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Connection Handbook 1 BACKGROUND AND THEORY

Handbook 1: Design of Structural Steel Connections

Handbook 1: Design of Structural Steel Connections

First Edition 2007 Author T.J. Hogan Contributing author and editor S.A. Munter Level 13, 99 Mount Street, North Sydney. NSW 2060. Phone 9931 6666. Email [email protected] Website: www.steel.org.au

Handbook 1. Design of structural steel connections.

by

T.J.Hogan

contributing author & editor S.A.Munter

first edition - 2007

AUSTRALIAN STEEL INSTITUTE (ABN)/ACN (94) 000 973 839 Handbook 1. Design of structural steel connections Copyright © 2007 by AUSTRALIAN STEEL INSTITUTE

Published by: AUSTRALIAN STEEL INSTITUTE

All rights reserved. This book or any part thereof must not be reproduced in any form without the written permission of Australian Steel Institute. Note to commercial software developers: Copyright of the information contained within this publication is held by Australian Steel Institute (ASI). Written permission must be obtained from ASI for the use of any information contained herein which is subsequently used in any commercially available software package. FIRST EDITION 2007 (LIMIT STATES) National Library of Australia Cataloguing-in-Publication entry:

Hogan, T.J. Handbook 1: Design of structural steel connections 1 st ed. Bibliography. ISBN 978 0 909945947 (pbk.). 1. Steel, Structural—Standards - Australia. 2. Steel, Structural—Specifications - Australia. 3. Joints, (Engineering)—Design and construction. I. Munter, S.A. II. Australian Steel Institute. III. Title (Series: Structural steel connection series; 1).

This publication originated as part of Design of structural connections First edition 1978 Second edition 1981 Third edition 1988 Fourth edition 1994

Also in this series: Design capacity tables for structural steel, Volume 3: Simple connections – open sections Design Guide 1: Bolting in structural steel connections Design Guide 2: Welding in structural steel connections Design Guide 3: Web side plate connections Design Guide 4: Flexible end plate connections Design Guide 5: Angle cleat connections Design Guide 6: Seated connections

Disclaimer: The information presented by the Australian Steel Institute in this publication has been prepared for general information only and does not in any way constitute recommendations or professional advice. While every effort has been made and all reasonable care taken to ensure the accuracy of the information contained in this publication, this information should not be used or relied upon for any specific application without investigation and verification as to its accuracy, suitability and applicability by a competent professional person in this regard. The Australian Steel Institute, its officers and employees and the authors and editors of this publication do not give any warranties or make any representations in relation to the information provided herein and to the extent permitted by law (a) will not be held liable or responsible in any way; and (b) expressly disclaim any liability or responsibility for any loss or damage costs or expenses incurred in connection with this publication by any person, whether that person is the purchaser of this publication or not. Without limitation, this includes loss, damage, costs and expenses incurred as a result of the negligence of the authors, editors or publishers. The information in this publication should not be relied upon as a substitute for independent due diligence, professional or legal advice and in this regards the services of a competent professional person or persons should be sought. handbook 1 design of structural steel connections, first edition

ii

CONTENTS Page List of figures List of tables Preface About the author About the contributing author and editor Acknowledgements

iv v vi vii vii viii

1 CONCEPT OF DESIGN GUIDES............... 1 1.1 Background 1 2 BACKGROUND DISCUSSION................... 2 2.1 General considerations 2 2.2 Forms of construction 3 2.3 Connection design models 6 2.4 Connection characteristics 7 3 BOLTS AND BOLT GROUPS .................. 10 3.1 Bolt types and bolting categories 10 3.2 Bolt dimensions 11 3.3 Dimensions of wrenches for installing bolts 12 3.4 Bolt mechanical properties 14 3.5 Design requirements for bolts 15 3.6 AS 4100 Design requirements— Strength limit state 17 3.7 AS 4100 design requirements— Serviceability limit state 23 3.8 Geometric requirements of AS 4100 for bolted connections 26 3.9 Bolt group loaded in-plane 28 3.10 Design example No. 1— Design of bolts in lap splice connection 39 3.11 Design example No. 2— Design of bolt group loaded in-plane 41 3.12 Bolt group loaded out-of-plane 44 3.13 Prying action 46 3.14 Design example No. 3— Design of bolt group loaded out-of-plane 50 4 WELDS AND WELD GROUPS................. 52 4.1 Weld types 52 4.2 Standard weld symbols 53 4.3 Selection of prequalified welding consumables 54 4.4 Weld categories 55 4.5 Design of butt welds— Strength limit state 56 4.6 Design of fillet welds— Strength limit state 58 4.7 Weld group loaded in-plane 62 4.8 Weld group loaded out-of-plane 66

Page 4.9 Weld group loaded by general set of design actions 4.10 Properties of common fillet weld groups 4.11 Practical fillet weld groups 4.12 Design example No. 4— Design of fillet weld group loaded in-plane 4.13 Design example No. 5— Design of fillet weld group loaded out-of-plane

67 69 71

75

76

5 CONNECTION COMPONENTS ................77 5.1 Angle components 77 5.2 Flat bar components 79 5.3 Plate components 80 5.4 Design capacities 81 6 SUPPORTED MEMBERS .........................86 6.1 General 86 6.2 Uncoped sections 87 6.3 Design example No. 6— UB unholed and holed moment and shear capacity 93 6.4 Single web coped sections 95 6.5 Design example No. 7— UB single web coped moment and shear capacity 101 6.6 Double web coped sections 102 6.7 Design example No. 8— UB double web coped moment and shear capacity 105 6.8 Lateral torsional buckling 106 6.9 Block shear failure of coped sections 107 6.10 Web reinforcement of coped supported members 109 7 SUPPORTING MEMBERS......................110 7.1 Rationalised dimensions 110 7.2 Gauge lines 113 8 MINIMUM DESIGN ACTIONS ON CONNECTIONS......................................116 8.1 AS 4100 Requirements 116 9 REFERENCES........................................118 APPENDICES A Limcon software B ASI Handbook 1 comment form

handbook 1 design of structural steel connections, first edition

120 125

iii

LIST OF FIGURES Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14

Figure 15 Figure 16

Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22

Figure 23

Figure 24 Figure 25 Figure 26 Figure 27 Figure 28 Figure 29 Figure 30 Figure 31 Figure 32

Page Rigid connections ........................... 4 Simple connections ........................ 5 Moment rotation characteristics of typical connections ..................... 7 End plate tear-out failure edge distances ...................................... 16 End plate tear-out failure force components .................................. 16 End plate tear-out, simple case .... 16 Lap joint and brace/gusset connection .................................... 21 Bolt group subject to in-plane moment ........................................ 28 Bolt group subject to shear forces at centroid .......................... 29 Bolt group subject to a general load set......................................... 29 Graphical relationship—Bolt force to component displacement......... 30 Horizontal and vertical bolt forces at an extreme bolt .............. 31 Single bolt column loaded in-plane......................................... 32 Single bolt column–Forces and edge distances for end plate tear-out or bearing failure ............. 33 Double bolt column loaded in-plane......................................... 35 Double bolt column–Forces and edge distances for end plate tear-out or bearing failure ............. 36 Bolted plate splice ........................ 39 Bolt group loaded in-plane............ 41 Bolt group loaded out-of-plane— Design actons............................... 44 Double bolt column geometry ....... 45 Prying mechanism in T-stub connection .................................... 46 Graphical relationship—Bolt load/applied load for a stiff T-stub flange ................................ 47 Graphical relationship—Bolt load/applied load for a flexible T-stub flange ................................ 47 T-stub critical dimensions and design actions .............................. 48 T-stub parameters ........................ 48 Bolt group loaded out-of-plane ..... 50 T-stub geometry ........................... 51 Weld types.................................... 52 Symbols for welds on drawings .... 53 Design throat thickness of incomplete penetration butt weld .. 57 Design throat thickness of fillet welds..................................... 58 Design actions on a fillet weld ...... 60

Page Figure 33 Design forces per unit length parallel to weld group axes x, y, z .61 Figure 34 Fillet weld subject to longitudinal and transverse shear forces ..........61 Figure 35 General fillet weld group................63 Figure 36 Horizontal and vertical weld component forces at a point in a weld group ..............................65 Figure 37 Fillet weld group loaded out-of-plane ...................................66 Figure 38 General fillet weld group................67 Figure 39 Possible critical points in particular fillet weld group..............71 Figure 40 Fillet weld group loaded inand out-of-plane ............................72 Figure 41 Two parallel vertical welds loaded out-of-plane .......................72 Figure 42 Two parallel horizontal welds loaded out-of-plane .......................74 Figure 43 Fillet weld group loaded in-plane ...75 Figure 44 Fillet weld group loaded out-of-plane ...................................76 Figure 45 Rectangular connection component geometry.....................81 Figure 46 Rectangular component design moment capacity—Major axis........82 Figure 47 Rectangular component design moment capacity—Minor axis........82 Figure 48 Rectangular component design capacity in axial tension ...............83 Figure 49 Examples of block shear failure in components ....................84 Figure 50 Block shear area in components ...85 Figure 51 Section with holes in both flanges .88 Figure 52 Section with holes in one flange ....88 Figure 53 Section with holes in one flange ....89 Figure 54 Single web coped (SWC) sections 95 Figure 55 SWC universal beam (UB) ............95 Figure 56 T-Section of SWC UB showing elastic neutral axis.........................96 Figure 57 SWC UB T-section with plastic neutral axis in web.........................96 Figure 58 SWC UB T-section with plastic neutral axis in the flange ...............97 Figure 59 SWC universal beam example ....101 Figure 60 Double web coped (DWC) sections .......................................102 Figure 61 Elastic neutral axis in DWC section ...............................103 Figure 62 DWC universal beam example ....105 Figure 63 Block shear failure in DWC members .....................................107 Figure 64 Block shear area in SWC and DWC members .....................108 Figure 65 Web reinforcement of coped supported members.....................109


iv

LIST OF TABLES Table 1 Table 2 Table 3 Table 4

Table 5 Table 6 Table 7 Table 8 Table 9 Table 10

Table 11 Table 12

Table 13

Table 14 Table 15 Table 16 Table 17 Table 18 Table 19 Table 20 Table 21 Table 22 Table 23

Table 24

Table 25 Table 26 Table 27

Page

Page

Bolt category identification system .......................................... 10 Dimensions of commercial bolts and nuts ............................... 11 Dimensions of high strength structural bolts and nuts ............... 11 Dimensions of wrenches for determining erection clearances ................................12,13 Metric hexagon commercial bolts . 14 High strength structural bolts ........ 14 AS 4100 Clause 9.3.2 provisions, strength limit state, static loads..... 17 Design areas of bolts.................... 18 Strength limit state commercial bolts 4.6/S bolting category .......... 19 Strength limit state high strength structural bolts 8.8/S, 8.8/TB, 8.8/TF bolting categories .............. 20 Reduction factor for lap connections .................................. 22 AS 4100 Clause 9.3.3 provisions serviceability limit state—Static loads ................ 24 Serviceability limit state high strength structural bolts 8.8/TF bolting category ............................ 25 Minimum edge distances .............. 26 AS 4100 provisions for slotted and oversize holes........................ 27 Single bolt column ........................ 32 Bolt group design factors for single column of bolts .............. 34 Double bolt column....................... 35 Bolt group factors for double column of bolts ............................. 37 Bolt group factors for double column of bolts ............................. 38 Prequalified welding consumables ................................ 54 Strength of weld metal .................. 54 Design capacities of equal leg fillet welds per unit length Category SP ................................. 59 Design capacities of equal leg fillet welds per unit length Category GP................................. 59 Properties of common fillet weld groups treated as line elements.... 69 Equal angles—Rationalised dimensions for detailing ................ 77 Unequal angles—Rationalised dimensions for detailing ................ 77

Table 28 Gauge lines for angles ..................78 Table 29 Strengths of angles to AS/NZS 3679.1 Grade 300............78 Table 30 Flats ..............................................79 Table 31 Strength of plate to AS/NZS 3678 Grade 250 .....................................80 Table 32A Universal beams, Grade 300— Design section moment and web capacities...............................91 Table 32B Parallel flange channels, Grade 300—Design section moment and web capacities ..........91 Table 32C Welded beams, Grade 300— Design section moment and web capacities...............................92 Table 33A Single web coped universal beams, Grade 300—Design section moment and shear capacities ......................................99 Table 33B Single web coped parallel flange channels, Grade 300— Design section moment and shear capacities ..........................100 Table 34A Double web coped universal beams, Grade 300—Design section moment and shear capacities ....................................104 Table 34B Double web coped parallel flange channels, Grade 300— Design section moment and shear capacities ..........................104 Table 35 Universal beams rationalised dimensions for detailing...............110 Table 36 Universal columns rationalised dimensions for detailing...............110 Table 37 Welded beams rationalised dimensions for detailing...............111 Table 38 Welded columns rationalised dimensions for detailing...............111 Table 39 Parallel flange channels rationalised dimensions for detailing.......................................112 Table 40 Gauge lines for universal sections .......................................113 Table 41 Gauge lines for welded section flanges.........................................114 Table 42 Gauge lines for welded section webs............................................114 Table 43 Gauge lines for parallel flange channels......................................115


v

PREFACE This new series of connection publications by the Australian Institute of Steel (ASI) covering capacity tables, theory and design of individual simple connections will be known as the Structural Steel Connections Series, Part 1: 1 st ed. 2007 (“Connection Series, Part 1”). This Connection Series, Part 1 details the method of design and provides capacity tables and detailing parameters for a range of simple connections commonly used for structural steelwork in Australia. Connections have a major engineering and economic importance in steel structures influencing design, detailing, fabrication and erection costs. Standardisation of design approach integrated with industry detailing is the key to minimum costs at each stage. This Connections Series, Part 1 in conjunction with the future Connection Series, Part 2 for rigid connections (collectively the Structural Steel Connections Series or “Connection Series”) replaces and enhances an ASI flagship publication first released in 1978 at which time connection design theories were developed for the purpose of generating and releasing connection capacity tables. The first three editions were released in permissible stress format. The fourth edition Design of Structural Connections (often referred to as the Green Book) was released in 1994 in limit state format but there was no subsequent release of a limit state companion document containing connection design capacity tables. Handbook 1: Design of structural steel connections is the hub of a new Connections Series expanding and revising the elemental connection theory contained in previous editions of Design of Structural Connections. This has been achieved through extensive local and international literature reviews using ASI’s close association with like organisations and searching the wealth of material contained in the ASI Library facility (the largest in the Southern Hemisphere). This process consolidated industry best practice, references and research papers. Handbook 1 formulates the elemental equations and procedures for the assessment of bolts, bolt groups, welds, weld groups, connection components and supporting members in standardised structural connections. Dimensions and clearances for bolt installation have been revised and new theory for bolt groups loaded out-of-plane added. The new Connections Series format with separate design guides for individual connection types is intended to facilitate addition to or revision of connection model theory using relevant new local or international research as deemed appropriate by the ASI. Connection models developed using the Handbook 1 theory follow a stylised page format with a numbered DESIGN CHECK procedure to simplify connection capacity assessment. This Connection Series, Part 1 also revises the third edition of Bolting of steel structures in Design Guide 1 now known as Bolting in structural steel connections. Another important design guide (Design Guide 2) has been specifically developed called Welding in structural steel connections. Design Capacity Tables V3: Simple Connections – Open Sections consolidates design capacity tables contained in the individual connection design guides (specifically Design Guide 3: Web Side Plate, Design Guide 4: Flexible End Plate and Design Guide 5: Angle Cleat Connections) and is known as the Design Capacity Tables for Structural Steel V3, Simple Connections (“Simple Connection DCTs V3). Engineering Systems has worked closely with the ASI to further develop Limcon as the companion program for this new Connection Series. The latest version of Limcon (V3.5) fully implements the new connection design models and was employed in checking the design tables. The Limcon output for one or more of the worked examples is included in an appendix to each design guide for each connection design type. The program is an efficient tool covering the full range of structural connections, including those beyond the scope of capacity tables provided in the Connection Series. An appendix to each publication in the series also contains an ASI comment form. Users of this Connections Series are encouraged to photocopy this one page form and forward any suggested improvements which may be incorporated into future editions.

T.J. Hogan S.A. Munter


vi

ABOUT THE AUTHOR Tim Hogan is Director of SCP Consulting Pty Ltd. His academic achievements include a Bachelor of Engineering from the University of NSW with 1st Class Honours and the University Medal. Post graduate qualifications include a Master of Engineering Science and a Master of Business Administration. Tim is a Member of the Institution of Engineers Australia with CPEng and FIE Aust. status. His early experience was on bridge design and construction with the NSW Public Works Department and subsequently as Development Engineer and then Engineering Manager with the Australian Institute of Steel Construction until 1980. Consulting experience with SCP Consulting since 1980 has included design and supervision of large steel framed buildings, industrial buildings, mill buildings, retail developments, defence infrastructure and composite steel-concrete buildings. His published works deal primarily with the areas of composite construction, steel connections, fabrication and erection of steel structures and he was a major contributor and editor of the Commentary to AS 4100. He is a member of a number of Standards Australia Committees dealing with steel and composite structures and is currently Chairman of Committee BD-001 Steel Structures and BD-032 Composite Construction. He received an award from Standards Australia for his contributions to writing of Australian Standards.

ABOUT THE CONTRIBUTING AUTHOR AND EDITOR Scott Munter is now the National Structural Decking Manager for BlueScope Lysaght. He was formerly the National Manager—Engineering & Construction for the Australian Steel Institute (ASI) and worked in this role from 2000 to 2007. This key role involved setting the technical leadership of ASI in support of design and construction to enable the efficient specification and use of steel in construction. Responsibilities included ASI technical publications, advice on industry best practice, ASI and Code committees, presentations and lecturing. Scott is a Member of the Institution of Engineers Australia with CP Eng & NPER (Structural) status. He holds a Bachelor of Structural Engineering from the University of Technology, Sydney with 1 st Class Honours and the University Medal. His professional career includes 15 years in consulting civil and structural engineering working for Tim Hogan at SCP Consulting. His consulting experience includes a strong steel focus with major infrastructure, industrial and commercial developments plus domestic construction.


vii

ACKNOWLEDGEMENTS The authors would like to extend special thanks to: The ASI Connections Steering Ccommittee consisting of Richard Collins (Engineering Systems), Anthony Ng (OneSteel Market Mills), Arun Syam (Smorgon Steel Tube Mills) for their respective contributions with the development and review of the technical and editorial content of the revised ASI Connection Manual. Significant contributions were made by: •

Richard Collins—Engineering Systems in the development and upgrade of the Limcon software code in parallel with the design theory aiding in the editing and validation of the revised models.

•

Standards Australia for providing their technical typesetting expertise.

•

Whizzcad Pty Ltd with drafting and graphics for publishing.

•

ASI State Engineering & Construction Special engineering and industry review of manuscripts.

Sub-Committees

for

progressive

Together with support of: •

All facets of the ASI membership including design engineers, steelwork detailers and fabricators in contributing industry best practice and standards through ASI surveys and direct consultation to establish the theory and geometry in this new ASI Connection Manual.


viii

1

CONCEPT OF DESIGN GUIDES

1.1

Background

The ASI was formed in 2002 through the merger of Australian Institute of Steel Construction (AISC) and Steel Institute of Australia (SIA). The former AISC published a design manual giving guidance on the design of structural connections in steelwork (Ref. 2). ASI is updating Reference 2 by way of the Connection Series including design guides, dealing with connection parts and individual connection types. The overall series of connections publications will be known as the Connections Series. The former AISC also published a manual containing standardised detailing for simple connections, accompanied by load tables (Ref. 3). Wherever possible each design guide for individual connection types contains standardised detailing and design capacity tables for the connection type covered by that design guide derived using the design models in that design guide. The Connection Series is a specialist series devoted to the design of connections in structural steel in accordance with current Australian Standard AS4100 (Ref 1.), reflecting the current state of knowledge of connection behaviour from test results. In some instances, the test evidence is sparse and in other instances the evidence is contradictory or clouded. Each design guide in the Connection Series has been written by weighing the evidence to provide recommended design procedures based in part on the design procedures used in equivalent manuals and/or published papers. Each design guide is intended to provide a design model which gives a reasonable estimate of connection design capacity and effort has been expended in researching and developing design models which can be justified on the basis of the available research and current design practice. It is to be emphasised that for the connections model presented, the design model is not the only possible model. It is therefore not intended to suggest that other models may not result in adequate connection capacity and further reference is made to the Disclaimer on page ii of this publication as to the required investigation and verification by a competent professional person or persons in regards to the accuracy, suitability and applicability of the materials provided in this Connections Series. The connections dealt with are those presently in common use in Australia and reflect the types of connections covered within the earlier AISC Standardized Structural Connections (Ref. 3).


1

2

BACKGROUND DISCUSSION

2.1

General considerations

In structural steel connections, there are two fundamental considerations: (a)

the connection designer requires a realistic estimate of connection strength in order that a connection will be economical (not over-designed) and safe (design capacity exceeds design actions); and

(b)

the connection must be detailed in such a way that it is economic to fabricate and erect, while recognising that the connection detailing may have an important impact on the strength of the connection.

Any design model for assessing the strength of a connection must take account of the following four elements: (i)

the strength of the fasteners (bolts and welds);

(ii)

the strength of the connection components (plates, flat bars, angles, gusset plates);

(iii)

the strength of the connected member in the vicinity of the connection;

(iv)

the strength of the supporting member in the vicinity of the connection.

Codes for the design of steel structures primarily deal with member design as a whole, rather than specifically allowing for local effects, and provide only the basic information on fastener design. No code specifies a detailed design procedure for any type of connection, leaving the assessment of how a connection behaves and how its behaviour should be allowed for in design to the individual designer. This presents the designer with a considerable task considering the large number of different connection types that may be encountered, each requiring individual research and assessment. A series such as this seeks to assist the designer by providing guidance in order to reduce the task considerably.


2

2


2.2

Forms of construction

AS 4100 allows for three forms of construction which relate to the behaviour of the connections. It then requires that the design of the connections be such that the structure is capable of resisting all design actions, calculated by assuming that the connections are appropriate to the form of construction of the structure or structural part. The design of the connections required is to be consistent with the form of construction assumed. The three forms of construction are: Rigid construction—For rigid construction, the connections are assumed to have sufficient rigidity to hold the original angles between the members unchanged. The joint deformations must be such that they have no significant influence on the distribution of the action effects nor on the overall deformation of the frame. Semi-rigid construction—For semi-rigid construction, the connections may not have sufficient rigidity to hold the original angles between the members unchanged, but are required to have the capacity to furnish dependable and known degree of flexural restraint. The relationship between the degree of flexural restraint and the level of the load effects is required to be established by methods based on test results. Simple construction—For simple construction, the connections at the ends of members are assumed not to develop bending moments. Connections between members in simple construction must be capable of deforming to provide the required rotation at the connection and are required to not develop a level of restraining bending moment which adversely affects any part of the structure. The rotation capacity of the connection must be provided by the detailing of the connection and must have been demonstrated experimentally. The connection is then required to be considered as subject to reaction shear forces acting at an eccentricity appropriate to the connection detailing. Examples of rigid connections include (Figure 1): —welded moment connection —bolted moment end plate —moment splice (bolted or welded) —moment transmitting base plate. Examples of simple connections include (Figure 2): —angle seat —bearing pad —flexible end plate —angle cleat —web side plate or fin plate.


3

FIGURE 1 RIGID CONNECTIONS


4

FIGURE 2 SIMPLE CONNECTIONS


5

2


2.3

Connection design models

Clause 9.1.3 of AS 4100 (Ref. 1) nominates the basic requirements that any design model must have for the design of a steel connection if the design model is to be acceptable. These requirements are as follows: ‘Each element in a connection shall be designed so that the structure is capable of resisting all design actions. The design capacities of each element shall be not less than the calculated design action effects. Connections and the adjacent areas of members shall be designed by distributing the design action effects so that they comply with the following requirements: (a)

The distributed design action effects are in equilibrium with the design action effects acting on the connection.

(b)

The deformations in the connection are within the deformation capacities of the connection elements.

(c)

All of the connection elements and the adjacent areas of members are capable of resisting the design action effects acting on them.

(d)

The connection elements shall remain stable under the design action effects and deformations.

Design shall be on the basis of a recognised method supported by experimental evidence. Residual actions due to the installation of bolts need not be considered.’ The onus is placed on the structural steel designer to ensure that the actual behaviour of a connection does not have a deleterious effect on the members of the steel frame and that the connection conforms to the requirements specified in AS 4100 (Ref. 1). AS 4100 attempts to correct for the difference between assumed and real behaviour only in the case of simple construction. AS 4100 recognises that real simple connections will actually transmit some bending moment as well as the shear force for which such connections are designed (see Section 2.4). These bending moments are conservatively neglected in proportioning the beams, since their magnitudes are at present not reliably known, but they are accounted for in proportioning the columns through the application of AS 4100 Clause 4.3.4, which requires the line of action of a beam reaction to be taken at 100 mm from the face of the column towards the span, or at the centre of bearing, whichever is the greater. Thus all building columns in practice become beamcolumns, being designed for at least this minimum level of bending moment from a connection. Note that loss of rigidity in real ‘rigid’ connections will cause a redistribution of bending moments in a frame which may adversely affect some members (see Section 2.4).


6

2


2.4

Connection characteristics

Figure 3 illustrates typical moment-rotation characteristics for a variety of both ‘simple’ and ‘rigid’ connections. It is clear from this figure that no connection is either fully rigid (vertical axis) or truly pinned (horizontal axis) and it is also apparent that whether a connection is ‘rigid’ or ‘simple’ may well depend on the rotation which is imposed on it by the supported member. Although no connections are ideal pins, all of the typical simple connections would be suitable for simple design within the meaning of Clause 4.2 of AS 4100. Connections connect a ‘member’ to a ‘support’. In the case of simple connections, supports may be considered to be ‘flexible’ or ‘stiff’, in the extreme. In practice, no support is purely ‘flexible’ (i.e. all beam end rotation is accommodated by movement of the support) nor purely ‘stiff’ (i.e. all beam end rotation is accommodated by deformation within the connection), but rather lies somewhere between the two extremes.

FIGURE 3 MOMENT ROTATION CHARACTERISTICS OF TYPICAL CONNECTIONS In a true flexible support situation, the laws of statics demand that the bolt or weld groups and the connection components must resist the full effect of the bending moment and shear at the position of the connection. The bending moment at the support is a function of the stiffness and strength of the support and of the supported member, the detailing and strength of the bolt and weld groups, and the stiffness and strength of the connection components. Significant rotation may take place in the bolt group or in the connection components. There are two extremes of design approach possible with a stiff support situation: (a)

maintain a significant stiffness and strength throughout all elements of the connection;

(b)

arrange that some element of the connection is rotationally flexible (while not impairing the load carrying capability of the connection). handbook 1 design of structural steel connections, first edition

7

It is generally assumed that the angle seat, bearing pad, flexible end plate and the angle cleat connections can be detailed into category (b). It is, however, necessary in dimensioning the components for these connections to ensure that as much flexibility as possible is achieved. Making the ‘flexible’ component too stiff places unnecessary rotation requirements and bending moments on the other components and the support. The web side plate connection nominally seems to fit into category (a). The weld is stiff and possesses little ductile rotational capacity. The plate may be capable of significant rotation if a plastic hinge can form in it. The bolt group is also capable of significant rotation and tests suggest that most of the rotation occurs in the bolt group. Obviously, where the rotation occurs is a function of the relative stiffnesses and strengths of the components, and their interactions. A further complication is that it is possible to have two extremes of behaviour with a simple connection attached to a stiff support: (a)

rotation capacity provided directly adjacent to the support (flexible end plate, flexible angle cleat);

(b)

rotation capacity provided at a distance from the support (angle seat, web side plate).

Note that case (b) requires that the support and the components between the hinge and the support always be subject to bending moment as well as shear force. Using the recommended design models for simple connections in relevant Design Guides of this Manual, the possibility of either a stiff or a flexible support is accounted for in the formulation of the design model. Another observation also should be made. In determining the design model to be adopted for a simple or rigid connection, the detailing practice, the effect of tolerances and the magnitude of the design capacities of connection elements must all be considered. Connection detailing practice differs between countries, as do the tolerances on the lengths of members, the tolerances on the positioning of members and the design capacities in many of the connection elements. These factors may alter the significance of some aspects of any design model and consequently different design models may be appropriate in different countries. These factors can also create problems with the analysis of results from much of the research data, as the failure loads of the connection are often compared with the relevant design capacities of the time rather than being compared with the measured strength of the individual components within the connection. It is very important to note that virtually all of the reported testing of simple connections has been carried out in the stiff support situation. This is of some significance in assessing the results and the reported connection behaviour, and is another reason why there is no distinction in any of the Design Guides of this Manual between a stiff and a flexible support condition in the recommended design models for any simple connection. This Manual meets the requirements of AS 4100 by providing a rational and recognised design model for a range of common steel connections, each design model reflecting engineering principles and known connection behaviour from experimental data in each Design Guide. The emphasis in this Manual is on practical design models whose assumptions are transparent to the user. The model in each Design Guide is related to current codes of Standards Australia in respect of member and fastener design, and member and fastener mechanical properties, which are presented in this Design Guide. The philosophy of the Manual is the same as that espoused in Reference 4, being as follows: (i)

take into account overall connection behaviour, carry out an appropriate analysis in order to determine a realistic distribution of forces within the connection;

(ii)

ensure that each component or fastener in each action path has sufficient capacity to transmit the applied action;

(iii)

recognise that this procedure can only give a connection where equilibrium is capable of being achieved but where compatibility is unlikely to be satisfied, and therefore ensure that the connection elements are capable of ductile behaviour.


8

Connections are considered in the Manual and in AS 4100 to consist of the following connection elements: (A)

fasteners (bolts or welds);

(B)

components (plates, gussets, cleats);

(C)

supported members;

(D)

supporting members,

all of whose design capacities must be evaluated in order to estimate the design capacity of a connection. This Guide deals with the design capacity of these elements as isolated elements so that the formulae derived can be used in later Guides concerned with individual connections. The design models contained within this Manual are considered to be applicable only to connections which are essentially statically loaded. Connections subject to dynamic loads, earthquake loads or fatigue applications may require additional considerations.


9

3

BOLTS AND BOLT GROUPS

3.1

Bolt types and bolting categories

In Australia a standard bolting category identification system has been adopted in AS 4100 for use by designers and detailers. This system is summarised in Table 1. TABLE 1 BOLT CATEGORY IDENTIFICATION SYSTEM Details of bolt used Property class

Min. bolt tensile strength (MPa)

Min. bolt yield strength (MPa)

4.6/S

4.6

400

240

Commercial bolt

8.8/S

8.8

830

660

High strength AS/NZS 1252 Structural (Ref. 6) Bolt

Bolts are used Snug tightened. Now the most common procedure used in simple connections in Australia.

8.8/TF

8.8

830

660

8.8/TB

8.8

830

660

High Strength Structural Bolt—Friction type AS/NZS 1252 connection (Ref. 6) High strength Structural Bolt— Bearing type connection

In both applications, bolts are fully Tensioned to the requirements of AS 4100. Cost of tensioning is an important consideration in the use of these bolting procedures.

Bolting category

8.8/T

Bolt name

Australian Standard AS 1111.1 (Ref. 5)

Remarks

Least costly and most commonly available is Grade 4.6 bolt. Use Snug tightened.

The use of the various bolting categories is discussed in Reference 7 while the appropriate bolting category for each connection type is identified in the Design Guide for that connection type. Generally, bolting categories 4.6/S and 8.8/S are used in simple connections while category 8.8/TB is used in rigid connections and bolted splices. Category 8.8/TF is recommended only for use in connections where a no-slip connection under serviceability loads is essential. 8.8/TF is the only bolting category which requires consideration of the condition of the contact surfaces in a bolted connection. Design drawings and shop detail drawings should both contain notes summarising Table 1. The dimensions of bolts conforming to AS 1111.1 may be found in Table 2, while the dimensions of bolts conforming to AS/NZS 1252 may be found in Table 3. These dimensions are required for checking clearances in connections. Connections also require detailing so that there is sufficient clearance for wrenches used to tighten the nut. Clearances for three common types of wrench are given in Table 4. The mechanical properties of bolts specified in AS 1111.1 and AS/NZS 1252 are given in Tables 5 and 6. A more detailed discussion of bolting generally may be found in Design Guide 1 (Reference 7).


10

3


3.2

Bolt dimensions

TABLE 2 DIMENSIONS OF COMMERCIAL BOLTS AND NUTS AS 1111.1 Bolts (Ref. 5), AS 1112.3 Nuts (Ref. 33) Bolt

Nut

Desig- Thread Shank Width Width Height Width nation pitch dia. across across of head across flats corners flats nom.

max.

min.

nom.

Width across corners

Washer Height of Outside Nominal normal dia. thickness nuts

max.

min.

max.

max.

M12

1.75

12

18

20

8

18

20

12

24

2.5

M16

2.0

16

24

26

10

24

26

16

30

3

M20

2.5

20

30

33

13

30

33

19

37

3

M24

3.0

24

36

40

15

36

40

22

44

4

M30

3.5

30

46

51

19

46

51

26

56

4

M36

4.0

36

55

61

23

55

61

32

66

5

TABLE 3 DIMENSIONS OF HIGH STRENGTH STRUCTURAL BOLTS AND NUTS AS/NZS 1252 (Ref. 6) Bolt

Nut

Desig- Thread Shank Width Width Height Width nation pitch dia. across across of head across flats corners flats nom.

max.

max.

max.

Width across corners

Washer Height of Outside Nominal normal dia. thickness nuts

max.

max.

max.

max.

nom.

M16

2.0

16

27

31

11

27

31

17

34

4

M20*

2.5

20

34

39

13

32

39

21

42

4

M24

3.0

24

41

47

16

41

47

24

50

4

M30

3.5

30

50

58

20

50

58

31

60

4

M36

4.0

36

60

69

24

60

69

37

72

4

*NOTE: At the time of developing this design guide M20 high strength structural bolts and nuts are still typically being supplied in Australia with dimensions complying to AS 1252—1983 despite this code being superseded by the ISO aligned standard AS/NZS 1252:1996. The 1996 Standard specified a new across flat (AF) dimension of 34 mm for M20 bolts compared to 32 mm specified in the 1983 Standard. The dimensions listed in Table 3 are in accordance with the current 1996 standard. International manufacturers have been reluctant to adopt the ISO AF sizes. Australian suppliers of structural bolts are typically ordering the mechanical properties to AS/NZS 1252:1996.

M

Used in this guide to designate metric bolts with thread complying with AS 1275.


11

3


3.3

Dimensions of wrenches for installing bolts

TABLE 4 DIMENSIONS OF WRENCHES FOR DETERMINING ERECTION CLEARANCES DIMENSIONS OF OPEN ENDED WRENCHES ISO 3318 (Ref. 34) CLEARANCES—4.6/S CATEGORY Nom. bolt dia. 12 16 20 24 30 36

AF

Clearance X max.

(mm)

(mm)

18 24 30 36 46 55

45 57 70 83 104 123

CLEARANCES—8.8/S CATEGORY AF

Clearance X max.

(mm)

(mm)

27 34 41 50 60

64 78 93 112 133

Nom. bolt dia. 16 20 24 30 36

DIMENSIONS OF SOCKETS—HAND WRENCHES ISO 2725-1 (Ref. 35) CLEARANCES—8.8/TF AND 8.8/TB CATEGORIES Sockets* 20 mm drive

Clearance

C max. (Normal)

C min. (Long)

D max.

E

(mm)

(mm)

(mm)

(mm)

16

60

85

40

25

20

65

85

48.3

30

24

70

85

57.1

35

Nom. bolt dia.

*Bolt diameters above M24 cannot be tensioned with a hand wrench.

Please Note: Australian rigging crews can interchange between metric, UNC and imperial sockets for erection of steelwork. This factor combined with the numerous global manufacturers of erection equipment of both high and low quality makes the task of locking in exact equipment dimensions from suppliers virtually impossible. Dimensions for open ended wrench clearances and all sockets have been tabulated from the nominated International Standards (ISO). All other equipment dimensions are supplied as a guide only from supplier specifications. Sockets meeting M20 AS/NZS 1252:1996 may be in limited supply in Australia and not available across all ranges for reasons noted at Table 3.


12

TABLE 4 (continued) DIMENSIONS OF WRENCHES FOR DETERMINING ERECTION CLEARANCES DIMENSIONS OF IMPACT WRENCHES ISO 2725-2 (Ref. 36) CLEARANCES—8.8/TF AND 8.8/TB CATEGORIES Impact wrench type Normal wrenches Heavy wrenches

B (mm)

A (mm)

to 370 some to 600

55 65

Sockets 20 mm drive

Clearance

Nom. bolt dia.

C

D

E

(mm)

(mm)

(mm)

16

54

48

30

20

57

58

35

24

58

61.1

35

Sockets 25 mm drive

Clearance

Nom. bolt dia.

C

D

E

(mm)

(mm)

(mm)

16

60

58

35

20

63

58

35

24

70

68

40

Please Note: Australian rigging crews can interchange between metric, UNC and imperial sockets for erection of steelwork. This factor combined with the numerous global manufacturers of erection equipment of both high and low quality makes the task of locking in exact equipment dimensions from suppliers virtually impossible. Dimensions for open ended wrench clearances and all sockets have been tabulated from the nominated International Standards (ISO). All other equipment dimensions are supplied as a guide only from supplier specifications. Sockets meeting M20 AS/NZS 1252:1996 may be in limited supply in Australia and not available across all ranges for reasons noted at Table 3.


13

3


3.4

Bolt mechanical properties

TABLE 5 METRIC HEXAGON COMMERCIAL BOLTS

STANDARD SPECIFICATION: PROPERTY CLASS: NORMAL METHOD OF MANUFACTURE: MECHANICAL PROPERTIES:

MOST COMMONLY USED SIZES: TENSILE AND PROOF LOADS:

AS 1111.1 (Ref. 5) 4.6 Hot or cold forging (generally cold) Tensile strength 400 MPa (nom. and min.) Yield stress 240 MPa (min.) Stress under proof load 225 MPa (min.) M12, M16, M20, M24, M30, M36 Tensile Minimum Proof load Designation stress area breaking load (mm 2 ) (kN) (kN) M12 84.3 33.7 19.0 M16 157 62.8 35.3 M20 245 98.0 55.1 M24 353 141 79.4 M30 561 224 126 M36 817 327 184 NOTE: Elongation after fracture = 22% min. Hardness = 114 HB min.

TABLE 6 HIGH STRENGTH STRUCTURAL BOLTS

STANDARD SPECIFICATION: PROPERTY CLASS: NORMAL METHOD OF MANUFACTURE: MECHANICAL PROPERTIES:

MOST COMMONLY USED SIZES: TENSILE AND PROOF LOADS:

AS/NZS 1252 (Ref. 6) 8.8 Hot or cold forging, hardened and tempered Tensile strength 800 MPa (nom.), 830 MPa (min.) Stress at perm. set 640 MPa (nom.), 660 MPa (min.) Stress under proof load 600 MPa (M16), M20, M24, (M30), (M36)/ ( )available but rarely used Tensile Minimum Proof load Designation stress area breaking load (mm 2 ) (kN) (kN) M16 157 130 94.5 M20 245 203 147 M24 353 293 212 M30 561 466 337 M36 817 678 490 NOTE: Elongation after fracture = 12% min. Impact strength = 30 J min. Hardness = 242 HB min.


14

3


3.5

Design requirements for bolts

AS 4100 is a design code written in limit state format, in which two limit states might require consideration in the design of bolted connections: STRENGTH LIMIT STATE

(requires consideration for all bolted connections)

SERVICEABILITY LIMIT STATE

(requires consideration only for that class of connections which are required not to slip under serviceability loads)

A commentary on AS 4100 is found in Reference 8. In any bolted connection, there are three modes of force transfer to be considered, these modes being: (a)

shear/bearing mode where the forces are perpendicular to the bolt axis and are transferred by shear and bearing on the bolt and bearing on the ply material;

(b)

friction mode where the forces are perpendicular to the bolt axis but are transferred by frictional resistance between the mating surfaces, the frictional resistance being improved by applying an initial clamping force;

(c)

axial tension where the forces to be transferred are parallel to the bolt axis.

Most connections have bolts which transfer load in the shear/bearing mode, with the exception of the bolted moment end plate and the column base plate in which the bolts can be subject to both shear force and axial tension. A bolt in shear/bearing mode (bolting categories 4.6/S, 8.8/S and 8.8/TB) bears against the sides of the bolt holes and load is transferred by shear in the bolts and bearing on the connected plies. The shear strength of the bolt is affected by the strength of the bolt material and by the available bolt area across the shear plane. Consequently, the situation of whether plain shank or thread intercepts the shear plane affects the strength of the connection, as discussed in detail in Reference 7. In practice, it is very difficult to ensure that threads are excluded from the shear plane in many practical connections for reasons discussed in Reference 7, since the practice requires that the erector install a bolt of the correct minimum length into the bolt hole and the practice often leads to bolts of excessive length. Most connections—especially the simple connections—are designed on the assumption that threads will be included in the shear plane, as this assumption most accurately reflects the field situation and is a conservative basis for design. The failure in the connected plies may occur in one of two ways: (i)

local bearing failure;

(ii)

tear-out failure of the plies behind a bolt.

Local bearing type failures involve a piling up of ply material in front of the hole around the bolt shank, either the plain shank or threaded length. End plate tear-out failure occurs in connections in which the end distance (ae1 or a e2 in Figure 4) falls below 3.2 times the bolt diameter, the end distance representing the length of ply which must fail in shear for failure of the connected ply to occur. The end distance is defined in AS 4100 as ‘the minimum distance from the edge of a hole to the edge of a ply in the direction of the component of force plus half the bolt diameter.’ Plate tear-out type failures are observed in joints subject to a force which acts towards a free edge.


15

Defining— dh

= hole diameter = df + 2 mm

df

= bolt diameter

sp

= bolt pitch

ae

= distance from hole edge to an edge in the direction of a component of force plus half the hole diameter

Since the end distance is defined from the hole edge and the hole is usually 2 mm larger than the bolt diameter then: a e1 = (a e – 1 mm) a e2 = (sp – 0.5d h – 1 mm)

FIGURE 4 END PLATE TEAR-OUT FAILURE EDGE DISTANCES Note that an edge may not only mean the physical edge of a connection component or a beam web or flange, but may also include the edge of an adjacent hole (see Figure 4), which reflects the fact that plate tear-out is theoretically possible between holes, although in practice bolt centres are such that it is normally not observed. In many cases, the end tear-out mode is relatively straightforward, as in Figure 4 or Figures 5 and 6. However, in bolt groups components of force may act in many directions if the bolt group is subject to an in-plane moment. It is to be remembered that end tear-out design requirements apply to connection components, connected members and supporting members as appropriate, each of which will have a different end distance and ply thickness.

FIGURE 5 END PLATE TEAR-OUT FAILURE FORCE COMPONENTS

FIGURE 6 END PLATE TEAROUT, SIMPLE CASE


16

3


3.6

AS 4100 Design requirements— Strength limit state

The strength limit state design provisions which apply for static load applications are found in Clause 9.3.2 of AS 4100. These provisions are summarised in Table 7. TABLE 7 AS 4100 CLAUSE 9.3.2 PROVISIONS, STRENGTH LIMIT STATE, STATIC LOADS Limit state Bolt in shear

AS 4100 Clause 9.3.2.1

Design requirement

Vf

*

≤

φV f

V f* = design shear force Vf

= nominal capacity in shear = 0.62 f uf k r A v

φ

= capacity factor = 0.8

f uf

= minimum tensile strength of bolt (Tables 1, 5, 6) = 400 MPa Property Class 4.6 to AS 1111.1 (Ref. 5) = 830 MPa Property Class 8.8 to AS/NZS 1252 (Ref. 6)

kr

= reduction factor for bolted lap splice connections. For all other connections, k r = 1.0.

Av

= available bolt shear area. For a single bolt with single shear plane, threads included, A v = A c core area. For a single bolt with single shear plane, threads excluded, A v = A o shank area.

Bolt in tension

9.3.2.2

N tf* ≤ φN tf N tf* = design tension force N tf

= nominal capacity in tension = A s f uf

φ


As

= tensile stress area

Bolt in shear and 9.3.2.3 tension

⎡ V f * ⎤ 2 ⎡ N tf* ⎤ 2 ⎥ ≤ 1. 0 ⎥ +⎢ ⎢ ⎣⎢ φV f ⎥⎦ ⎣⎢ φN tf ⎥⎦

Ply in bearing

Vb* ≤ φV b Vb* = design bearing force on a ply

9.3.2.4

Vb

= nominal capacity of ply in bearing

Vb

≤

3.2 d f t pf up (local failure in bearing)

≤

a e t p f up (tear-out failure)

φ


df

= bolt diameter

tp

= thickness of the ply

ae

= minimum distance from the edge of a hole to the edge of a ply in the direction of the component of force plus half the bolt diameter

f up

= tensile strength of the ply

Note—Filler plates: Where filler plates exceed 6 mm but are less than 20 mm in total thickness, the nominal shear capacity Vf specified in Table 7 is required by Clause 9.3.2.5 of AS 4100 to be reduced by 15%. Filler plates greater than 20 mm in total thickness should not be used as no design guidance is available in AS 4100. handbook 1 design of structural steel connections, first edition

17

Design areas of bolts Bolted connections subject to shear may be either installed with the threads of the bolt crossing the shear plane or with the plain shank of the bolt crossing the shear plane. The alternative arrangements are discussed in Reference 7. In a joint with a number of shear planes, some shear planes may cross the threaded part of the bolt while other shear planes may cross the shank. Clause 9.3.2.1 of AS 4100 recognises that the strength of the bolt across any shear plane is dependent upon the available shear area of the bolt at that plane. It allows for all possible combinations by defining the shear area as: Av

= available bolt shear area = n n Ac + n x Ao

where: Ac

= core area (see Table 8)

Ao = plain shank area (see Table 8) nn

= number of shear planes with threads intercepting the shear plane

nx

= number of shear planes with shank intercepting the shear plane

Usually either: n n = 1 and nx = 0 when there are two plies and threads intercept the shear plane (thus giving Av = A c) OR n n = 0 and nx = 1 when there are two plies and the shank intercepts the shear plane (thus giving Av = A o). The core area and plain shank area for bolt diameters commonly used are given in Table 8. Also given in Table 8 is the tensile stress area used when bolts are subject to tension. TABLE 8 DESIGN AREAS OF BOLTS Nom. dia. (mm)

Areas (mm 2 )

Designation A c core

df

76.2

A s tensile stress 84.3

A o shank

12

M12

16

M16

144

157

201

20

M20

225

245

314

24

M24

324

353

452

30

M30

519

561

706

36

M36

759

817

1016


113

18

TABLE 9 STRENGTH LIMIT STATE COMMERCIAL BOLTS 4.6/S BOLTING CATEGORY (f uf = 400 MPa, φ = 0.8) Designation

Axial tension

Shear values (single shear)

φN tf

Threads included in shear plane—N φV fn

Threads excluded from shear plane—X φV fx

kN

kN

kN

M12

27.0

15.1

22.4

M16

50.2

28.6

39.9

M20

78.4

44.6

62.3

64.3

89.7

M24

113

M30

180

103

140

M36

261

151

202 φ = 0.8

φ = 0.8 4.6N/S

4.6X/S

NOTE: Bearing/Plate tear-out design capacity. For all reasonable combinations of ply thickness, bolt diameter and end distance, the design capacity for a ply in bearing (φV b ) exceeds both φV fn and φV fx, and does not control design.

SHEAR–TENSION INTERACTION DIAGRAM


19

TABLE 10 STRENGTH LIMIT STATE HIGH STRENGTH STRUCTURAL BOLTS 8.8/S, 8.8/TB, 8.8/TF BOLTING CATEGORIES (f uf = 830 MPa) Desig- Axial nation tension

Single shear

Plate tear-out in kN

Bearing in kN

Threads Threads included in excluded from shear shear plane X plane N

φV b for t p and a e of:

φV b for t p

tp = 6

tp = 8

t p = 10

t p = 12

6

8

10

φN tf

φV fn

φV fx

kN

kN

kN

M16

104

59.3

82.7

113 151 189

M20

163

92.6

129

78 89 100 103 118 133 129 148 166 155 177 199 142 189 236

M24

234

133

186

170 227 283

M30

373

214

291

213 283 354

35 40

45

35

40

45

35

40

45

35

40

45

a e
φ = 0.8 8.8N/S

8.8X/S

φ = 0.9

φ = 0.9

f up =410 MPa

f up =410 MPa

NOTE: The above table lists the design capacity of a ply in bearing for Grade 250 (f up = 410 MPa) plate only. For design capacities for ply failure in other grades of steel, multiply the above values by the ratio of the actual f up to 410 MPa.

SHEAR–TENSION INTERACTION DIAGRAM


20

Lap splice connections

FIGURE 7 LAP JOINT AND BRACE/GUSSET CONNECTION For lap splice connections of the type shown in Figure 7 in which the bolts are in shear/bearing mode, theoretical and experimental studies have shown that the measured strength of the connection is affected by the length of the connection. Conventional theories of bolted lap splice connection design assume that rigid plate theory applies and that all bolts in the connection are equally loaded. However, studies show that the longer the connection is, the less uniform is the load distribution among the bolts in the connection while the behaviour is elastic. As a connection is loaded so that yielding of the plies or bolts or both occur, plastic deformations permit a redistribution of load resulting in a more uniform load distribution—if the redistribution proceeds without premature failure of either bolts or plies. Some connections may be so long that redistribution does not completely occur. AS 4100 Clause 9.3.2.1 uses a reduction factor k r to account for this effect, and the expression for k r is given in Table 11. The source of the expression used is explained in Reference 8. Connections affected by the requirement for lap splice connections and for which k r may not be taken as 1.0 without calculation using Table 11 are: (a)

bracing cleat (unusually long connections, relatively rare);

(b)

bolted flange splice.

For all other connections, generally k r = 1.0. Values of k r for various bolt pitches and numbers of bolts in a line are given in Table 11.


21

TABLE 11 REDUCTION FACTOR FOR LAP CONNECTIONS (k r) Length

L j < 300

300 ≤ L j ≤ 1300

L j > 1300

1.0

1.075–L j /4000

0.75

mm kr

VALUES OF k r FOR VARIOUS BOLT PITCHES Pitch

Values of k r for n of

sp

4

5

6

7

8

9

65

1.0

1.0

0.994

0.978

0.961

0.945

70

1.0

1.0

0.988

0.970

0.953

0.935

75

1.0

1.0

0.981

0.963

0.944

0.925

80

1.0

0.995

0.975

0.955

0.935

0.915

85

1.0

0.990

0.969

0.948

0.926

0.905

90

1.0

0.985

0.963

0.940

0.918

0.895


22

3


3.7

AS 4100 design requirements— Serviceability limit state

General Under certain conditions, a bolted connection which does not slip under the serviceability shear force may be specified. This type of connection is known as a friction-type joint and employs the 8.8/TF bolting category. The no slip requirement applies for the serviceability limit state—it would be totally unrealistic to have no slip for the strength limit state—though a separate check is also required by AS 4100 for the strength limit state, under the assumption that slip has occurred before this state is reached. The design requirements of AS 4100 for 8.8/TF bolting category are summarised in Table 12. With the bolt hole clearances permitted by AS 4100, the maximum amount of slip that can occur with a single bolt in a single hole is 2–3 mm. In actual connections, as the number of bolts in a connection increases, so the potential for slip decreases since the normal inaccuracies in fabrication and erection mean that some bolts in the connection are most likely to be in bearing mode even before the connection is loaded in shear. Slip under the applied shear force only needs to be restricted where such slip affects the serviceability or behaviour of the structure. Such instances are rare and are mostly restricted to cases of continually reversing loading or fatigue loading. Design parameters Initial bolt tension There can be considerable variation in the level of bolt tension possible, unless control is exercised over the bolt installation procedure. The procedures within Section 15 of AS 4100 for bolt installation are intended to ensure that a reliable level of installed bolt tension is achieved so that the design provisions against slip under the serviceability shear force are themselves reliable. Hole types Different hole types—round, short slotted, long slotted and oversize—are permitted by Section 14 of AS 4100. All of the hole types, except the standard round hole with 2–3 mm clearance, may cause a loss of clamping force in the vicinity of the bolt because of loss of area due to the bigger hole. The clamping force is highly localised around the hole and any loss of hole area has a significant effect on the tension achieved, which in turn affects the slip resistance at the interface. The factor for different hole types, k h, is intended to compensate for this effect, and varies from 0.70 to 1.00 according to hole type (see Table 12). Contact surface condition The value of the slip factor, μ, is highly dependent on the condition of the contact or faying surfaces. This slip factor should be determined using a test procedure as laid down in Appendix J of AS 4100. The slip factor used in AS 4100 for bare steel surfaces is 0.35.


23

TABLE 12 AS 4100 CLAUSE 9.3.3 PROVISIONS SERVICEABILITY LIMIT STATE—STATIC LOADS Limit state Bolt in shear

AS 4100 Clause 9.3.3.1

Design requirement Vsf* * sf

≤

φV sf

V

= design shear force—serviceability limit state

φ


V sf

= nominal shear capacity—serviceability limit state = μn ei N ti k h

μ

= slip factor = 0.35 for clean as-rolled surfaces or as determined by testing in accordance with Appendix J of AS 4100

n ei

= number of effective interfaces

N ti

= minimum bolt tension at installation (see Table 13)

kh

= factor for different hole types = 1.0 for standard holes = 0.85 for oversize holes = 0.85 for short slotted holes

for the hole dimensions permitted by AS 4100

= 0.70 for long slotted holes Bolt in shear and tension

9.3.3.3

⎡ Vsf* ⎤ ⎡ N tf* ⎤ ⎢ ⎥+⎢ ⎥ ≤ 1 .0 ⎣ φVsf ⎦ ⎣ φN tf ⎦ N tf* = design tension force—serviceability limit state

N tf = nominal tension capacity of the bolt = N ti (see Table 13)


24

TABLE 13 SERVICEABILITY LIMIT STATE HIGH STRENGTH STRUCTURAL BOLTS 8.8/TF BOLTING CATEGORY Slip factor, μ = 0.35 Number of effective interfaces, n ei = 1 Capacity factor, φ = 0.7—for bolt serviceability limit state

Designation

N ti , bolt tension at installation

φN tf = φN ti

kN

kN

M16

95

M20

145

M24 M30

66.5

φV sf = Design capacity in shear (kN) for kh = 1

k h = 0.85

k h = 0.7

Standard holes

Oversize holes short slotted holes

Long slotted holes

23.3

19.8

16.3

101

35.5

30.2

24.9

210

147

51.5

43.7

36.0

335

234

82.1

69.8

57.5

NOTE: N ti is given in Clause 15.2.5.1 of AS 4100.

SHEAR–TENSION INTERACTION DIAGRAM k h = 1.0


25

3


3.8

Geometric requirements of AS 4100 for bolted connections

Minimum edge distance Minimum edge distances from the centre of a bolt hole to the edge of a plate or the flange of a rolled section are specified in AS 4100 as follows: 1.75 d f for sheared or hand flame cut edges 1.50 d f for machine flame cut, sawn or planed edges 1.25 d f for rolled edges or rolled sections —where d f is the nominal diameter of the fastener. Table 14 lists these minimum edge distances for commonly used bolt diameters. TABLE 14 MINIMUM EDGE DISTANCES Nominal diameter of fastener d f

Sheared or hand flame cut edge

Rolled plate; machine flame cut, sawn or planed edge

Rolled edge of a rolled section

mm

mm

mm

mm

12

21

18

15

16

28

24

20

20

35

30

25

24

42

36

30

30

53

45

38

36

63

54

45

Maximum edge distance AS 4100 specifies the maximum edge distance from the centre of a bolt to the nearest edge. This is limited to 12tp or 150 mm, whichever is the lesser, where tp is the thickness of the thinner outer ply. Minimum pitch of bolts Minimum pitch of bolts is specified in AS 4100 to be 2.5 times the nominal diameter of the bolt. However, if it is intended to tension bolts with a special tensioning tool, the minimum distance between the centres of bolt holes shall be appropriate to the type of tool used (Table 4). Maximum pitch of bolts Maximum pitch of bolts is stipulated in AS 4100 to be the lesser of 15tp and 200 mm where tp may be taken as the thickness of the thinner outside ply. However, in the following cases the maximum distances are required to be: (a)

For fasteners which are not required to carry design actions in regions not liable to corrosion: the lesser of 32tp and 300 mm.

(b)

For an outside line of fasteners in the direction of the design force: the lesser of 4tp + 100 mm, and 200 mm.


26

Bolt holes The diameter of bolt holes in bolted connections is stipulated in AS 4100 to be larger than the bolt diameter by either: 2 mm for M24 bolts or smaller 3 mm for bolts larger than M24 6 mm for holes in base plates The large oversize holes permitted in base plates is to assist in column erection and is related to the out-of-position tolerance for anchor bolts permitted in AS 4100. In some applications, the use of slotted or oversize holes may be justified in order to ease erection difficulties. AS 4100 makes provision for the use of short and long slotted holes and oversize holes, and the detailed provisions for such holes are summarised in Table 15. TABLE 15 AS 4100 PROVISIONS FOR SLOTTED AND OVERSIZED HOLES (df = nominal bolt diameter) Hole type

Maximum size (mm) General

Short slotted

Long slotted

Oversize

Limitations

M20

M24

Width: d f + 2

22

26

Length: ≤1.33 d f or d f + 10 (whichever is the greater)

30

34

Width: d f + 2

22

26

Length: ≤2.5 d f

50

60

≤1.25 d f or ≤d f + 8 (whichever is the greater)

28

32

May be used in shear connections. In friction-type joints, slots may be used without regard to direction of loading. In bearing-type joints, slots must be normal to the direction of the load; bolts must bear uniformly; joint cannot be eccentrically loaded. May be used in any or all plies of both types provided hardened washers or plate washers are used under bolt head and nut. May be used in shear connections, but only in alternate plies. In friction-type joints, may be used without regard to direction of loading. In bearing-type joints, slots must be normal to the direction of the load; bolts must bear uniformly and the joint cannot be eccentrically loaded. Special washer or plate (≥8 mm thick) to cover all exposed long slotted holes. May be used in any or all plies of bearing-type and friction-type connections provided hardened washers or plate washers are installed over the oversize holes.


27

3


3.9

Bolt group loaded in-plane

AS 4100 Clause 9.4 specifies the assumptions which must be made when analysing any bolt group so that the design actions on individual bolts in the group may be determined. Clause 9.4.1 deals specifically with a bolt group subject to in-plane loading which generates only shear force on the bolts in the group. This Clause specifies that the design method to be used must comply with the following assumptions: (a)

The connection plates are considered to be rigid and to rotate relative to each other about a point known as the instantaneous centre of rotation of the bolt group.

(b)

In the case of a bolt group subject to a pure couple only, the instantaneous centre of rotation coincides with the bolt group centroid. In the case of a bolt group subject to an in-plane shear force applied at the group centroid, the instantaneous centre of rotation is at infinity and the design shear force is uniformly distributed throughout the group. In all other cases, either the results of independent analyses for a pure couple alone and for an in-plane shear force applied at the bolt group centroid shall be superposed, or a recognised method of analysis shall be used.

(c)

The design shear force in each bolt shall be assumed to act at right angles to the radius from the bolt to the instantaneous centre, and shall be taken as proportional to that radius.

FIGURE 8 BOLT GROUP SUBJECT TO IN-PLANE MOMENT * ) is applied, Clause For the situation shown in Figure 8 where only an in-plane torque (M bm 9.4.1(b) of AS 4100 nominates that the instantaneous centre of rotation coincides with the bolt group centroid. Noting that for bolt 'n':

sin θ n =

yn rn

cos θ n =

xn rn

equilibrium requires that:

∑V

xn =0 rn

(Eqn 3.9.1)

∑V

yn =0 rn

(Eqn 3.9.2)

* n

* n

∑V r

* n n

* = +Mbm

(Eqn 3.9.3)


28

FIGURE 9 BOLT GROUP SUBJECT TO SHEAR FORCES AT CENTROID For the situation shown in Figure 9 where both V *bv and V *bh act at the bolt group centroid, Clause 9.4.1(b) of AS 4100 gives the result: * Vv* (= design shear force on a bolt due to action V bv )=

Vbv* nb

(Eqn 3.9.4)

* Vh* (= design shear force on a bolt due to action V bh )=

Vbh* nb

(Eqn 3.9.5)

n b = number of bolts in bolt group For the general case of a bolt group loaded by vertical shear, horizontal shear, and an in-plane moment generated by the vertical shear force acting at an eccentricity (e) from the bolt group centroid, as in Figure 10, three equations can be generated which satisfy force and moment equilibrium.

FIGURE 10 BOLT GROUP SUBJECT TO A GENERAL LOAD SET

∑V ∑V ∑V

* n

cos θ n + Vbv* = 0

(Eqn 3.9.6)

* n

sin θ n − Vbh* = 0

(Eqn 3.9.7)

r + Vbv* (e − x e ) + Vbh* y e = 0

(Eqn 3.9.8)

* n n

In order to solve these equations for Vn* —the design shear force on bolt n —one further equation is required and the form of this equation depends on the analysis method used. Various methods of analysis have been proposed for bolt groups including the ‘linear’ or ‘elastic’ method, the ‘plastic’ and the ‘force/displacement’ or ‘elastic/plastic’ method. These can all be developed from the centre of rotation concept which forms the basis of Clause 9.4.1 of AS 4100.


29

Traditionally, design has been done using the elastic method of analysis, which is readily amenable to a closed-form solution and to hand calculations. Reference 8 notes that there is little benefit arising from the use of other methods of analysis. The relationship between the force on a bolt and the component displacement may be thought of that as shown in Figure 11. ‘The linear’ assumption assumes that the bolt force is linearly related to the displacement and has the advantage that it leads to a closed form solution which is not available with any other assumption. Typically, assumption (c) of Clause 9.4.1 of AS 4100 leads to a linear equation of the form F* (bolt force) = k × r where k is a constant and r is the distance from the centre of rotation to an individual bolt.

FIGURE 11 GRAPHICAL RELATIONSHIP—BOLT FORCE TO COMPONENT DISPLACEMENT Historically, rivet and bolt groups have been designed using the ‘linear’ (elastic) method and tests have indicated that the method is generally conservative. The ‘plastic’ method of analysis assumes that all bolts not at the centre of rotation are deformed sufficiently to become fully plastic and that all transmit the same force at the point of failure of the group. The method requires an iterative solution by computer, since it is not possible to solve Equations 3.9.6 to 3.9.8 explicitly. Other methods available (Ref. 10) have attempted to measure the relationship between the relative displacement of the connected components and the force developed on the bolt (this method is often termed displacement-compatibility). They then use this relationship in solving Equations 3.9.6 to 3.9.8. The method used to obtain a solution is again an iterative one, generally requiring the use of a computer to provide a satisfactory solution. The relationship between the relative displacement and the bolt force is dependent on a number of factors including (Ref. 10): (i)

the thickness of the connected components, and

(ii)

the yield strengths of these components.

Because much of the deformation which occurs in realistic cases is due to bearing failure of the connected material, a single definition of this relationship is really only suited to the application for which it was derived by tests. The AISC Manual (Ref. 9) now has design aids as well as rapid design methods available, particularly for routine bolt group configurations. * The method for bolt groups loaded by in-plane design action set ( Vbv* , Vbh* , Mbm ) in this Guide uses the linear method. The method was also used in Reference 2, and is used in a number of equivalent Manuals as either the primary method of analysis or as an alternative method (Reference 9). As Reference 9 notes, the load-deformation method is more accurate but requires tabulated values or an iterative solution while the linear method is simplified but conservative as it neglects the ductility of the bolt group and potential for load redistribution.


30

Using the linear method, Clause 9.4.1 (c) of AS 4100 relates the design shear force on any bolt * ) on the bolt furthest from the centre of rotation by the linear ( Vn* ) to the design shear force ( Vmb relationship Vn*

rn * Vmb rmax

=

(Eqn 3.9.9)

where: r max

= maximum value of r n

* mb

V is the value of interest for design being the design shear force on the extreme bolt which can be found by substituting Eqn 3.9.9 into Eqn 3.9.3 giving * Vmb rmax

∑r

2 n

* = Mbm

or * Vmb

=

* Mbm rmax rn2

∑

letting l bp

= (polar moment of area of bolt group)

∑r = ∑ (x =

2 n 2 n

+ y n2

)

then * Vmb

=

* Mbm rmax l bp

(Eqn 3.9.10)

* * * Vmb can be resolved into horizontal ( Vmh ) and vertical components ( Vmv )—as in Figure 12(a). * Vmh

y max * * y max * = M bm = Vmb sin θ max = Vmb r l bp max

(Eqn 3.9.11)

* Vmv

x max * * x max * = M bm = Vmb cos θ max = Vmb r l bp max

(Eqn 3.9.12)

FIGURE 12 HORIZONTAL AND VERTICAL BOLT FORCES AT AN EXTREME BOLT For the situation shown in Figure 10, where Vbv* is eccentric to the bolt group centroid by x = e and is acting simultaneously with Vbh* (through the centroid), the principle of superposition may be used (as permitted by Clause 9.4.1(b) of AS 4100). That is, the effects of a torque (equivalent to Vbv* e in magnitude and direction) acting on the bolt group are summed with the effects of Vbv* and Vbh* acting at the bolt group centroid so as to simulate the situation in Figure 10. Using the principle of superposition, the maximum design force on the extreme bolt in the group can be found by summation of the design shear forces from each design action taken separately. handbook 1 design of structural steel connections, first edition

31

* Using vectorial addition to obtain the resultant design shear force ( Vres ) on the extreme bolt—as in Figure 12(b) * Vres

=

(V

=

* * ⎡Vbv* Mbm x max ⎤ 2 ⎡Vbh* Mbm y max ⎤ 2 + + ⎥ ⎥ +⎢ ⎢ l bp l bp ⎥⎦ ⎥⎦ ⎢⎣ nb ⎢⎣ nb

* v

* + Vmv

) + (V 2

* h

* + Vmh

)

2

(Eqn 3.9.13)

This equation can also be used to solve any general problem for a bolt group subject to in-plane actions. The design requirement considering only shear on the bolt becomes: * Vres

≤ φV f

where φVf = design capacity of single bolt in shear (Section 3.6).

For bolt groups subject to a combination of in-plane vertical shear, in-plane horizontal shear and in-plane bending moment, general equations governing the design of such bolt groups can be derived. A summary of the governing expressions is given herein, while a full derivation of the expressions is given in Reference 2. The purpose of deriving such expressions is to have simple expressions available for use with specific connections in other Design Guides. Governing equations for common cases are given in Tables 16 and 18. TABLE 16 SINGLE BOLT COLUMN The governing interaction equation for a single column bolt group considering bolt shear failure can be obtained as follows:

Equation 3.9.13 can be transformed to: 2

2

⎡ Vbh* ⎡ V* ⎤ M* ⎤ + bm ⎥ + ⎢ bv ⎥ ≤ 1.0 ⎢ ⎣ φVdh φMdm ⎦ ⎣ φVdv ⎦

(Eqn 3.9.14)

where φMdm , φVdh and φVdv are functions of φVf as follows (see Reference 2):

φV dh = np( φV f) φV dv = np( φV f) φM dm =

npsp (np + 1) 6

(φVf )

for np ≠ 1

= 0 for np = 1 * If V = 0 and M bm = Vbv* e (e = eccentricity of Vbv* ) —a common case in many simple connections * bh

Vbv* ≤ Zb ( φVf) becomes the simple design requirement

(Eqn 3.9.15)

where

Zb is a function of e, s p and np FIGURE 13 SINGLE BOLT COLUMN LOADED IN-PLANE

In Reference 2, it is shown that: np Zb = for np ≠ 1 2 ⎡ ⎤ 6e 1+ ⎢ ⎥ ⎣⎢ s p (n p + 1)⎦⎥ =0

(Eqn 3.9.16)

for np = 1

In the above expressions, Vf = nominal capacity of a single bolt in shear-strength limit state

φ = 0.8 as discussed in section 3.6. Tables of values of Zb can be developed to allow rapid design (Table 17). handbook 1 design of structural steel connections, first edition

32

The governing interaction equation for end plate tear-out/bearing failure for a single column bolt group can be obtained as follows:

It is also necessary in bolted connections to check the components of forces acting towards the edge of a component or supported member to ensure that end plate tear-out or bearing failure will not occur. The derivation of expressions to cover this situation may be found in Reference 2. The equations derived may be summarized as follows for the case of: * Vbh* = 0 and M bm = V bv* e

(V ) + (V )

* Vres =

* 2 v

* 2 mb

≤ φVbf (bearing failure)

Vbv* ≤ ( φV ev) n p

(vertical tear-out)

Vbv* ≤ Ze( φVeh) n p

(horizontal tear-out)

where: Vv*

=

Vbv* np

* * Vmb = Vbv

np ≠ 1 6e np sp (np + 1)

np = 1 np ≠ 1

= 0

Ze

=

sp (np + 1)

np = 1

6e

= 0

(Section 3.6)

φV bf = φ3.2 d f tp fup

(Section 3.6)

φV ev = φa ev t p fup

(Section 3.6)

φV eh = φa eh t p fup fup

= tensile strength of ply

tp

= thickness of ply

a ev = vertical edge distance

(Figure 14) (Figure 14)

aeh = horizontal edge distance φ

= 0.9

df

= bolt diameter

np

= number of bolts in single column

FIGURE 14 SINGLE BOLT COLUMN— FORCES AND EDGE DISTANCES FOR END PLATE TEAR-OUT FAILURE OR BEARING FAILURE

Tables of values of Ze can be developed to speed up the design process (Table 17).


33

TABLE 17 BOLT GROUP DESIGN FACTORS FOR SINGLE COLUMN OF BOLTS s p = 70 mm np

2

3

4

5

6

7

8

9

φV dh /φV f

2

3

4

5

6

7

8

9

φV dv/φV f

2

3

4

5

6

7

8

9

φM dm /φV f

0.070

0.140

0.233

0.350

0.490

0.653

0.840

1.05

l bp × 10

2.45

9.80

24.5

49.0

85.75

137

206

294

3

3

NOTE: V dh , Vdv and V f are in kN. M dm is in kNm. l bp is in mm .

Zb FOR SINGLE COLUMN OF BOLTS s p = 70 mm e

Values of Z b for n p =

mm

2

0 10 20 30 40 50

2.00 1.92 1.74 1.52 1.32 1.15

60 70 80 90 100 110 120 130 140 150

3

4

5

6

7

8

9

3.00 2.93 2.76 2.52 2.28 2.05

4.00 3.94 3.78 3.56 3.30 3.04

5.00 4.95 4.81 4.60 4.34 4.07

6.00 5.96 5.83 5.63 5.39 5.12

7.00 6.96 6.84 6.66 6.43 6.17

8.00 7.96 7.86 7.69 7.48 7.22

9.00 8.97 8.87 8.72 8.51 8.27

1.01 0.894 0.802 0.725 0.661

1.84 1.66 1.51 1.38 1.27

2.79 2.56 2.36 2.18 2.02

3.80 3.54 3.29 3.07 2.87

4.84 4.56 4.29 4.03 3.80

5.89 5.60 5.31 5.04 4.78

6.95 6.66 6.36 6.07 5.79

8.00 7.72 7.42 7.13 6.83

0.606 0.560 0.520 0.485 0.454

1.17 1.09 1.01 0.949 0.891

1.87 1.75 1.64 1.54 1.45

2.68 2.52 2.37 2.24 2.11

3.58 3.38 3.19 3.02 2.87

4.53 4.30 4.08 3.88 3.70

5.52 5.27 5.03 4.80 4.59

6.55 6.27 6.01 5.76 5.53

Ze FOR SINGLE COLUMN OF BOLTS s p = 70 mm e mm

Values of Z e for n p = 2

3

4

5

6

7

8

9

10 20 30 40 50

3.50 1.75 1.17 0.875 0.700

4.67 2.33 1.56 1.17 0.933

5.83 2.92 1.94 1.46 1.17

7.00 3.50 2.33 1.75 1.40

8.17 4.08 2.72 2.04 1.63

9.33 4.67 3.11 2.33 1.87

10.5 5.25 3.50 2.63 2.10

11.67 5.83 3.89 2.92 2.33

60 70 80 90 100

0.583 0.500 0.438 0.389 0.350

0.778 0.667 0.583 0.519 0.467

0.972 0.833 0.729 0.648 0.583

1.17 1.00 0.875 0.778 0.700

1.36 1.17 1.02 0.907 0.817

1.56 1.33 1.17 1.04 0.933

1.75 1.50 1.31 1.17 1.05

1.94 1.67 1.46 1.30 1.17

110 120 130 140 150

0.318 0.292 0.269 0.250 0.233

0.424 0.389 0.359 0.333 0.311

0.530 0.486 0.449 0.417 0.389

0.636 0.583 0.538 0.500 0.467

0.742 0.681 0.628 0.583 0.544

0.848 0.778 0.718 0.667 0.622

0.955 0.875 0.808 0.750 0.700

1.06 0.972 0.897 0.833 0.778


34

TABLE 18 DOUBLE BOLT COLUMN The governing interaction equation for a double bolt column bolt group considering bolt shear failure can be obtained as follows: 2

⎡ Vbv* ⎢ ⎢⎣ φVdv

2s pg ⎤ ⎥ + 2 ⎥⎦ 1 + s pg

+

2 2 1 + s pg

⎡ Vbv* ⎢ ⎢⎣ φVdv

* * ⎤ ⎡ M bm ⎤ ⎡ M bm ⎤ ⎥⎢ ⎥+⎢ ⎥ ⎥⎦ ⎢⎣ φM dm ⎥⎦ ⎢⎣ φM dm ⎥⎦

* ⎡ Vbh* ⎤ ⎡ M bm ⎤ ⎡ Vbh* ⎤ ⎢ ⎥⎢ ⎥+⎢ ⎥ ⎢⎣ φV dh ⎥⎦ ⎢⎣ φM dm ⎥⎦ ⎢⎣ φVdh ⎥⎦

2

2

≤ 1 .0

(Eqn 3.9.17)

where φVdv, φVdh and φM dm are functions of φVdf as follows (see Reference 2): φV dv

=

2n p (φV f)

φV dh

=

2n p (φV f)

φM dm = = s pg

=

(

FIGURE 15 DOUBLE BOLT COLUMN LOADED IN-PLANE φ

) )

2

2

npsp (φVf )

s g (φVf)

(n

p

Vf

) ( (

1 2 np − 1 + sg / sp 3 (np − 1)2+ sg / sp

for np ≠ 1 for np = 1

sg

− 1)sp

=

nominal capacity of single bolt in shearstrength limit state

=

0.8

* If Vbh* = 0 and M bm = V bv* e (e = eccentricity of Vbv* ) —a common case in many simple connections

Vbv* ≤Zb (φVf) becomes the simple design requirement

(Eqn 3.9.18)

where Zb is a function of e, s p, np, s g and s pg The formula for Zb is derived in Reference 2 as follows: Zb

2n p

=

⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ e s s 2e / s g 2 / pg g 2 ⎢1 + ⎥ ⎢ ⎥2 + + 1 2 2 ⎢ ⎥ ⎢ 1 np + 1 ⎡ 1 ⎤ 1 np + 1 ⎡ 1 ⎤ ⎥ ⎢ 1+ ⎢ ⎥ ⎥ ⎢ 1+ ⎢ ⎥ ⎥ 3 n p − 1 ⎢⎣ s pg ⎥⎦ ⎥⎦ ⎢ 3 n p − 1 ⎢⎣ s pg ⎥⎦ ⎥ ⎢⎣ ⎣ ⎦

(

=

2n p

[1 + Z 1 ] 2 + [Z 1 / s pg ] 2

)

for n p ≠ 1

(Eqn 3.9.19)

where Z1

=

2e / s g 1 np + 1 ⎡ 1 ⎤ ⎢ ⎥ 3 n p − 1 ⎢⎣ s pg ⎦⎥ 2 1 + 2e / sg

2

1+

Zb

=

for n p = 1

Tables of values of Zb can be developed to allow rapid design (Table 18). handbook 1 design of structural steel connections, first edition

35

The governing interaction equation for end plate tear-out/bearing failure for a double column bolt group can be obtained as follows:

It is also necessary in bolted connections to check the components of forces acting towards the edge of a component or supported member to ensure that end plate tear-out or bearing failure will not occur. The derivation of expressions to cover this situation may be found in Reference 2. The equations derived may be summarized as follows for the case of: * Vbh* = 0 and Mbm = Vbv* e

(V

* Vres =

* v

* + Vmv

) + (V ) 2

* 2 mh

≤ φVbf (bearing failure)

Vbv*

≤ Zev(φVev) 2n p

(vertical tear-out)

Vbv*

≤ Zeh (φVeh) 2n p

(horiz. tear-out)

where Vv*

=

Vbv* 2np

* * Vmv = Vbv

* * Vmh = Vbv

lbp

=

Zev =

Zeh =

es g 2lbp e(np − 1)sp 2lbp

np sp2 6

1+

[(n − 1) + 3(s 2 p

1 npes g

g

/ sp

)

2

]

np ≠ 1

lbp

l bp

FIGURE 16 DOUBLE BOLT COLUMN—FORCES AND EDGE DISTANCES FOR END PLATE TEAROUT FAILURE OR BEARING FAILURE

np ≠ 1

e(np − 1)sp np

⎡ sg ⎤ Zev = ⎢ ⎥ ⎣⎢ sg + 2e ⎦⎥

np = 1

Zeh = 0

np = 1

φV bf = φ3.2 d f tp fup

(Section 3.6)

φV ev = φa ev t p fup

(Section 3.6)

φV eh = φa eh t p fup

(Section 3.6)

fup

= tensile strength of ply

tp

= thickness of ply

aev

= vertical edge distance

a eh = horizontal edge distance

(Figure 16) (Figure 16)

φ

= 0.9

df

= bolt diameter

np

= number of bolts in each bolt column

Tables of values of Zex and Zeh can be developed to expedite the design process (Table 19).


36

TABLE 19 BOLT GROUP FACTORS FOR DOUBLE COLUMN OF BOLTS s g = 70 mm s p = 70 mm np

1

2

3

4

5

6

7

8

9

φV dh /φV f φV dv/φV f φM dm /φV f

2 2 0.070

4 4 0.198

6 6 0.344

8 8 0.531

10 10 0.764

12 12 1.04

14 14 1.37

16 16 1.74

18 18 2.16

2 2 / 1 + spg

0

1.41

1.79

1.90

1.94

1.96

1.97

1.98

1.98

2 2spg / 1 + spg

2.00

1.41

0.894

0.632

0.485

0.392

0.329

0.283

0.248

I bp × 103

2.45

9.80

26.95

58.80 110.25 186.20 291.55 431.20 610.05

NOTE: V dh , Vdv and V f are in kN. M dm is in kNm. l bp is in mm 3 .

Zb FOR DOUBLE COLUMN OF BOLTS s p = 70 mm s g = 70 mm e


mm 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

1 2.00 1.56 1.27 1.08 0.933 0.824 0.737 0.667 0.609 0.560 0.519 0.483 0.452 0.424 0.400 0.378

2 4.00 3.47 3.04 2.68 2.39 2.15 1.96 1.79 1.65 1.53 1.42 1.33 1.25 1.17 1.11 1.05

3 6.00 5.51 5.01 4.55 4.13 3.77 3.45 3.17 2.93 2.72 2.54 2.37 2.23 2.10 1.99 1.88

4 8.00 7.57 7.07 6.55 6.06 5.60 5.18 4.80 4.46 4.16 3.89 3.65 3.44 3.25 3.07 2.92

5 10.0 9.62 9.15 8.62 8.09 7.57 7.08 6.62 6.20 5.81 5.47 5.15 4.86 4.60 4.37 4.15

6 12.0 11.7 11.2 10.7 10.2 9.62 9.08 8.56 8.08 7.62 7.20 6.82 6.46 6.14 5.84 5.56

7 14.0 13.7 13.3 12.8 12.3 11.7 11.1 10.6 10.1 9.55 9.07 8.63 8.21 7.82 7.46 7.13

8 16.0 15.7 15.4 14.9 14.4 13.8 13.2 12.7 12.1 11.6 11.0 10.5 10.1 9.63 9.21 8.83

9 18.0 17.8 17.4 17.0 16.5 15.9 15.4 14.8 14.2 13.6 13.1 12.5 12.0 11.5 11.1 10.6

Zev, Zeh FOR DOUBLE COLUMN OF BOLTS s p = 70 mm s g = 70 mm e mm

Values of Z ev for n p = 1 .778 .636 .538 .467 .411 .368 .333 .304 .280 .259 .241 .225 .212 .200 .189

2 .875 .778 .700 .636 .583 .538 .500 .467 .437 .412 .389 .368 .350 .333 .318

3 .928 .865 .811 .762 .720 .681 .647 .616 .588 .562 .538 .517 .497 .478 .461

4 .955 .913 .875 .840 .808 .778 .750 .724 .700 .677 .656 .636 .618 .600 .583

5 .969 .940 .913 .887 .863 .840 .818 .797 .778 .759 .741 .724 .708 .692 .677

6 .978 .957 .937 .917 .899 .881 .864 .847 .831 .816 .801 .787 .773 .760 .747

7 .983 .967 .952 .937 .922 .908 .895 .881 .869 .856 .844 .832 .821 .810 .799

Values of Z eh for n p = 8 .987 .975 .963 .951 .939 .928 .917 .906 .895 .885 .875 .865 .856 .846 .837

9 .990 .980 .970 .960 .951 .942 .933 .924 .915 .906 .898 .890 .882 .874 .866

2 7.00 3.50 2.33 1.75 1.40 1.17 1.00 .875 .778 .700 .636 .583 .538 .500 .467

3 6.42 3.21 2.14 1.60 1.28 1.07 .917 .802 .713 .642 .583 .535 .494 .458 .428

4 7.00 3.50 2.33 1.75 1.40 1.17 1.00 .875 .778 .700 .636 .583 .538 .500 .467

5 7.88 3.94 2.63 1.97 1.58 1.31 1.13 .984 .875 .788 .716 .656 .606 .563 .525


6 8.87 4.43 2.98 2.22 1.77 1.48 1.27 1.11 .985 .887 .806 .739 .682 .633 .591

7 9.92 4.96 3.31 2.48 1.98 1.65 1.42 1.24 1.10 .992 .902 .826 .763 .708 .661

8 11.0 5.50 3.67 2.75 2.20 1.83 1.57 1.38 1.22 1.10 1.00 .917 .846 .786 .733

9 12.1 6.05 4.04 3.03 2.42 2.02 1.73 1.51 1.35 1.21 1.10 1.01 .931 .865 .807

37

TABLE 20 BOLT GROUP FACTORS FOR DOUBLE COLUMN OF BOLTS s g = 90 mm s p = 70 mm np

1

2

3

4

5

6

7

8

9

φV dh /φV f φV dv/φV f φM dm /φV f

2 2 0.090

4 4 0.228

6 6 0.382

10 10 0.804

2 2 / 1 + spg

0

1.23

1.68

8 8 0.571 1.84

1.90

12 12 1.08 1.94

14 14 1.41 1.96

16 16 1.78 1.97

18 18 2.20 1.97

2 2spg / 1 + spg

2.00

1.58

1.08

0.788

0.612

0.498 0.419

0.361

0.317

I bp × 10

4.05

13.0

31.75

3

65.20 118.25 195.80 302.76 444.00 624.46

NOTE: V dh , Vdv and V f are in kN. M dm is in kNm. l bp is in mm 3 .

Zb FOR DOUBLE COLUMN OF BOLTS s p = 70 mm s g = 90 mm e


mm 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

1 2.00 1.64 1.38 1.20 1.06 0.947 0.857 0.783 0.720 0.667 0.621 0.581 0.545 0.514 0.486 0.462

2 4.00 3.50 3.09 2.76 2.48 2.25 2.06 1.90 1.76 1.64 1.53 1.44 1.35 1.28 1.21 1.15

3 6.00 5.49 5.00 4.56 4.16 3.82 3.52 3.25 3.02 2.82 2.64 2.48 2.34 2.21 2.09 1.99

4 8.00 7.53 7.02 6.51 6.04 5.60 5.20 4.84 4.51 4.23 3.97 3.73 3.52 3.33 3.16 3.01

5 10.0 9.57 9.08 8.55 8.03 7.52 7.05 6.61 6.20 5.83 5.50 5.19 4.91 4.66 4.43 4.22

6 12.0 11.6 11.1 10.6 10.1 9.54 9.01 8.51 8.04 7.61 7.20 6.83 6.48 6.16 5.87 5.60

7 14.0 13.7 13.2 12.7 12.2 11.6 11.1 10.5 9.99 9.50 9.03 8.60 8.19 7.82 7.47 7.14

8 16.0 15.7 15.3 14.8 14.3 13.7 13.1 12.6 12.0 11.5 11.0 10.5 10.0 9.59 9.19 8.81

9 18.0 17.7 17.3 16.9 16.4 15.8 15.2 14.7 14.1 13.5 13.0 12.4 11.9 11.5 11.0 10.6

Zev, Zeh FOR DOUBLE COLUMN OF BOLTS s p = 70 mm s g = 90 mm e mm

Values of Z ev for n p = 1 .818 .692 .600 .529 .474 .429 .391 .360 .333 .310 .290 .273 .257 .243 .231

2 .903 .823 .756 .699 .650 .607 .570 .537 .508 .481 .458 .436 .417 .399 .382

3 .938 .883 .834 .791 .751 .716 .684 .654 .627 .602 .579 .558 .538 .519 .502

4 .959 .921 .886 .853 .823 .795 .769 .744 .721 .700 .679 .660 .642 .625 .608

5 .971 .944 .918 .894 .871 .849 .828 .809 .790 .772 .754 .738 .722 .707 .693

6 .979 .959 .940 .921 .903 .886 .869 .854 .838 .823 .809 .795 .782 .769 .757

7 .984 .969 .954 .939 .925 .911 .898 .885 .873 .861 .849 .837 .826 .815 .805

Values of Z eh for n p = 8 .988 .975 .964 .952 .941 .930 .919 .908 .989 .888 .878 .869 .859 .850 .841

9 .990 .980 .971 .961 .952 .943 .934 .925 .917 .908 .900 .892 .884 .876 .869

2 9.29 4.64 3.10 2.32 1.86 1.55 1.33 1.16 1.03 .929 .844 .774 .714 .663 .619

3 7.56 3.78 2.52 1.89 1.51 1.26 1.08 .945 .840 .756 .687 .630 .582 .540 .504

4 7.76 3.88 2.59 1.94 1.55 1.29 1.11 .970 .862 .776 .706 .647 .597 .554 .517

5 8.45 4.22 2.82 2.11 1.69 1.41 1.21 1.06 .938 .845 .768 .704 .650 .603 .563


6 9.32 4.66 3.11 2.33 1.87 1.55 1.33 1.17 1.04 .932 .848 .777 .717 .668 .622

7 10.30 5.15 3.43 2.57 2.06 1.72 1.47 1.29 1.14 1.03 .936 .858 .792 .736 .687

8 11.33 5.66 3.78 2.83 2.26 1.89 1.62 1.42 1.26 1.13 1.03 .944 .871 .809 .755

9 12.39 6.20 4.13 3.10 2.48 2.07 1.77 1.55 1.38 1.24 1.13 1.03 .953 .885 .826

38

3


3.10 Design example No. 1— Design of bolts in lap splice connection

Check a bolted splice in a 180 × 20 plate in the following configuration to ensure that it can transmit the design tension capacity of the plate being spliced.

FIGURE 17 BOLTED PLATE SPLICE Plates:

Grade 250 to AS/NZS 3678

Spliced plate:

20 mm thick

fy = 250 MPa

Ag

= 180 × 20 = 3600 mm 2

An

= 3600 – 2 × 22 × 20 = 2720 mm2

AS 4100, Clause 7.2 N t Nt

fu = 410 MPa

≤ 3600 × 250/10 3 = 900 kN ≤ 0.85 × 1.0 × 2720 × 410/10 3 = 948 kN

Design capacity:

φN t = 0.9 × 900 = 810 kN

Bolts and splice plates are to be able to transmit this design capacity

Splice plates:

2 No × 10 mm thick

fy = 260 MPa

Ag

= 2 × 180 × 10 = 3600 mm

An

= 2 × (180 × 10 – 2 × 22 × 10) = 2720 mm 2

Nt

≤ 3600 × 260/10 3 = 936 kN

Nt

≤ 0.85 × 1.0 × 2720 × 410/10 3 = 948 kN

Design capacity:

φN t = 0.9 × 936 = 842 kN >810 kN

Bolts:

M20 category 8.8/S in 22 mm diameter holes grip = 40 mm

fu = 410 MPa

2

bolt length = 70 mm

minimum plain shank length = 16.5 mm

SATISFACTORY

(Ref. 7) (Ref. 7)

Hence, threads intercept one shear plane, plain shank intercepts the other shear plane—bolts subject to shear on two planes.


39

Design capacity of bolts in shear = φVfn + φV fx = 92.6 + 129 = 221.6 kN (Table 10)

L j = 70 mm (first to last bolt, each side of splice location) hence, k r = 1.0 Plate crushing and tear-out:

Spliced plate in bearing: From Table 7

Vb

M20 bolts a e1 = 39 mm

d f = 20 mm fup = 410 MPa

tp = 20 mm

≤ 3.2 × 410 × 20 × 20/10 = 525 kN 3

≤ 39 × 20 × 410/10 3 = 320 kN

Splice plates: From Table 7

φV b (= 0.9 × 320 kN) > φVf (= 221.6 kN)

DOES NOT CONTROL

a e1 = 34 mm

tp = 10 mm

Vb

fup = 410 MPa

≤ 3.2 × 410 × 10 × 20/10 = 262 kN 3

≤ 34× 10 × 410/10 3 = 139 kN φV b = 0.9 × 139 kN > 92.6 kN threads included = 125.5 < 129 kN threads excluded

DOES NOT CONTROL DOES CONTROL

Design capacity on two shear planes per bolt reduces to = 92.6 + 125.5 = 218 kN. Total design capacity of 4 bolts each side of splice location = 4 × 218 = 872 kN > 810 kN SATISFACTORY


40

3


3.11 Design example No. 2— Design of bolt group loaded inplane

If the bolts in the connection shown in Figure 18 are M20 bolts in 8.8/S bolting category, determine the maximum design vertical force that the bolts in the bolt group can sustain.

FIGURE 18 BOLT GROUP LOADED IN-PLANE Design actions at bolt group centroid:

Vbv*

= V* kN

* Mbm

= 0.5 V* kNm

Using first principles approach of Eqns 3.9.10 to 3.9.13

Design capacity of bolt group based on design shear capacity of bolts nb

= 8

Ibp

=

∑ (x

2 n

+ y n2

)

r max

=

45 2 + 105 2 = 114.2 mm

= 8 × 45 2 + 4 × 105 2 + 4 × 35 2 = 65200 mm2

Vv*

=

Vbv* nb

= 0.125V*

Vh*

=

Vbh* nb

=0

* M bm r max I bp

=

* Vmb =

0.5V * × 1000 × 114.2 = 0.876V* 65200


41

Using Eqns 3.9.11 and 3.9.12: * Vmh =

* M bm y max I bp

=

* Vmv =

* M bm x max Ibp

=

0.5V * × 1000 × 105 = 0.805V* 65200 0.5V * × 1000 × 45 = 0.345V* 65200

(V ) + (V )

2 * mv

2 * mh

* Note that Vmb =

= 0.876V* as before

Using Eqn 3.9.13:

(V

* = Vres

* v

* + Vmv

) + (V 2

* h

* + Vmh

)

= ⎛⎜ ⎝

2

(0.125 + 0.345 ) 2 + 0.805 2 ⎞⎟V * ⎠

= 0.932V* ≤ φVf Bolt design capacity: M20 bolts 8.8/S bolting category

grip = 15.4 + 8 = 23.4 mm From Reference 7, 55 mm long bolt is shortest possible bolt 55 mm long bolt has minimum plain shank of 10 mm (<15.4) ∴ threads intercept shear plane Vdf = φV fn = 92.6 kN (Table 10) Crushing on 8 mm ply, φVb = 3.2 × 20 × 8 × 410/10 3 = 210 kN

BOLT SHEAR CONTROLS

(Plate tear-out assessed for components of bolt forces separately.) * ∴ Vres = 0.932 V*≤ 92.6 kN

V*≤ 99.4 kN Design capacity of bolt group based on end plate tear-out considerations:

Now vertical end plate tear-out is not likely in either column or bracket, while horizontal end plate tear-out will occur in the 8 mm web of the channel member before occurring in column flange. Hence, tp = 8 mm,

fup = 410 MPa

φ = 0.9

a eh – 1 = 50 – 1 mm = 49 mm

* Vmh on top bolt = 0.805V* ≤ φV b = φa e tpfup

V* ≤

0.9 × 49 × 8 × 410 = 180 kN 0.805 × 10 3

DOES NOT CONTROL

Using the closed form solution approach of Table 18 Bolt group design parameters (Table 18):

s p = 70 mm 2 1+ s

Z1 =

Zb =

s g = 90 mm

np = 4

2spg

= 0.788

= 1.84

2 1 + spg

2 pg

spg =

90 = 0.4286 e = 500 mm s g/s p = 1.2857 3 × 70 ⎡1 2 2 ⎤ ⎢ 3 np − 1 + s g / s p ⎥ ⎢ ⎥ n p s p = 570.7 ⎢ (n p − 1) 2 + s g / s p 2 ⎥ ⎣⎢ ⎦⎥

(

) ( (

) )

2 × 500 / 90 = 2.761 1 5 1 1+ × × 3 3 0.4286 2 2× 4 3.761 + (2.761 / 0.4286 ) 2 2

= 1.072


42

Design capacity of bolt group based on design shear capacity of bolts:

Using Table 18,

Vbv* ≤ Zb (φVf ) = 1.072 × 92.6 = 99.4 kN

Method (a) using Z b:

since Vbv* = V * then V * ≤99.4 kN Using Eqn 3.9.17, Method (b) using interaction equation: Vbh* = 0 φV dv = 8 × 92.6 = 740.8 kN φM dm = 571 × 92.6 = 52847 kNmm = 52.8 kNm 2

⎡ V* ⎤2 ⎡ V * ⎤ ⎡ 0.5V * ⎤ ⎡ 0.5V * ⎤ ⎢ 740.8 ⎥ + 0.788 ⎢ 740.8 ⎥ ⎢ 52.8 ⎥ + ⎢ 52.8 ⎥ ≤ 1.0 ⎣ ⎦ ⎣ ⎦⎣ ⎦ ⎣ ⎦

[V *] 2 [1.8222 + 10.054 + 89.336 ]× 10 -6 ≤ 1.0 Solving,

V * ≤99.4 kN (as method (a))

Design capacity of bolt group based on end plate tear-out considerations:

Using Table 18, l bp =

[

]

4 × 70 2 2 15 + 3 × (90 / 70 ) = 65200 mm3 6

Now, vertical end plate tear-out is not likely in either column or bracket, while horizontal end plate tear-out will occur in the 8 mm web of the channel member before occurring in column flange. Hence, tp

= 8 mm,

φ = 0.9

f up = 410 MPa

a eh – 1 = 50 – 1 mm = 49 mm

φV eh = 0.9 × 49 × 8 × 410/10 = 145 kN 3

φV bf = 0.9 × 3.2 × 20 × 8 × 410/10 3 = 189 kN Then using Table 18, with Vbv* = 99.4 kN (maximum capacity controlled by bolt shear) Vv*

=

99.4 = 12.4 kN 2× 4

* Vmh

=

99.4 × 500 × 3 × 70 = 80.0 kN ≤ φVeh = 145 kN 2 × 65200

* Vmv

=

99.4 × 500 × 90 = 34.3 kN 2 × 65200

* Vres

=

(12.4 + 34.3) 2 + 80.0 2

= 92.6 kN ≤ φVbf = 189 kN

SATISFACTORY

SATISFACTORY

CONCLUSION: Plate tear-out does not control the design capacity of the connection.

DESIGN CAPACITY OF BOLT GROUP = 99.4 kN


AS BEFORE

43

3


3.12 Bolt group loaded out-of-plane

AS 4100 Clause 9.4.2 specifies that for a bolt group loaded such that it is subject to out-ofplane loading, the design actions shall be determined in accordance with Clause 9.1.3. Clause 9.1.3 of AS 4100 nominates the basic requirements that any design model must have for the design of a steel connection if the design model is to be acceptable. These requirements are as follows: ‘Each element in a connection shall be designed so that the structure is capable of resisting all design actions. The design capacities of each element shall be not less than the calculated design action effects. Connections and the adjacent areas of members shall be designed by distributing the design action effects so that they comply with the following requirements: (a)

The distributed design action effects are in equilibrium with the design action effects acting on the connection.

(b)

The deformations in the connection are within the deformation capacities of the connection elements.

(c)

All of the connection elements and the adjacent areas of members are capable of resisting the design action effects acting on them.

(d)

The connection elements shall remain stable under the design action effects and deformations.

Design shall be on the basis of a recognised method supported by experimental evidence. Residual actions due to the installation of bolts need not be considered.’ A bolt group loaded out-of-plane can be subject to a bending moment applied normal to the mating surface (M*) and a coincident vertical shear force (V*) and horizontal tension force N t* . If n b = number of bolts in the connection, then V* and N t* can be assumed to be equally distributed among the bolts, giving: Vv* = design shear force per bolt due to vertical shear V* =

V* nb

N tn* = design tension force per bolt due to horizontal axial tension N t* =

N t* nb

The method used in this Design Guide to determine the design tension force in the bolts due to the design action M* is based on the following assumptions: (1)

the neutral axis is at the centroid of the bolt group (Figure 19);

(2)

the bolts above the neutral axis are all in tension and the bolts below the neutral axis are assumed to be notionally in ‘compression’;

(3)

a plastic distribution of bolt force is assumed on both sides of the neutral axis.

The method is one suggested in Reference 9, Case II (neutral axis at centre of gravity).

FIGURE 19 BOLT GROUP LOADED OUT-OF-PLANE—DESIGN ACTIONS handbook 1 design of structural steel connections, first edition

44

* Using these assumptions, the design axial tension in the bolts on the tension side ( N tm ) is given

by: * = design force per bolt in tension due to design bending moment M* N tm

=

M* nt y m

(Eqn 3.12.1)

nt

= number of bolts above the neutral axis

ym

= lever arm between resultant tensile force and resultant ‘compression’ force

For the common case of a double column of bolts (Figure 20) n b = 2n p = number of bolts in connection when n p = odd number (3,5,7, etc.) n t = (np – 1)

ym =

(n

p

+ 1) s p 2

(Eqn 3.12.2)

when n p = even number (2,4,6, etc.) nt = np

ym =

np sp 2

(Eqn 3.12.3)

FIGURE 20 DOUBLE BOLT COLUMN GEOMETRY Reference 9 also offers an alternative formulation—Case I (neutral axis not at centre of gravity), which is a direct but less conservative method. Governing bolt interaction equations for a double column bolt group:

The bolts above the neutral axis are subject to shear force and tension force and must satisfy the interaction equation of Table 7. * ⎤2 ⎡ Vv* ⎤ 2 ⎡ N tn* + N tm ⎥ ≤ 1 .0 ⎢ ⎥ +⎢ φ φ V N tf ⎣ f⎦ ⎣ ⎦

(Eqn 3.12.4)

The bolts below the neutral axis have a notional ‘compression’ force due to the design bending moment M*. This would normally be ignored, so that the bolts below the neutral axis would normally only need to satisfy ⎡ Vv* ⎤ 2 ⎡ N tn* ⎤ 2 ⎥ ≤ 1 .0 ⎢ ⎥ +⎢ ⎣ φVf ⎦ ⎣ φN tf ⎦

(Eqn 3.12.5)

which would not be a critical design criterion. The bolts may be subject to Prying Action under the design action N t* and under design action M* for bolts on the tension side. Prying action may increase the design tension force in the bolts above the values calculated using this Section. Prying action is discussed in Section 3.13. handbook 1 design of structural steel connections, first edition

45

3


3.13 Prying action

Bolt groups subject to out-of-plane moment or direct tension may be subject to an additional tensile force due to the flexural behaviour of the plate which the bolts connect to a support. This phenomenon is known as prying action and is illustrated in Figure 21. Any increase in tension force in the bolt due to prying should be taken into account in the design of the bolts and the connected plate. The mechanism of prying can be understood by reference to Figure 21. Considering a T-stub under tensile load, the contact pressure between the T-stub flange and the base will be reduced and additional prying forces develop in the general region of the flange tip, thus increasing the tensile force in the bolts, as the flange of the T-stub deforms.

FIGURE 21 PRYING MECHANISM IN T-STUB CONNECTION A review of the literature relating to prying may be found in References 2 and 10. This Section is based primarily on Reference 10, which suggests that the level of prying force is influenced by a number of items, including: (a)

the stiffness of the connected plate;

(b)

the stiffness of the bolt;

(c)

the magnitude of the clamping forces induced into the bolts at installation;

(d)

the bolt grip;

(e)

the number of lines of fasteners;

(f)

the stiffness of the support;

(g)

the dimensions of the bolt position relative to the edge of the connected plate and the point of application of the force.

If the connected plate is sufficiently stiff (‘thick plate’), the flexural deformations of the plate will be small compared to the elongation of the bolts and very little prying force will be developed (refer to Figure 22). The connected plate will bend in single curvature. If the connected plate is sufficiently flexible (‘thin plate’), the flexural deformations of the plate will be large and prying force will develop (refer to Figure 23). Bending of the plate develops a prying force acting between the bolt line and the edge of the plate, which may continue up until bolt failure. The connected plate may bend in either single or double curvature.


46

The test results plotted in Reference 10 show that experimentally measured levels of prying force may vary between 0% and 40% depending on the exact test arrangement. Precise evaluation by calculation is difficult despite the various studies on the subject reported in References 2 and 10.

FIGURE 22 GRAPHICAL RELATIONSHIP—BOLT LOAD/APPLIED LOAD FOR A STIFF T-STUB FLANGE

FIGURE 23 GRAPHICAL RELATIONSHIP— BOLT LOAD/APPLIED LOAD FOR A FLEXIBLE T-STUB FLANGE

A further complication is that if there are more than one line of bolts either side of the point of application of the design action, tests have shown that the outer line of bolts is not very effective in carrying the applied design action unless the connected plate is thick or stiffened (Ref. 10). The assessment of prying force for such arrangements is little studied and is not further developed in this Guide. A simple approach is as follows: (i)

for thick connected plates to a rigid support—use an allowance for prying of 0% to 10% by increasing the calculated tension force in a bolt by the selected percentage.

(ii)

for thin connected plates—use an allowance for prying of 20% to 40% by increasing the calculated tension force in a bolt by the selected percentage.

What constitutes a plate that is sufficiently thick so as to reduce prying is discussed later. If an analytical approach is desired to be used, the following method taken from Reference 10 is suggested. It is an approach also used in References 9 and 11. In using this analytical approach, it needs to be recognised that a lot of the experimental research is based on tee stubs bolted to supports and subject to tension. Some T-stub research has the T-stubs also bolted to the flanges of an I-section. Few realistic connections in Australia where prying is of interest involve a genuine T-stub detail as most involve plates bolted to I -section supports. Figure 24(a) shows a tee stub connection and identifies two critical dimensions (a e and a f). Figure 24(b) shows the same T-stub in a deformed condition when subject to a tension force N t* . If the T-stub deforms as shown, it presses against the support (assumed to be rigid) at the ends of the T-stub and generates a reaction—it is this reaction which is the prying force ( Nq* ).


47

FIGURE 24 T-STUB CRITICAL DIMENSIONS AND DESIGN ACTIONS If the flange part of the T-stub is very stiff, then the bolt force versus applied tension force relationship will be like that in Figure 22. If the flange part of the T-stub is very flexible, then the bolt force versus applied tension force relationship will be like that in Figure 23. The relevant parameters for an analytical method are given in Figure 25.

FIGURE 25 T-STUB PARAMETERS Equilibrium of forces gives: N t* + 2N q* = 2N tf*

(Eqn 3.13.1)

Equilibrium of moments about the centre of the bolt gives: M l* + M 2* = 0.5N t* af

(Eqn 3.13.2)

where M 2*

=

design bending moment acting on the net cross-section of the flange of the T-stub, through the bolt centreline

Ml*

=

design bending moment acting on the gross cross-section of the flange of the T-stub, at the face of the T-stub stem

letting δ

=

net cross - section area at bolt hole location gross cross - section area at face of stem

α

=

M 2* M l* then M 2* normalised becomes = αδ Ml*

and

then Eqn 3.13.2 can be expressed in a different form as: M 1* (1 + αδ) = 0.5N t* af handbook 1 design of structural steel connections, first edition

(Eqn 3.13.4) 48

Solving for M 1* results in: M 1*

=

0.5N t* a f N t* a f = (1 + αδ ) 2(1 + αδ )

(Eqn 3.13.4)

For the design of the plate/flange of the T-stub M 1*

≤

φM s (design section moment capacity of T-stub flange)

Methods of determining φMs for connection components (such as the T-stub flange) are discussed in Section 5 of this Guide. In order to determine the design tension force in the bolt, it is to be noted that: M 2*

=

N q* a e = αδM 1*

=

αδN t* a f αδM 1* = ae 2(1 + αδ ) a e

(Eqn 3.13.5)

Hence, Nq*

using Eqn 3.13.4

(Eqn 3.13.6)

The total design force in the bolt ( N tf* ) is then given by: N tf*

=

⎡ αδ ⎤ a 0.5Nt* + Nq* = Nt* ⎢0.5 + f ⎥ ae 2(1 + αδ ) ⎦ ⎣

(Eqn 3.13.7)

The behaviour of the flange of the T-stub as observed experimentally suggests that flange deformation is such that modified values of a e and a f should be used, as follows: ae′

=

a e + 0.5d h

af′

=

a f – 0.5d h

dh

=

bolt hole diameter

where

Using these modified parameters, the equations of interest become the following equations: ⎡ a′ αδ ⎤ N tf* = N t* ⎢0.5 + f ⎥ a e′ 2(1 + αδ ) ⎦ ⎣

M 1* =

N t* a f′ 2(1 + αδ )

(Eqn 3.13.8)

(Eqn 3.13.9)

The structural connection designer has a multitude of solutions to choose from by varying α—as Thornton illustrates in Reference 12—these being Option 1—

Choose α = 0, single curvature bending in the T-stub flange. There is zero prying, so Ntf* = 0.5Nt* , but a thicker plate is required that satisfies M 1* = 0.5N t* a f′ ≤ φM s

Option 2—

Choose α = 1, double curvature bending in the T-stub flange. Equations 3.13.8 and 3.13.9 apply directly and M1* ≤ φMs, N tf* ≤ φN tf

Option 3—

Choose any value of α. Thornton in Reference 12 illustrates a family of curves showing how the prying force values vary with values of α.

Equations 3.13.8 and 3.13.9 are a consistent set of equations which relate plate thickness and bolt force. The foregoing is a general treatment which is adapted in other Design Guides for individual connections as required—notably the Bolted Moment End Plate and Column Base Plate subject to bending moment. The AISC Manual (Ref. 9) contains an alternative formulation which is claimed to provide better correlation with available test data handbook 1 design of structural steel connections, first edition

49

3


3.14 Design example No. 3— Design of bolt group loaded out-of-plane

If the bolts in the connection shown in Figure 26 are M20 bolts in 8.8/S bolting category, determine if they are satisfactory under the design action shown.

FIGURE 26 BOLT GROUP LOADED OUT-OF-PLANE Bolt design capacities:

From Table 10, φV fx = 129 kN

No threads intersect shear plane

φN tf = 163 kN φV b > φVfx

since tp = 25 mm bearing or end plate tear-out is not critical.

Bolt group design parameters:

Using Section 3.12,

nb = 8

s p = 70 mm

nt = np = 4

ym =

np sp 2

n p = 4 (even numbering)

= 140 mm

Design actions: 250 = 31.3 kN 8 250 × 250 M* = = 111.6 kN N tf* = nt y m 4 × 140

Vv* =


50

Design capacity—Bolt and plate:

Using Section 3.13 to consider prying: (A)

Assume α = 0, no prying, N tf* =111.6 kN ⎛ 31.3 ⎞ 2 ⎛ 111 .6 ⎞ 2 Bolt interaction equation (Section 3.12) ⎜ ⎟ +⎜ ⎟ = 0.53 < 1.0 ⎝ 129 ⎠ ⎝ 163 ⎠

SATISFACTORY

Checking plate thickness using Sections 5.3 and 3.13: treating area around top two bolts as a T-stub as in Figure 27:

FIGURE 27 T-STUB GEOMETRY Section 3.13

a f = 50 mm

a f′ = 50 – 11 = 39 mm

d h = 22 mm

N t* = 2 ×111.6 kN = 223.2 kN

For α =0,

M1* = 223.2 × 39/2 = 4352 kNmm

(Section 5.3)

φM s =

0.9 × 250 × 25 2 × 70 4 × 10 3

= 2460 kNmm < M1*

NOT SATISFACTORY

since the plate is ‘thin’, prying will occur and the design tension force on the bolts must be reassessed. (B)

Assume α = 1 δ=

70 − 22 = 0.685 70

af′ = 39 mm

ae′ = 40 + 11 = 51 mm

a f′ αδ 39 1 × 0.685 = × = 0.155 (Total prying force is 31%) a ′e 2(1 + αδ ) 51 2 × (1.685 ) N tf* = N t* [0.5 + 0.155 ] = 223.2 × 0.655 = 146 kN

⎛ 31.3 ⎞ 2 ⎛ 146 ⎞ 2 Bolt Interaction Equation (Section 3.12) ⎜ ⎟ +⎜ ⎟ = 0.86 ≤ 1.0 ⎝ 129 ⎠ ⎝ 163 ⎠ M1* =

223 × 39 2 × 1.685

= 2580 kNm

SATISFACTORY

(compare to 4350 kNm if no prying is assumed)

≈ φM s = 2460 kNm (from before)

SATISFACTORY

CONCLUSIONS

(1)

Bolts are satisfactory even if prying is considered

(2)

25 mm thick plate is just satisfactory, will bend in double curvature and 31% prying force will be involved. The plate is not thick enough for no prying to occur. For no prying to occur, a plate thickness of 36 mm is required for which: φM s =

0.9 × 250 × 36 2 × 70 4 × 10 3

= 5130 kNm >4352 kNm = M1*


51

4

WELDS AND WELD GROUPS

4.1

Weld types

Six types of weld are included in AS 4100 (see Figure 28): Complete penetration butt weld—a weld where fusion exists between weld metal and the parent metal throughout the entire depth of the joint. A butt weld is one in which the weld lies substantially within the extension of the planes of the surfaces of one or more of the parts joined. Incomplete penetration butt weld—a butt weld where, by design, fusion does not extend throughout the full depth of the joint. Fillet weld—a weld of approximately triangular cross-section which is formed in the corner between the surfaces of two components. Plug weld—a weld made by completely or partially filling a circular hole in one component with filler metal, with the filler metal fusing to the contiguous component exposed through the hole. Slot weld—a weld made by depositing a fillet weld around the periphery of an elongated hole in one component so as to join it to the surface of a contiguous component exposed through the hole. Compound weld—a weld comprising a fillet weld superimposed on a butt weld.

AS 4100 restricts the use of plug and slot welds to applications where these welds either transmit shear in lap joints or where they prevent buckling of lapped parts or where they join component parts of built-up members.

FIGURE 28 WELD TYPES The design and detailing of the six types of weld included in AS 4100 are extensively dealt with in AS 4100 (Ref. 1) and its associated commentary (Ref. 8) as well as in AS 1554.1 (Ref. 14) and Design Guide 2. handbook 1 design of structural steel connections, first edition

52

4


4.1

Standard weld symbols

NOTES: 1. The letters CP in the tail of the arrow indicate a complete penetration butt weld. 2. The tail should be omitted if no reference T is required. 3. The size of a fillet weld shall be to the left of the symbol. 4. For an incomplete penetration butt weld, the design throat thickness shall be to the left of the symbol. Where no design throat thickness is shown, a complete penetration butt weld is assumed required. 5. Arrow side and other side welds are made the same size unless otherwise dimensioned. 6. Symbols only apply between abrupt changes in direction of welding unless governed by the ’weld all round’ symbol or otherwise dimensioned.

FIGURE 29 SYMBOLS FOR WELDS ON DRAWINGS (from AS 1101.3, Ref. 13)


53

4


4.2

Selection of prequalified welding consumables

TABLE 21 PREQUALIFIED WELDING CONSUMABLES Steel grade in AS/NZS 3678 (Ref. 27) AS/NZS 3679.1 (Ref. 29)

Steel type

Weld metal classification Manual metal-arc AS 1553.1 (Ref. 15)

Submerged arc—AS 1858.1 (Ref. 16)

Classification

Grade

Flux cored—AS 2203.1 (Ref. 17) Gas metal arc—AS/NZS 2717.1 (Ref. 18)

200, 250, 300

1

E41XX, E48XX

0 and 1

W40X, W50X

250L0

2

E41XX, E48XX

2

W402, W502

250L15, 300L15

3

E41XX, E48XX

3

W403, W503

350, WR350, 400

4

E48XX, E41XX

0 and 1

W50X, W40X

350L0, WR350L0

5

E48XX, E41XX

2

W502, W402

350L15, 400L15

6

E48XX, E41XX

3

W503, W403

NOTE: See expanded version of this table in AS 1554.1 (Ref. 14).

TABLE 22 STRENGTH OF WELD METAL Weld metal designation

f uw (MPa)

E41XX, W40X

410

E48XX, W50X

480

NOTE: fuw is the nominal tensile strength of the deposited weld metal used for design.

As required by AS 4100, all welding must comply with AS 1554.1 (Ref. 14). Table 21 is based on Table 4.5.1 of AS 1554.1 (Ref. 14) and matches weld metal strength and ductility to base metal strength and ductility, when using any of the welding procedures complying with AS 1554.1. In Tables 21 and 22, X or XX indicates any number(s) representing a variety of different electrode compositions may be used.


54

4


4.3

Weld categories

AS 4100 permits the use of two weld categories as follows: SP—structural purpose GP—general purpose The difference between these weld categories lies in the level of permissible imperfections allowed by AS 1554.1 (Ref. 14). SP weld category has smaller permitted imperfections—and is accordingly more reliable—than category GP. Once the permitted level of imperfections is exceeded the imperfections are classed as defects. Each category of weld cannot be accepted under AS 1554.1 if the level of permitted imperfections for that category is exceeded, unless it can be demonstrated by a fracture mechanics assessment that the defects will not be injurious to the performance of the structure (refer to Design Guide 3 for a more detailed explanation). The selection of weld category is at the discretion of the designer but it is expected that most welds will be weld category SP in practice. Capacity factors for each weld category are as follows: Complete penetration butt welds GP (general purpose)

φ = 0.6 (Table 3.4 of AS 4100)

Category GP may be selected where the weld is essentially statically loaded and is not loaded above 66.7% of the design capacity of a SP weld. SP (structural purpose)

φ = 0.9 (Table 3.4 of AS 4100)

Category SP shall be selected where a GP quality weld is not appropriate. The cut-off value of 66.7% for the two weld types is due to the ratio of GP to SP capacity factors (φ), i.e.: 0.6/0.9 ×100 = 66.7% Fillet weld/Incomplete penetration butt weld/Plug or slot weld/Weld group GP (general purpose)

φ = 0.6 (Table 3.4 of AS 4100)

Category GP may be selected where the weld is essentially statically loaded and is not loaded above 75% of the design capacity of a SP weld. SP (structural purpose)

φ = 0.8 (Table 3.4 of AS 4100)

Category SP shall be selected where a GP weld quality is not appropriate. The cut-off value of 75% for the two weld types is due to the ratio of GP to SP capacity factors (φ), i.e.: 0.6/0.8 ×100 = 75%


55

4


4.4

Design of butt welds—Strength limit state

Complete penetration butt weld AS 4100 Clause 9.7.2.7 requires that the design capacity is taken as equal to the nominal capacity of the weaker part of the parts joined multiplied by the capacity factor (φ) of: 0.90—weld category SP 0.60—weld category GP provided that the weld procedure is qualified in accordance with AS 1554.1 (Ref. 14). To specify this type of weld on a drawing, the term ‘complete penetration butt weld’ or the appropriate symbol from AS 1101.3 is sufficient (Fig. 29). The design throat thickness is then the size of the weld which is the minimum depth which the weld extends from its face into a joint—that is the thickness of the thinner part. Incomplete penetration butt weld AS 4100 Clause 9.7.2.7 requires that the design capacity shall be calculated as for a fillet weld using a design throat thickness determined using Clause 9.7.2.3(b) of AS 4100. The size of an incomplete penetration butt weld is a function of: (a)

the required design throat thickness

(b)

the welding process

(c)

the details of the weld preparation

and rather than specifying the size of such a weld on the drawings it is usual to specify the required design throat thickness. This then allows the fabricator to produce the required weld by selecting the most advantageous combination of welding process, weld preparation and welding position. The whole procedure must be qualified in terms of AS 1554.1 before fabrication commences. AS 4100 Clause 9.7.2.3 specifies the design throat thickness of a butt weld as follows: (a)

Complete penetration butt weld—The design throat thickness for a complete penetration butt weld shall be the size of the weld.

(b)

Incomplete penetration butt weld—The design throat thickness for an incomplete penetration butt weld shall be as follows: (i)

Prequalified preparation for incomplete penetration butt weld, except as provided in (iii), as specified in AS 1554.1 (Ref. 14).

(ii)

Non-pre-qualified preparation for incomplete penetration butt weld, except as provided in (iii)— (A)

where θ < 60° …

(d – 3) mm, for single V weld; [(d 3 + d 4) –6] mm, for double V weld

(B)

where θ >60° …

d mm, for single V weld; (d 3 + d 4) mm, for double V weld

where d

= depth of preparation (d 3 and d 4 are the values of d for each side of the weld)

θ

= angle of preparation.


56

(iii)

For an incomplete penetration butt weld made by an automatic arc welding process for which it can be demonstrated by means of a macro test on a production weld that the required penetration has been achieved, an increase in design throat thickness up to the depth of preparation may be allowed. If the macro test shows penetration beyond the depth of preparation, an increase in design throat thickness up to that shown in Figure 9.7.3.4 (of AS 4100) may be allowed.’

For fully-automatic arc welding processes, Clause 9.7.2.3(b)(iii) permits advantage to be taken of the penetration achievable with such processes to reduce the size of the weld deposited, provided a macro test demonstrates the viability of the procedure (see Figure 30).

(a) Incomplete penetration butt weld made by other than a fully automatic process

(b) Incomplete penetration butt weld made by a fully automatic process

FIGURE 30 DESIGN THROAT THICKNESS OF INCOMPLETE PENETRATION BUTT WELD


57

4


4.5

Design of fillet welds—Strength limit state

AS 4100 Clause 9.7.3.10 specifies that a fillet weld subject to a design force per unit length v w* (kN/mm) shall satisfy: v w* ≤ φv w

where: φ

= capacity factor = 0.80 SP category fillet weld = 0.60 GP category fillet weld

vw

= nominal capacity of fillet weld per unit length (kN/mm)—see Tables 23, 24 = 0.6 fuw tt k r

fuw = nominal tensile strength of deposited weld metal—see Table 22 tt

= design throat thickness

kr

= reduction factor to account for the length of a welded lap connection = 1.0 for most connections except long lap splices

The design throat thickness is the smallest dimension from the root of the weld to the hypotenuse of the triangular weld profile, drawn perpendicular to the hypotenuse (see Figure 31).

FIGURE 31 DESIGN THROAT THICKNESS OF FILLET WELDS Advantage may be taken of the increased penetration achievable with a fully automatic welding process, in order to reduce the size (but not the design throat thickness) of a fillet weld—85% of the penetration being considered as part of the design throat thickness (see Figure 31(c)). The viability of the increased penetration must be demonstrated by means of a macro test. handbook 1 design of structural steel connections, first edition

58

Remarks on (equal) fillet weld leg sizes, tw are as follows: 1)

for tw = 3–5 mm: Used for a minimum size fillet weld

2)

for tw = 6–8 mm: Sizes preferred for structural connections—single pass welds.

3)

for tw = 10–12 mm: Not recommended for all cases—cannot be guaranteed as single pass welds. Check with fabricator before specifying. TABLE 23 STRENGTH LIMIT STATE DESIGN CAPACITIES OF EQUAL LEG FILLET WELDS PER UNIT LENGTH Category SP, φ = 0.8, k r = 1.0 Weld size

Design capacity per unit length of weld, φv w

(mm)

(kN/mm) Leg: tw

Throat: t t

E41XX/W40X

E48XX/W50X

3

2.12

0.417

0.489

4

2.83

0.557

0.652

5

3.54

0.696

0.815

6

4.24

0.835

0.978

8

5.66

1.11

1.30

10

7.07

1.39

1.63

12

8.49

1.67

1.96

f uw = 410 MPa

f uw = 480 MPa

t t = t w/ 2

where: f uw = nominal tensile strength of the weld metal (Table 22)

TABLE 24 STRENGTH LIMIT STATE DESIGN CAPACITIES OF EQUAL LEG FILLET WELDS PER UNIT LENGTH Category GP, φ = 0.6, k r = 1.0 Weld size

Design capacity per unit length of weld, φv w

(mm)

(kN/mm) Leg: tw

Throat: t t

E41XX/W40X

E48XX/W50X

3

2.12

0.313

0.367

4

2.83

0.417

0.489

5

3.54

0.522

0.611

6

4.24

0.626

0.733

8

5.66

0.835

0.978

10

7.07

1.04

1.22

12

8.49

1.25

1.47

t t = t w/ 2

f uw = 410 MPa

f uw = 480 MPa

where: f uw = nominal tensile strength of the weld metal (Table 22)

Theoretical and experimental work indicates that longitudinally loaded fillet welds provide lower strength but higher ductility than transversely loaded fillet welds (Refs. 19, 20). This is not reflected in the nominal capacity expression of AS 4100 but the lower bound longitudinally loaded strength is used together with an average capacity factor, to give the design capacity. The increase in strength for transversely loaded fillet welds is variously estimated at 13% (Ref. 19) to 44% (Ref. 20) but the decrease in ductility is a factor of 4 (Ref. 20). handbook 1 design of structural steel connections, first edition

59

AS 4100 Clause 9.7.3.10 specifies that the design force per unit length on a fillet weld shall be determined as the vectorial sum of the design forces per unit length on the effective area of the weld. The effective area is taken as the product of the effective length and the design throat thickness (AS 4100 Clause 9.7.3.6). For the design of a fillet weld, AS 4100 Clause 9.7.3.10 specifies that the nominal capacity be based on a failure stress of 0.6fuw in shear on the design weld throat (tt) which is assumed to be the failure plane (see Figure 32). Considering the design actions in terms of force per unit length ( v n* , v vt* , v vl* )on the fillet weld throat in Figure 32, a general form of a failure criterion may be written as (Ref. 21):

(

)

v n*2 + k v v vl*2 + v vt*2 ≤ φk w (0.6 fuw t t )

≤ φk wv w

where kv

= coefficient which varies according to the failure criteria used

v n*

= design force per unit length of weld normal to the plane of the fillet weld throat

v vl*

= design force per unit length of weld longitudinal to the plane of the fillet weld throat

v vt* = design force per unit length of weld transverse to the plane of the fillet weld throat

φ

= capacity factor

kw

= a factor to account for the failure criteria of a single weld element determined from test data

For Clause 9.7.3.10 of AS 4100, values of k v = 1.0 and k w = 1.0 were adopted based on the studies reported in Reference 21. Accordingly, AS 4100 requires that the design force per unit length be the vectorial sum of all design forces per unit length acting on the effective area of the fillet weld.

FIGURE 32 DESIGN ACTIONS ON A FILLET WELD Hence, if the design forces per unit length are resolved into three mutually orthogonal components relative to the throat of the fillet weld—as in Figure 32—then: * = vectorial sum of the three components, resultant design force per unit length v res

=

(v ) + (v ) + (v ) * 2 n

* vt

2

* vl

2

≤ φv w * The design requirement then becomes: v res ≤φv w, where values of φv w are given in Tables 23 and 24.

The design method of AS 4100 involving the calculation of fillet weld force per unit length using linear methods combined with vectorial addition of component forces is conservative, but the chosen value of the capacity factor (φ) reflects this conservatism (Ref. 21). Any other combination of design criteria would involve the use of a smaller capacity factor to arrive at essentially the same result.


60

In many actual fillet welds, it is more convenient to define a fillet weld orientation with respect to three mutually orthogonal axes, usually arranged so that the fillet weld lies in the x-y plane—as in Figure 33.

FIGURE 33 DESIGN FORCES PER UNIT LENGTH PARALLEL TO WELD GROUP AXES (x, y, z) Using this approach, three mutually orthogonal components of design force per unit length exist, being: one parallel to the fillet weld x-axis ( v x* ) one parallel to the fillet weld y-axis ( v y* ) one parallel to the fillet weld z-axis ( v z* ) * = so that v res

v x*2 + v y*2 + v z*2

≤ φv w

is the design requirement

Specifically, for a fillet weld subject only to longitudinal shear force—as in Figure 34(a)—the design capacity per unit length of fillet weld is given by: φv w = φf uw tt and

* v res = v z* since v n* = v vt* = 0, v vl* = v z*

(a) Fillet weld subject to longitudinal shear force

(b) Fillet weld subject to transverse shear force

FIGURE 34 FILLET WELD SUBJECT TO LONGITUDINAL AND TRANSVERSE SHEAR FORCES For a fillet weld subject only to transverse shear force—as in Figure 34(b)—the design capacity per unit length of fillet weld is also: φv w = φf uw tt In this case, using components resolved with respect to the throat (as Figure 32): v n* = v y* / 2 * v res =

(v

* y

/ 2

v vt* = v y* / 2

) + (v 2

* y

/ 2

)

2

= v y* ≤ φv w

v vl* = 0

is the design requirement


61

4


4.6

Weld group loaded in-plane

Fillet weld groups—Types and analysis AS 4100 Clause 9.8 specifies the assumptions which must be made in analysing fillet weld groups. No mention is made of a butt weld group because most usual connections involving a weld group are made using fillet welds. AS 4100 Clause 9.8 deals with three types of fillet weld groups, as follows: —weld group subject to in-plane loading (Clause 9.8.1) —weld group subject to out-of-plane loading (Clause 9.8.2) —weld group subject to both in-plane and out-of-plane loading (Clause 9.8.3) For each type of fillet weld group, both a general and an alternative method of analysis are permitted. It is convenient to use the general method for most connections but the alternative method for others. The above three sub-clauses nominate the assumptions which must be made for the analysis of a fillet weld group in order to determine the design force per unit length at any point in the fillet weld group. Once this design value is determined, the fillet weld must satisfy the requirements of Clause 9.7.3.10 at all points in the group. In the general method of analysis, the nominal capacity of a welded connection with a constant size weld is assessed by treating that connection as a weld group of unit thickness in isolation from the attached elements or members. The alternative method of analysis for all three types of loading on fillet weld groups states that the design force per unit length in the fillet weld group shall be determined by considering the fillet weld group to be an extension of the member connected by the fillet weld group and by proportioning the design force per unit length to satisfy equilibrium between the fillet weld group and the elements of the connected member. That is, an assumption is made about the distribution of forces so that equilibrium is satisfied at the weld/member interface. This method is specific to each connection type and will be demonstrated in Example No. 5 and when used in a relevant Design Guide. Fillet weld group loaded in-plane Clause 9.8.1.1 of AS 4100 deals specifically with a fillet weld group subject to in-plane loading which generates in-plane shear forces on the fillet weld group. The Clause restricts the design method to be used to the following assumptions: (a)

The connection plates shall be considered to be rigid and to rotate relative to each other about a point known as the instantaneous centre of rotation of the weld group.

(b)

In the case of a weld group subject to a pure couple only, the instantaneous centre of rotation coincides with the weld group centroid. In the case of a weld group subject to an in-plane shear force applied at the group centroid, the instantaneous centre of the rotation is at infinity and the design force per unit length ( v w* ) is uniformly distributed throughout the group. In all other cases, either the results of independent analyses for a pure couple alone and for an in-plane shear force applied at the weld group centroid shall be superposed, or a recognised method of analysis shall be used.

(c)

The design force per unit length ( v w* ) at any point in the fillet weld group shall be assumed to act at right angles to the radius from that point to the instantaneous centre, and shall be taken as proportional to that radius.

Note that the Clause permits the use of superposition under (b) and this method will be used extensively in this Section. Also note the similarity in wording to that for bolt groups loaded inplane—essentially the method for fillet weld groups is identical to that for such bolt groups and the development in this Section will reflect this. If a connection at the end of a member is viewed as a weld group in isolation from that member then the nominal capacity of the weld group may be determined by either an elastic or an handbook 1 design of structural steel connections, first edition

62

ultimate strength approach. Both methods are based upon assumptions (a) and (b) of Clause 9.8.1.1, that is the rotation being assumed about an instantaneous centre. The elastic or linear method is the traditional approach to the assessment of the load capacity of a weld group. The design force per unit length of weld is considered to be proportional to the distance from the instantaneous centre, as in assumption (c) of Clause 9.8.1.1, quoted above. This method has been adopted in AS 4100 because reliability studies reported in Reference 21 have indicated that the method is sufficiently reliable, while having the virtue of being simpler to apply than the alternative methods and being amenable to hand calculation. Applying the provisions of Clause 9.8.1.1 of AS 4100 to the general fillet weld group of Figure 35 the analysis proceeds as follows:

FIGURE 35 GENERAL FILLET WELD GROUP Letting

Lw ds

= length of weld = unit length of weld at point (x s, y s)

v s*

= calculated force per unit length at point (x s, y s)

then, equilibrium requires that:

Fy* =

∑ (v ∑ (v

M z* =

∑ [v

Fx* =

)

(Eqn 4.7.1)

)

(Eqn 4.7.2)

* s

d s sin θ s

* s

d s cos θ s

* s

d s sin θ s (y s − y p ) +

s

s

] ∑ [v

s

* s

]

d s cos θ s (x s − x p )

(Eqn 4.7.3)

s

Noting that Clause 9.8.1.1(c) of AS 4100 specifies that v s* = k wr s where k w = constant of proportionality (in units of force per unit length) and r s = radius from the instantaneous centre of rotation to length d s, and further noting that: cosθs = (x s – x e)/r s

sinθs = (ys – y e)/r s

these expressions reduce to: Fx* = k w

∑ (y

s

− y e )d s

(Eqn 4.7.4)

Fy* = k w

∑ (x

s

− x e )d s

(Eqn 4.7.5)

M z* = k w

∑ (y

s

− y e ) (y s − y p )d s + k w

s

s

− x e ) (x s − x p )d s

(Eqn 4.7.6)


63

s

∑ (x

s

s

With the origin at the weld group centroid:

∑x d s

s

=

s

s

s

∑d

ds = 0

2 s

s

s

s

= L w = total length of fillet weld

s

∑y d 2 s

= lwy

∑x d +∑y d 2 s

s

s

∑x d 2 s

∑y

s

s

= lwx

= l wy + l wx = l wp

s

where lwx, l wy, and l wp are second moments of area of a weld group of unit throat thickness calculated about weld group centroid, for the x -axis, y -axis and polar axis respectively. Using these substitutions, the three equations of equilibrium may be re-written as: Fx* = – k wLwy e

(Eqn 4.7.7)

Fy* = – k wLwx e

(Eqn 4.7.8)

M z* = k w[l wp + Lw( x ex p + y ey p)]

(Eqn 4.7.9)

Rearranging these equations gives explicit solutions for the three unknowns ( x e, y e, k w):

xe

= −

ye

= −

kw

=

Fy*

(Eqn 4.7.10)

k w Lw

Fx* k w Lw

(Eqn 4.7.11)

M z* + Fx* y p + Fy* xp

(Eqn 4.7.12)

l wp

Hence, the design force per unit length ( v w* ) at any point ( x s, y s) is given by: v w* = k wr s

where r s =

(xs − xe ) 2 + (y s − y e ) 2

(Eqn 4.7.13)

v w* must be less than φv w (design capacity per unit length), given in Tables 22 and 23.

An alternative method of solution is to apply the principle of superposition permitted in AS 4100 Clause 9.8.1.1(b). For the weld group of Figure 35, the applied design actions may be * transferred to the weld group centroid to give a design action set ( Fx* , Fy* , M zo ) where: * * * * M zo = M z + Fx y p − Fy x p

(Eqn 4.7.14)

From Clause 9.8.1.1(b) of AS 4100, in-plane shear forces are uniformly distributed so that: v x*

= force per unit length in x -axis direction due to Fx* = Fx* / Lw

v y*

* = force per unit length in y -axis direction due to Fy * = Fy / Lw

* ) applied at the weld group centroid, For the pure couple ( M zo

xe

= ye = 0

then

kw

=

with

v m* = k wr s

and

* M zo and rs = l wp

Fy* = Fx* = 0

x s2 + y s2

* * Taking components of v m* parallel to the x – ( v mx ) and y – ( v my ) axes gives (see Figure 36)

* * * v mx = − v m sin θ s = − v m

* * * v my = + v m cos θ s = + v m

ys M* y = − zo s rs l wp

(Eqn 4.7.15)

xs M* x = + zo s rs l wp

(Eqn 4.7.16)


64

FIGURE 36 HORIZONTAL AND VERTICAL WELD COMPONENT FORCES AT A POINT IN A WELD GROUP Superposition of the components due to each design action gives: v x*

=

v y*

=

* ys Fx* M zo − Lw l wp

Fy* Lw

+

* M zo xs l wp

(Eqn 4.7.17) (Eqn 4.7.18)

with the resultant force per unit length being given as: * v res =

(v ) + (v ) * 2 x

* 2 y

(Eqn 4.7.19)

which must be less than φv w (design capacity per unit length). Equations 4.7.13 and 4.7.19 are alternative design requirements—either may be used as desired—each of which complies with the requirements of AS 4100.


65

4


4.7

Weld group loaded out-of-plane

Clause 9.8.2.1 of AS 4100 deals specifically with a fillet weld group subject to out-of-plane loading which generates out-of-plane shear forces on the fillet weld group. The Clause restricts the design method to be used to the following assumptions: (a)

The fillet weld group shall be considered in isolation from the connected element; and

(b)

The design force per unit length in the fillet weld resulting from a design bending moment shall be considered to vary linearly with the distance from the relevant centroidal axes. The design force per unit length in the fillet weld group resulting from any shear force or axial force shall be considered to be uniformly distributed over the length of the fillet weld group.

Clause 9.8.2.1 of AS 4100 does not specifically mention that superposition is permitted but the Commentary (Ref. 8) states that the same comments as were made about Clause 9.8.1.1 apply. Superposition is thus assumed to be permitted for out-of-plane loading in this Guide. As with the analysis for in-plane loading, the weld group loaded out-of-plane is analysed by treating it as a weld group of unit thickness and is considered in isolation from the member (Figure 37). Once again, the nominal capacity could be determined by either a linear or an ultimate strength approach. However, Clause 9.8.2.1(b) of AS 4100 specifically mentions a linear relationship for determining the design force per unit length in the fillet weld resulting from the design bending moment. The same comments made earlier about the reasons for AS 4100 using the linear method in relation to in-plane loading also apply for out-of-plane loading.

FIGURE 37 FILLET WELD GROUP LOADED OUT-OF-PLANE For out-of-plane loading, AS 4100 Clause 9.8.2.1(b) is quite specific in stating that for a fillet weld group subject to moment the design force per unit length is related to distance from the weld group centroid. Accordingly, for the weld group of Figure 37, analogous equations to Eqns in Section 4.7 can be written as follows: v

or

* x

Fx* = Lw

(Eqn 4.8.1)

Fy*

v y*

=

v z*

=

Fz* M x* y for moment M x* about x-axis as in Figure 37 + Lw l wx

(Eqn 4.8.3)

v z*

=

* Fz* M y x for moment M y* about y-axis (not shown in Figure 37) + Lw l wy

(Eqn 4.8.4)

(Eqn 4.8.2)

Lw

The resultant design force per unit length is: * v res =

(v ) + (v ) + (v ) * 2 x

* 2 y

* 2 z

using Clause 9.7.3.10 of AS 4100

which must be less than φv w (design capacity per unit length). handbook 1 design of structural steel connections, first edition

66

4


4.8

Weld group loaded by general set of design actions

Page 1 of 2

For a fillet weld group subject to both in-plane and out-of-plane loading simultaneously, Clause 9.8.3.1 of AS 4100 states that the design action shall be obtained using the previous methods for in-plane and out-of-plane loading separately such that Clause 9.7.3.10 of AS 4100 is satisfied at all points, and the design shear forces per unit length in different directions being combined using vectorial addition. Hence, for the general fillet weld group of Figure 38, subject to both in-plane and out-of-plane loading:

FIGURE 38 GENERAL FILLET WELD GROUP the general design expressions become—by combining Eqns 4.7.17, 4.7.18, 4.8.1, 4.8.2, 4.8.3 and 4.8.4 v x*

=

v y*

=

v z*

=

Fx* M z* y − Lw l wp

Fy* Lw

+

M z* x l wp

* Fz* M x* y M y x + − Lw l wx l wy

(Eqn 4.9.1)

(Eqn 4.9.2)

(Eqn 4.9.3)

where v x* , v y* and v z* are the design forces per unit length in the x , y , z directions respectively on an

elemental length of weld. The x and y -axes are the principal axes of the weld group and the z -axis is perpendicular to the weld group and through the centroid. Fx* , Fy* and Fz* are the design forces applied to the weld group along the x , y , z axes

respectively. M x* , M y* and M z* are the design bending moments applied to the weld group about the

respective x , y , z-axes, with M z* moments due to in-plane forces being determined relative to weld centroid location.


67

lwx and lwy are the second moment of areas of the weld group for a unit thickness of weld about the x and y-axes respectively. l wp(= lwx + l wy) is the polar moment of inertia about the z -axis, and L w is the total length of weld. It is also legitimate for the above expressions to be slightly modified in order to allow them to reflect realistic distributions of the force set ( Fx* , Fy* and Fz* ) between components of the total weld group, as follows: v x*

=

v y*

=

v

* z

Fx* M z* y − Lwx l wp

Fy* Lwy

+

(Eqn 4.9.4)

M z* x l wp

(Eqn 4.9.5)

* Fz* M x* y M y x + − = Lwz l wx l wy

(Eqn 4.9.6)

where

L wx, L wy , L wz = the lengths of weld assumed to receive the component forces along the individual x , y and z -axes respectively; The resultant design force per unit length is: * v res =

(v ) + (v ) + (v ) * 2 x

* 2 y

* 2 z

which must be less than φv w as before.


68

4


4.9

Properties of common fillet weld groups

TABLE 25 PROPERTIES OF COMMON FILLET WELD GROUPS TREATED AS LINE ELEMENTS Type of fillet weld group

x

y

lwx

lwy

lwp

—

d 2

d3 12

0

d3 12

d3 + 6 b 2d a 3 + + 2 3 2 a(b − a )

ad 2 + ad 2 +

b 2

d 2

b 2

d 2

For a = 0

For a = b

b

2

(2b + d )

2ab + b 2a + 2b + d 2

For a = 0 2

b (2b + d )

(2a + d )d 2(a + b + d ) For a = b

d 2

d 2 For a = 0

d 2

For a = 0

d3 6

b 2d 2

bd 2 a 3 + + 2 3 2 a(d − a )

b3 + ab 2 6

For a = 0 bd 2

a2 + b2 2(a + b + d )

b 2d a 3 2 + + a(b − a ) 2 3

d3 6

(

)

d 3 b 2d + 6 2 bd 2 a 3 + + 2 3 b3 2 a(d − a ) + + ab 2 6

For a = 0

For a = 0

b3 6

2

a d − y 2+

For a = 0

a3 ⎛a ⎞ + a⎜ − x ⎟ 2 + 12 ⎝2 ⎠ 3 2 b dx + + 12 ⎛b ⎞ b⎜ − x ⎟ 2 ⎝2 ⎠

3

d + 12

2 ⎛d ⎞ d ⎜ − y ⎟ 2 + by ⎝2 ⎠

For a = b d2 (6b + d ) 12

a 3 a(d − a ) 2 + 6 2 bd 2 d 3 + + 2 12 For a = 0 d2 (6b + d ) 12

bd 2 b 3 + 2 6

l wx + l wy

For a = b

b 3 (b + 2d ) 3 (2b + d )

(

)

2a b − x 2 + d x +

2

2b 3 ⎛b ⎞ + 2b⎜ − x ⎟ 2 12 ⎝2 ⎠

For a = 0

l wx + l wy

b 3 (b + 2d ) 3 (2b + d )


69

TABLE 25 ( continued) PROPERTIES OF COMMON FILLET WELD GROUPS TREATED AS LINE ELEMENTS Type of fillet weld group

x

lwx

y

lwy

b 2

d 2

d bd + 6 2

b 2

d 2

bd 2 +

d 2

d 2

πd 3 8

3

2

d3 6

3

b db + 6 2

b3 3

πd 3 8


lwp

2

d 3 bd 2 + 6 2 3 b db 2 + + 6 2

bd 2 +

d 3 b3 + 6 3

I wx + I wy

70

4


4.10 Practical fillet weld groups

Critical points Many fillet weld groups comprise lines of welds parallel to the x and y axes. For such relatively regular fillet weld groups, the identification of possible critical points is correspondingly more straightforward.

FIGURE 39 POSSIBLE CRITICAL POINTS IN PARTICULAR FILLET WELD GROUP The possible critical points for a fillet weld group consisting of lines of weld parallel to the x and y axes only are shown numbered 1 to 8, in Figure 39. Governing design equation * v res =

(v ) + (v ) + (v ) * 2 x

* 2 y

* 2 z

≤ φv w = φ (0.6 fuw t t )

(Section 4.9)

Design procedure The design of any general fillet weld group subject to a general design action set ( Fx* , Fy* , Fz* , M x* , M y* , M z* ) may be obtained by evaluating the design action set ( v x* , v y* , v z* ) using the

equations given in Section 4.9, using the property set ( L wx, L wy , L wz , I wx , I wY, I wp ,) from Table 24, and checking that the governing inequality given above is satisfied, at each of the critical points (1-8).


71

Restricted cases of forces on weld elements For a fillet weld group loaded ‘in-plane’ by a common design action set of forces ( Fx* , Fy* ) and design moment ( M z* ), the design force equations reduce to the expressions: Fx* M z* y − v x* = Lwx I wp v y* v

* z

=

Fy* Lwy

−

M z* x I wp

= 0

For a fillet weld group loaded ‘out-of-plane’ by a common design action set of forces ( Fy* , Fz* ) and design moment ( M x* ), the design force equations reduce to the expressions: v x*

= 0

v y*

=

v z*

=

Fy* L wy Fz* M*y + x L wz I wx

FIGURE 40 FILLET WELD GROUP LOADED IN- AND OUT-OF-PLANE Examining two types of weld groups common to a number of connections in order to obtain simple closed-form solutions for subsequent use in other Design Guides gives the following: (a)

Two parallel vertical welds loaded out-of-plane Consider the fillet weld group shown in Figure 41 which is loaded by an out-of-plane moment ( M x* ) and design vertical ( Fy* ) and horizontal ( Fz* ) shear forces acting at the weld group centroid. Weld group properties are: L wx = L wy = L wz =2 L w

I wx

=

y

=

(L ) w

6

±

Lw 2

3

(Table 24) at points 3, 4, 7, 8 (+ve at 3, 8,

-ve at 4, 7 in Figure 41) Design forces per unit length using the above equations 4.9.4 to 4.9.6 and the above weld group properties are: v x*

= 0

v y*

* = Fy / (2Lw )

v z*

=

Fz* M *L / 2 + x w3 at points 3, 8 (top) 2Lw (Lw ) / 6

=

Fz* M *L / 2 at points 4, 7 (bottom) − x w3 (Lw ) / 6 2Lw

FIGURE 41 TWO PARALLEL VERTICAL WELDS LOADED OUT-OF-PLANE


72

(v ) + (v )

Governing equation—vectorial addition

* 2 y

* 2 z

≤ φv w

Substitution of the appropriate design forces per unit length ( v y* , v z* ) into this equation enables the fillet weld group to be rapidly designed for any action set ( Fy* , Fz* , M x* ). For Fz* = 0, M x* = 0

since v z* = 0, the design requirement reduces to v y* ≤ φv w since v y* = Fy* /(2 L w) then Fy* ≤ 2 L w ( φv w)

Hence, φv dv = design capacity of fillet weld group subject to vertical shear only = 2 L w( φv w) since v y* = 0, the design requirement reduces to v z* ≤ φv w For Fy* = 0, M x* = 0 since v z*

= Fz* /(2 L w) then Fz* ≤ 2 L w ( φv w)

Hence, φv dh = design capacity of fillet weld group subject to horizontal shear only = 2 L w( φv w) For Fy* = 0, Fz* = 0

since v y*

* = 0 and v z ±

3M x* L2w

the design requirement reduces to v z* ≤φv w

∴ M z* ≤ Hence, φMdm

1 2 Lw (φv w ) 3

= design capacity of fillet weld group subject only to moment applied at the weld group centroid =

1 2 Lw (φv w ) 3

For Fz* = 0, M x* = Fy* e, e = eccentricity of Fy* v y* =

Fy* 2Lw

v z* = ±

3M x* L2w

=±

3Fy* e L2w

On substitution into the governing equation of Section 4.9: ⎡ Fy* ⎢ ⎢⎣ 2L w then Fy* ≤

⎤ 2 ⎡ 3Fy* e ⎤ 2 ⎥ + ⎢ 2 ⎥ ≤ (φv w ) 2 ⎥⎦ ⎢⎣ L w ⎥⎦ 2Lw (φv w )

(the design capacity of a fillet weld group subject to a vertical shear force ⎛ 6e ⎞ 2 ⎟ 1 + ⎜⎜ ⎟ ⎝ Lw ⎠ only at an eccentricity of e).


73

(b)

Two parallel horizontal welds loaded out-ofplane

Consider the fillet weld group shown in Figure 42 which is loaded out-of-plane by a moment ( M x* ) and design vertical ( Fy* ) and horizontal ( Fz* ) shear forces acting at the weld group centroid. Weld group properties are: L wx

= L wy = L wz = 2L w

I wx

=

Lw t 2 (Table 24) 2

at points 1, 2, 5, 6 y = t/2 in Figure 42 Design forces per unit length using previous equations and the above weld group properties are: v x*

= 0

v y*

= Fy* / (2Lw )

v z*

=

Fz* M * (t / 2) + x 2 2Lw Lw t / 2

=

Fz* M* + x at points 1, 2 in Figure 42 2Lw Lw t

=

Fz* M * (t / 2) − x 2 2Lw Lw t / 2

=

Fz* M* − x at points 5, 6 in Figure 42 2Lw Lw t

FIGURE 42

Governing equation—vectorial addition ( v x* = 0) For Fz* = 0, M z* = 0

(v ) + (v ) * y

2

* z

2

≤ φv w

* since v z* = 0, the design requirement reduces to v y ≤ φv w

since v y* = Fy* /(2 L w) then Fy* ≤ 2 L w ( φv w) Hence, φv dv = design capacity of fillet weld group subject to vertical shear only = 2 L w( φv w) For Fy* = 0, M x* = 0

since v y* = 0, the design requirement reduces to v z* ≤ φv w since v z* = Fz* /(2 L w) then Fz* ≤ 2 L w ( φv w)

Hence, φv dh = design capacity of fillet weld group subject to horizontal shear only = 2 L w( φv w) For Fy* = 0, Fz* = 0

M x* then M x* ≤L wt( φv w) Lw ⋅ t

since v z* = ± Hence, φMdm

∴ v z* ≤φv w (as above)

since v y* = 0

= design capacity of fillet weld group subject only to moment applied at the weld group centroid = L wt( φv w)

For Fz* = 0, M x* = Fy* e, (e = eccentricity of Fy* ) v y* =

Fy*

2Lw

*

v z* = ±

Fy e M x* (at points 1, 2, 5, 6) =± Lw t Lw t

On substitution into the governing equation of Section 4.9: ⎡ Fy* ⎤ 2 ⎡ Fy*e ⎤ 2 2 ⎥ ≤ (φv w ) ⎥ +⎢ ⎢ ⎢⎣ 2Lw ⎥⎦ ⎢⎣ Lw t ⎥⎦ 2Lw (the design capacity of a fillet weld group subject to a vertical shear then Fy* ≤ (φv w ) 1 + 4(e / t ) 2

force only at an eccentricity of e ). handbook 1 design of structural steel connections, first edition

74

4


4.11 Design example No. 4— Design of fillet weld group loaded in-plane

Using Table 25, type 4 weld group with a = b = 275 mm; d = 300 mm Weld centroid:

=

x

b2 2b + d

= 89.0 mm Design actions: F = 0 Fy* = –180 kN (Figure 40a) M z* = –180 × (275 + 175 – 89.0) * x

= –64980 kNmm

FIGURE 43 FILLET WELD GROUP LOADED IN-PLANE Weld group properties:

L wx I wp

= 2 × 275 + 300 = 850 mm = L wy = L wz = L w = 850 mm (total weld length resists shear force) = I wx + I wy

I wp

=

Lw

assume

300 2 (6 × 275 + 300 ) 275 3 (275 + 2 × 300 ) + (Table 25) 12 3(2 × 275 + 300 )

= 21.8 × 10 6 mm3 at points 1, 6:

x y

at points 2, 3, 4, 5: x

= 275 – 89.0 = +186 = ± 300/2 = ± 150 y = ± 150

= –89.0

Design forces per unit length: v x*

=

− M z* y − 64980 × 150 =− I wp 21.8 × 10 6

= +0.447 at points 1, 2, 3 ( y = +150) = –0.447 at points 4, 5, 6 ( y = –150) v y*

=

Fy* L wy

+

M z* x − 180 − 64980 × 186 = + 850 I wp 21.8 × 10 6

= –0.767 at points 1, 6 =

(critical)

−180 −64980 × (−89.0 ) + 850 21.8 × 106

= +0.054 at points 2, 3, 4,5

(not critical)

Resultant design force per unit length: points 1, 6 (critical points) * v res =

(± 0.447 ) +(− 0.767 ) 2

2

= 0.888 kN/mm From Table 25—SP weld category 6 mm E48XX fillet weld * φv w = 0.978 kN/mm > v res


SATISFACTORY 75

4


4.12 Design example No. 5— Design of fillet weld group loaded out-of-plane

FIGURE 44 FILLET WELD GROUP LOADED OUT-OF-PLANE Design actions:

Fy* = –450 kN M x*

Fz* = 0

= 90 kNm = 90000 kNmm

Weld group properties: L w = 2(300 + 200) = 1000 mm (Table 25)

Use AS 4100 Clause 9.8.2.2 Alternative analysis due to the connection type. It can be assumed that the vertical shear is primarily taken by the webs of the box section. If so this vertical shear must be assumed to be transferred through the vertical fillet weld only. Hence, L wy = 2 × 300 = 600 mm For weld group, = 300 mm d = 200 mm b I wx =

at points 1, 2, 3, 8 y at points 4, 5, 6, 7 y

d 3 bd 2 + (Table 25, type no. 6 weld group) 6 2

= 13.5 × 10 6 mm3 on substitution = 150 mm = –150 mm

Design forces per unit length: v x* = 0 v y*

= =

v z*

= = =

−450 = −0.75 at points 3, 4, 7, 8 600 0 at points 1, 2, 5, 6 90000 × (± 150 ) 13.5 × 10 6 +1.00 at points 1, 2, 3, 8 ( y = +150) –1.00 at points 4, 5, 6, 7 ( y = –150)

Resultant design force per unit length: * v res =

(− 0.75) 2 +(± 1.00 ) 2

= 1.25 kN/mm From Table 23—SP weld category 8 mm E48XX fillet weld * φv w = 1.30 kN/mm > v res


SATISFACTORY 76

5

CONNECTION COMPONENTS

5.1

Angle components

NOTES: 1

Only sizes likely to be used in structural connections are included.

2

Grade—commonly available only in Grade 300 to AS/NZS 3679.1 (Ref. 29).

TABLE 26 EQUAL ANGLES— RATIONALISED DIMENSIONS FOR DETAILING Designation Leg size Ration’d thickness b1 × b1 mm mm 200×200×

150×150×

125×125×

100×100×

90× 90×

75× 75×

mm 26EA 20EA 18EA 16EA 13EA 19EA 16EA 12EA 10EA 16EA 12EA 10EA 8EA 12EA 10EA 8EA 6EA 10EA 8EA 6EA 10EA 8EA 6EA 5EA

Mass per m kg/m 76.8 60.1 54.4 48.7 40.0 42.1 35.4 27.3 21.9 29.1 22.5 18.0 14.9 17.7 14.2 11.8 9.2 12.7 10.6 8.22 10.5 8.73 6.81 5.27

Dimensions Actual thickness t r1 mm mm 26.0 18 20.0 18 18.0 18 16.0 18 13.0 18 19.0 13 15.8 13 12.0 13 9.5 13 15.8 10 12.0 10 9.5 10 7.8 10 12.0 8 9.5 8 7.8 8 6.0 8 9.5 8 7.8 8 6.0 8 9.5 8 7.8 8 6.0 8 4.6 8

Centre of area r2 mm 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

pB = nL mm 59 57 56 55 54 44 43 42 41 37 35 34 34 29 28 28 27 26 25 24 22 21 21 20

Designation Leg size Ration’d thickness b1 × b1 mm mm 65×65×

55×55× 50×50×

mm 10EA 8EA 6EA 5EA 6EA 5EA 8EA 6EA 5EA 3EA

Mass per m kg/m 9.02 7.51 5.87 4.56 4.93 3.84 5.68 4.46 3.48 2.91

Dimensions Actual thickness r2 t r1 mm mm mm 9.5 6 3 7.8 6 3 6.0 6 3 4.6 6 3 6.0 6 3 4.6 6 3 7.8 6 3 6.0 6 3 4.6 6 3 3.0 6 3

Centre of area pB = nL mm 20 19 18 18 16 15 15 15 14 13

NOTE: Dimensions may not add correctly due to rounding.

TABLE 27 UNEQUAL ANGLES— RATIONALISED DIMENSIONS FOR DETAILING Designation Leg size b1 × b2

Ration’d thickness

mm mm 150×100×

mm 12UA 10UA 16UA 12UA 10UA 8UA 12UA 10UA 8UA 6UA 10UA 8UA 6UA

150× 90×

125× 75×

100× 75×

Mass per m kg/m 22.5 18.0 27.9 21.6 17.3 14.3 17.7 14.2 11.8 9.16 12.4 10.3 7.98

Dimensions Actual thickness r2 t r1 mm mm mm 12.0 10 5 9.5 10 5 15.8 10 5 12.0 10 5 9.5 10 5 7.8 10 5 12.0 8 5 9.5 8 5 7.8 8 5 6.0 8 5 9.5 8 5 7.8 8 5 6.0 8 5


Centre of area pB mm 49 48 52 51 50 49 43 42 42 41 32 31 30

nL mm 24 23 23 21 20 20 18 17 17 16 19 19 18

77

TABLE 28 GAUGE LINES FOR ANGLES

Nominal leg length

s g1

s g2

s g3

Bolt

Nominal leg length

s g3

Bolt

200

75

75

120

M24

100

55

M20

150

55

55

90

M20

90

55

M20

125

45

50

75

M20

75

45

M20

65

35

M16

55

35

M16

50

30

M16

NOTES: 1

The gauges given are suitable for general use in member detailing. When angles are used as components in connections, gauge lines may be varied from the values given above in order to suit a particular connection.

2

The bolt diameters listed are the maximum that can be accommodated on the thickest angles of each leg length, using either: (a)

high strength structural bolts with washers to AS/NZS 1252 (Ref. 6); or

(b)

commercial bolts with ‘large series’ washers to AS 1237 (Ref. 23).

For thinner legs and commercial bolts with ‘normal series’ washers, it may be possible to accommodate a larger bolt diameter.

TABLE 29 STRENGTHS OF ANGLES TO AS/NZS 3679.1 (Ref. 29) GRADE 300 Thickness of angle

Yield stress

Tensile strength

mm

MPa

MPa

<11

320

440

≥11, ≤17

300

440

>17

280

440


78

5


5.2

Flat bar components

NOTES: 1

Only sizes likely to be used in structural connections are included.

2

Only a limited range of sizes listed may be available at the time of fabrication. Check manufacturer or steel merchant catalogues for current availability.

3

Commonly available in Grade 300 to AS/NZS 3679.1 (Ref. 29).

TABLE 30 FLATS Width × thickness

Width × thickness

mm mm 50 × 5 50 × 6 50 × 8 50 × 10 50 × 12 50 × 16 50 × 20 50 × 25

Mass per metre kg/m 1.96 2.36 3.14 3.92 4.71 6.28 7.85 9.81

mm mm 110 × 6 110 × 8 110 × 10 110 × 12 130 × 5 130 × 6 130 × 8 130 × 10


65 × 5 65 × 6 65 × 8 65 × 10 65 × 12

2.55 3.06 4.08 5.10 6.12

130 × 12 130 × 16 130 × 20 130 × 25 150 × 5

12.2 16.3 20.4 25.5 5.89

65 × 16 65 × 20 75 × 5

8.16 10.2 2.94

150 × 6 150 × 8 150 × 10

7.06 9.42 11.8

Thickness of bar mm

Yield stress MPa

Tensile strength MPa

75 × 6 75 × 8 75 × 10

3.53 4.71 5.89

150 × 12 150 × 16 150 × 20

14.1 18.8 23.5

<11 ≥11, ≤17 >17

320 300 280

440 440 440

75 × 12 75 × 16 75 × 20 75 × 25 75 × 40 90 × 6 90 × 8 90 × 10 90 × 12 100 × 5 100 × 6 100 × 8 100 × 10

7.06 9.42 11.8 14.7 23.6 4.24 5.65 7.06 8.48 3.92 4.71 6.28 7.85

150 × 25 150 × 50 180 × 6 180 × 10 180 ×12 180 × 20 200 × 6 200 × 8 200 × 10 200 × 12 200 × 16 200 × 20 200 × 25

29.4 58.9 8.48 14.1 17.0 28.3 9.42 12.6 15.7 18.8 25.1 31.4 39.2

× × × × ×

9.42 12.6 15.7 19.6 39.2

100 100 100 100 100

12 16 20 25 50

Width × thickness

mm mm 250 × 6 250 × 8 250 × 10 250 × 12 300 × 6 300 × 8 300 × 10 300 × 12


Strength of flat bars to AS/NZS 3679.1 (Ref. 29) Grade 300


79

5


5.3

Plate components

Standard thicknesses of plate available in Grade 250 to AS/NZS 3678 (Ref. 27) are as follows: 5, 6, 8, 10, 12, 16, 20, 25, 28, 32, 36, 40, 45, 50 mm Typical applications for connection components cut from plate are: —end plates (flexible, rigid) —column base plates —fin plates —gusset plates —stiffeners —splice plates TABLE 31 STRENGTH OF PLATE TO AS/NZS 3678 (Ref. 27) GRADE 250 Thickness of plate mm ≤8 > 8, ≤ 12 >12, ≤ 50 >50, ≤ 80 >80, ≤150

Yield stress MPa 280 260 250 240 230

Tensile strength MPa 410 410 410 410 410


80

5


5.4

Design capacities

General Connection components (cleats, gusset plates, brackets) must have their strength assessed in order to determine the strength of a connection as a whole. AS 4100 Clause 9.1.9 specifies that connection components shall have their capacities assessed using the provisions of Sections 5, 6, 7 or 8 of AS 4100 as applicable. AS 4100 Table 3.4 specifies a capacity factor of 0.90 for connection components. A connection component is typically of rectangular cross-section (d i × ti ) as shown in Figure 45, with or without a single line of holes of diameter d h (as in Figure 45) or multiple lines of holes.

FIGURE 45 RECTANGULAR CONNECTION COMPONENT GEOMETRY Design shear capacity of rectangular component Since the shear distribution in a rectangular cross-section is non-uniform, Clause 5.11.3 of AS 4100 is applicable. This specifies the nominal shear capacity (Vv) as: 2Vu ⎛f* 0.9 + ⎜⎜ vm* ⎝ f va

=

Vv

⎞ ⎟ ⎟ ⎠

≤ Vu

where Vu

= the nominal shear capacity of a web with a uniform shear stress distribution determined in accordance with Clause 5.11.2 of AS 4100

* fvm , fva* = the maximum and average design shear stress respectively in the web

determined by a rational elastic analysis

Now, for a rectangular section (d i × ti ) subject to a design shear force of V*: Vu = Vw = 0.60 fyi d i ti * fvm

V *Q = Ib

fva*

3

I

=

Hence, fvm* Vv

t id i 12

Q=

(Clause 5.11.4 of AS 4100—no allowance required for holes)

V* = d it i t id i 8

2

b = ti

⎛ 1 .5 ⎞ f* ⎟⎟ therefore vm* = 1.5 = V * ⎜⎜ f va ⎝ d it i ⎠

=

2Vu = 0.833 Vu = 0.50 fyi d i ti on substitution of Vu = 0.60 fyi d i ti 0 .9 + 1 .5

∴φV v = design shear capacity of rectangular component = 0.9 Vv = 0.45 fyi d i ti ≥ V*, the design shear force handbook 1 design of structural steel connections, first edition

81

Design moment capacity—Major axis for rectangular component The rectangular component when bent about its major axis (Figure 46) would be considered compact in most connections. Thus Clause 5.2.1 of AS 4100 specifies the nominal moment capacity as: Ms = fyZ e Clause 5.2.3 gives: Ze = lesser of S (=ti d i 2/4) and 1.5 Z (= 1.5 × ti d i 2/6) Hence, Ms =

f yit i d i

2

4

and φM s = design moment capacity=

0.90 f yit id i 4

2

FIGURE 46

= 0.225 fyi ti d i 2 ≥M*, design bending moment

Local buckling in flexure is not normally a problem with connection components. Table 5.2 of AS 4100 does not provide a plasticity slenderness limit for elements with compression at one edge and tension at the other but both edges unsupported, which is the way most components are used. Usually attachment to a member prevents local buckling of the component. Clause 5.2.6 of AS 4100 only specifies an allowance for holes be made in flanges, which a rectangular component does not possess (Fig. 46). Design moment capacity—Minor axis for rectangular component

FIGURE 47 The rectangular component when bent about its minor axis would be considered compact. Thus Clause 5.21 of AS 4100 specifies the nominal moment capacity as: Ms = f yi Z e

Ze = lesser of S = d i ti 2/4

where:

1.5Z= (d i ti 2/6) × 1.5 Hence, Ms = fyi d i ti 2/4 φM s = 0.9 fyi d i ti 2/4 = 0.225 fyi d i ti 2 ≥ M* design bending moment Design capacity in axial compression for rectangular component Usually, connection components are so short that only gross section yielding can occur without any local or member buckling. Any exceptions for an individual connection will be covered in the relevant Design Guide. Accordingly, Section 6 of AS 4100 specifies the nominal capacity in axial compression as the nominal section capacity given by Clause 6.2.1, which results in: N s = k f An f yi where kf

= the form factor given in Clause 6.2.2

An = the net area of the cross-section, except that for sections with penetrations or unfilled holes that reduce the section area by less than 100 {1–[fy/(0.85fu )]}%, the gross area may be used. Deductions for fastener holes shall be made in accordance with Clause 9.1.10 of AS 4100. In the absence of local buckling, k f may be taken as 1.0 while: An = Ag for all holes filled with bolts (which is the usual case) = d i ti = (d i ti –n pd h) if holes are not filled and unfilled holes reduce gross area by more than 100 {1–[fy/(0.85fu)]}% Then, φN s = design capacity in axial compression = 0.9 Anf yi ≥ N*, the design axial compression force handbook 1 design of structural steel connections, first edition

82

Design capacity in axial tension for rectangular component Clause 7.2 of AS 4100 specifies the nominal section capacity in tension as the lesser of: Nt

= Ag f yi

Nt

= 0.85 k t An fui

and

where Ag = the gross area of the cross-section fyi

= the yield stress used in design

kt

= the correction factor for distribution of forces determined in accordance with Clause 7.3

An = the net area of the cross-section, obtained by deducting from the gross area the sectional area of all penetrations and holes, including fastener holes. The deduction for all fastener holes shall be made in accordance with Clause 9.1.10 of AS 4100 fui

= the tensile strength used in design

For components in connections, a uniform force distribution usually applies for which k t = 1.0. Now Ag = d i ti and An = d i ti – n p d h ti (Figure 48) so

Nt

≤ fyi d i ti and ≤ 0.85 fui (d i ti – n p d h ti )

∴

φN t ≤ 0.90 fyi d i t i and ≤ 0.765 fui (d i ti – n p d h ti )

and

φN t ≥ N*, the design axial force in tension

FIGURE 48 RECTANGULAR COMPONENT DESIGN CAPACITY IN AXIAL TENSION Design capacity against rupture due to block shear failure for rectangular component A connection component may fail when a block of material ruptures as illustrated in Figure 49. Figure 49(a) shows block shear failure of a gusset plate subject to tension while Figure 49(b) shows block shear failure of a cleat component subject to a shear force. AS 4100 does not address the failure mechanism of rupture due to block shear. The AISC Specification (Ref. 22) Clause J4.3 contains provisions which apply to plates, gussets, angles and brackets for block shear strength.


83

FIGURE 49 EXAMPLES OF BLOCK SHEAR FAILURE IN COMPONENTS (after Ref. 11) The following explanation of block shear failure is based on Reference 11. Block shear failure involves both shear and tensile failure, a fact which is evident in the connections shown in Figure 49. If the region subject to direct tension fractures, it will be through the bolt holes. Regions subject to shear are more difficult to assess because it is unclear whether the assessment should be on the basis of net section through the holes or gross section along a plane parallel to the applied load. Tests of gusset plates show that when the net section fractures in tension, shear action is one of yield acting on planes generally parallel to the direction of load but not through the bolt holes. Tests also show that fracture at the net tension section is reached before shear fracture takes place on the other surfaces. Clause J4.3 of the AISC Specification (Ref. 22) provides a design provision in which the design capacity is determined by the sum of the shear strength along the parallel failure surface and tensile strength on the perpendicular failure surface. The design capacity is then given by the following expression in Clause J4.3 of Ref. 22: φV bs = φ[0.6 f u Anv + fu Ant U bs ] ≤ φ[0.6f y Agv + fu Ant U bs ] where φ

= 0.75

fu

= specified minimum tensile strength of component (fui in this Guide)

fy

= specified minimum yield stress of component (fyi in this Guide)

Agv = gross area subject to shear Agt = gross area subject to tension Anv = net area subject to shear Ant = net area subject to tension U bs = 1 when tension stress is uniform = 0.5 when tension stress is non-uniform Reference 11 argues that separate equations for design capacity are required for: (a)

gusset plates, cleats, angles (connection components)—this Section.

(b)

coped beam webs (supported members)—see Section 6.9.


84

The design capacity recommended by Kulak at Reference 11 and this Design Guide for connection components such as gusset plates, angle cleats, web cleats is as follows: φV bs = φ[Ant f ui + 0.6fyi Agv) where terms are as defined above. The AISC Specification (Ref. 22) Clause J4.3 gives the same expression as above for the upper bound using U bs = 1 which the Commentary implies applies for other than multiple row shear connections in coped beam webs. The application to connection components subject to shear force is not specifically addressed in the Commentary. Relevant areas Ant and Agv are defined as shown in Figure 50.

SHEAR FORCE

TENSION FORCE

A nt = ( l t – 0.5dh ) t i

A nt

A gv = l vt i

A gv = l vt i

A gv = l vt i

dh

= hole diameter

nh = no. of holes in vertical line

ti

= thickness of component

= ( l t – 1.5dh ) t i

A nt = ( l t – ( nh – 1) dh ) t i

FIGURE 50 BLOCK SHEAR AREA IN COMPONENTS The Steel Construction Institute publication (Ref. 24) contains provisions for the assessment of block shear in connection components which appears to be based on shear yielding rather than rupture.


85

6

SUPPORTED MEMBERS

6.1

General

For the design of some connections, an assessment is required of the design capacity of the supported member in bending, shear, bearing, etc. (in particular for flexible connections) while for other connections it is useful to know the design capacity in shear or bending because the connection may be designed for a selected proportion of the member capacity (such as rigid connections or splices). Sections 6.2 to 6.4 are intended to give a summary of the relevant design capacities in bending and shear for: uncoped sections

—Section 6.2

single web coped sections

—Section 6.3

double web coped sections —Section 6.4 for use in other Design Guides when assessing connected member strength locally at a connection. Since the concern is the member strength locally at a connection, only section capacity is considered, not member capacity, which is separately assessed as part of the design of the member. For coped and uncoped sections the relevant design capacities are moment and shear (yield and buckling). The nominal capacities are derived using in Clauses 5.2, 5.11, 5.12 and 5.13 of AS 4100. So that the design capacities of coped beams do not control the design capacity of the connection it is important that the length and depth of the cope must be kept as small as practical. AS 4100 requires that the re-entrant corner at the cope be radiused to at least 10 mm (Clause 14.3.3).


86

6

SUPPORTED MEMBERS

6.2

Uncoped sections

Moment capacity The nominal section moment capacity (Ms) is calculated as follows: Ms = fyZe

(AS 4100, Clause 5.2.1)

where Ze = effective section modulus = Zc ⎡⎛ λ sy − λ s ⎞ ⎤ ⎟ (Z c − Z )⎥ ⎟ ⎢⎣⎝ λ sy − λ sp ⎠ ⎥⎦

= Z + ⎢⎜⎜

if λ s ≤ λ sp

(Clause 5.2.3)

if λ sp < λ s≤ λsy

(Clause 5.2.4)

Z = elastic section modulus S = plastic section modulus Zc = effective section modulus for a compact section = [S; 1.5Z]min Clause 5.2.2 specifies that for a section with flat compression plate elements, the section slenderness (λ s) shall be taken as the value of the plate element slenderness (λ e) for the element of the cross-section which has the greatest value of λ e/λ ey– where ⎛b⎞ ⎛ f

⎞

y ⎟ λ e = ⎜ ⎟ ⎜⎜ ⎟ ⎝ t ⎠ ⎝ 250 ⎠

λ ey = the plate element yield slenderness limit (see Table 5.2 of AS 4100, Ref. 1) b = the clear width of the element outstand from the face of the supporting plate element or the clear width of the element between the faces of supporting plate elements t

= the element thickness

The section plasticity and yield slenderness limits (λ sp) and (λsy) respectively shall be taken as the values of the element slenderness limits (λ ep) and (λ ey) respectively given in Table 5.2 of AS 4100 for the element of the cross-section which has the greatest value of λ e/λ ey . Rolled sections (HR) λ ep = 9 for a flange outstand = 82 for a web λ ey = 16 for a flange outstand = 115 for a web

Welded sections (LW) λ ep = 8 for a flange outstand = 82 for a web λ ey = 15 for a flange outstand = 115 for a web

In terms of Clause 5.2.6 of AS 4100, for sections without holes, or for sections with holes that reduce either of the flange areas by not more than 100 {1 – [f y/(0.85fu)]}%, the elastic and plastic section moduli may be calculated using the gross section. If the holes reduce either of the flange areas by more than this, Z and S shall be calculated using either: (a)

(An/Ag) times the value for the gross section, in which An is the sum of the net areas of the flanges and the gross area of the web, and Ag the gross area of the section; or

(b)

the net section.

The design section moment capacity (φMs) is calculated from the nominal section moment capacity (Ms) and the capacity factor (φ = 0.9), so that: φM s = φfy Z e Tables of Ze and φMs for rolled and welded I sections are contained in Reference 25 while tables of φMs for hollow sections are contained in Reference 26.


87

Where the area of bolt holes in the flanges are such that the limit in AS 4100 is exceeded, the following formulae for Z and S may be used to determine Ze. Using the approach based on method (b) above: SECTION WITH HOLES IN BOTH FLANGES

Defining: A = area of unholed section (gross area) Ix = second moment of area about x-axis of unholed section Sx = plastic section modulus about x-axis of unholed section n h holes × d h diameter each flange tf = flange thickness

FIGURE 51 SECTION WITH HOLES IN BOTH FLANGES A′ holed section = A – 2n h d h tf = An I x′ holed section = Ix – 2n h d h tf ⎡ d − t f ⎤ 2 ⎢ 2 ⎥ ⎣ ⎦ I ′ holed section Z x′ holed section = x d/2 Sx′ holed section = Sx – 2n h d h tf ⎡ d − t f ⎤ ⎢ 2 ⎥ ⎣ ⎦ Z e′ = min of [1.5 Z x′ , Sx′ ] for compact sections or use formula in Clause 5.2.4 of AS 4100 (Page 1 of this Section) for non-compact sections

SECTION WITH HOLES IN ONE FLANGE Defining— A = area of unholed section Ix = second moment of area about x-axis of unholed section n h holes × d h diameter bottom flange tf = flange thickness FIGURE 52 SECTION WITH HOLES IN ONE FLANGE y bh =

A d 2 − nh d h t f t f 2 A − nh d h t f

y th = d – y bh

Δy

=

I x′

holed section

Z x′

holed section top flange

Z x′

holed section bottom flange =

A′ holed section = A – n hd htf = An

y bh – d/2 nhd ht f3 – n h d h tf ⎡ d − t f ⎤ 2 – [A – n h d h t f ] Δy 2 ⎢ 2 ⎥ 12 ⎣ ⎦ I x′ holed section = y th

= Ix –

I x′ holed section y bh


88

For plastic section modulus, equating areas above/below plastic section neutral axis: bf t f + (d 1 − y bp )t w = bf t f − nh d h t f + y bp t w

solving gives y bp =

(Figure 53)

d1t w + nhd ht f 2t w

FIGURE 53 SECTION WITH HOLES IN ONE FLANGE Sx′ holed section = bf t f (d1 − y bp + t f / 2) + (d1 − y bp ) 2t w / 2 + Z e′

2 y bp tw

2

+ (bf − nhd h )t f (y bp + t f / 2)

= min of [1.5 Z x′ , Sx′ ] compact sections, formula in Clause 5.2.4 of AS 4100 (page 1 of this Section) for non-compact sections

′ = 0.9fy Ze′ φ M sx

Under method (a) of AS 4100: An Z Z x′ = A An S S x′ = A

which is a lot simpler but less exact than using method (b). The AS 4100 limits for rolled sections above which holes must be accounted for are as follows: for Grade 300 rolled sections, fu = 440 MPa fy = 280 MPa, limit is 25.1% = 300 MPa, limit is 19.8% = 320 MPa, limit is 14.4% If the deduction for holes is below these values, then the Z and S of the gross section may be used. for Grade 300 welded plate sections, fu = 430 MPa fy = 280 MPa, limit is 23.4% = 300 MPa, limit is 17.9% = 310 MPa, limit is 15.2% If the deduction for holes is below these values, then the Z and S of the gross section may be used. Note that Clause 5.2.6 of AS 4100 only requires deductions be made for holes in flanges—no deduction need be made for holes in webs. handbook 1 design of structural steel connections, first edition

89

Shear capacity

The shear stress distribution of H and channel shaped sections can be assumed to be approximately uniform, in terms of Clauses 5.11.1 and 5.11.2 of AS 4100. Hence, provided the maximum web panel depth to thickness ratio (dp/t w) of the section satisfies— dp tw

≤

82 ⎛ fy ⎞ ⎜⎜ ⎟⎟ ⎝ 250 ⎠

where dp = depth of web panel = d –2tf d

= depth of a section

tf

= thickness of flange

t w = thickness of the web the nominal shear capacity of the web (Vv) is determined as: Vv = Vw, the nominal shear yield capacity of the web = 0.6 fyA w where Aw = gross sectional area of the web = dptw (for welded sections) = dtw (for hot-rolled sections) If the above dp/t w inequality is not satisfied, then for an unstiffened web: Vv = Vb = αvV w ⎡ ⎢ ⎢ where αv = ⎢ ⎢⎛ dp ⎢ ⎜⎜ ⎢⎣ ⎝ t w

⎤ ⎥ ⎥ 82 ⎥ 2 ≤ 1 .0 ⎞ ⎛ fy ⎞ ⎥ ⎟ ⎟ ⎜ ⎟ ⎜ 250 ⎟ ⎥⎥ ⎠ ⎝ ⎠⎦

The design shear capacity of a web (φV v) is calculated from the nominal shear capacity of the web (Vv) and the capacity factor (φ = 0.9). Therefore, for an uncoped section: φVvo = 0.54fy Aw

where Aw is as defined above. AS 4100 does not have any requirement to adjust φV vo for the presence of bolt holes in the web of a connection presumably because such holes are usually filled with bolts. When a cross-section is subject to both shear force and bending moment simultaneously, AS 4100 Clause 5.12.3 provides that the nominal web shear capacity in the presence of bending moment be given by: for M* ≤0.75φM s; and

Vvm = Vv ⎡ ⎛ 1.6M * ⎞⎤ = Vv ⎢2.2 − ⎜⎜ φM ⎟⎟⎥ ⎢⎣ s ⎠⎥ ⎝ ⎦

for 0.75φMs ≤M* ≤φMs

where Vv

= the nominal shear capacity of a web in shear alone = Vvo (noted above)

Ms = the nominal section moment capacity = Mso (noted above) the design capacity being given by φVvm , where φ = 0.9. handbook 1 design of structural steel connections, first edition

90

TABLE 32A UNIVERSAL BEAMS GRADE 300 DESIGN SECTION MOMENT AND WEB CAPACITIES Holed one Holed two Holed/ flanges Unholed NOTES: flange ′ ′ φM sx φM ′sx φV v ′ φM sx calculated for two diameter holes in one flange kNm kNm kN ′sx ′ φ M calculated for two 927* 927* 1180 diameter holes in both flanges 829* 829* 1100

Unholed Designation

φM sx kNm

610UB 125 113 101

927 829 782

530UB 92.4 82.0

782*

782*

1100

640 558

578 504

544 478

939 876

460UB 82.1 74.6 67.1

496 449 399

443 401 356

412 372 333

788 719 667

410UB 59.7 53.7

324 304

286 269

264 251

548 529

360UB 56.7 50.7 44.7

273 242 222

239 212 196

219 195 180

496 449 420

310UB 46.2 40.4 32.0

197 182 134

170 157 115

155 144 105

356 320 283

250UB 37.3 31.4 25.7

140 114 92.0

118 96.9 74.0

106 87.5 67.5

283 265 214

200UB 29.8 25.4 22.3 18.2

90.0 74.6 65.3 51.8

75.2 62.1 55.0 †

67.0 55.4 48.1 †

225 204 174 154

180UB 22.2 18.1 16.1

56.2 45.2 39.8

† † †

† † †

186 151 135

150UB 18.0 14.0

38.9 29.3

† †

† †

161 130

22 mm 22 mm

* loss of area in flange is below AS 4100 limit, so gross section value may be used. † M20 bolts will not fit.

TABLE 32B PARALLEL FLANGE CHANNELS GRADE 300 DESIGN SECTION MOMENT AND WEB CAPACITIES

Designation

Mass per metre

Unholed

φM sx

φV v

kg/m

kNm

kN

380PFC

55.2

238

657

300PFC

40.1

152

415

250PFC

35.5

114

346

230PFC

25.1

73.3

258

200PFC

22.9

59.7

207

180PFC

20.9

49.0

187

150PFC

17.7

37.0

156


91

TABLE 32C WELDED BEAMS GRADE 300 DESIGN SECTION MOMENT AND WEB CAPACITIES Unholed Holed one Holed two Unholed/ flange flanges Holed Designation

NOTES:

φM sx

′ φM sx

′ φM ′sx

φV v

′ φM sx

kNm

kNm

kNm

kN

1200WB 455 423 392 342 317 278 249

7110 6510 5910 4980 4500 3790 3250

7110* 6510* 5910* 4980* 4500* 3790* 3250*

7110* 6510* 5910* 4980* 4500* 3790* 3250*

2900 2900 2900 2900 2900 2900 2900

diameter holes in one flange ′′ φM sx calculated for two 24 mm diameter holes in both flanges

1000WB322 296 258 215

4130 3720 3100 2580

4130* 3720* 3100* 2580*

4130* 3720* 3100* 2580*

2490 2490 2490 2490

900WB282 257 218 175

3440 3070 2510 2020

3440* 3070* 2510* 2020*

3440* 3070* 2510* 2020*

1730 1730 1730 1730

800WB192 168 146 122

2030 1720 1540 1220

2030* 1720* 1430 1140

2030* 1720* 1330 1050

1190 1190 1190 1190

700WB173 150 130 115

1610 1350 1210 1020

1610* 1350* 1110 944

1610* 1350* 1020 868

1100 1100 1100 1100

calculated for two 24 mm

* loss of area in flange is below AS 4100 limit, so gross section value may be used.


92

6

SUPPORTED MEMBERS

6.3

Design example No. 6— UB unholed and holed moment and shear capacity

Determine the unholed and holed moment and shear capacity of a 250UB31.4 universal beam, Grade 300, Yield stress, f y = 320 MPa. Moment capacity

Flange slenderness

λ ef =

bf − t w 2t f

Web slenderness

λ ew =

d1 tw

fy 250 fy

250

= 8.13

= 38.4

320 = 9.19 250

320 = 43.4 250

To calculate Zex the plate element slenderness values are compared with the plate element slenderness limits in Table 5.2 of AS 4100. Bending about the x-axis puts the flange in uniform compression. Hence λ ef = 9.19

λ ep = 9

λ ey = 16

λ ef / λ ey = 0.574

(Table 5.2 of AS 4100)

Bending about the x-axis places one edge of the web in tension and the other in compression. Hence λ ep = 82

λ ew = 43.4

λ ey = 115

λ ew / λ ey = 0.377

(Table 5.2 of AS 4100)

The flange has the higher value of λ e / λ ey and hence is the critical element in the section. From Clause 5.2.2 of AS 4100 the section slenderness and slenderness limits are the flange values, i.e. λ sp = 9 λ sy = 16 λ s = 9.19 Now λ sp < λs ≤ λ sy.

∴The section is NON-COMPACT. 3

Zx

= 354 × 10 mm3

Sx = 397 × 103 mm3 (Ref. 25)

Zc

= min [Sx, 1.5 Z x]

= min [397, 1.5 × 354] × 103 = 397 ×103 mm3

( (

⎡ λ sy − λ s =Z+⎢ ⎣⎢ λ sy − λ sp

Z ex

) ) (Z

c

⎤ − Z )⎥ ⎦⎥

⎡ (16 − 9.19 ) (397 − 354 )⎤⎥ × 10 3 = 354 × 10 3 + ⎢ ⎣ (16 − 9 ) ⎦

= 395 × 10 3 mm 3

φM sx = 0.9 × 320 × 395 × 103 /106 = 114 kNm (refer Table 32A) Moment capacity with 2 × 22 mm dia. holes on one flange

nh = 2

dh = 22 mm

Check AS 4100 limit area of holes area of flange ratio of areas AS 4100 limit

= = = =

t f = 8.6 mm

A = 4010 mm2

d = 252 mm (Ref. 25)

2 ×22 × 8.6 = 378 mm2 146 × 8.6 = 1256 mm2 0.30 [1 – 320/0.85 × 440] = 0.144

Hence, holes must be accounted for. y bh =

4010 × 126 − 2 × 22 × 8.6 × 4.3 = 138.7 mm 4010 − 2 × 22 × 8.6

y th = 252 − 138.7 = 113.3 mm

Δy = 138.7 − 126.0 = 12.7 mm I x′

2

= 44.5 × 106 −

2 × 22 × 8.63 ⎡ 252 − 8.6 ⎤ 2 − 2 × 22 × 8.6 × ⎢ ⎥ − [4010 − 2 × 22 × 8.6]× 12.7 2 12 ⎦ ⎣

= 38.3 × 106 mm 4 handbook 1 design of structural steel connections, first edition

93

min Z x′ =

38.3 × 10 6 = 276 × 10 3 138.7

d1 = 234 mm y bp =

t w = 6.1 mm

bf = 146 mm

234 × 6.1 + 2 × 22 × 8.6 = 148.0 mm 2 × 6.1

S ′ = 146 × 8.6(234 − 148.0 + 4.3 ) + (234 − 148 ) 2× 3.05 + 148.0 2 × 3.05 + (146 − 2 × 22) × 8.6 × (148.0 + 3.05 )

= 336 × 103 mm3 Z e′ = min of [1.5 × 276, 336] × 10 3

= 336 × 103 mm3

3 6 M x′ =0.9 × 320 × 336 × 10 /10

= 96.9 kNm (refer Table 32A)

Shear capacity

dp

= d1 = 234 mm

dp

=

tw

234 = 38.4 ≤ 6. 1

82 320 250

= 72.5

φV vo =0.54 × 320 × (252 × 6.1)/103 = 265 kN (refer Table 32A)


94

6

SUPPORTED MEMBERS

6.4

Single web coped sections

FIGURE 54 SINGLE WEB COPED (SWC) SECTIONS Design moment capacity

The formulae quoted in Section 6.2 also apply for determining the nominal section moment capacity of a single web coped section, except that for a SWC section (which is a tee section in cross section (Fig. 54)): λep = 9, for a flange outstand or web subject to either uniform compression or maximum compression at unsupported edge and tension at supported edge λey = 16, for flange outstand subject to uniform compression = 25, for a web subject to maximum compression at unsupported edge and tension at supported edge The assumption made for single coped sections is that local buckling of the web, which is in compression due to the bending moment induced by the end reaction, does not occur. This assumption is made on the basis that the cope length involved is small (usually of the order of 100–150 mm) and that the stiffening effect of the connection itself inhibits local buckling. Reference 9 also contains a similar assumption. Where individual connections require additional assessment for local bucking of the supported member, a method that may be used is presented later in this Section (following the plastic modulus formulation). Assuming the full tee section as effective locally at the connection, Ze = [Ss; 1.5 Zs]min

where the plastic modulus ( Ss) and the elastic modulus (Zs) of a single web coped section are given by the expressions following. Notation used is shown in Figure 55.

FIGURE 55 SWC UNIVERSAL BEAM (UB) handbook 1 design of structural steel connections, first edition

95

Elastic Modulus Z s (Figure 56)

Zs = min of:

⎡ Ix ; ⎢ ( + d ⎣ w tf − yc )

Ix ⎤ ⎥ yc ⎦

FIGURE 56 T-SECTION OF SWC UB SHOWING ELASTIC NEUTRAL AXIS where Ix =

bf t f3 t d3 + bf t f (y c − 0.5t f ) 2 + 0.0152r 4 + 0.4292r 2 (y c − t f − 0.223r ) 2 + w w + t w d w (t f + 0.5d w − y c ) 2 12 12

yc =

0.5bf t f2 + 0.4292r 2 (t f + 0.223r ) + d w t w (t f + 0.5d w ) bf t f + 0.4292r 2 + d w t w

Plastic Modulus Ss

There are two situations to consider, namely: (a)

plastic section neutral axis in web.

(b)

plastic section neutral axis in bottom flange.

(a)

N.A. in web (Figure 57)

FIGURE 57 SWC UB T-SECTION WITH PLASTIC NEUTRAL AXIS IN WEB b ftf + 0.4292 r 2 + (y s – tf) tw = (d w + tf – y s) tw for equal areas either side of neutral axis. ∴y s

=

d w t w + 2t f t w − bf t f − 0.4292r 2 2t w

≥ tf + r

∴Ss

= b f t f (y s − t f / 2) + 0.4292r 2 (y s − t f − 0.223r ) + t w (y s − t f )

(y s − t f ) 2

+ (d w + t f − y s ) t w

(d w

+ tf − ys ) 2


96

(b)

N.A. in flange (Figure 58)

FIGURE 58 SWC UB T-SECTION WITH PLASTIC NEUTRAL AXIS IN THE FLANGE bfys

= bf (t f − y s ) + 0.4292r 2 + d w t w for equal areas either side of neutral axis

∴y s

=

∴Ss

= bf y s

bf t f + 0.4292r 2 + d w t w ≤ tf 2bf

(t − y s ) + 0.4292r 2 (t − y + 0.223r ) + d t (t + d / 2 − y ) ys + bf (t f − y s ) f f s w w f w s 2 2

The design capacity of a single web coped section is hence: φM ss = 0.9f yZ e

where Ze = [Ss, 1.5Zs ]min

f y = [f yf ,f yw] min

Where local buckling is desired to be assessed for a SWC beam, Reference 9 contains in Part 9 a design moment capacity which is based on work by Cheng et al. This assessment can be summarised as follows: φM ss = 0.9 fcr Zs where fcr E

υ f

k

tw tf dw d Lc

π2E = 12 1 − υ 2

(

)

⎛ tw ⎜⎜ ⎝ dw + tf

2

⎞ ⎟⎟ f k ≤ f y ⎠

= 200 × 10 3 MPa = poissons ratio = 0.3 = plate buckling model adjustment factor = 2L c/d when L c/d ≤ 1.0 1+ L c/d when L c/d > 1.0 ⎛d +t = 2.2⎜⎜ w f ⎝ Lc

⎞ 1.65 ⎟⎟ ⎠

when

=

2.2(d w + t f ) Lc

= = = = =

web thickness flange thickness web depth (Figure 55) uncoped section depth (Figure 55) length of cope (Figure 55)

when

Lc

(d w + t f )

≤ 1. 0

Lc > 1. 0 (d w + t f )

Note that if there are holes in the flange of the tee section at the SWC, then a deduction for holes must be made in accordance with Clause 5.2.6 of AS 4100, in the same manner as illustrated in Section 6.2. Coped sections rarely have holes in the remaining flange at simple connections. handbook 1 design of structural steel connections, first edition

97

Design shear capacity

A tee shaped section such as a single web coped section will have a non-uniform shear stress distribution. Using AS 4100 Clauses 5.11.1 and 5.11.3, the nominal shear capacity (Vv) is given by: Vv

=

2Vu ⎛f * 0.9 + ⎜⎜ vm * ⎝ f va

⎞ ⎟ ⎟ ⎠

≤ Vu

where Vu * fvm , fva*

= the nominal shear capacity of a web with a uniform shear stress distribution determined in accordance with Clause 5.11.2 = the maximum and average design shear stresses respectively in the web determined by a rational elastic analysis.

Now since dw /d w ≤

82 fy / 250

for all rolled sections to AS/NZS 3679.1, and using Clause 5.11.4 of

AS 4100: Vu = Vw = 0.6 f y A w = 0.6 f y d w t w Now fva* and

=

* = fvm

V* dwtw V * Qc Qd f* = c w so that vm Ix Ixtw fva*

First Moment of Area Qc (using the notation in Figure 56) Qc

= first moment of area of section at cope =

∫ y dA

= b f tf (y c – 0.5tf) + 0.4292r 2 (y c – tf – 0.223r) + tw (y c – tf ) 2/2 Second Moment of Area I x—as defined earlier in this Section. The design capacity is hence: φV ws = 0.9 Vv =

1.08 f y d w t w ≤ 0.54 f y d w t w where fy = f y of web Qc d w 0 .9 + Ix

When a cross-section is subject to both shear force and bending moment simultaneously, AS 4100 Clause 5.12.3 provides that the nominal web shear capacity in the presence of bending moment be given by: for M* ≤ 0.75φM s; and

Vvm = Vv ⎡ ⎛ 1.6M * ⎞⎤ ⎟⎟⎥ = Vv ⎢2.2 − ⎜⎜ ⎢⎣ ⎝ φM s ⎠⎥⎦

for 0.75φMs ≤ M* ≤ φMs

where Vv

= the nominal shear capacity of a web in shear alone = Vws above

Ms = the nominal section moment capacity = Mss above the design capacity being given by φVvm , where φ = 0.9. AS 4100 does not have a requirement to adjust φV ws for the presence of bolt holes in the web at a SWC connection presumably because such holes are usually filled with bolts.


98

TABLE 33A SINGLE WEB COPED UNIVERSAL BEAMS GRADE 300 COPE DEPTH = 65 mm DESIGN SECTION MOMENT AND SHEAR CAPACITIES φM ss

φV ws

kNm

kN

610UB125 113 101

342 315 310

919 860 863

530UB 92.4 82.0

231 210

720 673

460UB 82.1 74.6 67.1

161 146 134

586 536 499

Designation

410UB 59.7 53.7

96.4 97.2

399 387

360UB 56.7 50.7 44.7

74.1 66.4 64.6

350 318 298

310UB 46.2 40.4 32.0

43.2 41.0 34.5

239 216 192

250UB 37.3 31.4 25.7

27.4 24.8 19.5

179 169 136

200UB 29.8 25.4 22.3 18.2

15.0 13.0 11.2 9.3

130 117 101 88


99

Variations to formulae for PFC section

For a PFC, the following equations apply in lieu of those derived for a universal section given above. b t3 t d3 2 Ix = f f + bf t f (y c − 0.5t f ) 2 + 0.0076r 4 + 0.2146r 2 (y c − t f − 0.223r ) + w w + t w d w (t f + 0.5d w − y c ) 2 12 12 2 2 0.5bf t f + 0.2146r (t f + 0.223r ) + d w t w (t f + 0.5d w ) yc = bf t f + 0.2146r 2 + d w t w Qc = b ftf(y c – 0.5tf) + 0.2146 r 2 (y c – tf – 0.223r) + tw(y c – tf) 2/2 Plastic Neutral Axis in Web d w t w + 2t f t w − bf t f − 0.2146r 2 ≥ tf + r 2t w

ys

=

Ss

= b ftf(y s – tf/2) + 0.2146r2 (ys – tf – 0.223r) (y s − t f ) + (d + t − y )t (d w + t f − y s ) + tw(y s – tf) w f s w 2 2

Plastic Neutral Axis in Flange b t + 0.2146r 2 + d w t w ≤ tf ys = f f 2bf Ss

= bf y s

(t − y s ) + 0.2146r 2 (t − y + 0.223r ) + d t (t + d 2 − y ) ys + bf (t f − y s ) f f s w w f w s 2 2 TABLE 33B SINGLE WEB COPED PARALLEL FLANGE CHANNELS GRADE 300 COPE DEPTH = 65 mm DESIGN SECTION MOMENT AND SHEAR CAPACITIES Designation

φM ss

φV ws

kNm

kN

380PFC

89.9

467

300PFC

44.6

276

250PFC

28.0

215

230PFC

18.0

157

200PFC

11.4

117


100

6

SUPPORTED MEMBERS

6.5

Design example No. 7— UB single web coped moment and shear capacity

Determine the design moment and shear capacity of a single web coped 410UB53.7 universal beam, Grade 300.

FIGURE 59 SWC UNIVERSAL BEAM EXAMPLE bf dw Ix yc Qc ys Ze Ss 1.5Z Ze φM ss Qc d w Ix φV ws

= 178 mm = 403 – 65 – 10.9 = 327 mm 6

tf = 10.9 mm

fyf = 320 MPa

t wb = 7.6 mm

fyw = 320 MPa

4

= 53.7 × 10 mm = 99.2 mm on substitution into the expressions given earlier = 216 × 10 3 mm3 = 43.1 mm on substitution into the expression given in Section 6.4 hence, plastic neutral axis is in member web, i.e. y s > tf + r = [Ss; 1.5Z]min = 409 × 10 3 mm3 on substitution into the expression given in Section 6.4 = 1.5 × 53.7 × 10 6/(327 + 10.9 – 99.2) = 338 × 10 3 mm3 = [409 × 10 3; 338 × 10 3]min = 338 × 10 3 mm = 0.9 × 320 × 338 × 10 3/106 = 97.2 kNm (as in Table 33A) 216 × 10 3 × 327 = 1.313 = 53.7 × 10 6 0.9 × 1.2 × 320 × 327 × 7.6 = = 387 kN 10 3 × (0.9 + 1.313 ) 3 < 0.9 × 0.6 × 320 × 327 × 7.6/10 = 429 kN

(value in Table 33A is 387 kN)


101

6

SUPPORTED MEMBERS

6.6

Double web coped sections

FIGURE 60 DOUBLE WEB COPED (DWC) SECTIONS Design moment capacity

In this case, both edges are unsupported and AS 4100 contains no provisions for local buckling of such a section. The assumption is usually made that local buckling of the web in triangular compression above the neutral axis does not occur locally at connection. Reference 9 contains a similar assumption. For a rectangular section, (d w × t w—Figure 60)

Z x = t w d w2 6

S = t w d w2 4

Z e = [1.5Z x , Sx ]min

= t w d w2 4

Hence, design moment capacity φMsd = 0.9 fy 0.25 t w d w2 = 0.225fyt w d w2 Where local buckling is desired to be assessed for a DWC beam, Reference 9 contains in Part 9 a design moment capacity which is based on the work of Cheng et al. This assessment can be summarised as follows using the notation in Figure 60. φM sd = 0.9 fcr Zx where = 0.62πE

fd fcr

= 3.5 – 7.5 (d ct/d) = fyfe = 1.0

fe

= (1.34 – 0.486λ) = (1.30/λ 2) λ

=

where L c ≤ 2d, d ct ≤0.2d d cb ≤0.2d

t w2 fd Lc d w

fcr

fy 1 d w 438 K 2t w

where d ct > 0.2d,

d cb > 0.2d

for λ ≤ 0.7 for 0.7 < λ ≤ 1.41 for λ > 1.41 and K is a function of (2Lc/d w) as set out below (interpolate for intermediate values)

2L c/d w

0.25

0.3

0.4

0.5

0.6

0.75

1

1.5

2

3

≥4

K

16

13

10

6

4.5

2.5

1.3

0.8

0.6

0.5

0.425


102

Design shear capacity

FIGURE 61 ELASTIC NEUTRAL AXIS IN DWC SECTION A double web coped section leaves a rectangular cross-section of web dw × t w. In Section 5.4, the design shear capacity for a rectangular cross-section of a component was derived and using that result design shear capacity of a DWC section is φV wd = 0.45 fy t w d w. When a cross-section is subject to both shear force and bending moment simultaneously, AS 4100 Clause 5.12.3 provides that the nominal web shear capacity in the presence of bending moment be given by: Vvm = Vv for M* ≤ 0.75 φMs; and ⎡ ⎛ 1.6M * ⎞⎤ ⎟⎟⎥ = Vv ⎢2.2 − ⎜⎜ ⎝ φM s ⎠⎦⎥ ⎣⎢

for 0.75 φMs ≤ M* ≤ φM s

where Vv = the nominal shear capacity of a web in shear alone = Vwd above Ms = the nominal section moment capacity = Msd above the design capacity being given by φVvm , where φ = 0.9. Holes in DWC sections:

AS 4100 only requires that deductions for holes be made in flanges (Clause 5.2.6) when calculating section moment capacity. Since a DWC section has no flanges, no deduction for holes in the web need be made when calculating section moment capacity. AS 4100 does not require an adjustment to φV wd for the presence of bolt holes in the web at a connection presumably because such holes are usually filled with bolts.


103

TABLE 34A DOUBLE WEB COPED UNIVERSAL BEAMS GRADE 300 DESIGN SECTION MOMENT AND SHEAR CAPACITIES d

d ct

d cb

dw

tw

φM sd

φV wd

mm

mm

mm

mm

mm

kNm

kN

610UB125 113 101

612 607 602

65 65 65

52 52 52

495 490 485

11.9 11.2 10.6

197 182 180

795 741 740

530UB 92.4 82.0

533 528

65 65

53 53

415 410

10.2 9.6

126 116

610 567

460UB 82.1 74.6 67.1

460 457 454

65 65 65

50 52 54

345 340 335

9.9 9.1 8.5

84.8 75.7 68.7

492 446 410

410UB 59.7 53.7

406 403

65 65

51 53

290 285

7.8 7.6

47.2 44.4

326 312

360UB 56.7 50.7 44.7

359 356 352

65 65 65

49 51 52

245 240 235

8.0 7.3 6.9

34.6 30.3 27.4

282 252 233

310UB 46.2 40.4 32.0

307 304 298

65 65 65

52 54 53

190 185 180

6.7 6.1 5.5

17.4 15.0 12.8

183 163 143

250UB 37.3 31.4 25.7

256 252 248

65 65 65

51 52 53

140 135 130

6.4 6.1 5.0

9.0 8.0 6.1

129 119 93.6

Designation

TABLE 34B DOUBLE WEB COPED PARALLEL FLANGE CHANNELS GRADE 300 DESIGN SECTION MOMENT AND SHEAR CAPACITIES d

d ct

d cb

dw

tw

φM sd

φV wd

mm

mm

mm

mm

mm

kNm

kN

380PFC

380

65

50

265

10.0

50.6

382

300PFC

300

65

50

185

8.0

19.7

213

250PFC

250

65

50

135

8.0

10.5

156

230PFC

230

65

50

115

6.5

6.2

108

Designation


104

6

SUPPORTED MEMBERS

6.7

Design example No. 8— UB double web coped moment and shear capacity

Determine the design moment and shear capacity of a double web coped 410UB53.7 universal beam, Grade 300.

FIGURE 62 DWC UNIVERSAL BEAM EXAMPLE d Ze φM sd

= 403 mm d w = 285 mm t w = 7.6 mm 2 3 3 = 7.6 × 285 /4 = 154.3 × 10 mm = 44.4 kNm (as Table 34A) = 0.9 × 320 ×154.3 ×10 3/106

φV wd = 0.45 × 320 × 285 × 7.6/10 3

= 312 kN

fyw = 320 MPa

(as Table 34A)


105

6

SUPPORTED MEMBERS

6.8

Lateral torsional buckling

Connection components and coped sections are generally so short that lateral torsional buckling of neither the connection elements nor of the coped section will occur. Coping of beam ends may reduce the elastic critical buckling moment of a laterally unsupported flexural member, particularly if exceptionally long copes are involved. In AS 4100, no specific guidance is given about the effect of web coping on the buckling capacity of a laterally unrestrained beam, but it would be prudent to either perform a buckling analysis using Reference 28 (permitted by Clause 5.6.4) or assume only partial restraint at the coped end when calculating the twist restraint factor (k t) and the lateral restraint factor (k r ) in terms of Clause 5.6.3. A k r value of 1.0 should always be used for supported members connected by angle cleats or web plates only, whether the members are coped or uncoped due to the lack of restraint to the top flange. Guidance on the restraint provided by specific connections where the supported members are either uncoped or coped may be found in Reference 30. Guidance on the lateral torsional buckling analysis of I -section beams with copes at the support may be found in References 28 and 31, while testing is reported in Reference 32. In References 28 and 31, the situation is analysed as an interaction problem involving buckling of the uncoped length and coped length separately, and then combining the effects of each.


106

6

SUPPORTED MEMBERS

6.9

Block shear failure of coped sections

Page 1 of 2

A coped member may fail when a block of web material pulls out as illustrated in Figure 63. AS 4100 does not address the failure mechanism of rupture due to block shear. The AISC Specification (Ref. 22) Clause J5 contains provisions which apply to plates, gussets, angles and brackets by reference to Clause J4.3 of the Specification.

FIGURE 63 BLOCK SHEAR FAILURE IN DWC MEMBERS The following explanation of block shear failure is based on Reference 11. Block shear failure involves both shear and tensile failure, a fact which is evident in the supported beam web shown in Figure 63. Failure by block shear was discussed in Section 5.4 for connection components and gusset plates in particular. The mode of failure by block shear is different in coped beams than for gusset plates. Because the shear resistance is present on only one surface in a coped beam compared to two with a gusset plate (see Figure 49(a)), the block of failing material must rotate (Figure 63). Although tensile failure is observed on the horizontal plane through the net section in tests on coped sections, the distribution of tensile stress is not uniform, with higher tensile stress toward the end of the web. There are relatively few test results for block shear failure in coped beams (Ref. 11). A coverage of earlier work on block shear failure in coped beams is contained in Reference 2. Clause J4.3 of the AISC Specification (Ref. 22) provides a design provision in which the design capacity is determined by the sum of the shear strength along the parallel failure surface and tensile strength on the perpendicular failure surface. The design capacity is then given by the following expressions in Clause J4.3 of Ref. 22: φV bs = φ[0.6f u Anv+fu Ant U bs ] ≤ φ[0.6f y Agv + fu A nt U bs ] where φ fu fy Agv Agt Anv Ant U bs

= 0.75 = = = = = = = =

specified minimum tensile strength of component specified minimum yield stress of component gross area subject to shear gross area subject to tension net area subject to shear net area subject to tension 1 when tension stress is uniform 0.5 when tension stress is non-uniform

Reference 11 argues that separate equations for design capacity are required for: (a)

gusset plates, cleats, angles (see Section 5.4); handbook 1 design of structural steel connections, first edition

107

(b)

coped beam webs (following).

The design capacity recommended by Kulak at Reference 11 and this Design Guide for coped beam webs is as follows: φV bs = φ[0.5Ant fui + 0.6fyi Agv] where terms are as defined above. The AISC Specification (Ref. 22) Clause J4.3 gives the following expressions for the upper bound based on guidance given in the Commentary to the Specification: φV bs = φ[A nt fui + 0.6fyi Agv] = φ[0.5Ant fui + 0.6fyi A gv]

single column of bolts to beam web double column of bolts to beam web

Relevant areas Ant and Agv are defined as shown in Figure 64.

For both SWC and DWC, Ant = ltt w – 0.5d htw (single column of bolts) Agv = l vt w where

lt

= distance from end of member to centreline of holes

lv

= distance from top of coped member to centreline of bottom hole

dh

= hole diameter

tw

= thickness of web FIGURE 64 BLOCK SHEAR AREAS IN SWC AND DWC MEMBERS


108

6

SUPPORTED MEMBERS

6.10 Web reinforcement of coped supported members

The following guidance is taken directly from Reference 9, Part 9. When the strength of a coped beam is inadequate, either a different beam can be selected to eliminate the need for reinforcement, or reinforcement can be provided to increase the strength. In spite of the increase in material cost, the former solution may be the most economical option due to the appreciable labour cost associated with adding stiffeners and/or doubler plates. When the latter solution is required, some typical reinforcing details are illustrated in Figure 65. The doubler plate illustrated in Figure 65(a) and the longitudinal stiffening illustrated in Figure 65(b) are used with rolled sections where d w/t w ≤ 60. When a doubler plate is used, the required doubler-plate thickness td req is determined by substituting the quantity (tw + td req) for tw in the calculations of the design capacities for coped sections given earlier. To prevent local crippling of the beam web, the doubler plate must be extended at least a distance d c (depth of cope) beyond the cope as illustrated in Figure 65(a). When longitudinal stiffening is used, the stiffening elements must be proportioned to meet the width-thickness ratios specified in AS 4100. The stiffened cross-section must then be checked for moment capacity but local web buckling need not be checked. To prevent local buckling of the beam web, the longitudinal stiffening must be extended a distance d c beyond the cope as illustrated in Figure 65(b). The combination of longitudinal and transverse stiffeners shown in Figure 63(c) may be required for thin-web plate-girders, where d w/t w > 60. When longitudinal and transverse stiffening is used, the stiffening elements must be proportioned to meet the width-thickness ratios specified in AS 4100. The stiffened cross-section must then be checked for moment capacity, but local web buckling need not be checked. To prevent local buckling of the beam web, longitudinal stiffeners must be extended a distance L c/3 beyond the cope as illustrated in Figure 65(c).

FIGURE 65 WEB REINFORCEMENT OF COPED SUPPORTED MEMBERS


109

7

SUPPORTING MEMBERS

7.1

Rationalised dimensions

TABLE 35 UNIVERSAL BEAMS RATIONALISED DIMENSIONS FOR DETAILING Flange

Depth of section

Width

Thickness

d

bf

tf

tw

Designation

kg/m

Web thickness tw

Dimensions

a

w

k

m

r

2

mm

mm

mm

mm

mm

mm

mm

mm

mm

mm

610UB 125 113 101

612 607 602

229 228 228

20 17 15

12 11 11

6 6 5

109 108 109

544 544 544

34 31 29

653 648 644

14 14 14

530UB 92.4 82.0

533 528

209 209

16 13

10 10

5 5

99 100

474 474

30 27

573 568

14 14

460UB 82.1 74.6 67.1

460 457 454

191 190 190

16 15 13

10 9 9

5 5 4

91 90 91

406 406 406

27 26 24

498 495 492

11 11 11

410UB 59.7 53.7

406 403

178 178

13 11

8 8

4 4

85 85

358 358

24 22

444 440

11 11

360UB 56.7 50.7 44.7

359 356 352

172 171 171

13 12 10

8 7 7

4 4 3

82 82 82

310 310 310

24 23 21

398 395 391

11 11 11

310UB 46.2 40.4 32.0

307 304 298

166 165 149

12 10 8

7 6 6

3 3 3

80 79 72

261 261 256

23 22 21

349 346 333

11 11 13

250UB 37.3 31.4 25.7

256 252 248

146 146 124

11 9 8

6 6 5

3 3 3

70 70 60

217 217 208

20 18 20

295 291 277

9 9 12

200UB 29.8 25.4 22.3 18.2

207 203 202 198

134 133 133 99

10 8 7 7

6 6 5 5

3 3 3 2

64 64 64 47

170 170 170 162

19 17 16 18

247 243 242 221

9 9 9 11

180UB 22.2 18.1 16.1

179 175 173

90 90 90

10 8 7

6 5 5

3 3 2

42 43 43

141 141 141

19 17 16

201 197 195

9 9 9

150UB 18.0 14.0

155 150

75 75

10 7

6 5

3 3

35 35

120 120

18 15

172 168

8 8

TABLE 36 UNIVERSAL COLUMNS RATIONALISED DIMENSIONS FOR DETAILING Flange

Depth of section

Width

Thickness

d

bf

tf

tw mm

Designation

Web thickness tw

Dimensions

a

w

k

m

r

2

kg/m

mm

mm

mm

mm

mm

mm

mm

mm

mm

310UC 158 137 118 96.8

327 321 315 308

311 309 307 305

25 22 19 15

16 14 12 10

8 7 6 5

148 148 148 148

244 244 244 244

42 38 35 32

451 445 440 433

17 17 17 17

250UC 89.5 72.9

260 254

256 254

17 14

11 9

5 4

123 123

197 197

31 28

365 359

14 14

200UC 59.5 52.2 46.2

210 206 203

205 204 203

14 13 11

9 8 7

5 4 4

98 98 98

159 159 159

26 24 22

293 290 287

11 11 11

150UC 37.2 30.0 23.4

162 158 152

154 153 152

12 9 7

8 7 6

4 3 3

73 73 73

121 121 121

20 18 16

223 220 215

9 9 9

100UC 14.8

97

99

7

5

3

47

63

17

139

10

NOTE: Dimensions in Tables 35 and 36 may not add correctly due to rounding. handbook 1 design of structural steel connections, first edition

110

TABLE 37 WELDED BEAMS RATIONALISED DIMENSIONS FOR DETAILING Flange

Depth of section

Width

Thickness

d

bf

tf

tw

Designation

kg/m

Web thickness tw

Dimensions

a

w

k

m

2

mm

mm

mm

mm

mm

mm

mm

mm

mm

1200WB 455 423 392 342 317 278 249

1200 1192 1184 1184 1176 1170 1170

500 500 500 400 400 350 275

40 36 32 32 28 25 25

16 16 16 16 16 16 16

8 8 8 8 8 8 8

242 242 242 192 192 167 130

1104 1104 1104 1104 1104 1104 1104

48 44 40 40 36 33 33

1300 1293 1285 1250 1242 1221 1202

1000WB 322 296 258 215

1024 1016 1010 1000

400 400 350 300

32 28 25 20

16 16 16 16

8 8 8 8

192 192 167 142

944 944 944 944

40 36 33 28

1099 1092 1069 1044

900WB 282 257 218 175

924 916 910 900

400 400 350 300

32 28 25 20

12 12 12 12

6 6 6 6

194 194 169 144

848 848 848 848

38 34 31 26

1007 1000 975 949

800WB 192 168 146 122

816 810 800 792

300 275 275 250

28 25 20 16

10 10 10 10

5 5 5 5

145 133 133 120

748 748 748 748

34 31 26 22

869 855 846 831

700WB 173 150 130 115

716 710 700 692

275 250 250 250

28 25 20 16

10 10 10 10

5 5 5 5

133 120 120 120

648 648 648 648

34 31 26 22

767 753 743 736

TABLE 38 WELDED COLUMNS RATIONALISED DIMENSIONS FOR DETAILING Flange

Depth of section

Width

Thickness

d

bf

tf

tw

Designation

kg/m

Web thickness tw

Dimensions

a

w

k

m

2

mm

mm

mm

mm

mm

mm

mm

mm

mm

500WC 440 414 383 340 290 267 228

480 480 472 514 506 500 490

500 500 500 500 500 500 500

40 40 36 32 28 25 20

40 32 32 25 20 20 20

20 16 16 13 10 10 10

230 234 234 238 240 240 240

384 384 384 434 434 434 434

48 48 44 40 36 33 28

693 693 688 717 711 707 700

400WC 361 328 303 270 212 181 144

430 430 422 414 400 390 382

400 400 400 400 400 400 400

40 40 36 32 25 20 16

40 28 28 25 20 20 16

20 14 14 13 10 10 8

180 186 186 188 190 190 192

334 334 334 334 334 334 334

48 48 44 40 33 28 24

587 587 581 576 566 559 553

350WC 280 258 230 197

355 347 339 331

350 350 350 350

40 36 32 28

28 28 25 20

14 14 13 10

161 161 163 165

259 259 259 259

48 44 40 36

499 493 487 482

NOTE: Dimensions in Tables 37 and 38 may not add correctly due to rounding.


111

TABLE 39 PARALLEL FLANGE CHANNELS RATIONALISED DIMENSIONS FOR DETAILING Depth of Mass section Designation per m kg/m

Flange Width

Thickness

Web thickness

d

bf

tf

mm

mm

mm

tw mm

Dimensions a

w

k

r

mm

mm

mm

mm

380PFC

55.2

380

100

18

10

90

317

32

14

300PFC

40.1

300

90

16

8

82

240

30

14

250PFC

35.5

250

90

15

8

82

196

27

12

230PFC

25.1

230

75

12

7

89

182

24

12

200PFC

22.9

200

75

12

6

69

152

24

12

180PFC

20.9

180

75

11

6

69

134

23

12

150PFC

17.7

150

75

10

6

69

111

20

10


112

7

SUPPORTING MEMBERS

7.2

Gauge lines

TABLE 40 GAUGE LINES FOR UNIVERSAL SECTIONS Section

Flange s gf M20

Web s gw M24

M20

M24

Universal beams 610UB 530UB

140 140

90 90

140 140

460UB 410UB 360UB,310UB 310UB32.0

90 90 90 70

140 70 70

90 90 90

250UB 250UB25.7* 200UB 200UB18.2* 180UB 150UB

70 70 70 50 b b

90

140 140 140 90 60

90 90 90 70

140 140 140 90 b

1

2

1

90 90

140 140

90 90

70 70

140 140

90 90

70 70

90 90 90 90

70 70 70 70

140 140 140 140

90 90 90 90

70 70 70 70

140 140 140 140

70 70 70 70 70 70

90 90 90 90 90

140 140

70 70 70 70 70 70

90 90 90 90 90

140 140

90 90 90

90 90 90 70 c

70 70 70

140 140

90 90 90 70 c

70 70 70

140 140

2

1

2

3

1

2

3

Universal columns 310UC 250UC 200UC 150UC 100UC Preference NOTES: *Gauge listed for 250UB25.7 and 200UB18.2 are for M16 bolts. b—Indicates that the flange will not accommodate this size of bolt. c—Indicates that the web will not accommodate two lines of bolts with a gauge of 50 mm or more. All dimensions are in mm.


113

TABLE 41 GAUGE LINES FOR WELDED SECTION FLANGES M20

Section

M24 s gf2

s gf1

s gf1

s gf2

Welded beams 1200WB455-392

140

90

280

1200WB342-278

140

90

280

1200WB249

140

90

1000WB322-258

140

90

1000WB215

420

280

140

90

280

140

90

280

140

90

140

90

140

90

140

90

140

90

900WB282,218

140

90

900WB175

140

90

140

90

800WB

140

90

140

90

700WB

140

90

140

90

280

280 280

Welded columns 500WC

140

280

400WC

140

280

350WC

140

Preference

1

420

140

280

140

280

140 2

1

2

1

2

1

2

NOTE: All dimensions are in mm.

TABLE 42 GAUGE LINES FOR WELDED SECTION WEBS Web s gw

Section

M24

M20

Welded beams 1200WB

140

90

70

140

90

70

1000WB

140

90

70

140

90

70

900WB

140

90

70

140

90

70

800WB

140

90

70

140

90

70

700WB

140

90

70

140

90

70

500WC

140

90

70

140

90

70

400WC

140

90

70

140

90

70

350WC

140

90

70

140

90

70

1

2

3

1

2

3

Welded columns

Preference

NOTE: All dimensions are in mm. handbook 1 design of structural steel connections, first edition

114

TABLE 43 GAUGE LINES FOR PARALLEL FLANGE CHANNELS Section

Flange s gf

Web s gw

M16

M20

M24

M16

M20

M24

380×100

55

55

55

140

90

70

140

90

70

140

90

70

300× 90

55

55

b

140

90

70

140

90

70

140

90

70

250× 90

55

55

b

140

90

70

140

90

70

140

90

70

230× 75

45

45

b

140

90

70

90

70

90

70

200× 75

45

45

b

90

70

90

70

90

70

180× 75

45

45

b

70

90

70

90

70

150× 75

45

45

b

70

1

1

1

1

Parallel flange channels

Preference

65 2

3

1

55 2

3

1

2

3

NOTES: b—Indicates that the flange will not accommodate this size of bolt. c—Indicates that the web will not accommodate two lines of bolts with a gauge of 50 mm or more. All dimensions are in mm.


115

8

MINIMUM DESIGN ACTIONS ON CONNECTIONS

8.1

AS 4100 Requirements

AS 4100 Clause 9.1.4 provides that connections shall be designed at the strength limit state for the greater of: (a)

the design action in the member; and

(b)

the minimum design action effects expressed either as the value or the factor times the member design capacity for the minimum size of member required by the strength limit state, specified in items (i) to (vii) below: (i)

Connections in rigid construction—a bending moment of 0.5 times the member design moment capacity.

(ii)

Connections to beams in simple construction—a shear force of 40 kN or 0.15 × member design shear capacity, whichever is the lesser.

(iii)

Connections at the ends of tension or compression members—a force of 0.3 times the member design capacity, except that for the threaded rod acting as a bracing member with turnbuckles, the minimum tension force shall be equal to the member design capacity.

(iv)

Splices in members subject to axial tension—a force of 0.3 times the member design capacity in tension.

(v)

Splices in members subject to axial compression—for ends prepared for full contact in accordance with Clause 14.4.4.2 of AS 4100, it shall be permissible to carry compressive actions by bearing on contact surfaces. When members are prepared for full contact to bear at splices, there shall be sufficient fasteners to hold all parts securely in place. The fasteners shall be sufficient to transmit a force of 0.15 times the member design capacity in axial compression. In addition, splices located between points of effective lateral support shall be designed for the design axial force (N*) plus a design bending moment not less than the design bending moment (M*) where— M* = δ

δN * Ls 1000

= appropriate amplification factor δb or δs determined in accordance with Clause 4.4 of AS 4100

L s = distance between points of effective lateral support When members are not prepared for full contact, the splice material and its fasteners shall be arranged to hold all parts in line and shall be designed to transmit a force of 0.3 times the member design capacity in axial compression. (vi)

Splices in flexural members—a bending moment of 0.3 times the member design capacity in bending. This provision shall not apply to splices designed to transmit shear force only. A splice subjected to a shear force only shall be designed to transmit the design shear force together with any bending moment resulting from the eccentricity of the force with respect to the centroid of the connector group.

(vii)

Splices in members subject to combined actions—a splice in a member subject to a combination of design axial tension or design axial compression and design bending moment shall satisfy (iv), (v) and (vi) simultaneously.

The action to be designed for is the greater of the calculated design actions or the minimum specified in (i) to (vii), as appropriate.


116

The minimum is generally expressed as a factor times the design capacity (φR u ) for the minimum size of member required by the strength limit state. Hence, if a member is increased in size above the minimum size for whatever reason (rationalisation of member sizes, slenderness or serviceability considerations), it is only necessary to use the design capacity of the minimum size required by the strength limit state for the purpose of determining the minimum design action. For example, columns which may be subject to large compressive forces and only minor tensile forces, any splice has to be designed for both the specified value for the minimum member size required to resist the compression, and for the specified value for the minimum member size required to resist the tension. Minimum design actions for an individual connection are discussed in detail in the Design Guide relevant for that connection.


117

9

REFERENCES

1

STANDARDS AUSTRALIA, AS 4100—1998 ‘Steel structures’.

2

AUSTRALIAN INSTITUTE OF STEEL CONSTRUCTION, ‘Design of structural connections’, 4th edition, Authors Hogan, T.J. and Thomas, I.R., Editor Syam, A.A., 1994.

3

AUSTRALIAN INSTITUTE OF connections’, 3rd edition, 1985.

4

Owens, G.W. and Cheal, B.D. ‘Structural steelwork connections’, Butterworths, London, 1989.

5

STANDARDS AUSTRALIA, AS 1111.1—2000 ‘ISO Metric hexagon bolts and screws— Product Grade C, Part 1: Bolts’.

6

STANDARDS AUSTRALIA/STANDARDS NEW ZEALAND, AS/NZS 1252:1996 ‘Highstrength steel bolts with associated nuts and washers for structural engineering’.

7

AUSTRALIAN STEEL INSTITUTE, ‘Design guide 2:, Bolting in structural steel connections’, Author Hogan, T.J., Contributing author and editor Munter, S.A., 2007.

8

STANDARDS Commentary’.

9

AMERICAN INSTITUTE OF STEEL CONSTRUCTION, ‘Steel Construction manual’, 13th edition, 2005.

10

Kulak, G.L., Fisher, J.W. and Struik, J.H.A. ‘Guide to design criteria for bolted and riveted joints’, 2 nd edition (2001 -Published by American Institute of Steel Construction).

11

Kulak, G. ‘High strength bolts—A Primer for structural engineers’, American Institute of Steel Construction, Steel Design Guide 17, 2002.

12

Thornton, W.A. ‘Prying action—A general treatment’, Engineering Journal, American Institute of Steel Construction, Vol. 22, No. 2, 1985, pp 67-75.

13

STANDARDS AUSTRALIA, AS 1101.3—2005 ‘Graphical symbols for general engineering, Part 3: Welding and non-destructive examination’.

14

STANDARDS AUSTRALIA/STANDARDS NEW ZEALAND, ‘Structural steel welding, Part 1: Welding of steel structures’.

15

STANDARDS AUSTRALIA/STANDARDS NEW ZEALAND, AS/NZS 1553.1:1995 ‘Covered electrodes for welding, Part 1: Low carbon steel electrodes for manual metal-arc welding of carbon and carbon-manganese steels’.

16

STANDARDS AUSTRALIA, AS 1858.1—2003 ‘Electrodes and fluxes for submerged arc welding, Part 1: Carbon steel and carbon-manganese steels’.

17

STANDARDS AUSTRALIA, AS 2203.1—1990 Part 1: Ferritic steel electrodes’.

18

STANDARDS AUSTRALIA/STANDARDS NEW ZEALAND, AS/NZS 2717.1:1996 ‘Welding—Electrodes—Gas metal arc, Part 1: Ferritic steel electrodes’.

19

Lay, M.G. ‘Fillet weld design stresses in AS 1250’, Proceedings, 23rd National Conference of the Australian Welding Institute, Hobart, Sept., 1975, pp. 87–92.

20

Butler, L.J. and Kulak, G.L. ‘Strength of fillet welds as a function of direction of load’, Welding Journal, Welding Research Council, Vol. 36, No. 5, May 1971, pp. 231s–234s.

21

Pham, L. and Bennetts, I.D. ‘Reliability study of fillet weld design’, Civil Engineering Transactions, Institution of Engineers Australia, Vol. CE26, No. 2, May 1984, pp. 119– 124.

22

AMERICAN INSTITUTE OF STEEL CONSTRUCTION, ‘Specification for structural steel buildings’, March 2005.

AUSTRALIA,

STEEL

AS 4100

CONSTRUCTION,

Supplement

‘Cored

‘Standardized

1—1999

‘Steel

structures—

AS/NZS 1554.1:2004

electrodes


structural

for

arc-welding,

118

23

STANDARDS AUSTRALIA, AS 1237.2—2002 ‘Plain washers for metric bolts, screws and nuts for general purposes, Part 2: Tolerances’.

24

STEEL CONSTRUCTION INSTITUTE AND BRITISH CONSTRUCTIONAL STEELWORK ASSOCIATION, ‘Joints in steel construction: Simple connections’, Publication P212, 2002.

25

AUSTRALIAN INSTITUTE OF STEEL CONSTRUCTION, ‘Design capacity tables for structural steel, Vol 1: Open sections’, 3 rd edition, 1999.

26

AUSTRALIAN STEEL INSTITUTE, ‘Design capacity tables for structural steel, Vol 2: Hollow sections’, 2 nd edition, 2004.

27

STANDARDS AUSTRALIA/STANDARDS NEW ZEALAND, AS/NZS 3678:1996 ‘Structural steel—Hot rolled plates, floor-plates and slabs’.

28

Cheng, J.R., Yura, J.A. and Johnson, C.P. ‘Lateral buckling of coped steel beams’, Journal of Structural Engineering, ASCE, Vol. 114, No .1, Jan 1988, pp. 1–15.

29

STANDARDS AUSTRALIA/STANDARDS NEW ZEALAND, AS/NZS 3679.1:1996, ‘Structural steel, Part 1: Hot rolled bars and sections’ and AS/NZS 3679.2:1996, ‘Part 2: Welded I sections’.

30

Trahair, N.S., Hogan, T.J. and Syam, A.A. ‘Design of unbraced beams’, Steel Construction, Australian Institute of Steel Construction, Vol. 27, No. 1, Feb 1993.

31

Gupta, A.K. ‘Buckling of coped steel beams’, Journal of Structural Engineering, ASCE, Vol. 110, No. ST9, Sept 1984, pp. 1977–1987.

32

Cheng, J.R. and Yura, J.A., ‘Lateral buckling tests on coped steel beams’, Journal of Structural Engineering, ASCE, Vol. 114, No. ST1, Jan 1988, pp. 16–30.

33

STANDARDS AUSTRALIA, AS 1112.3—2000 ‘ISO metric hexagon nuts, Part 3: Product grade C’.

34

INTERNATIONAL STANDARD, ISO 3318—1990 ‘Assembly tools for screws and nuts— Double-headed open-ended wrenches, double-headed ring wrenches and combination wrenches—Maximum widths of heads’.

35

INTERNATIONAL STANDARD, ISO 2725-1—1996 ‘Assembly tools for screws and nuts— Square drive sockets, Part 1: Hand-operated sockets—Dimensions’.

36

INTERNATIONAL STANDARD, ISO 2725-2—1996 ‘Assembly tools for screws and nuts— Square drive sockets, Part 2: Machine-operated sockets (“impact”)—Dimensions’.


119

APPENDIX A—Limcon software

A1

Introduction

A1.1 General This Appendix contains the output from the Limcon computer program for two of the examples for which detailed hand calculations are included in the Design Guide. Limcon undertakes all DESIGN CHECKS set out in the ASI design model and lists the capacity and capacity ratio for each limit state. A detail diagram is included at the beginning of the Limcon output. A virtual reality image of the connection can be displayed on the computer screen to facilitate checking. Note: To express the result of each limit state check Limcon uses the capacity ratio. This is the ratio of the design capacity to the design action effect and the minimum capacity ratio for all limit states must not be less than 1.0.

A1.2 Bolt group—Limcon design example In Appendix A2 Design example No. 2—Design of bolt group loaded in-plane, as calculated by hand in Section 3.11, is assessed using Limcon. Limcon checks bearing and tearing by determining the force on each bolt and comparing this with computed capacities. Bolts in the outside rows and columns are checked for external tearing where a force component is directed towards an edge. Internal tearing checks are performed on each bolt in the direction of the force components. Each result is displayed for the critical bolt only. Limcon uses the specified horizontal and vertical edge distances to compute external tearing capacity. It is assumed that the horizontal edge distance applies to both sides of the bolt group but clearly, in this example, only the edge distance on the left is of interest. A large value has been entered for the top and bottom edge distance, as tearing checks are not relevant owing to the presence of the beam flanges rather than free edges. In this example, tearing is checked only for the beam web because it is clear that tear-out is not going to occur in the column flange. Thus, plate thickness and grade are entered for the beam web. If it were not clear which part of the connection was critical, it would be necessary to consider bolt groups in web and flange separately. A1.3 Weld group—Limcon design example In Appendix A3 Design example No. 5—Design of fillet weld group loaded out-of-plane, as calculated by hand in Section 4.13, is assessed using Limcon. The weld group is assessed according to the alternative analysis permitted by AS 4100 Clause 9.8.2.2, which treats the weld group as an extension of the connected member for determining the distribution of shear forces. This is more conservative and, in this case, more realistic than the assumption in Clause 9.8.1.1(b) that the shear force is uniformly distributed throughout the group.


120

APPENDIX A

A2

Limcon output—Design example No. 2—Design of bolt group loaded in-plane


121


122

APPENDIX A

A3

Limcon output—Design example No. 5—Design of fillet weld group loaded out-of-plane


123


124

APPENDIX B—ASI Handbook 1 comment form

(Please photocopy this comment form and fax to ASI)

FAX: (02) 9931 6633 ATTENTION:

National Manager—Engineering & Construction Australian Steel Institute Level 13, 99 Mount Street, North Sydney NSW 2060 Telephone: (02) 9931 6666

Notice: This facsimile message and any attached files may hold confidential information. If you are not the intended recipient any use, disclosure, forwarding or copying of this facsimile is unauthorised. If you have received this facsimile in error please notify the sender immediately by reply facsimile or telephone. Thank you for your co-operation on this.

Name:

Date:

Company:

Address:

Tel: Mobile: Email:

Reference: (eg Section, Page No, line)

Comment:


125

Asi Steel Connections

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