.>p

"','1'

0

NR'",Jk,

Y"."

U

8

N

=NJiJc ,.. O~

y"

9

10

C

" 6 § -5 " ~
Steel Failure

N",.,5.N,., ...

Anchorage (bond) failure

N~,

NJ/J,,..

=N..,,,, Y'h,,,

'5.NRJ ,.

N,., .. =ill N.d,,11>
a

1.1

oj Verification required for the most unfavourable anchor Verification required for channel bolt with highcst tension load c) Partial factors see Section 3.4.2

b)

fib Bulletin 58: Design 01 anchorages in concrete

251

ParI V: 26 Ultimale limit state - elastic design approach

252

26.2.1.2 Steel failure Section 26.1.1.2 applies.

26.2.1.3

Pullout failure


26.2.1.4 Concrete cone failure Concrete cone failure does not need to be verified when sufficient anchor reinforcement is provided.

26.2.1.5

Splitting failure


26.2.1.6 No tests with anchor channels with anchor reinforcement close to an edge are available in which blowout failure occurred. It is assumed that the model given in section 26.1.1.6 applies. The model might be conservative.

Blowout failure

Section 26.1.1.6 applies. However, verification for blowout failure should be perfonned in all applications.

26.2.1.7 Steel failure of anchor reinforcement Section 19.2.1.7 applies.

26.2.1.8 Anchorage failure of anchor reinforcement in the concrete cone Section 19.2.1.8 applies.

}r~NSd'" fL~ CSd

~5Cl ~

a)

26.2.2 L=Nsd ."

b)

Figure 26.2-2: Reinforcement to take up shear forces; detailing of reinforcement: a) cross section; b) plane view with simplified strut and tie model

Resistance to shear failure

For anchor channels with anchor reinforcement to take up shear loads the requirements given in Section 19.2.2 should be met. However, the reinforcement configurations shown in Figure 19.2-3 are not as effective for anchor channels as for headed anchors and should therefore not be used. Only anchor reinforcement in the fonn of surface reinforcement as shown in Figure 19.2-4 and Figure 26.2-2 is covered in this Design Guide. The force acting on the reinforcement, Nsd.rc, should be calculated according to Equation (19.2-3).

26.2.2.1



Table 26.2-2:

Reqllired verifications for anchor channels with anchor reinforcement under shear loading

Failure Mode Channel

.. 2

2

~

lip

Channel

Anchor')

Channel bolt bj

Design resistance c) V"",,J '" V... ~,I

v..,,.;; v""",

y"",1 V",,.;;V,,,,.,

Channel bolt

d)

d,

V"".,'" v...., Y.,.

"

V

V"':::;v..,~..

v....... "

'"

y,"

.J,>

3

i

4

"

Pullout

V;:::;V...,.P

Pryout

V~:::;

0

0

RJ,p

v:

v...,,,..

Steel failure

V;"" :>NI
~ , Anchorage ; (bond) failure

V;':::;N..".

5

V

"',cp

N RJ.,<

'" v... , Y.u" = v...
Y.1k

",NRln Y.I".",

5

~

0

6

NM ..

'"

" .,,·d,·....l!iL f, Llj a /.1

.J Verification required for most unfavourable anchor or channel bolt

Verification required for channel bolt wit highest shear load oj Partial factors see Section 3.4.2 d) Shear load without lever ann cj Shear load with lever ann

b)

26.2.2.2 Steel failure Section 26.1.2.2 applies.

fib Bulletin 58: Design of anchorages ill concrete

253


254

26.2.2.3

Pullout failure

Section 19.1.2.3 applies. However, the factor k3 in Equation (10.2-3) should be taken as 1.5.

26.2.2.4 Concrete pryout failure Section 26.1.2.4 applies. However, the factor k4 in Equation (26.1-4) should be multiplied by 0.75.

26.2.2.5 Concrete edge failure Concrete edge failure does not need to be verified when sufficient anchor reinforcement is provided.

26.2.2.6 Steel failure of the anchor reinforcement Section 19.2.2.6 applies. However, the reinforcement configurations in Figure 19.2-3 should not be used for anchor channels and are therefore not covered in this Design Guide.

26.2.2.7 Anchorage failure of the anchor reinforcement in the concrete breakout body Section 19.2.2.7 applies. However, the reinforcement configurations in Figure 19.2-3 should not be used for anchor channels and are therefore not covered in this Design Guide.

26.2.3

Resistance to combined tension and shear loads

For anchor channels with anchor reinforcement, Section 26.1.3 applies with the following modifications. Failure of the anchor reinforcement should be treated as concrete failure.

26.2.3.1

Anchor channels with anchor reinforcement to take up tension and shear loads

For verification of the channel of anchor channels with anchor reinforcement to take up tension and shear loads Section 26.1.3.1 (simplified approach) or Section 26.1.3.2 (alternative approach) are valid.

26.2.3.2

Anchorages with anchor reinforcement to take up tension or shear loads only

For verification of the channel of anchor channels with anchor reinforcement to take up tension or shear loads, the following provisions apply: For anchorages close to an edge with an anchor reinforcement to take up shear loads, failure cracks will occur in the concrete well before reaching the ultimate load (see cracks 1 in Figure 19.2-5). These cracks will reduce the tension capacity of the anchorage. Also, the shear capacity of anchorages with anchor reinforcement to take up tension loads might be reduced by the early fonnation of a concrete cone. According to Potthoff (2008) a linear interaction equation is adequate.

In the simplified approach Equation (1O.3-ld) with a= 1.0 should conservatively be used. In the alternative approach, steel and concrete failure modes may be verified separately. For steel failure modes Section 26.1.3.2 is valid. For the verification of concrete failure modes of anchor channels Equation (10.3-3) with a = 1.0 should be used.

27 If the characteristic displacements under tension and shear load are not given in the Approval or have not been evaluated by prequalification tests, then the following information should be considered as a first approximation.


Section 21 applies.

The displacement of an anchor channel under tension load is composed of the displacement of the anchor and the displacement of the channel due to bending and local opening of the channel lips and deformation in the area of the connection of the anchor and the channel. The displacement of the anchors can be calculated according to Section 21. The displacement due to bending of the channel may conservatively be calculated using simple beam analysis. No formulas are currently available for calculating the displacement due to local opening of the channel lips and this displacement should therefore be determined from suitable tests. No method for calculating the displacement of an anchor channel under shear loading is currently available.

28

Fatigue loading

Fatigue loading of anchor channels is not covered in this Design Guide.

29

Seismic loading

Seismic loading of anchor channels is not covered in this Design Guide.


255

References ACI 355.2 (2007): ACI 355.2-07: Qualification a/post-installed mechanical anchors in concrete and

commentary. American Concrete Institute (ACI), Farmington Hills, Michigan, USA, 2007. ACI 318 (2008): Building code requirements for sintclura! concrete (Ae] 318-08) and commentary (Ae! 3JBR-08). American Concrete Institute (AeI), Farmington Hills, Michigan, USA, 2008.

ACI 318 (2011): BUilding code requirements for simciural concrete, Appendix D: Anchoring to

concrete. American Concrete Institute (ACI), Farmington Hills, Michigan, USA, to be published in 2011. ANSI (1994): ANSI B212.15-94: American national standard for cutting tools - Carbide-tipped masonry drills and blanks for carbide-tipped masonry drills. American National Standard Institute (ANSI), New York, New York, USA, 1994. ASCE (2006): ASCE/SEI 7-05: Minimum design loads for buildings and other stn/ctl/res. American Society of Civil Engineers (ASCE), Reston, Virginia, USA, 2006. ASTM (2009): ASTM AI93-09: Standard specification for alloy-steel and stainless steel bolting materials for high temperature or high pressure service and other special purpose applications. American Society for Testing and Materials (ASTM), Philadelphia, Pennsylvania, USA, 2009. Anderson, Meinheit (2000): Anderson, N. S.; Meinheit D. F.: Design Criteria for Headed Stud Groups in Shear. Part I - Steel Capacity and Edge Effects. PCI Journal, September-October 200, pp.

46-75. Anderson, Meinheit (2005): Anderson, N. S.; Meinheit D. F.: PCl's headed stud design redefined. Structure Magazine, April 2005, pp. 26-29. Anderson, Meinheit (2007): Anderson, N. S.; Meinheit D. F.: A review ofheaded-stud design criteria in the sixth edition of the PCI design handbook. PCI Journal, V. 52, No. 1,2007, pp. 2-20. Appl (2009): Appl, J.: Tragverhalten von Verbunddiibeln linter Zugbelaslung (Load carrying behaviour of bonded anchors under tension loading. PhD thesis, University of Stuttgart, Stuttgart, Germany, 2009 (in Gennan). Asmus (2007): Asmus, J.: Design Methodfor Splitting Failure Mode of Fastenings. Eligehausen, R.; Fuchs, W.; Genesio, G.; Grosser, P. (Editors): "Connections between Steel and Concrete". IbidemVerlag, Stuttgart, Gennany, 2007, pp. 505-517. Bruckner et al. (20ot): Bruckner, M.; Eligehausen, R.; Ozbolt, J.: Influence of bending compression stresses on the concrete cone capacity. In: Eligehausen, R. (Editor): "Connections between Steel and Concrete". RILEM Publications, eachan, France, 2001, pp. 647-657. CEB (1991): Fire design of concrete sln/ctures in accordance with CEB-F1P Model Code 90. Comite Eura-International du Beton (CEB), CEB, Bulletin d'lnfonnation 208, Lausanne, Switzerland, 1991. CEB (1993): CEB-F1P Model Code 1990. Comite Euro-International du Beton (CEB), Thomas Telford, London, UK, 1993. CEB (1994): Fastenings to concrete and masonry structures, state of the art report. Comite EuraInternational du Beton (CEB), Thomas Telford, London, UK, 1994. CEB (1997): Design of fastenings in concrete - Design Guide - Parts I to 3. Comite EuroInternational du Beton (CEB), CEB Bulletin d'Information 233, Thomas Telford, London, UK, 1997. CEN (2000): EN 206-1:2000: Concrete. Part 1: Specification, peiformance, production and conformity. Comite Europeen de Nonnalisation (CEN), Brussels, Belgium, 2000.


257

CEN (2002-1): EN 1990:2002: Eurocode: Basis of structural design. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2002. CEN (2002-2): EN 1991:2002: Eurocode 1: Actions on structures. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2002. Part 1-1: General actions - Densities, self-weight, imposed loads for buildings

Part 1-2: Part 1-3: Part 1-4: Part 1-5: Part 1-6: Part 1-7: Part 2: Part 3: Part 4:

(EN 1991-1-U002) General actions - Actions on structures exposed tofire (EN 1991-1-2:2002) General actions - Snow loads (EN 1991-1-3:2003) General actions - Wind actions (EN 1991-1-4:2005) General actions - Thermal actions (EN 1991-1-5:2003) General actions - Actions during execution (EN 1991-1-6:2005 General actions - Accidental actions (EN1991-1-7:2006) Traffic loads on bridges (EN1991-2:2003) Actions induced by cranes and machinery (EN1991-3:2006) Silos and tanks (EN1991-4:2006)

CEN (2004-1): EN 1992-1-1:2004: Eurocode 2: Design of concrete structures. Part 1-1: General rules and rules for buildings and civil engineering structures. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2004. CEN (2004-2): EN 1992-1-2:2004: Eurocode 2: Design of concrete structures. Part 1-2: General rules. Structuralfire design. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2004. CEN (2005): EN 1993-1-8:2005: Eurocode 3: Design of steel structures. Part 1-8: Design ofjoints. Comite Europeen de Normalisation (CEN), Brussels, Belgium 2005. CEN (2007): EN 13501-2:2007: Fire classification of construction products and building elements. Part 2: Classification using data jiwn fire resistance tests, excluding venti/ation services. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2007. CEN (2009): CEN/TS 1992-4:2009: Design offasteningsfor use in concrete. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2009. Part 4-1: General (CENITS 1992-4-1:2009) Part 4-2: Headedfasteners (CEN/TS 1992-4-2:2009) Anchor channels (CENfTS 1992-4-3:2009) Part 4-3: Post-installedfasteners - Mechanical systems (CENITS 1992-4-4:2009) Part 4-4: Post-installedfasteners - Chemical systems (CENITS 1992-4-5:2009) Part 4-5:

DIEt (2009): Approval Certificate Z-30.3-6: Erzeugnisse, Verbindungsmittel lind Bauteile aus nichtrostenden Stahlen (Products, fasteners and components made of stainless steels). Deutsches Institut fUr Bautechnik (DIDt), Berlin, Germany, 2009 (in German). Eligehausen et al. (1992): Eligehausen, R.; Fuchs, W.; Ick, U.; MalIee, R.; Reuter, M.; Schimmelpfennig, K.; Schmal, B.: Tragverhalten von Kopjbolzenverankenmgen bei zentrischer Zugbeanspruchung (Behavior of headed anchors under centric tension loading tension). Bauingenieur 67,1992, pp. 183-196 (in German). Eligehausen et al. (2006-1): Eligehausen, R.; Cook, R. A.; Appl, J.: Behavior and design of adhesive bonded anchors. ACI Structural Journal, V. 103, No.6, 2006, pp. 822-831. Eligehausen et al. (2006-2): Eligehausen, R.; Mailee, R.; Silva, J. F.: Anchorage in Concrete Construction. Ernst & Sohn, Berlin, Germany, 2006. Eligehausen, Grosser (2007): Eligehausen, R.; Grosser, P.: Experimentelle und numerische

Untersuchungen zur Bemessung von Befestigungen am Bautei/rand unter Querlasten (Experimental and numerical investigations on anchorages close to the edge under shear loading). Research Report EL 72/13-2, University of Stuttgart, Stuttgart, Gennany, 2007, (in German). Eligehausen et al. (2010): Eligehausen, R.; Blochwitz, R.; Fuchs, W.: Behavior. testing and design of bonded anchors under sustained tension load in concrete. ACI Spring Convention, March 2010, Chicago, Illinois, USA. EOTA (1997): ETA G 001: Guideline for European Technical Approval of Metal Anchors for Use in Concrete. European Organisation for Technical Approvals (EOTA), Brussels, Belgium, 1997. Part 1: Anchors hi general (1997), amended 2006 Torque-controlled expansion anchors (1997), amended 2006 Part 2: Undercut anchors (1997). amended 2010 Part 3: Deformation-controlled expansion anchors (1998), amended 2006 Part 4: Bonded anchors (2002), amended 2006 and 2008 Part 5: Part 6: Anchorsfor mUltiple usefor non-structural applications (2003), amended 2010 Annex A: Details oftest (1997), amended 2001 and 2006 AnnexB: Tests for admissible service conditions, detailed information (1997). amended

Annex C

2001 and 2006 Design methods for anchorages (1997), amended 2001,2006 and 2010

EOTA (2003-1): Technical Report TR 018: Assessment of torque-controlled bonded anchors. European Organisation for Technical Approvals (EOTA), Brussels, Belgium, 2003.

Cook, Klingner (1992): Cook, R. A.; Klingner, R. E.: Ducti/e Multiple-Anchor Steel-to-Concrete Connections. Journal of Structural Engineering, ASCE, V. 118, No.6, 1992, pp. 1645-1665.

EOTA (2003-2): Steel plate wlfh cast-in anchor(s) - Common Understanding of Assessment Procedure (CUAP) for a European Technical Approval. European Organisation for Technical

Cook et al. (1998): Cook, R. A.; Kunz, J.; Fuchs, W.; Konz, R. c.: Behavior and design of single adhesive anchors under tensile load in uncracked concrete. ACI Structural Journal, V. 95, No.1, 1998, pp. 9-26.

Approvals (EOTA), Brussels, Belgium, 2003.

DAfStb (1991): Hi/ftmittel zur Berechmmg der SchnittgrdfJen und Formveranderungen von

Belgium, 2004.

Stahlbetontragwerken: nach DIN 1045, Ausg. Juli 1988 (Aids for the calculation of action effects and deflections in concrete structures: according to DIN 1045, verso July 1988). Deutscher Ausschuss fUr Stahlbeton (DAfStb), Heft 240, Ernst & Sohn, Berlin, Germany, 1991 (in German).

EOTA (2004-2): Technical Report TR 020: Evaluation of Anchorages in Concrete concerning Resistance to Fire. European Organisation for Technical Approvals (EOTA), Brussels, Belgium, 2004.

DIOt (2002): Merkblatt iiber die Kennwerte, Anforderungen und Priifimgen von Mauerbohrern mit Schneidkorpern aus Hartmetall, die zllr Herstellung der Bohrlocher von Diibelverankerungen venvendet werden (Technical bulletin for characteristic values, requirements and tests for masonry drill bits with carbide cutting edges which are used to drill holes for anchors). Deutsches Institut fUr Bautechnik (DIEt), Berlin, Germany, 2002.

258

References

EOTA (2004-1): Anchor channels - Common Understanding of Assessment Procedure (CUAP) for a European Technical Approval. European Organisation for Technical Approvals (EOTA), Brussels,

EOTA (2007): Technical Report TR 029: Design of Bonded Anchors. European Organisation for Technical Approvals (EOTA), Brussels, Belgium, 2007. Fichtner, Eligehausen (2007): Fichtner, S.; Eligehausen, R.: Stiffness requirements for baseplates. In: Eligehausen, R.; Fuchs, W.; Genesio, G.; Grosser, P. (Editors): "Connections between Steel and Concrete". Ibidem-Verlag, Stuttgart, Germany, 2007, pp. 1059-1072.

fib Bullelin 58: Design ofanchorages in concrete

259

Fuchs, Eligehausen (1989): Fuchs, W.; Eligehausen, R.: Tragverhalten von Befestigungsmitteln im gerissenen Beton bei Querzllgbeanspntchung (Load-bearing behaviour of fasteners in cracked concrete under shear load). Test report No. 1141-89115 (in German), University of Stuttgart, Germany,

ICC-ES (2010-1): AC193: Acceptance criteria for mechanical anchors in concrete elements. International Code Council-Evaluation Service (ICC-ES), Whittier, California, USA, 2010.

1989.

ICC-ES (2010-2): AC232: Acceptance criteria for anchor channels in concrete elements. International Code Council-Evaluation Service (ICC-ES), Whittier, California, USA, 2010.

Fuchs (1992): Fuchs, W.: Tragverhalten von Btifestigungen unter QlIerlasten in ungerissenem Beton (Load-bearing behaviour of fastenings under shear loading in uncracked concrete). Deutscher Ausschuss fUr Stahlbeton (DAfStb), Heft 424, Beuth Verlag, Berlin, Germany, 1992 (in German).

ISO (1992): ISO 898-2: 1992: Mechanical properties offasteners made ofcarbon steel and alloy steel. ParI 2: Nuts with specified proof load values, coarse thread. International Organization for

Fuchs ct a!. (1995): Fuchs, W.; Eligehausen, R.; Breen, J.E.: Concrete Capacity Design (CCD) Approachfor Fastening to Concrete. ACI Structural Journal, V. 92, No.1, 1995, pp. 73-94. Furche, Eligehausen (1991): Furche, J.; Eligehausen, R.: Lateral blow-ollt failure of headed studs near a free edge. In: Senkiw, G. A.; Lancelot, H. B. (Editors): Anchors in Concrete - Design and Behavior. ACI Special Publication l30, Detroit, Michigan, USA, 1991, pp. 235-252. Furche (1994): Forche, J.: Zum Trag- und Verschiebllngsverhalten von Kopjbolzen bei zentrischem Zug (Load-bearing and displacement behaviour of headed anchors under axial tension loading). PhD thesis, University of Stuttgart, Stuttgart, Germany, 1994 (in German). Grosser,

ISO (1999): ISO 834-1:1999 "Fire resistance test-elements of building constructions. Part 1: General requirements". International Organization for Standardization (ISO), Geneva, Switzerland, 1999. ISO (2009-1): ISO 898-1 :2009: Mechanical properties offasteners made of carbon steel and alloy steel. Part 1: Bolts, screws and studs with specified property classes - coarse thread and fine pitch thread. International Organization for Standardization (ISO), Geneva, Switzerland, 2009. ISO (2009-2): ISO 3506-1:2009: Mechanical properties of corrosion-resistant stainless steelfasteners. Part I: Bolts, screws and studs". International Organization for Standardization (ISO), Geneva, Switzerland, 2009.

Tragverhalten von parallel zum Bauteilrand angeordneten Zweifachbefestigungen unter Torsionsbeanspntchung im lmgerissenen Beton (Load-bearing behaviour of groups with two anchors arranged parallel to the edge under torsion loading in uncracked concrete). Test report No. E 08/01 - G07100/02, University of Stuttgart, Germany, 2008 Grosser (2008):

Standardization (ISO), Geneva, Switzerland, 1992.

P.:

(in German). Grosser, Eligehausen (2008): Grosser, P.; Eligehausen, R.: Fastenings under shear loading parallel to the edge. Test report No. E 08/02 - G07100103, University of Stuttgart, Germany, 2008. Grosser, Cook (2009): Grosser, P.; Cook, R.: Load bearing behavior of anchor groups arranged perpendicular to the edge and loaded by shear towards the free edge. UF Structures Report 2009-1, University of Florida, Florida, USA, 2009. Grosser et a!. (2010): Grosser, P.; Eligehausen, R.; Ozbolt, J.: 3D FE analysis ofanchor channels and headed anchors under shear load close to the edge. In: Proceedings of the 7th International Conference on Fracture Mechanics of Concrete and Concrete Structures, Jeju, Korea, May 23 - 27, 2010, Korea Concrete Institute, 2010, Seoul, Republic of Korea. Grosser (2011): Grosser, P.: Adhesive anchors with deep embedments under shear load located close to the edge and loaded perpendicular to the edge. Test report No. fHW/17-11l01, University of Stuttgart, Germany, 2011.

ISO (2009-3): ISO 3506-2:2009: Mechanical properties of corrosion-resistant stainless steel fasteners. Part 2: Nu/s. International Organization for Standardization (ISO), Geneva, Switzerland, 2009. Klingner, Mendonca (1982): Klingner, R. E.; Mendonca, J. A.: Shear Capacity of Short Anchor Bolts and Welded Studs: A Literature Review. ACI-Journal, September 1 October 1982, pp. 339-349. Kraus (2003): Kraus, J.: Tragverhalten lind Bemessung von Ankerschienen unter zentrischer Zugbelastllng (Load-bearing behaviour and design of anchor channels under axial tension). PhD thesis, University of Stuttgart, Stuttgart, Germany, 2003 (in German). Lee et al. (2007): Lee, N.H.; Kang, S.K.; Chang, J.B.; Park, K.R.: Tensile-headed anchors with large diameter and deep embedment in concrete. ACI Structural Journal, V. 104, No.4, 2007, pp. 479-486. Lee et al. (2010): Lee, N.H.; Park, K.R.; Suh, Y.P.: Shear behavior of headed anchors with large diameters and deep embedments. ACI Structural Journal, V. 107, No.2, 2010, pp. 146-156. Lieberum et al. (1987): Lieberum, K. W.; Reinhardt, H.-W.; Walraven, J. C.: Fastenings of anchors in the shear zone ofconcrete slabs. Beton + Fertigteil-Technik 1987, No. 10, pp. 708-715. Lotze (1993): Lotze, D.: Tragverhalten und Anwendung von Diibeln linter oflmals wiederholter Belastllng (Load-bearing behaviour and application of anchors under frequently repeated loading).

Hoehler (2006): Hoehler, M. S.: Behavior and testing of fastenings to concrete for lise in seismic applications. PhD thesis, University of Stuttgart, Stuttgart, Germany, 2006.

PhD thesis, University of Stuttgart, Stuttgart, Germany, 1993 (in German).

Hofmann (2005): Hofmann, J.: Tragverhalten lind Bemessung von Befestigllngen am Bauteilrand

Mallee (2001): MaBee, R.: "Behaviour and design of anchors close to an edge under torsion". In: Eligehausen, R. (Editor): "Connections between Steel and Concrete". RILEM Publications, Cachan, France, 2001, pp. 178-187.

unter Querlasten mit beliebigem Winkel zur Bauteilkante (Load-bearing behaviour and design of fasteners close to an edge under shear loading under an arbitrary angle to the edge). PhD thesis, University of Stuttgart, Stuttgart, Germany, 2005 (in German). Hofmann, Eligehausen (2009): Hofmann, J., Eligehausen, R.: Trag[cihigkeit von randnahen Kopjbolzen bei der Versagensart seitlicher Betonausbruch (Load bearing capacity of headed stllds in case of blowout failure mode. Beton- und Stahlbetonbau 104 (2009), Heft 7, pp. 386-393 (in German). ICC-ES (2009): AC308: Acceptance criteria for post-installed adhesive anchors in concrete elements. International Code Council-Evaluation Service (lCC-ES), Whittier, California, USA, 2009.

260

References

Malice (2002): MaBee, R.: Diibelgntppen am Bal/tei/rand unter Torsionsbeanspruchl/ng (Anchor groups close to an edge under torsion). Beton- und Stahlbetonbau, V. 97, No.2, 2002, pp. 69-77 (in German). Malice, Pusill-Wachtsmuth (2007): Mal1ee, R.; Pusill-Wachtsmuth, P.: Design ofanchors close to an edge under shear loading - Engineering approach for consideration of load direction. Beton- und Stahlbetonban V. 102,2007, Special Edition, pp 7-15.

fib Bulletin 58: Design ofonchoroges in concrete

261

Nilsson, Elfgren (2009): Nilsson M.; Elfgren, L.: Fastenings (Anchor Bolts) in Concrete StructuresEffect ofSwface Reinforcement. Proceedings of Nordic Symposium on Nuclear Technology, Inspecta, Stockholm 25-26 Nov 2009, Paper B2-4.

Scheer ct ai. (1987): Scheer, J.; Peil, U; Nolle, P.: Schrallben mit planmiijJiger Biegebeansprllchung (Screws under bending). Report No. 6079, TU Braunschweig, Braunschweig, Gennany, 1987 (in Gennan).

Naithani ct al. (1988): Naithani, K. c.; Gupta, V. K.; Gudh, A D.: Behavior of shear connection under dynamic loads. Materials and Structures V. 21, No.5, 1988, pp. 359-363.

Schmid (2010): Schmid, K.: Der Einflllss einer Riickhiingebewehnmg auf das Tragverhalten von Befestigungsmitteln unter Querlastell senkrecht zum Rand (Influence of anchor reinforcement on the behaviour ofanchors loaded by shear towards the edge). PhD thesis, University of Stuttgart, Stuttgart, Gennany, 2010 (in Gennan).

Newmark, Hall (1982): Newmark, N. M.; Hall, W. J.: Earthquake spectra and design. Engineering monographs on earthquake criteria, structural design, and strong motion records, No.3, Earthquake Engineering Research Institute (EERI), Oakland, California, USA, 1982. Ozbolt, Eligehausen (1990): Ozbolt, J.; Eligehausen, R.: Numerical analysis of headed studs embedded in large plain concrete blocks. In: Bicanic, N., Mang, H. (Editors): Computer Aided Analysis and Design of Concrete Structures. Pineridge Press, London, 1990. Periskic (2006): Periskic, G.: Einzel- und Zweifachbefestigllngen mit Verbunddiibel senkrecht zum Rand unter Querlast zum Rand im ungerissenen Beton (Single anchors and Groups with two anchors loaded in shear towards the edge in uncracked concrete). Report No. E06/01-E01301l1, University of Stuttgart, Stuttgart, 2006 (in Gennan). Peri~kic (2010): Periskic, G.: Entwicklllng eines 3D thermo-hygro-mechanischen Modells fiir Beton unter Brandbeansprllchung und Anwendung auf Befestigungen unter Zuglasten (Development of a thermo-hydra-mechanical Model for concrete under fire and application to fastenings loaded in tension). PhD thesis, University of Stuttgart, Stuttgart, 2010 (in Gennan).

Potthoff (2008): Potthoff, M.: Tragverhalten und Bemessung von Ankerschienen unter Querbelastung (Load bearing behavior and design of channel bars under shear load). PhD thesis, University of Stuttgart, Stuttgart, Gennany, 2008 (in Gennan). Ramm, Grciner (1991): Ramm, W.; Greiner, U.: Verankenmgen mit Kopjbolzen - Randnahe Verankenmgen linter Querzugbeanspruchung und ramfferne Verankenmgen unter zentrischer ZlIgbeanspntchung - Untersuchung des Einjlusses von speziellen Riickhiingebewehrungen (Anchorages with headed anchors - anchors close to an edge under shear loading and anchors remote from an edge under axial tension loading - Investigation of the influence of special supplementary reinforcement). Research Report, Universitat Kaiserslautern, Kaiserslautern, Gennany, 1991 (in Gennan).

Silva (2002): Silva, J. F.: Design Considerations for Earthquake Resistant Anchorages. In: Fuchs, W.; Reinhardt, H.-W. (Editors): "Befestigungstechnik, Bewehrungstechnik und.. . Festschrift zu Ehren von Prof. Dr. -Ing. Rolf Eligehausen anlasslich seines 60. Geburtstages - aktuelle Beitrage aus Forschung und Praxis". Ibidem Verlag, Stuttgart, Gennany, 2002, pp. 511-521. Spieth (2002): Spieth, H. A.: Tragverhalten und Bemessllng von eingemortelten Bewehrungsstiiben (Behavior and design ofpost-installed rein/arcing bars). PhD thesis, University of Stuttgart, Stuttgart, Gennany, 2002 (in Gennan). Usami ct ai. (1988): Usami, S.; Abe, Y.; Nagano, T.; Kowada, A; Kobayashi, J.; Kodama, J.; Koike, K.: Studies on the fatigue strength of anchors for supporting equipment and piping. Tensile fatigue strength against cone-shaped concrete failure. Proceedings of the Annual Meeting of Kanton Branch of Architectural Institute of Japan, Tokyo, Japan, 1988. Utescher (1978): Utescher, G.: Beurteillingsgrundiagen fijr Fassadenverankerungen (Assessment principles for fastening of favades). Verlag Wilhelm Ernst & Sohn, Berlin, Gennany, 1978 (in Gennan). Zhao et al. (1989): Zhao, G.; Fuchs, W.; Eligehausen, R.: EinjIuss der Balltei/dicke auf das Tragverhalten von Diibelbefestigungen im ungerissenen Beton unter QlIerzllgbeansprllchung (InjIuence of member thickness on the behaviour of anchors in non-cracked concrete under shear loading). Report No. 1O/12A-89/5, University of Stuttgart, Stuttgart, Gennany, March 1989 (in Gennan). Zhao (1993): Zhao, G.: Tragverhalten von randfernen Kopjbolzenverankerungen bei Betonbruch (Behaviour of headed anchors remote to an edge at concrete failure). PhD thesis, University of Stuttgart, Stuttgart, Gennany, 1993 (in Gennan).

Reick (2001): Reick, M.: Brandverhalten von Befestigllngen mit grofiem Randabstand in Beton bei zentrischer Zugbeanspruchung (Behavior offastenings remote from an edge in concrete under axial tension). PhD thesis, University of Stuttgart, Stuttgart, Gennany, 2001 (in Gennan). Reuter, Eligehausen (1992): Reuter, M.; Eligehausen, R.: EinflujJ der Lasteinleitllng durch Befestigllngen auf die Tragfiihigkeit von Stahlbetonbauteilen (Influence of load transmission by fastenings on the load-bearing capacity ofreinforced concrete elements). Bauingenieur V. 67, No. 10, 1992, pp. 461-474 (in Gennan). Rieder, Bergmeister (2010): Rieder, A; Bergmeister, K.: Simulated and tested seismic response of post-installed metal anchors in concrete. Proceedings of 3'd fib International Congress, 2010, Washington, DC, USA Roik (1982): Roik, K.: Verbundkonstntktion (Composite construction). Stahlbau-Handbuch, Vol. 1, Stahlbau-Verlags-GmbH, Koln, Gennany, pp. 627-672 (in Gennan). Roik (2009): Roik, M.: Tastversuche zum Tragverhalten von senkrecht zllln Rand eingeballten Ankerschienen, belastet durch Querzug parallel zum Rand (Preliminary tests to anchor channels arranged perpendicular to the edge and loaded by a shear load parallel to the edge). Halfen GmbH, Langenfeld, Gennany, 2009 (in Gennan).

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References

fib Bulletin 58: Design ofonchorages in concrete

263

Related documents ACI 355.1 (1991): ACI 355.1R-91: Stale of the art report on anchorage to concrete. American Concrete Institute (ACI), Detroit, Michigan, USA, 1991.

CEN (2005-6): EN 10088-3:2005: Stainless steels. Part 3: Technical delivery conditions for semifinished products, bars, rods. wire. sections and bright products of corrosion resisting steels for general purposes. Comite Europeen de Normalisation (CEN), Brussels, Belgium 2005. CEN (2008): EN 1S0 13918:2008: Welding - Studs and ceramic fernlles for arc stud welding. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2008.

CEB (1978): International system of unified codes of practice for structures. Volume 1: Common unified ntfes for different types of construction and material. Comit6 Euro-Intemational du Beton (CEB), Bulletin d'Information 125, Paris, France, 1978.

Eligehausen (2001): Eligehausen, R. (Editor): Connections between Steel and Concrete. RILEM Proceedings PRO 21, RILEM, Cachan, France, 200 I.

CEB (1988): General principles on reliability for structures - a commentary on ISO 2394. Comite Euro-Intemational du Beton (CEB): CEB, Bulletin d'Infonnation 191, Lausanne, Switzerland, 1988.

Eligehausen et al. (2007): Eligehausen, R.; Fuchs, W.; Genesio, G.; Grosser, P. (Editors): Connections between Steel and Concrete. Ibidem-Verlag, Stuttgart, Germany, 2007.

eEN (2000-2): EN 12390-1:2000 Testing hardened concrete. Part 1: Shape, dimensions and other requirements for specimens and moulds. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2000.

Fichtner (2011): Fichtner, S.: Untersuchungen zum Tragverhalten von Gnlppenbefestigungen 1I111er Beriicksichtigung der Ankerplattendicke lind einer Ausgleichsschicht (Investigations on the behavior of anchor groups taking into account baseplate thickness and thickness of mortar layer). PhD thesis,

CEN (2000-3): EN 12390-2:2000 Testing hardened concrete. Part 2: Making and curing specimens for strength tests. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2000. CEN (2000-4): EN 12390-5:2000 Testing hardened concrete. Part 5: Flexural strength of test specimens. Comite Europeen de Normalisation (CEN). Brussels, Belgium, 2000. CEN (2000-5): European Committee for Standardization (CEN) (2000): EN 12390-6:2000 Testing of hardened concrete. Part 6: Tensile splitting strength of test specimens. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2000. CEN (2000-6): EN 12390-7:2000: Testing hardened concrete. Part 7: Density of hardened concrete. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2000.

University of Stuttgart, Stuttgart, Germany, 2011 (in German). ISO (1979): ISO 273:1979 Fasteners clearance holes for bolts and screws. International Organization for Standardization (ISO), Geneva, Switzerland, 1979. ISO (1997-3): ISO 1803:1997 Building constmction, tolerances. expression ofdimensional accuracy, principles and terminology. International Organization for Standardization (ISO), Geneva, Switzerland,1997. ISO (2005): ISO 5922:2005 Malleable cast iron. International Organization for Standardization (ISO), Geneva, Switzerland, 2005.

CEN (2000-7): EN 12504-1:2000: Testing concrete in stnlctures. Part 1: Cored specimens - Taking, examining and testing in compression. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2000. CEN (2001): EN 10002-1:2001: Metallic materials - Tensile testing of metallic materials. Part 1: Method oftest at ambient temperature. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2001. CEN (2004-2): EN 1994-1-1:2004: Eurocode 4: Design of composite steel and concrete stnlctures. Part 1-1: General rules and rules for buildings. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2004. CEN (2004-3): EN 1998-1:2004: Eurocode 8: Design ofstnlctures for earthquake resistance. Part 1: General rules. seismic actions and rilles for buildings. Comite Europeen de Normalisation (CEN), Brussels, Belgium, 2004. CEN (2005-1): EN 1993-1-1:2005: Eurocode 3: Design of steel structures. Part 1-1: General rules and rules for buildings". Comite Europeen de Normalisation (CEN), Brussels, Belgium 2005. CEN (2005-3): EN 1998-3:2005: Eurocode 8: Design ofstnlcturesfor earthquake resistance. Part 3: Assessment and retrofitting of bUildings. Comite Europeen de Normalisation (CEN), Brussels, Belgium 2005. CEN (2005-4): EN 10080-1 :2005: Steelfor the reinforcement of concrete. Weldable reinforcing steel. Part 1: General. Comite Europeen de Normalisation (CEN), Brussels, Belgium 2005. CEN (2005-5): EN 10088-2:2005: Stainless steels. Part 2: Technical delivery conditions for sheet/plate and strip of corrosion resisting steels for general purposes. Comite Europeen de Normalisation (CEN), Brussels, Belgium 2005.

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