SK ASCE

Cover photo courtesy of Susan Dowty, S.E., S. K. Ghosh Associates Inc.

Seismic Design Using Structural Dynamics based on 2012 IBC, 2015 IBC, and ASCE/SEI 7-10

ISBN: 978-1-936039-24-1

Copyright 2014 S. K. Ghosh Associates Inc. and International Code Council

ALL RIGHTS RESERVED. This publication is a copyrighted work owned jointly by S. K. Ghosh Associates Inc. (SKGA) and the International Code Council, Inc (ICC). Without advance written permission from the copyright owners, no part of this book may be reproduced, distributed or transmitted in any form or by any means, including, without limitation, electronic, optical or mechanical means (by way of example, and not limitation, photocopying or recording by or in an information storage retrieval system). For information on permission to copy material exceeding fair use, please contact: SKGA: 334 Colfax St., Unit E, Palatine, IL 60067. Phone 1-847-991-2700 ICC:

Publications, 4051 West Flossmoor Road, Country Club Hills, IL 60478. Phone 1-888-ICC-SAFE (422-7233).

The information contained in this document is believed to be accurate; however, it is being provided for informational purposes only and is intended for use only as a guide. Publication of this document by SKGA and the ICC should not be construed as SKGA and the ICC engaging in or rendering engineering, legal or other professional services. Use of the information contained in this workbook should not be considered by the user to be a substitute for the advice of a registered professional engineer, attorney or other professional. If such advice is required, it should be sought through the services of a registered professional engineer, licensed attorney or other professional. Trademarks: “International Code Council,” the “International Code Council” logo and the “International Building Code” are trademarks of the International Code Council, Inc.

First Printing (Based on ACI 318-11): April 2014 PRINTED IN THE U.S.A.

TABLE OF CONTENTS

Preface ……………………………….…..……………………………… v Acknowledgements….…………….……………………………...….… vi Chapter 1: Modal Response Spectrum Analysis: Background and Implementation……………..………………………………….1 Chapter 2: Design of Reinforced Concrete Structures for Earthquake Forces ………………….………………………. 68 Appendix A: Member Forces from Modal Analysis ...……………. 151 References ……………………..……………………………………. 167

Seismic Design Usign Structural Dynamics (2012 IBC, 2015 IBC, and ASCE 7-10)

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PREFACE This publication addresses the methods by which a designer may comply with the seismic design requirements of the 2012 International Building Code (IBC)/2015 IBC/ASCE 710: Equivalent Lateral Force Procedure (ASCE 7-10 Section 12.8), Modal Response Spectrum Analysis (ASCE 7-10 Section 12.9), or Seismic Response History Analysis (ASCE 7-10 Chapter 16). The procedures in ASCE 7-10 Section 12.9 and Chapter 16 are more complicated than the Equivalent Lateral Force Procedure, but are required to be used under certain conditions of irregularity, occupancy, and height. Over the years, many questions have been asked about code provisions concerning these procedures and this publication has been created to answer these questions and demystify the application of the code with respect to modal response spectrum analysis. Although ASCE 7-10 (the 2012 and the 2015 IBC) formally recognizes modal response spectrum analysis as well as seismic response history analyses, the modal response spectrum analysis is more common in design office usage and is therefore the primary subject of this publication. The background and details are explained in the first half (Chapter 1) of this publication where a step-by-step analysis procedure is given, and a three-story, one-bay frame example is solved entirely manually to illustrate application of the procedure. The second half (Chapter 2) of this publication is devoted exclusively to the detailed design of a 20-story reinforced concrete building that utilizes a dual system consisting of specially detailed shear walls and frames for earthquake resistance. Modal response spectrum analysis is used as the basis of design. Design utilizing the Equivalent Lateral Force Procedure is also illustrated because it is basically a prerequisite to design using the Modal Response Spectrum Analysis Procedure. A key feature of this 20-story design example that would be of particular interest to users is the design of reinforced concrete shear walls by the procedure in the 2011 edition of ACI 318 Building Code Requirements for Structural Concrete. ACI 318-14 is the reference standard for concrete design and construction in the 2015 IBC. However, it is still under development. A 45-day public comment period is expected to commence around May 15, 2014 and publications is not expected until late fall, 2014. SKGA plans to update Part 2 of this publication to ACI 318-14, once that standard gets finalized, and issue a second printing based on ACI 318-14. ACI Committee 318 undertook a major reorganization effort following the publication of ACI 318-11, which is now about to culminate in ACI 318-14.Thus the update to Chapter 2 of this publication will be more challenging than it would have been in the absence of the extensive reorganization. The resulting update, however, would be highly valuable because it will steer the reader through a large part of the reorganized ACI 318-14.


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ACKNOWLEDGEMENTS Parts of this publication are influenced by an earlier book (Ghosh, S.K., Domel, Jr., A.W., and Fanella, D.A., Design of Concrete Buildings for Earthquake and Wind Forces, Publication EB 113.02D) from the Portland Cement Association, an organization to which the senior author owes much gratitude. This publication started out as a version, modified for the 2000 IBC, of an earlier publication: Seismic Design Using Structural Dynamics (1997 UBC), published by the International Conference of Building Officials. Dr. Madhu Khuntia, formerly of S. K. Ghosh Associates Inc., contributed much to the 1997 UBC publication. Dr. Kihak Lee, Saravanan Panchacharam, and Dr. David Fanella, formerly of S. K. Ghosh Associates Inc. played key roles in the first IBC update. The 2000 IBC edition of the publication was subsequently updated to conform to the provisions of 2006 IBC/2009 IBC/ASCE 7-05. Dr. Jaehong Kim and Dr. Pro Dasgupta of S. K. Ghosh Associates Inc. and Dr. Farhad Shad of Ramboll Engineering Consultants contributed greatly to that update. The contributions of Dr. Ali Hajihashemi of S. K. Ghosh Associates Inc. in the development of this edition of the publication are much appreciated.

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About S. K. Ghosh Associates Inc. The company provides seismic and code-related consulting services to engineers, businesses, trade associations, code-writing bodies, and governmental agencies involved in the design and construction of buildings and other structures that are impacted by the provisions of building codes. The company serves as a technical resource on structural codes and standards for code development and enforcement agencies and personnel; design professionals; academics; and the material industries. Technical support is provided through publications, seminars, peer reviews, research projects, computer programs, code interpretations and comparisons, a website, and other means. Main Office: 334 E. Colfax St., Unit E, Palatine, IL 60067 West Coast Office: 43 Vantis Drive, Aliso Viejo, CA 92656 1-847-991-2700 www.skghoshassociates.com

About the International Code Council The International Code Council is a member-focused association. It is dedicated to developing model codes and standards used in the design, build and compliance process to construct safe, sustainable, affordable and resilient structures. Most U.S. communities and many global markets choose the International Codes. ICC Evaluation Service (ICCES) is the industry leader in performing technical evaluations for code compliance fostering safe and sustainable design and construction. Headquarters: 500 New Jersey Avenue, NW, 6th Floor, Washington, DC 20001-2070 District Offices: Birmingham, AL; Chicago, IL; Los Angeles, CA 1-888-422-7233 www.iccsafe.org


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CHAPTER 1

MODAL RESPONSE SPECTRUM ANALYSIS: BACKGROUND AND IMPLEMENTATION 1.1

The Nature of Earthquake Forces in a Structure

The forces that a structure subjected to earthquake motions must resist result directly from the distortions induced by the motion of the ground on which it rests. The response (i.e., the magnitude and distribution of forces and displacements) of a structure resulting from such a base motion is influenced by the properties of both the structure and the foundation, as well as the particular characteristics of the exciting motion. A simplified picture of the behavior of a building during an earthquake may be obtained by considering Figure 1-11. As the ground on which the building rests is displaced, the base of the building moves with it. However, the inertia of the building mass resists this motion, which induces distortions in the building (greatly exaggerated in the figure). This distortion wave travels along the height of the structure1. The continued shaking of the base causes the building to undergo a complex series of oscillations. (A)

(B)

Seismic Waves

Figure 1-1. Behavior of Buildings during an Earthquake

It is important to draw a distinction between forces due to wind and those produced by earthquakes. Occasionally, even engineers tend to think of these forces as belonging to the same category just because codes specify design wind as well as earthquake forces in terms of equivalent static forces. Although both wind and earthquake forces are dynamic in character, a basic difference exists in the manner in which they are induced in a

Seismic Design using Structural Dynamics (2012 IBC, 2015 IBC, and ASCE 7-10)

1

Figure 1-2. 1940 El Centro (California) Earthquake Accelerogram: N-S Component and Corresponding Derived Velocity and Displacement Plots

1.3 Response of Structures to Earthquakes 1.3.1 Dynamic versus static structural analysis In a structural dynamic problem, the loading and all aspects of the structural response vary with time, so that a solution must be obtained for each instant during the history of response. There is a more important distinction between a static and a dynamic problem.3,4 When the simple column of Figure 1-3(a) is subjected to a static lateral load, the internal forces may be evaluated by simple statics. If the same load is applied dynamically, the timevarying deflections involve accelerations, which in turn generate inertia forces resisting the motion (Figure 1-3(b)). The external loading, p(t), that causes the motion and the inertia forces, fI(t), that resist its acceleration act simultaneously. The internal forces in the column must equilibrate this combined load system, so that it is necessary to know the inertia forces before the internal forces can be determined. The inertia forces depend upon the rate of loading and on the flexibility and mass characteristics of the structure. The basic difficulty of dynamic analysis lies in that the deflections that lead to the development of inertia forces are themselves influenced by the inertia forces.


3

Figure 1-4. Lumped SDOF System Subjected to Base Translation

where m, c, and k are the mass, damping coefficient, and stiffness, respectively, as shown in Figure 1-4. Equation (1-1) may be rewritten as x  2x  2 x  x g

(1-2)

where 2 = (2/T)2 = k/m, T is the natural period of vibration (Figure 1-5a), and  = c/ccr = c/2m is the fraction of critical damping* (Figure 1-5b). The solution to Equation (1-2) leads to the deformation response x(t), which depends on: (a) the characteristics of the ground acceleration, x g ( t ) , (b) the natural circular frequency of vibration,  = 2/T (or equivalently the natural period of vibration, T), of the structure without damping, and (c) the damping ratio, , of the structure. The solution to Eq. (1-2) is given by

1 x ( t, , )  d

t



x g () exp   d ( t  )] sin d ( t  )d 

0

1 R ( t, , ) d

(1-3)

where d   1   2 . For  < 0.2,  d (= 2/TD) is practically equal to . ---------------------------------------------*Critical damping is defined as the least damping coefficient for which the free response of a system (i.e. in the absence of an external exciting force) is non-vibratory, i.e., for which the system returns to the static position without oscillation after any excitation.


5

Ground Acceleration, ẍg (t)

-0.4 g

El Centro S00E Component May 18, 1940

0 0.4 g

0

10

20 Time, sec.

30

10 T = 0.5 sec ξ = 0.02

xmax = 2.48 in.

Deformation, u, in.

0

T = 1 sec ξ = 0.02

T = 2 sec ξ = 0.02

-10 10 0 xmax = 6.61 in. -10 10 0 -10 0

20

10

20 Time, sec.

30

Deformation (or Displacement) Response Spectrum ξ = 2 Percent

15 Sd, in.

xmax = 8.84 in.

10 5 0

0

1 2 3 Natural Vibration Period, T, sec.

Figure 1-6. Computation of Displacement Response Spectrum6


9

subject to low levels of shaking. The latter evidence suggested a two-factor approach sketched in Figure 1-16. In this approach, adopted in the 1994 NEHRP Provisions,16 the short-period plateau, of height proportional to Aa, is multiplied by a short-period site coefficient, Fa, and the curve proportional to Av/T is multiplied by a long-period site coefficient, Fv. Both Fa and Fv depend on the site conditions and on the level of shaking, defined by the Aa and Av coefficients, respectively. The 1994 NEHRP Provisions introduced new seismic coefficients Ca and Cv such that Ca = AaFa and Cv = AvFv

(1-10)

Figure 1-16. Two-Factor Approach to Local Site Response

Six soil categories (called Site Classes), designated as A through F, were introduced in the 1994 NEHRP Provisions. The first five are based primarily on the average shear wave velocity, vs (ft/sec), in the upper 100 ft of the soil profile, and the sixth is based on a site-specific evaluation. The categories include: (A) hard rock (vs > 5000 ft/sec), (B) rock (2500 ft/sec < vs < 5000 ft/sec), (C) very dense soil and soft rock (1200 ft/sec < vs <2500 ft/sec), (D) stiff soil profile (600 ft/sec < vs < 1200 ft/sec), (E) soft soil profile (vs < 600 ft/sec), and (F) soils requiring site-specific calculations such as liquefiable and collapsible soils, sensitive clays, peats and highly organic clays, very high plasticity clays, and very thick soft/medium stiff clays. In recognition of the fact that in many cases the shear wave velocities may not be available, alternative definitions of the site categories were also included in the 1994 NEHRP Provisions. These alternative definitions use the standard penetration resistance


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however, they are uniformly defined as “the maximum level of earthquake ground shaking that is considered as reasonable to design buildings to resist.” This definition facilitates the development of a design approach that provides approximately uniform protection against collapse resulting from maximum considered earthquake (MCE) ground motions throughout the United States. It is widely recognized that the ground motion difference between 10-percent and 2percent probabilities of being exceeded in 50 years (henceforth referred to as 10%/50 and 2%/50 ground motions, respectively) in coastal California is typically smaller than the corresponding difference in inactive seismic areas such as the eastern and central United States. Figure 1-17, reproduced from the commentary to the 1997 NEHRP Provisions, plots the spectral acceleration at a period of 0.2 second, normalized at a 2-percent probability of being exceeded in 50 years (10 percent in 250 years), versus the annual frequency of being exceeded.

Figure 1-17. Hazard Curves for Selected Cities (1997 NEHRP)

The figure shows that in coastal California, the ratio between the 0.2-second spectral accelerations for the 2%/50 and 10%/50 ground motions is about 1.5, whereas the ratio varies between 2.0 and 5.0 in other parts of the United States. The question therefore arose as to whether the definition of design ground motion based on a constant probability for the entire United States would result in similar levels of seismic safety for all buildings.


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design provisions of ASCE 7-10 that are beyond the scope of this publication. For a comprehensive discussion of those revisions, please refer to the ASCE publication Significant Changes to the Seismic Load Provisions of ASCE 7-10: An Illustrated Guide.22

1.7 Dynamics of Multi-Degree-of-Freedom Systems 1.7.1 Equations of motion The building of Figure 1-20 is used to illustrate multi-degree-of-freedom analysis.3,4 The mass of the structure is assumed concentrated at the floor levels (lumped-mass idealization) and subject to lateral displacements only. The equations of dynamic equilibrium of the system may be written as

[m]{x}  [c]{x }  [k]{x}  {p(t )}

(1-15)

where {x} , {x } , and {x} are the acceleration, velocity, and displacement vectors, respectively; {p(t)} is the load vector; and [m], [c], and [k] are the mass, damping, and stiffness matrices, respectively. The mass matrix for a lumped mass system is diagonal, i.e. the inertia force corresponding to any degree of freedom depends only on the acceleration in that degree of freedom. In general, it is not practical to evaluate the damping coefficients in matrix [c], and damping is expressed in fractions of critical damping. The stiffness coefficient kij in matrix [k] is the force corresponding to displacement coordinate i resulting from a unit displacement of coordinate j.

Figure 1-20. Lumped MDOF System with Applied Loading and Resulting Displacements


29

m3

x2

m2

33

32

31

x3

21

23

22

(a) m1

Shape change

12

11

x1

Mode 1 Frequency 1

13



No change in shape x1 = 11X1 + 12X2 + 13X3 (b)

x2 = 21X1 + 22X2 + 23X3

or,

x3 = 31X1 + 32X2 + 33X3 or,

 x1   11    x 2    21 x     3   31

12 22 32

13   X1    23   X 2  33   X3 

{ x } = [{ 1 } { 2 } { 3 }] { X } { x } = [ { X }

(c)

xi = im

Free vibration in mode m

Tm = Period

2π ωm Frequency

Figure 1-21. Mode Superposition Analysis of Earthquake Response


31

Vt =

V12 + V22 + …+ Vn2

Step 9 – Distribute base shear for each mode over height of structure Fim =

w i  im Vm w i  im

where Fim = lateral force at level i in mode m Vm = base shear in mode m Step 10 – Perform lateral analysis for each mode…to determine member forces for each mode of vibration being considered (ASCE 7 Section 12.9.2) For rigid diaphragms, include accidental torsion (ASCE 7 Section 12.8.4.2) and amplified accidental torsion (ASCE 7 Section 12.8.4.3) in the distribution of story shears to lateralforce-resisting systems. Step 11 – Combine dynamic analysis results (moments, shears, axial forces, and displacements) for all considered modes using the square root of the sum of the squares (SRSS) combination or the complete quadratic combination (CQC) to approximate total structural response (ASCE 7 Section 12.9.3) or resultant design values. Step 12 – Scale story drifts from dynamic analysis results (ASCE 7 Section 12.9.4) Scale factor = 0.85 [0.5S1W/(R/Ie)]/Vt ≥ 1.0 Adjusted story drifts = 0.85 [0.5S1W/(R/Ie)]/Vt × (Original story drifts) Adjusted story drifts are to be smaller than the allowable story drifts given in ASCE 7 Table 12.12-1.

1.12 Response Spectrum Analysis Example 1.12.1 General A three-story reinforced concrete building (Figure 1-29) is designed following the requirements of the 2012/2015 IBC (ASCE 7-10). The building is located in Los Angeles (on Site Class D). The dynamic analysis procedure is used as the basis of design. 1.12.2 Design Criteria hs w E

56

= 10 ft = 386.4 kips/floor = 4000 ksi

(Figure 1-29(a))


Icol

= 4500 in.4 each column (taken equal to 0.7Ig)

The member sizes for the structure are chosen as follows: Beams 16.67 in. (depth)  12 in. (width) Columns 16.67  16.67 in. Material properties: Concrete (all members): fc = 4000 psi All members are constructed of normal weight concrete (wc = 145 pcf) Reinforcement: fy = 60,000 psi Service Loads: Assumed floor load Total weight W

= 386.4 kips/floor = 386.4 x 3 = 1159.2 kips

Seismic Design Data The risk-targeted maximum considered earthquake (MCER) spectral response acceleration (for 5% damping) at short period, SS = 1.5g, and that at 1-second period, S1 = 0.6g. Assume Risk Category: II and Seismic importance factor, Ie = 1.0

(ASCE 7 Table 1.5-2)

Site Class = D Site coefficient Fa = 1.0 Site coefficient Fv = 1.5

(ASCE 7 Table 11.4-1) (ASCE 7 Table 11.4-2)

Soil-modified SS = SMS= FaSS = 1.0  1.5g = 1.5g

(ASCE 7 Eq. 11.4-1)

Soil-modofied S1 = SM1= FvS1 = 1.5  0.6 = 0.9g

(ASCE 7 Eq. 11.4-2)

Design Spectral Response Acceleration Parameters (for 5% damping) At short periods:

SDS = 2/3(SMS/g) = 2/3  1.5 = 1.0

At 1-sec period: SD1 = 2/3(SM1/g) = 2/3  0.9 = 0.6

(ASCE 7 Eq. 11.4-3) (ASCE 7 Eq. 11.4-4)

Special Moment Frame system of reinforced concrete has R = 8 (ASCE 7 Table 12.2-1, Item C.5) Seismic Design Category: Based on both SDS (ASCE 7 Table 11.6-1) and SD1 (ASCE 7 Table 11.6-2), the Seismic Design Category for the example building is D.


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w

k

k

hs

k

hs

k

hs

w

k w

k

(a) k32 = -250

k31 = 0

1

k33 = 250

250

k21 = -250

1

k22 = 500

k23 = -250

k12 = -250

k13 = 0

250

1

k11 = 500

250

(b) Figure 1-29. Response Spectrum Analysis Example


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CHAPTER 2

DESIGN OF REINFORCED CONCRETE STRUCTURES FOR EARTHQUAKE FORCES 2.1

Introduction

2.1.1 General A 20-story reinforced concrete office building is designed following the requirements of the International Building Code (IBC), 2012 and 2015 editions, and ASCE 7-10. The building is located on IBC Site Class D. Both dynamic and static lateral force procedures are used as the basis of design. The building is symmetrical about both principal plan axes. Along each axis a dual system (special reinforced concrete shear walls with special moment-resisting frames or SMRF) is utilized for resistance to lateral forces. A Dual System is defined as a structural system with the following features (ASCE 7-10 Section 12.2.5.1): 12.2.5.1 Dual Systems. For a dual system, the moment frames shall be capable of resisting at least 25 percent of the design seismic forces. The total seismic force resistance is to be provided by the combination of the moment frames and the shear walls or braced frames in proportion to their rigidities. 2.1.2 Design criteria A typical plan and elevation of the example building are shown in Figures 2-1 and 22, respectively. The member sizes for the structure are chosen as follows: Beams Interior columns Exterior columns Shear walls: Grade to 10th floor 10th floor to 17th floor 17th floor to roof Shear wall boundary elements

68

34  24 in. (width = 34 in.) 40  40 in. 34  34 in. 16 in. thick 14 in. thick 12 in. thick 38  38 in.


Plan of shear wall

Figure 2-4. Reinforcement Details for Shear Wall C2-D2 (between Level 1 and Level 2) by Equivalent Lateral Force Procedure


91

Figure 2-5. Design Strength Interaction Diagram for Shear Wall C2-D2 (between Level 1 and Level 2) by Equivalent Lateral Force Procedure

Using 2-No. 5 vertical bars @ 11 in. o.c.  = 0.0035 > 0.0025

O.K.

ACI 318 Section 21.9.4.1 For hw/w = 8.64 > 2.0 c =2 For normal-weight concrete,  = 1 Vn

= Acv (c f c' + tfy)

(ACI 318 Eq. 21-7)

= 5664 [2×1× 4000 + 0.0043 × 60,000]/1000 = 2178 kips In accordance with ACI 318 Section 21.9.4.4, Vn must not exceed 8Acv f c'

92


Figure 2-10. Reinforcement Arrangements in End Beam A2-B2, Column A2-1 (between Level 1 and Level 2) and Column A2-2 (between Level 2 and Level 3)

In addition, center-to-center spacing of longitudinal bars that are transversely supported by a stirrup cannot exceed 14 in.

Top 

34  2 1.5  2  0.5  2  12 in.  14 in. .......OK 5

Since, the bottom bars will be placed based on the stirrup locations, maximum distance between two transversely supported bars is the same as above. 2.7.2.4 Negative reinforcing bar cutoff The negative reinforcement at the joint face is 6-No.8 bars. The location where 3 of the 6 bars can be terminated will be determined. Note that 3-No.8 bars must be continuous throughout the length of the beam to satisfy the minimum reinforcement requirements of ACI 318 Section 21.5.2.1. The loading used to find the cutoff point of the 3-No.8 bars is 0.7 times the dead load in combination with the probable flexural strengths (Mpr) at the ends of the members (fourth load combination, representing a condition where the vertical component of the earthquake counteracts dead load effects), as this combination will produce the longest bar cutoff lengths.


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Figure 2-13. Reinforcement Details for Interior Columns B2-1 and B2-2  0.8 Po =  0.8 {0.85fc (Ag - Ast)+ Astfy} = 4174 kips > 3506 kips for Column B2-1 > 3320 kips for Column B2-2

Figure 2-14 shows the P-M interaction diagram for the interior columns.

Figure 2-14. P-M Interaction Diagrams for Columns B2-1 (left) and B2-2 (right)

2.8.2.2 General ACI 318 Section 21.6 applies to frame members (i) resisting earthquake forces and

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SK ASCE

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