CUREe-Kajirna Research Project Final Project Report

Design Guidelines for Ductility and Drift Limits

Mr. Nobumasa Tanaka Dr. Norio Inoue Mr. Takaharu Fukuda Mr. Hitoshi Hatamoto Mr. Y oshio Sunasaka Mr. Satoshi Ohrui Mr. Tetsuya Tsujimoto

By

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Prof. Vitelmo V. Bertero Prof. Gary C. Hart Prof. James C. Anderson Prof. Helmut Krawinkler Prof. Jack P. Moehle Mr. Eduardo Miranda Mr. Aladdin Nassar Mr. Mohsen Rahnama Mr. Chukwuma G. Ekwueme Mr. Thomas A. Sabol \ \ Mr. Xiaoxuan Qi

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Report No. CK 92-03B February 1992

California Universities for Research in Earthquake Engineering ( CUREe)

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Kajirna Corporation

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CUREe (California Universities for Research in Earthquake Engineering)

California Institute of Technology Stanford University University of California, Berkeley University of California, Davis University of California, Irvine University of California, Los Angel~s University of California, San Diego University of Southern California

Kajima Corporation

Kajima Institute of Construction Technology Information Processing Center Structural Department, Architectural Design Division Civil Engineering Design Division Kobori Research Complex

' ', l t ABSTRAcr AND ACKNOWLEDGEMENTS

This report summarizes each of the studies that have been conducted in California as a part of the CUREe-Kajima Research Project #5, entitled .. Design Guidelines for Ductility and Drift Limits." This research project has been supponed by a grant provided by the Kajima Corporation and administered by CUREe (California Universities for Research in Earthquake Engineering). This financial support is gratefully acknowledged.

The report consists of seven chapters. The first six chapters summarize the six different srudies that have been conducted according to the agreed team research project plan. These srudies are described in ~etail in the seven CUREe-Kajima reports given below.

1.

2.

3.

4.

5.

REPORTS ..

Bertero, V. V ., Anderson, J.C., Krawinkler, H., Miranda, E., "Design Guidelines for Ductility and Drift Limits: Review of State-of-the-Practice and of-the-Art on Ductility and Drift-based Earthquake Resistant Design of Buildings," July, 1991.

Krawinlder, H., Nassar, A., and Rahnarna, M., "Evaluation of Damage Potential of Recorded Ground Motions, .. June, 1991.

Bertero, V. V., and Miranda, E., "Evaluation of Damage Potential of Recorded Ground :Motions and its Implications for Design of Structures, July, 1991.

Miranda, E., and Benero, V. V., "Evaluation of Seismic Performance of a Ten-Story RC Building," July, 1991.

Anderson, J.C., M"U"anda, E., and Bertero, V.V., "Evaluation of Seismic Perfonnance of a Thirty-Story RC Building, July, 1991.

6. Hart, G., and Ekwueme, C. G., Japanese Concrete Frame Building Response," July, 1991.

7. Qi, X., and Moehle, J.P., "Displacement Design Approach for Reinforced Concrete Structures Subjected to Earthquakes," January, 1991.

Chapter 7, after a brief review of the studies reported in the above seven reports, (summarized in the first six chapters), presents guidelines for the development of a reliable method for estimating the values of response reduction factor R and discusses how these values could be used to improve present U.S. and Japanese code procedures for earthquake resistant design.

This report summarizes only the work done by researchers of the C'UREe -team. The valuable contributions of the Kajima team to this joint research project are recognized and gratefully aclalowledged.

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Chapter 1

2

3

4

5

6

7

TABLE OF CONTENTS

Title Review of State-of-the-Practice and -of-the-Art on Ductility and Drift-based Earthquake-Resistant Design by Vitelmo V. Bertero, James C. Anderson, Helmut Krawinkler, and Eduardo Miranda

Evaluation of Damage Potential of Recorded Ground Motions b'y Helmut Krawinkler, Aladdin Nassar, and Mohsen Rahnama.

Evaluation of Damage Potential of Recorded Ground Motions and its Implications for Design of Structures by Vitelmo V. Bertero and Eduardo .Miranda

U.S. Concrete Frame -Building Response by James C. Anderson, Vitelmo, V. Bertero, and Eduardo Miranda

Japanese Concrete Frame Building Response by Gary C.Hart and C.G. Ekwueme

Member Details and Response Reduction by Jack P. Moehle

Summary, Conclusions, and Implications for Design by Helmut Krawinkler and Vitelmo V. Bertero

1.1-1.17

2.1- 2.19

3.1- 3.19

4.1- 4.50

5.1- 5.49

6.1 .. 6.22

7.1-7.9

DESIGN GUIDELINES FOR DUCfll.ITY AND DRIFT LIMITS: REVIEW OF STATE-OF-TilE-PRACTICE AND OF-THE-ART ON DUCTILITY AND DRIFT-BASED EAR1HQUAKE-RESISTANT

DESIGN OF BUILDINGS

A REPORT ON TASK 1 OF THE CUREe-KAJIMA RESEARCH PROJECT ON DESIGN GUIDELINES FOR DUCfll.ITY AND DRIFT LIMITS

by

Vitelmo V. Bertero

James C. Anderson

Helmut Krawinkler

Eduardo Miranda

and

The CUREe and The Kajima Research Teams /

A CUREe-KAJIMA RESEARCH REPORT

July 1991

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ACKNOWLEDGEMENTS This report summarizes the results obtained in the studies that have been conducted under task 1 of a research project on topic 5 entitled "Design Guidelines For Ductility And Drift Limits." This particular project is part of a program of research which is supported by a grant given by Kajima Corporation and administered by CUREe, the California Universities for Research in Earthquake Engineering. The financial support from Kajima is gratefully acknowledged.

The main authors of this research paper wish to thank Mr. Nobumasa Tanaka, Group Manager of the Kajima Research Team, and the members of this team for their valuable comments. Thanks are extended to Hatem Goucha and Brad Young for their assistance during the final preparation of this report.

TABLE OF CONTENTS

1. IN1'RODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -1-1. 1 INTRODUCTORY REMARKS ............................. -1-1. 2 OBJECTIVES ............ ............................... -3-1. 3 SCOPE ................................................ -4-

2. NEEDS FOR DUCTILITY AND CONTROL OF DRIFT AND TIIEIR PROPER USE IN ESTABLISHING RELIABLE EQRD CRITERIA ...... -5-2. 1 NEEDS FOR DUCTILITY ................................. -5-

2. 1. 1 General Remarks ................................... -5-2. 1. 1 (a) Needs for Recognizing the Differences Between

Deformability, Ductility and Ductility Ratio . . . . . . . . . . . -6-2. 1. 1 (b) Advantages of Providing Structural Components and

Their Connections with the Largest Ductility Economically Feasible .......................... -6-

2. 1. 1 (c) Quantification of the Ductility Ratio ............. -8-2. 1. 1 (d) Concluding Remarks ........................ -9-

2. 2 NEEDS FOR CONTROLLING INTERSTORY DRIFT INDEX (IDI) .................................................. -9-2. 2. 1 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -9-2. 2. 2 Drift Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -10-2. 2. 3 The Need for Drift Design ........................... -11-Table ................................................ -15-Figures ............................................... -17-

3. STATE-OF-THE-PRACTICE AND STATE-OF-THE-ART OF EQRD OF RC STRUCTURES ............................... -21-3. 1 PROBLEMS IN DESIGN AND CONSTRUCTION OF EQ-

RESISTANT STRUCTURES ............ ............. -21-3. 2 STATE-OF-THE-PRACTICE .............................. -22-

3. 2. 1 Estimation of Demands in Present Seismic Codes .......... -22-3. 2. 1 (a) Strength ................................. -22-3. 2. 1 (b) Stiffness and Drift ......................... -23-3. 2. 1 (c) P-A Effects .............................. -24-

3. 2. 2 Estimation of Supplies in Present Seismic Codes .......... -24-3. 2. 2 (a) Strength. . ............................... -24-3. 2. 2 (b) Stiffness, Deformation and Stability Capacities .... -25-

3.3 STATE-OF-THE-ART IN DUCTILITY AND STORY DRIFT-BASED EQRD ............................................... -26-3. 3. 1 General Introductory Remarks Regarding Importance of J..L 6

and IDI in Preliminary Design ......................... -26-3. 3. 1 (a) Examples ................................ -27-3. 3. 2 (b) Concluding Remarks ....................... -32-

3. 4 STATE-OF-THE-ART IN USING DUCTILITY RATIO J..L 6 IN PRELIMINARY EQRD .................................. -32-

3. 4. I Use of J. 6 in Establishing the Design EQs ................ -32-3. 4. 2 Use of J.6 in Preliminary Design ....................... -33-3. 4. 3 Concluding Remarks ............................... -34-

3. 5 STATE-OF-THE-ART IN USING INTERSTORY DRIFT INDEX (IDI) IN PRELIMINARY EQRD ........................... -35-3. 5. I Control of IDI at Serviceability Level ................... -35-3. 5. 2 Control of IDI at the Ultimate or Safety Limit State ....... -36-3. 5. 3 Choice of Member Stiffness for Drift and P-.i Analyses ...... -36-3. 5. 4 Recommended Practical Methods for Designing Considering

IDI. . ........................................... -38-3. 5. 5 Need to Consider the Effect of Multicomponent Seismic

Excitation and Direction in Estimating Structural Response (IDI) ...... .- .................................... -39-

Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -4I-

4. STATE-OF-THE-PRACTICE: REVIEW OF CODES ................... -45-4. 1 COMPARISON OF THE BASIC SLEDRS: UNITED STATES' UBC

AND JAPAN'S BUILDING STANDARD LAW (BSL) ........... -45-4. I. 1 Shape of the SLEDRS .............................. -45-4. I. 2 SLEDRS Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -45-

4.2 COMPARISON OF THE DESIGN SPECTRA .................. -45-4. 2. I Japan's BSL. . ..................................... -45-

4. 2. 1 (a) Service-Level Design Earthquake .............. -46-4. 2. 1 (b) Ultimate or Safety Level Design Earthquake. . .... -47-4. 2. 1 (c) Comparison of Japan's BSL and UBC Design

Earthquakes: Service Limit State Level . . . . . . . . . . . . -48-4. 3 OBSERVATIONS REGARDING DERIVATION OF SIDRS

DIRECTLY FROM SLEDRS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -52-4. 3. I Tri-Services Manual Approach ....................... -53-

4. 3. I (a) METHOD 1: ELASTIC ANALYSIS PROCEDURE ............................... -54-

4. 3. I (b) METHOD 2: CAPACITY SPECTRUM METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -54-

4. 3. 2 Comparative Designs of Buildings Using U.S. and Japanese Codes ........................................... -55-

4. 4 NEW ZEALAND CODE OF PRACTICE FOR GENERAL STRUCTURAL DESIGN AND DESIGN LOADING FOR BUILDINGS (NEW ZEALAND STANDARD NZS 4203: I984) .... -56-4. 4. 1 Material Code Format .............................. -56-4. 4. 2 Material Strength .................................. -56-4. 4. 3 Strength Reduction Factor ........................... -56-4. 4. 4 :Load Factor U .................................... -56-4. 4. 5 Special Observations or Aspects ....................... -57-

4. 4. 5 (a) Earthquake Provisions ....................... -57-4. 4. 5 (b) Method of Analysis ........................ -57-

4.4.6 Equivalent Static Force Analysis: Total Horizontal Seismic Force or Shear .................................... -57-

4. 5 COMPARISON OF REQUIRED DESIGN SEISMIC FORCES AT SAFETY LEVEL BY NZS WITH UBC AND JAPAN'S BSL ...... -59-

4.6 COMPARISON OF REQUIRED LIMITS FOR THE INTER-STORY DRIFT BY NZS, UBC AND BSL ........................... -61-4. 6. 1 NZS Requirements ................................ -61-

4. 6. 1 (a) Calculations of Deformations. . ............... -61-4. 6. 1 (b) Building Separation ........................ -62-

4. 6. 2 UBC Requirements ................................ -62-4. 6. 3 Japan's BSL Requirements. . ......................... -63-

4. 7 MEXICO: 1987 TECHNICAL NORMS (STANDARDS) FOR THE FEDERAL DISTRICT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -64-4. 7. 1 Mexico Required Strength at Ultimate (Safety) Limit State .. -65-4. 7. 2 Mexico Requirements for lnterstory Drift . . . . . . . . . . . . . . . . -65-

4. 8 DUCTILITY AND DRIFT CONSIDERATIONS IN EUROPEAN SEISMIC CODES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -66-4. 8. 1 Reference Documents .............................. -66-4. 8. 2 Summary of Relevant Aspects of Design Procedure ........ -66-

4. 8. 2 (a) Seismic Input ............................. -66-4. 8. 2 (b) Design Spectrum ........................... -67-4. 8. 2 (c) Behavior Factors. . ......................... -68-4. 8. 2 (d) Drift Considerations. . ...................... -68-4. 8. 2 (e) Other Relevant Considerations ................ -69-

4. 8. 3 Evaluation of Ductility Considerations .................. -69-4. 8. 4 Evaluation of Drift Considerations : .................... -71-4. 8. 5 Summary ........................................ -71-Tables ................................................ -73-Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -75-

5. SUMMARY OF STATE-OF-THE-PRACTICE ON DUCTILITY AND DRIFT-BASED EARTHQUAKE-RESISTANT DESIGN .......... -87-5. 1 GENERAL REMARKS ................................... -87-5.2 CODE SPECIFIED SLEDRS ............................... -88-

5. 2. 1 Sites with Firm Soils (Soil Type 1). . ................... -88-5. 2. 2 Sites with Soft Soils (Soil Type 3). . .................... -89-

5. 3 USE OF J.L6 TO REDUCE SLEDRS TO SIDRS ................. -89-5. 3. 1 Firm Soil (Soil Type 1). . ........................... -89-5. 3. 2 Sites with Soft Soils (Soil Type 3) ..................... -90-

5. 4 STATE-OF-THE-PRACTICE ON THE USE OF IDI LIMITATIONS IN EQRD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -90-5. 4. 1 Minimum Lateral Stiffness and Acceptable Limits on IDI at

Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -91-5. 4. 1 (a) Short T ................................. -91-5. 4. 1 (b) Long T ................................. -92-

5. 4. 2 Maximum Acceptable IDI at Ultimate Limit States (Collapse) . 0 -92-

Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -96-

6. RESEARCH, DEVELOPMENT, AND EDUCATIONAL NEEDS .......... -97-6. 1 GENERAL REMARKS REGARDING THE NEED FOR IDEAL

SOLUTION .................................. o -97-6. 2 RESEARCH AND DEVELOPMENT NEEDS TO IMPROVE THE

ESTABLISHMENT OF SLEDRS . . . . . . . . . . . . . . . . . . . . . . . . . . . -99-6. 2. 1 SLEDRS for Service Level EQs. . . . . . . . . . . . . . . . . . . . . . . -99-6. 2. 2 SLEDRS for Survivability .......................... -100-

6. 3 RESEARCH AND DEVELOPMENT NEEDS TO IMPROVE THE ESTABLISHMENT OF SIDRS ............................ -100-6. 3. 1 SIDRS for Strength, Cy ........................... . -101-

6. 3. 1 (a) Code Procedures to Determine SIDRS for Cy ... . -102-6. 3. 2 Implications of Recent Research Results with Respect to

Rationale for R Code Values ............ 0 -104-6. 3. 2 (a) The Case of Rock and Firm Soil Sites ........ . -106-6. 3. 2 (b) Case of Very Soft Soil Sites ............... . -106-6. 3. 2 (c) Recommendations for Improving Code SIDRS .. . -108-6. 3. 2 (d) SIDRS for Lateral Displacement and IDI ...... . -109-

Table -111-Figures ............................................. . -113-

7. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS ............ -131-7. 1 SUMMARY ................ o -131-7. 2 CONCLUSIONS ........................................ -132-7.3 RECOMMENDATIONS ................................. -144-

7. 3. 1 Recommendations for Improving Code SIDRS for Strength, Cy ............................................. -144-

. 7. 3. 2 Recommendations for Improving SDIRS for Lateral Displacement and IDI. ............................. -145-

8. REFERENCES -146-

1. INTRODUCfiON

1.1 INTRODUCfORY REMARKS One of the most promising approaches for developing efficient methods for improving earthquake-resistant design (EQRD) is predicting the response of structures to earthquake (EQ) ground motions through the use of an energy balance equation. The energy balance equation for a general oscillatory system subjected to base acceleration can be written as:

~ = Es + Eo (1. 1) where ~ = total input energy

Es = energy stored in the structure Eo = energy dissipated from the structure

The stored energy and dissipated energy can further be defined as

Es=~+~ and

where Eo = E, + ~ ~ = elastic strain energy

~ = kinetic energy E, = energy dissipated through viscous damping

~ = energy dissipated through hysteretic, inelastic deformations

For a linear elastic system the ~ can be expressed as follows

(F_J(v) 2

(1. 2)

(1. 3)

(1. 4)

where F. is the restoring elastic force and vis the relative displacement of the reactive mass, equal to F/K where K is the elastic stiffness.

From Eq. 1.4 it is clear that for any given linear elastic perfectly plastic system the maximum

~ that can be stored is reached when F. reaches the elastic limit or yielding force Fy of the system. Therefore to increase the ~ , and thereby the Es , it is necessary either to increase Fy and/or to increase the yield displacement vr by decreasing K. Because the increase of

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Fy usually demands large amounts of material, and therefore an increase in the weight and

cost of the structure, it would seem logical to try to increase vy as much as possible by decreasing K. However, because of the need to have a serviceable structure and to control damage of nonstructural components in general, there are restrictions on the maximum value that can be selected for vy (or for the minimum value forK). From this discussion it should be clear that lateral displacement (lateral drift) plays an important role in the EQRD of structures, and that there is a need to establish the maximum value that can properly be

selected. This is not an easy task.

From the above discussion it becomes clear that to achieve economical EQRD the E. must be minimized to the value required to achieve a serviceable structure. The problem, then is to find out what can be done to minimize E. . Combining and rearranging the above

equations results in the following expression for the energy stored in the structure.

Es = E. - (E( + EJ (1. 5) Although, strictly speaking, for any given structure undergoing given ground motions the

input energy depends on the behavior (elastic or inelastic) of the structure, for the sake of simplicity it may be assumed in the first approximation that E. is independent of structural behavior. Then, considering that to achieve economical EQRD the energy stored in the structure must be minimized, it is clear from Eq. 1.5 that it is necessary to dissipate a significant part of the total input energy either by viscous damping, by inelastic

deformations, or by a combination of the two.

Although the advantages of controlling the seismic response of civil engineering structures by increasing the equivalent viscous damping have long been recognized, the concept of using plastic deformation of the structural material to dissipate part of the seismic input

energy does not appear in the technical literature of the United States until the 1950s. In

1956, Housner discussed the use of limit design for EQRD [1]. The use of the concept of ductility and ductility ratio in EQRD of reinforced concrete (RC) structures was introduced in the United States for the first time in 1961 with the publication of the Portland Cement

Association (PCA) Manual, "Design of Multistory Reinforced Concrete Buildings for

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Earthquake Motions" [2]. Since the publication of the PCA Manual, significant experimental and analytical research efforts have been devoted to the development of

reliable methods of EQRD based on a combination of strength and ductility. In 1969, the advantages of using plastic methods for the EQRD of ductile moment-resistant steel frames was noted [3], and in 1975 and 1977 computer programs for the application of inelastic design methods for the EQRD of ductile moment-resistant RC frames based on the use of design ductility were developed and proposed for use in structural design practice [4 and 5]. Despite these accomplishments, the practical application of inelastic EQRD in the United States is not widely used. This also seems to be the case worldwide, except for countries

such as Mexico and New Zealand, where building codes have explicitly introduced the use

of ductility ratio, J.L, in the estimation of seismic design forces, and allow the use of limit design methods. In New Zealand, the seismic code is based on combined limit design and capacity design procedures which incorporate the concepts of strength and ductilit).

The slow progress in the use of limit design and capacity design procedures for EQRD is not surprising. The definition of the term "ductility ratio" and its evaluation are precise only

for the case of ideal linear elastic-perfectly plastic behavior, which, in reality, is the

exception rather than the rule. Furthermore, even though the advantages of providing a structure with the largest ductility that is economically feasible are generally recognized, the term "ductility" is used very loosely to express either the deformability of the structure or the ductility ratio. Although the deformability, ductility and ductility ratio are interrelated

parameters, their values and significance in the actual behavior of structures can be quite different. There is an urgent need to get a worldwide agreement regarding the proper use

of these technical terms and their proper evaluation and application to EQRD of structures.

1. 2 OBJECTIVES The ultimate goals of this report are to review the state-of-the-practice and the state-of-the-art in the use of the concepts of ductility, ductility ratio, and drift for attaining efficient

EQRD, and then to identify the research, development and educational needs required to improve the proper use of these concepts.

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1. 3 SCOPE

To achieve these goals, we will discuss both the need for applying the concepts of ductility and control of drift and their proper use. Initial emphasis is placed on the importance of recognizing the differences and interrelationships between deformability, ductility, and ductility ratio, and on the need to unify the ways in which the different types of ductility ratios are estimated from the actual seismic response of structures. It is then shown that to achieve high energy dissipation capacity and overall effective seismic performance, it is necessary to utilize highly redundant combined structural systems with multiple lines of structural defense. It is also necessary to provide the critical elements which control the

inelastic behavior of these systems with the highest ductility ratio that is economically feasible. The needs for controlling lateral deformation are discussed next. Different definitions of drift indices are presented, and their relationship to strength and ductility are discussed.

After a brief statement of EQRD problems, the state-of-the-practice and the state-of-the-art in the use of the concepts of ductility and drift limits are reviewed. The review of the state-of-the-practice focuses on how the concept of displacement ductility ratio (J..L,) and interstory drift index (IDI) are used in present building seismic codes. Although emphasis is placed on the Japanese and U.S. codes, the New Zealand, Mexican and European seismic codes are also analyzed. Results obtained from the analyses and critical comparisons of these five codes are summarized and discussed. The state-of-the-art in the use of J..L, and IDI is reviewed by assessing the implications of lessons learned from recent earthquakes and research results. Comparisons of the state-of-the-art and the state-of-the-practice are used to identify more fully research, development and educational needs. Short and long term

solutions are formulated for the proper use of the concepts of J..L, and IDI for EQRD of buildings, placing emphasis on the need for an energy approach.

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2. NEEDS FOR DUCI1LITY AND CONTROL OF DRIFT AND THEIR PROPER USE IN ESTABliSHING REUABLE EQRD CRITERIA

2. 1 NEEDS FOR DUCI1LITY

2. 1. 1 General Remarks It is well recognized and accepted that in EQRD all structural members and their connections and supports, i.e.,all critical regions whose yielding strength may be reached and exceeded by a severe earthquake, should be designed (sized and detailed) with large ductility and stable hysteretic behavior so that the entire structure will also be ductile and display stable hysteretic behavior. There are two main reasons for.this ductility requirement: first, it allows the structure as a whole, through distribution of

internal forces, to develop its maximum potential strength, which is given by the combination

of the maximum strength of all components; and second, large structural ductility allows the

structure to move as a mechanism under its maximum potential strength, which will result in the dissipation of large amounts of energy. (It should be noted that attempts should be mad, to develop a mechanism of a complete nature as opposed to a partial or local mechanism, as in the case of soft stories.) While these two reasons have been recognized in the past, only the second has been emphasized because the large dissipation of energy

was used to justify the reduction of the design strength that would be required if only linear elastic behavior were permitted. Although this reduction is justifiable in certain cases, the authors have previously expressed their concerns [6-9] about excessively large reductions in the required elastic strength or in the Linear Elastic Design Response Spectra (LEDRS) through the indiscriminate use of large values for the structural ductility ratio. For clarity and convenience in discussing the reasons for this concern, a glossary of the terms to be used in the discussion is given below.

Deformability: Capability of a material, structural component, or entire structure to deform before rupture.

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Ductility: Capability of a material, structural component, or entire structure to undergo

deformation after its initial yield without any significant reduction in yield strength.

Ductility Ratio or Ductility Factor, 1-': The ratio of the maximum deformation that a

structure or element can undergo without a significant loss of initial yielding resistance to

the initial yield deformation.

The above definitions are illustrated in Fig. 2.1 for the case of a Ductile Moment-Resistant

Space Frame (DMRSF).

2. 1. 1 (a) Needs for Recognizing the Differences Between Deformability. Ductility and Ductility Ratio. Although the ductility ratio depends on the ductility, which in turn depends

on the plastic deformability, so that the three terms are interrelated, there are essential

differences in their quantification that need to be recognized.

Defonnability vs. Ductility: While one structure can have significantly greater deformability

than another, its ductility (particularly its usable ductility) can be smaller. For example, this can be the case of a very flexible RC-DMRSF vs. a stiff but very ductile shear wall. It is

clear from analysis of Fig. 2.2 that if the DMRSF is too flexible, i.e. the .dfy is very large, and

the maximum lateral deformation, ~f"'' , that can be accepted or tolerated is limited, then the DMRSF ductility that can be used could be smaller than the available and usable shear

wall ductility.

Ductility vs. Ductility Ratio: The difference between these two terms is clearly illustrated

in Fig. 2.2. While the shear wall usually has smaller ductility than a DMRSF, it can have

a significantly higher ductility ratio.

2. 1. 1 (b) Advantages of Providing Structural Components and Their Connections with the Largest Ductility Economically Feasible. The minimum desirable ductility for each

component should be such that the structure has the opportunity to develop its maximum

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potential strength according to the maximum strength of its components. The need for this

is illustrated in Fig. 2.3, where the strengths of a simple structure composed of a ductile

moment-resisting frame and two coupled walls are depicted as the sum of the resistance functions of each of their components. This figure illustrates that, in order for a structure to develop its maximum potential strength RT as determined by the sum of the maximum

strength of each component (RT = R.... + R,..2 + RF), it is necessary that J...,1 2.. 4.3, J. 912 2_2.8 and J.i.F 2_1.0. To allow the structure to move as a mechanism under its maximum potential

strength, the ductility ratio of the walls, particularly wall w., must be significantly higher

than that of the DMRF. This figure also illustrates the difference between ductility ratio

and deformability. While the ductile moment-resisting frame has a larger deformability than the walls, its ductility ratio can be smaller than that of the individual walls. The available frame ductility ratio cannot be used effectively because the frame has significantly larger deformability (flexibility) than the wall components do, resulting in a relatively earlier failure of the wall components.

It should be noted that by providing large ductility and due to three-dimensional (3-D) interaction between DMRF and walls, it is possible that the maximum strength of the entire

structure will exceed the sum of its components if the strength of each is determined considering it as acting independently. This is illustrated in the schematic representation (Fig. 2.4) of the behavior observed in the experiments conducted on the 7-story RC DMRSF-wall structures of the U.S.-Japan Cooperative Research Program. Results of these

experiments are discussed in detail in Ref. 6. The beneficial 3-D interaction was identified

as a consequence of the effects of outriggering action of frames on the wall, as illustrated

in the isometric view of Fig. 2.5. The wall, rocking around the compressive edge during its ductile axial-flexural behavior, tends to lift up the surrounding girders of the DMRSF that frame into the walls. The girders resist this movement and, in doing so, develop higher shear forces and increase the axial compression in the wall, which results in an increase in

its axial-flexural capacity. This outriggering action results in a significant enhancement of

the lateral strength of the whole structure.

-8-

2. 1. 1 (c) Quantification of the Ductility Ratio. Though the use of the concept of ductility ratio for the EQRD of structures was introduced in U .~.earthquake engineering literature in the early 1950s, though its application to RC structures was presented in 1961 in the PCA

Manual [2], and though tremendous experimental and analytical research efforts have since been devoted to its evaluation and application, even today it continues to be an ambiguous parameter. In a workshop conducted in 1977 [10], a group of experts, including professors, researchers and practicing engineers, after recognizing the need to survey, analyze and

evaluate the main parameters (as well as the definitions) that are presently used in analytical and experimental research and in practice to describe the inelastic mechanical

characteristics of reinforced concrete materials, sections, regions, members, subassemblages,

structures and whole soil-building systems, made the following statement:

"One parameter of particular concern is ductility. While ductility is a useful

concept, it has a precise definition and quantitative meaning only for the

idealized case of monotonic, linear elasto-perfectly plastic behavior. Its use

in real cases where behavior significantly differs from this idealized case leads

to much ambiguity and confusion. It is thus difficult to make valid

comparisons of "available" ductility values reported by different researchers

because they are often based on different response parameters or on yielding values determined using different and/or unexplained definitions. These experimentally obtained "available" ductility values are also often misused in

analytical studies of the "demand" or "required" ductility due to the difficulty

of establishing realistic values for the "linear-elastic stiffness and yielding

strength." Attempts should be made to integrate the definitions of response

parameters that are used in experimental test programs and in analytical

investigations. Furthermore, it is highly questionable whether the performance of different building systems can be properly described and

evaluated on the sole basis of elastic stiffness, yielding strength, and ductility.

Consequently, there is a need to introduce additional parameters for

describing the total hysteretic energy dissipation, number of cycles of reversed

-9-

deformations, and the degradation in stiffness and strength that has been observed under seismic conditions."

The needs stated above are still valid today.

2. 1. 1 (d) Concluding Remarks. While in discussing the philosophy of ductility-based design, it is possible to use the concept of ductility and/or ductility ratio in a vague manner. But when such philosophy has to be applied in the EQRD of real structures, the philosophy has to be quantified, and therefore it is necessary to use unambiguous parameters which can

be evaluated numerically with reliability. Such parameters are usually the displacement

ductility ratio, JJ., , and/or the rotation ductility ratio, J.l.e Preliminary designs are usually

based on a selected maximum JJ.6 , which is determined based on the maximum values of JJ.e

which can be developed or which can be accepted at the critical regions of the structural

members.

Assuming that the values of JJ. 6 can be selected and evaluated reliably, the problem that

remains is to use this ratio or parameter correctly in the design process of a structure. To

discuss the solution of this problem it is advisable to review briefly the state-of-the-practice

and state-of-the-art in EQRD of RC structures. This is done after the discussion for the needs to control IDI.

2. 2 NEEDS FOR CONTROLLING INTERSTORY DRIFT INDEX (IDI)

2. 2. 1 General Remarks In Ref. 11 it is stated that

"While displacement ductility factors generally provide a good indication of

structural damage, they do not usually adequately reflect the damage to nonstructural elements. This is an important limitation in seismic-resistant design since a significant portion of the hazard to occupants and of the total

cost of repairing earthquake damage is a consequence of nonstructural

-10-

damage. Nonstructural damage is more dependent on the relative

displacements (drift) than on the overall displacements. To obtain a reliable measure of nonstructural damage, maximum drifts must remain unnormalized or be divided by the value of drift corresponding to the damage threshold.

Nonstructural damage estimates based on drift ductilities may be misleading.

For example, nonstructural damage for relatively rigid structures may be small

even for large values of displacement ductility since the yield displacement

may be well below the nonstructural damage threshold. On the other hand, the non structural damage and lateral displacements for flexible structures may become intolerably large even before significant yielding develops.

To produce safe and economical structures, seismic-resistant design methods

must incorporate drift (damage) control in addition to lateral displacement ductility as design constraints."

For clarity and convenience, in discussing the importance of control in the earthquake-resistant design of any engineering system, and particularly in case of building structures, the

following glossary of terms to be used in the discussion is introduced. The glossary is illustrated in Fig. 2.6 [12] and Fig. 2.7 [11].

2. 2. 2 Drift Definitions

Drift: Relative lateral displacement between two points (two floors).

Overall Drift = A .... (Fig. 2.6)

lnterstory Drift = A ; - A ~~ (Fig. 2. 6)

Overall Drift Index 11""' (F. 2 6) - Ig ..

H

lnterstory Drift Index - Ai-Ai-1 (Fig. 2. 6) h .

-11-

Tangential-Interstory Drift: = (4 ; -4 ... )... = Drift-Producing Damage (Fig. 2. 7)

Tangential-Interstory Drift Index: (IDI)... = RT (Fig. 2. 7)

2. 2. 3 The Need for Drift Design. As discussed in more detail in Ref. 12, the control of the

drift of a structural system under earthquake excitation is important for at least three

different reasons: (1) to maintain architectural integrity, thereby avoiding unacceptable damage to nonstructural components; (2) to limit structural damage and avoid structural instability (P - 4) problems; and (3) to avoid human discomfort under frequent minor or even occasional moderate earthquake shaking.

Story drifts and drift ductility factors may also be useful in providing information on the

distribution of structural damage. Unfortunately, conventionally computed story drifts may

not adequately reflect the potential structural or nonstructural damage to multistory

buildings. In some structures, a substantial portion of the horizontal displacements results

from axial deformations in the columns. Story drifts due to these deformations are not usually a source of damage [Fig. 2.7 (a)].

A better index of both structural and nonstructural damage is the tangential story drift

index, RT . As schematically indicated in Fig. 2.7 (b), the intent of this index is to measure the shearing distortion within a story. For the displacement components shown in Fig. 2. 7.

(c) and assuming that floor diaphragms are rigid in their own plane, the average tangential drift index is equal to

1 1 . R = - (u- -u ) + - (u + tL - u_ - u ' T H-:Jl L 6 Cl -z 4' (2. 1)

in which L is the bay width and H is the story height. This first term on the right-hand side

of Eq. 2.1 is the conventional story drift index, and the second is a correction applied for

each bay accounting for the slope of the floors above and below the story. It may not be

-12-

appropriate to average the values of RT for a story when the pattern of axial column

deformations varies greatly across the structure (e.g.,frames with structural walls).

Although drift indices and, in particular, tangential drift indices, provide a good measure of the distribution of structural deformations, it may be difficult to compute corresponding yield drifts. One possible method for computing the yield drift is taking the drift present at the appropriate location when the building, loaded with equivalent seismic lateral forces,

reaches its yield displacement; another is computing a story shear-drift relationship for a subassemblage consisting of the story in question with appropriate boundary conditions.

The general philosophy of EQRD for structures (particularly for building structures) other than essential facilities has been well established and proposes:

(1) to prevent nonstructural damage in frequent, minor earthquake ground shakings;

(2) to prevent structural damage and minimize nonstructural damage in occasional moderate earthquake ground shakings;

(3) to avoid collapse or serious damage in rare major earthquake ground shakings (where structure could be damaged but should not collapse).

The above philosophy is in complete accord with the concept of comprehensive design.

However, current design methodologies fall short of realizing the objectives of this general philosophy [13]. A typical hierarchy of earthquake limit states is shown in Table 2.1 [14].

As pointed out by Dowrick [14], even up to the present it has been common practice to design normal structures or equipment to meet only the two criteria designated above as (1) and (3). Indeed, design usually has only been carried out explicitly for criterion (3), on the assumption that the other two criteria (particularly criterion (1)) would be satisfied automatically.

-13-

The growing concern over the costs of earthquake damages (direct, functional and indirect) and the difficulty of repairing much postyield damage, points out the need for more

attention to be given to control of damage and repairability at the design stage. These

needs have been clearly emphasized by the 1989 Lorna Prieta earthquake. The control of

damage will, of course, also help to improve human safety, which is the traditional

fundamental criterion. The main source of damage is deformation; thus to control damage,

it is necessary to control deformation and particularly to control interstory drift.

In summary, achievement of reliable and efficient EQRD requires satisfaction not only of the criterion for strength and toughness but also the criteria for deformation and

repairability. It should be noted that strength, toughness, deflection control and repairability

are interrelated and hard to define.

Assuming that the values of the IDI can be estimated reliably, the problem that remains is

how to use correctly this ratio or index in the design process of a structure. To discuss the

solution of this problem it is beneficial to review briefly the state-of-the-practice and state-

of-the-art in earthquake-resistant design of RC structures.

Tahle 2.1 IIIERARCIIY OF LIMIT STATE DESIGN CRITERIA FOR DIFFERENT LEVELS OF EARTHQUAKE HAZARD [14]

(A) Serviceability

limit state

Serviceability eartiHJuake (or OBE)

Response (I) Undnmaged (2a) condition Elnstic

Normal st rue! ures

or (2b) equipment

Typical 5-10 return period (yr) or TA"'" T1115 (?)

Response Critical condition (4) Pre-yield st rue! urcs

or equipment Typical 500-1000

ret urn period (yr)

(D) Ultimate

limit state

'Usual' design cart hqua ke

No collapse Post-yield cycling Limited deformation (Repairable) pre-yield

50-100

-

(C) Survivability

- limit stale

Survivability earthquake

(or SSE) (3) Pre-collapse

500-1000

(5) As (2a) or

Pre-collapse

5000-10 000

-VI

Fig. 2.3

R (RESISTANCE)

~w J

-17-

~F, ~Wult A (DEFORWA TION)

Fig. 2.1 - DEFINITIONS OF DEFORMABILI'IY, DUCTILilY, AND DUCTILilY RATIO

R (RESISTANCE)

~. J

~ :~EAR ~ REAL 3-0 ...a.:ALL .EW. BEHAVIOR

f SUM OF INDIVIDUAL BEHAVIOR ,.. - - .. , OF WALL AND DMRSF

A (DEFORMATION)

Fig. 2.2 - DEFORMABILilY AND DUCTILI1Y OF AN RC WALL AND AN RC DMRSF

R (RESISTANCE)

.._. ___ DEFORMABILITY OF DNRSF ----1 DUCTILITY RATIO (I'- ~1~.,) OF OMRSF

~F. r A(OEFORMATION)

DUCTILI'IY REQUIREMENTS FOR BOTH WALLS AND FRAMES IN AN RC FRAME-WALL SYSTEM

-18-R (Resistance)

----- SHEAR WALL 1

w2 28 P.w267 -----..,SHEAR WALL 2

p.F 1 p.F-2~ 1-H--#-.,__-!--..l,---~--,._.....----------r D UCTJLE MOMENT

~w1 6w2 y y

RESISTING FRAME (DMRF)

f1 (Deformation) Fig. 2.4 THE EFFECTS OF A 3-D INTERACTION ON THE STRENGTH OF AN RC

FRAME-WALL SYSTEM

Fig. 2.5 - ISOMETRIC VIEW OF WALL ROTATION ILLUSTRATING 3-D OUTRIGGERING EFFECT

-19-

r II.

!" -r

l -r

h.

!'

. Fig. 2.6 - DEFINITION OF DRIFfS (12)

60 ,-DISPLACEMENTS (A A ) H RESULTING FROM / i - i-1 T ' CHORD ROTATION},~ DRIFT PRODUCING

I f-:-L-tf 7 DAMAGE 1 r--1 I

l l HORIZONTAL ++----~ --..;;._~,.. -~STORY DRIFT

Cal DRIFTS DUE TO AXIAL F~CES IN

FIRST STORY COLUMNS

(b) DRIFT DUE TO STORY DEFORMATION

r-----L----

(c) DISPLACEMENT COt.PONENTS FOR

COMPUTING R

Fig. 2.7 - COMPUTATION OF TANGENTIAL-INTERSTORY DRIFf INDEX [11]

-21-

3. STATE-OF-THE-PRACTICE AND STATE-OF-THE-ART OF EQRD OF RC STRUCfURES

3. 1 PROBLEMS IN DESIGN AND CONSTRUCTION OF EQ-RESISTANT STRUCfURES

The problem areas have been identified and discussed in detail by the authors in a series of publications [7-9]. Only the three main problem areas that have been identified are enumerated herein. The first problematical area in EQRD is in establishing the critical earthquake input (Design Earthquakes). The second includes problems involved in determining the demands on the entire soil-foundation-building (superstructure and nonstructural components) system by the critical earthquake. The third involves the visualization (for preliminary design) and prediction of the real supplies to the building at the moment that an earthquake strikes.

The supplies and demands, in general,, involve the mechanical characteristics of stiffness,

strength, stability, and energy absorption and dissipation capacities. Evaluation of the

demands and prediction of the supplies are not straightforward. The determination of the

demands, which is usually done by numerical analysis using mathematical models of the entire soil-foundation-building system, depends on the interaction of this system as a whole with the excitations that originate from changes in the system environment. The

determination also depends on the intimate interrelation betw~ the demand and supply itself. Specific problems encountered in the three problematical areas of the earthquake-

resistant design of structures -- critical earthquake input, demands on the building, and

supply capacities of the building --are discussed in Refs. 7-9.

While a sound preliminary structural design and reliable analyses of this design are necessary, they do not ensure an efficient earthquake-resistant structure. The seismic response of a structure depends on the state of the entire soil-foundation and superstructure

system at the time that earthquake shaking occurs, which means that the response depends

not only on construction, but on maintenance as well. A design will be effective only if the

-22-

model used can be constructed and maintained. Although the importance of construction

and maintenance in the seismic performance of structures has been recognized, insufficient

effort has been made to improve these practices --through, for example, supervision and

inspection.

3. 2 STATE-OF-THE-PRACTICE This review will focus only on the state-of-the-practice of EQRD of buildings as reflected by present building seismic codes, and will emphasize how the concepts of J.6 and IDI are

used and/or how they could be used to improve the state-of-the-practice according to

present knowledge. Before discussing and comparing the seismic codes for the United

States, Japan, New Zealand, Mexico and Europe, it is convenient to make the following

general remarks regarding code estimation of demands and supplies.

3. 2. 1 Estimation of Demands in Present Seismic Codes. Although the review has focused on U.S. seismic codes, the problems identified below are common to most codes in the

world. There are several sources of uncertainty in code-specified procedures for the

estimation of demands, uncertainties that can be grouped into two categories: (1) specified seismic forces; and (2) methods used to estimate response to these seismic forces.

3. 2. 1 (a) Strength For regular buildings, statically equivalent lateral seismic forces can be derived as follows.

For base shear: V = C.W =(C.., I R) W (3. 1) where V is base shear, c. is the design seismic coefficient, W is the weight of the reactive

mass (i.e., the mass that can induce inertial forces), c.p is the seismic coefficient equivalent to a Smoothed Linear Elastic Design Response Spectral (SLEDRS) for acceleration, S., (C.p = C.R = S/g), and R is the reduction factor. Although in most of the codes the values of R are given without any explicit relation to J.6 , these values implicitly depend on JJ. 6

-23-

Structural response is usually estimated using linear elastic analyses of the effects induced directly by the above statically equivalent lateral forces or by these forces multiplied by load factors depending on whether the design will be performed using allowable (service or working) stress or the strength method. There are only very few countries in which the codes recommend or encourage the use of limit analysis and limit design methods.

3. 2. 1 (b) Stiffness and Drift. Most of the seismic codes address design for lateral stiffness and for drift at service level. There are only a few codes that address estimations of the change in stiffness during the response to major shaking and the maximum drift that can occur. There are also only a few codes that explicitly require that the contribution of

torsion should be considered in estimating the maximum lateral drift, and very few give any guidelines regarding how to deal with the effect of multicomponent seismic excitations [15].

According to ATC 3-06, the deflections o. at ultimate (safety) limit state should be evaluated as follows:

where

(3. 2)

cd = the deflection amplification factor (this factor is specified for different types of structures)

oxe = the deflection determined by an elastic analysis for the seismic forces prescribed by the code considering the building fixed at the base

The ATC 3-06 [16] limits the maximum IDI, and consequently o., according to the seismic hazard group to which the building belongs. The limits vary from 0.010 to 0.015. For certain types of buildings and limited height, a one-third increase in IDI limitations is

allowed if there are no brittle types of finishes.

-24-

3. 2. 1 (c) P-.1 Effects. Few codes give explicit requirements and/or recommendations regarding how to estimate these effects. While ATC 3-06 [16] recommends that the P-.1 effect does not need to be considered when the stability coefficient e is less than 0.10

9 (3. 3)

where

.1 = the design-story drift

V, = the seismic shear force acting between level x and x-1

h,. = the story height below level x

P, = the total unfactored vertical design load at and above level x

In accordance with this method the commentary to A TC 3-06 recommends that when a is greater than 0. 10, the design story drifts be multiplied by a factor 1 I ( 1 - a) > 1. NEHRP-88 [17] requires multiplication by a factor 0.9 [11(1-a) > 1.

The 1988 UBC has a very vague requirement regarding P-.1 effects. This code requires

checking whether at working load level the ratio of secondary moment ( == P w c5 X&) to primary moment ( == V w h) does not exceed 0.1 (where P w is the total unfactored [working] dead and live load; V..., is the seismic shear at working load level; and h is the height of the story). There is no doubt that there is a need for more rational code procedures to estimate the demands regarding the stability effects at ultimate limit states.

3. 2. 2 Estimation of Suwlies in Present Seismic Codes.

3. 2. 2 (a) Strength. Most of the RC EQRD codes require that the supplied strength be estimated using a strength method in which nominal strength of critical sections are

i

I \

I

-25-

evaluated as a function of just the minimum specified strength of the materials, and then reduced by a strength reduction factor. There are a few codes, like the New Zealand Code,

in which the design and detailing of the critical regions of the structure is based on the probable supplied strength capacity to the members. Although most of the present RC EQRD codes specify minimum size and reinforcement detailing according to the ductility ratio that is expected to be developed, this is done in an implicit way. It can be concluded that the state-of-the-practice, as reflected by most of the present EQRD codes for RC buildings, does not appear to have included the use of the concept of energy dissipation

capacity in a rational and reliable way through the use of the ductility ratios.

3. 2. 2 (b) Stiffness. Deformation and Stability Capacities. Most of the RC codes give only empirical expressions to estimate the so-called "effective linear elastic stiffness." Some of them, such as the 1988 UBC which is based on the ACI (318-83) [19] (with some additional provisions), include the effect of cracking in the estimation of the effective linear stiffness. However, the UBC, as well as most of the present codes, does not specify how to evaluate

the changes in stiffness of the whole soil-foundation, superstructure and non-structural

components system induced by increasing damage. There is a need to develop code procedures that, based on the supplied local energy dissipation capacity of the structural members (rotational ductility ratio and degradation with repeated cycles, i.e. local hysteretic behavior), will lead to the estimation of the global deformational capacity of the structure under not only monotonically increasing deformation but also under generalized (repeated reversal) deformation.

The so-called Tri-Service Technical Manual [20], which will be discussed in more detail later, recommends a method called "Method 2; Capacity Spectrum Method" which requires estimating the "Force-Displacement Capacity Curve." Although the way that this curve is

used is questionable, there is no doubt that the requirement to estimate this curve is a step forward toward solution of this issue.

-26-

3. 3 STATE-OF-TIIE-ART IN DUCfiLITY AND STORY DRIFT-BASED EQRD The state-of-the-art with respect to each of the problem areas identified above is discussed in detail in Refs. 8, 9, and 21. Only the state-of-the-knowledge regarding the proper use of

the concept of ductility ratios and story drift in the EQRD process will be discussed herein.

It is well recognized that EQRD requires an iterative procedure in which a preliminary design is improved through a series of analyses. The importance of a proper preliminary design should be highly emphasized, because, if the design procedure is started with a poor preliminary design, the only thing that will be achieved at the end through its repeated

analyses will be an improved bad design. Before discussing separately the state-of-the-art

in J.J- 6 and in IDI, some general remarks about their use are presented.

3. 3. 1 General Introductory Remarks Regarding Importance of u. and IDI in Preliminary Design. Although it is generally well recognized that damage is due to deformation, there is no agreement regarding what is the main criterion for preliminary EQRD of structures. Perhaps as a consequence of past and present code requirements, present practice

emphasizes the use of strength in the preliminary design of structures. More specifically,

in most of the present codes, the preliminary design is based on only base shear strength

with a requirement to check the drift by elastic analysis. The insistence on only using strength as primary criterion is perhaps a consequence of the following two reasons: first, the practice of trying to design for ultimate or safety limit state by reducing the actual

inelastic design to one at working stress where linear elastic analysis can be used; and

second, the assumption that there is a unique relation between strength and stiffness without

recognizing that (particularly in the case of reinforced concrete structures) it is possible to change significantly the strength of a structure without changing its stiffness. While

preliminary design based on base shear strength could be justified for design where serviceability (elastic response) controls, it cannot be accepted for cases where the design is controlled by the ultimate (safety) limit state where large plastic deformation is accepted: at this limit state, base shear strength of a given designed structure is insensitive to variation

of deformation and, therefore, to damage. Once structures yield, the base shear strength

-27-

remains constant, while the deformation can take any value, from its yielding value up to the maximum value, at which collapse (sudden significant drop in resistance) occurs. In view of the above insensitivity of the base shear strength to damage in the inelastic (plastic) range of response (behavior), there have been some proposals to base preliminary design on only lateral stiffness, i.e. on only controlling the interstory drift. However, a practical

method for this type of design has yet to be developed.

The authors believe that the most rational approach is one which recognizes the importance of strength and stiffness (control of deformation) and which also recognizes that these two factors, while strongly interrelated in the case of elastic response, clearly have a weaker

relation to each other in the case of inelastic response. In this last case, the lateral

deformation at ultimate limit states depends on the yielding strength provided to the

structure. To control inelastic deformation, it is necessary to provide the structure with a minimum yielding strength. Therefore, to achieve an efficient preliminary EQRD, there is a need to consider two requirements simultaneously the strength (based on the rational use of J.1. 6 ) and the deformation (based on the limitation of IDI).

3. 3. 1 (a) Examples. The following two simple cases emphasize the need to consider strength and deformation simultaneously.

Given (See Fig. 3.1): (a) structure: SDOFS [Fig. 3.1.(a)] (b) ground motion: an impulsive EQ-ground motion, consisting of either

a rectangular acceleration pulse [Fig. 3.1. (b)] or a triangular acceleration pulse [Fig. 3.1. (c)], the two of which can be considered respectively as extreme cases

regarding probable shapes of pulse. (c) intensity of pulse: service level O.lOg = (v J.

Maximum Credible EQ = MCEQ, 0.40g = (vJ.

-28-

Required: To design a structure whose maximum deformation will not exceed the

following acceptable deformations.

(v)ocrvia: ~ 0.005h(v) ..... ~ 0.02h

Solution

FIRST CASE: Rectangular Acceleration Pulse [Fig. 3.1. (a)]

Assume a td I T: to be specific, say td I T = 514

Design for Serviceability: Linear elastic response. In this case, for td I T ;:: 0.5, the value of the maximum Dynamic Load Factor (DLF) ..... is 2.0. See Fig. 3.2 [22].

Strength (Resistance) Required: (R,.j..,,_.;"" = 2 x (O.lOg) m

(R,.joervioe = 0.20 W

Lateral Stiffness Required: Knowing the mass m, and value of the selected period T, it is

possible to compute the required stiffness k from

T = 21t lm ~ k = (21ti m ~k- T2 (3. 4)

Knowing k, it is possible to compute the service displacement [(v .. rvi"") = R_,.lk] and then to compare with the required limit for (IDI). = (v .. rvioe)lh, say (IDI). ~ 0.005

-29-

If (v oervia:)c~ooman:~ > (v oervia:)e>:>ep~ablc stiffness has to be increased. This will induce a change in T (decrease) and a new iteration in the design procedure has to be started. Assuming that the preliminary design for serviceability was satisfactory, then we can go to:

Design for Safety: [(vJ...J = 0.40g. Assuming that the supplied Ry = R, = 0.20W, for a linear elastic plastic response and for ~ I T = 514 from the graph (Fig. 3.3) with a

R,/F1 = 0.20W/(0.40g)m = 0.5

the graph indicates a v"'.)v.1 .. ,;. = 80 = J.L 6 This is a ductility ratio which not only cannot be developed but which also results in a vmax = 80 vclastic = 80 X 0.005h = 0.4h, i.e. an (IDI)~ -0.4, which obviously cannot be accepted.

From the above computations, it is clear that there is a need to:

(i) increase the yielding strength; or (ii) increase stiffness; or

(iii) a combination of (i) and (ii).

Increase in stiffness will lead to a decrease in the (v ...J .. rv1"'' but as the T will decrease the td I Twill increase and then the v"'/v.lasti will increase. Thus the solution is to try to increase the strength; but by how much? It depends on how much p,6 can be developed economically

and on how large (IDI)max can be tolerated to control damage. Assume that l.h < 6 and (IDI) < 0.02. From Fig. 3.3 it can be seen that to have a p,6 = vmax/vclastic = 6 -+ R,/FI = 1.05, then R, = 1.05 X 0.40g m = 0.42W. Note the significant increase in strength that is needed (0.4210.20) = 2.1.

Check lateral stiffness. If we keep the same k as for the service design,

vmax = (vclast;.)max X 6 = 2.1(vclastic), X 6, i.e. (v...J = 12.6(vclasti.) .. rvicc

-30-

If the (vewuc)oervia: i.e. under the F 1effcclive = 0.20W, was already 0.005h, the (v.....J = 0.063h. This results in an IDI which is too high. Usually the maximum acceptable is 0.02. Thus to limit

the IDI it will be necessary either to decrease acceptable J.6 or to increase stiffness or a

combination of these two solutions.

For example: doubling k (which will reduce the period T to a value equal to Tl ./2 and therefore

td --=1.4 td {f=l.8; TJ/2

and reducing J. 6 to 4 will result in a required yielding strength of

R,.. = 1.15, 0.40W = 0.46W. Then

vmax ::;: ( 0.46)( V elastic acceptable] X 4 ::;: 4.6(0.00Sh) 0.20 2

V max = 0.023h

The resulting IDI of 0.023 may be acceptable.

SECOND CASE: Triangular Acceleration Pulse [Fig. 3.1 (c)]

(3. 5)

(3. 6)

It can be legitimately claimed that the occurrence of a rectangular pulse is practically

impossible. To demonstrate that the same type of design is required even by the less

demanding type of acceleration pulse, which can be considered to be the triangular pulse,

the above example is repeated for this kind of pulse and considering a td I T = 1 rather than 1.25, and assuming T = I sec.

Design for Serviceability

For td I T = 1 and (vJ..,"';"" = O.lOg, from the graph of (Fig. 3.2), the

-31-

{R,.jelastic oervioe = 1.5(vJ .. rvi.,.m = 0.15W and

v .. rvi.,.= {R,.,J.~asuc .. rvi.,./k = 0.15W/(2rrYm/(1 ,y = 0.15g/39.48 = 1.47 in

Assume h = (294) in. Then IDI = 1.47 in/294 in = 0.005.

Design for Safety

F.trec~ive = 0.40W

Assuming R = R, = (R,.Jscl'\;a: from the graph (Fig. 3.4) it can be seen that for td I T = 1, and

R,,./F.rrecti-.: = R,.,.IF. = 0.15/0.40 = 0.375,

the required J.La = va.)v.lasti< = 22

This value is too large to be developed, and also results in an IDI = 22 x 0.005 = 0.11,

nearly five times more than can be accepted. Then, as discussed previously in the

improvement to the solution of the FIRST CASE, the supplied yielding resistance has to be

increased, either by a decrease of the acceptable J.La. and/or by an increase of the lateral

stiffness.

Assume that k is doubled; Tis decreased by T/ v'2 and consequently ~ I T = 1.41. With this value of td I T and considering a J. 6 = 6, the required R,,.,/F.trective = 0. 7. Then R_. = 0.28W and

vmax = (vewtJ0.28W X 6 = (0.005/2) h X (0.28/0.15) X 6 = 0.028

which, although closer to 0.02, still is not acceptable.

-32-

3. 3. 2 (b) Concluding Remarks Although none of the above assumed ground motions are realistic representations of usual EQ shaking, the examples illustrate very clearly the need to consider simultaneously the strength (through the proper use of JJ.6) as well as the deformations (through the acceptable limits of IDI). Similar procedures can be applied in the case of more realistic EQ ground motions. The only basic information that is needed is the:

SLEDRS for service EQs, SIDRS for maximum creditable EQ, Acceptable limits for IDI at service

as well as at safety limit states.

where SIDRS = Smoothed Inelastic Design Response Spectra

3. 4 STATE-OF-TilE-ART IN USING DUCTILITY RATIO JJ., IN PRELIMINARY EQRD According to the previous discussion, J1. 6 should be used throughout the whole design

procedure, and particularly in the final step, where the final designing and detailing of the

critical regions of the structures are done. However, as the importance of this last step

concerns other parts (phases) of the whole research project, only the use of JJ., in estimating the demands will be discussed herein, specifically in: (1) establishing the design EQs, and; (2) the preliminary design of the structure.

3. 4. 1 Use of u. in Establishing the Design EOs. The following two main different methods are being used.

A. REDUCTION OF THE LINEAR ELASTIC DESIGN RESPONSE SPECTRA

(LEDRS) THROUGH THE DIRECT USE OF THE VALUE OF JJ.6 (NEWMARK AND HALL PROCEDURE [23]), OR THROUGH THE USE OF STRUCTURAL MODIFICATION FACTORS, R, (ATC-3 PROCEDURE). R is a function not only

-33-

of J.J., but also of the provided overstrength, OVS, and of the increase in damping, ~. due to large deformations.

B. DERIVATION OF IDRS THROUGH STATISTICAL STUDIES OF THE

INELASTIC RESPONSE SPECTRA (IRS) OF STRUCTURES TO AVAILABLE RECORDED OR EXPECTED (PREDICTED) CRITICAL GROUND MOTIONS. These IRS are obtained through time history nonlinear dynamic analysis of structures

with different yielding strengths (Cy , or different degrees of J.J.,) and o [24]. This method can be considered as a part of the overall energy approach to the EQRD [25, 26].

Method A, which is very simple, is already widely used and has been included in codes of

several countries. However, as the proponents of this method point out, the method is only

valid for very limited types of structures. The application of this method to the design of

most real buildings is questionable [24-27].

Method B can be considered as the method of the future. Although it has already been

applied to simple cases, its general application in practice will require extensive integrated

analytical and experimental studies on real 3-D soil-foundation-superstructure and

nonstructural component systems. Once a reliable IDRS has been attained, the next

problem is how to use J.J., in the preliminary design of the structure.

3. 4. 2 Use of u. in Preliminary Design. For the purposes of this discussion, the different ways of conducting the preliminary design of EQ-resistant structures as regards the use of the ductility concept in the sizing of the structural members can be classified in the following

three groups: (a) #1a is not used at all. The critical internal forces in the members are obtained through linear elastic distribution (LED) of forces; (b) implicit and partial use of #1a Usually this is done by allowing a limited amount of redistribution of the internal

moments that have been obtained through a LED of forces; (c) use of limit design approach. Different methods, varying from the one based on simple plastic theory, which

-34-

assumes infinite ductility, to those based on a more general plastic theory which consider

"linear elastic serviceability conditions," as well as realistic limitation of IJ.e and J,6 ,

incorporating also stability considerations. These methods are usually classified as

compatibility and serviceability methods, with serviceability methods being the most promising of the two. This group also covers methods that include the possible occurrence of shakedown phenomena, which are, at present, being developed.

3. 4. 3 Concluding Remarks. In summary, the authors believe that the future of EQRD is an energy approach in which the concept of ductility is used by combining the methods B

and c, i.e., Be, with proper consideration of the possibility of shakedown phenomena.

However, this is considered a long-term approach. In present practice, as will be discussed later, most of the methods that are used can be classified as under the combination Aa. Although methods that can be classified as combined Ab are being used and have been

investigated recently [28-30], the results of these investigations indicate the need for further studies regarding: (1) the proper limits in the amount of redistribution; and (2) the adequate redistribution pattern through the height of the structures.

In view of the above remarks, and the fact that it is usually not practical to change radically the state-of-the-practice, the authors would like to formulate for the immediate or very near future the following compromise solution: to conduct the preliminary design using improved

Ab or Ac (or even Aa) methods; but ideally this should be complemented with time history nonlinear dynamic analyses of the response of the preliminary designed structure to the

predicted maximum credible EQ (MCEQ) ground shakings that can occur at the site of the structure during its service life. If this is not possible, the least that should be conducted is a static nonlinear analysis of the response of the structure under a monotonically increasing lateral load. Before this compromise solution can be applied in practice, it is first

necessary to identify the improvements needed, and then to carry out the studies required to achieve these improvements.

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3.5 STATE-OF-TIIE-ART IN USING INTERSTORY DRIFT INDEX (IDI) IN PRELIMINARY EQRD It is perhaps unfortunate that in the past most of the efforts in improving EQRD has been expended only in designing for strength without proper consideration of the role of

deformation. Damage is a consequence of deformations. For any structure that is

responding in the inelastic (plastic) range under practically a constant strength, the degree or level of damage depends upon the amount of the plastic deformation that the structure

undergoes. Thus, to control damage it is necessary to control deformations. The question

is how to achieve such control at the different levels of EQ shaking that can occur during the life of the structure. Although the general EQRD philosophy contemplates at least three different limit states, for a preliminary design it usually is convenient to try to satisfy

only the first (serviceability) and the last (safety) limit states.

3. 5. 1 Control of IDI at Serviceability Level. Because at service level the structure should respond in its elastic range, then for a structure with a given damping and a total mass and

its distribution, the control of IDI depends on the stiffness. The question is what is or are

proper limits for IDI to control nonstructural damage as well as to protect other contents

of the building and perhaps avoid human discomfort. At present it is generally recognized

that the limits for IDI depend on the function (occupancy) of the building, type of nonstructural , elements and how these nonstructural components are attached to the structure. Depending on these factors, acceptable limits for IDI vary from 0.0006 to 0.006.

Although the estimation of the IDI at the service level is usually based on linear elastic

analyses, there are many uncertainties regarding the effective stiffness of the structural

members (particularly on RC structures due to cracking), the deformation of the foundation, the effects of the nonstructural components, etc. Furthermore, analyses of the deformation

should be based on a realistic 3-D model that considers properly the effects of torsion under the multicomponents of ground motions. The estimation of torsional deformations offers serious difficulties.

-36-

The most practical procedure for including the criteria of IDI control in the preliminary design is to use the SLEDRS (tripartite on logarithmic scale or even the standard SLEDRS for displacement, Sd on normal scale). If the limit IDI is specified assuming uniform IDI along the structure (or, according to type of structure, considering possible concentrated IDI at top or bottom story by multiplying average IDI by a factor smaller than one), the maximum acceptable displacement can be estimated and from the SLEDRS the maximum acceptable period of the structure can be found. This preliminary estimation of the period facilitates the selection of the PSa that has to be used for the design for strength. Once the preliminary design for strength has been completed, a realistic 3-D model of this preliminary design can be used to estimate the maximum IDI that can occur under the multidirectional EQ ground motion.

3. 5. 2 Control of IDI at the IDtimate or Safety Limit State. The acceptable maximum IDI

to control damage varies with the type of structure and the function of the structure. Usually it varies from 0.01 to 0.03. The IDI demands for different types of EQs can be estimated by evaluating the IDRS for different values of J.L, or Cy. The problem is how to estimate the effective lateral stiffness or period T.

3. 5. 3 Choice of Member Stiffness for Drift and P-~ Analyses. [12] A common difficulty in seismic analysis of RC structures is the selection of a set of rational stiffness values to be used in force and displacement analyses. Should one use gross concrete-section properties? Should one use some reduced section properties? Or should the gross concrete properties be used for one type of analysis and reduced section properties for another? The seismic design codes in the U.S. are not specific about this matter. Thus, the choice of section properties used in lateral analysis in general, and in seismic analysis in particular, varies widely.

Contributing to the complexity of this issue are the following factors:

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1. Although elastic material behavior is usually assumed for the sake of simplicity,

reinforced concrete is not a homogeneous, linearly elastic material.

2. The stiffness and idealized elastic material properties of a reinforced concrete section vary with the state of behavior of this section (e.g. uncracked, cracked, yielding, and ultimate states).

3. Not all RC members in a structure, and not all cross sections along a particular member, are in the same state of behavior at the same time.

4. For many beams and other asymmetrically reinforced members, the stiffness properties for positive bending and negative bending are different.

5. Uncertainties regarding the actual contribution of the floor slab and of the deformations of the joints.

6. The stiffness of reinforced concrete members and structures varies with the time, and with the history of past exposure to wind forces and EQ ground motions.

7. The stiffness of RC members and structures varies with the level of deformations.

Analytical and experimental studies reported in Ref. 31 indicate that for motions which are within the working-stress design limits of members, the measured fundamental periods of concrete structures are generally slightly less than the periods computed using gross-concrete-section properties. According to these studies, in the case of large-amplitude

motions up to the yield level, the stiffness of the building is usually somewhere between the

computed values based on the gross concrete-section properties and the cracked-section

properties. Based on this observation, the same reference suggests that for force analysis,

the gross concrete-section properties and the clear-span dimensions be used, and the effect of nonseismic structural and nonstructural elements be considered. For drift calculations,

..

"'

-38-

either the lateral displacements determined using the above assumptions should be doubled,

or the center-to-center dimensions along with the average of the gross section and the cracked-section properties, or one-half of the gross section properties should be used. Furthermore, the nonseismic structural and nonstructural elements should be neglected if they do not create a potential torsional reaction.

Similar sets of assumptions have been proposed by research workers who have been

concerned about the choice of member stiffnesses to be used in the P-A analysis of concrete

structures. For example, for second-order analysis of concrete structures subjected to combinations of gravity and wind loads, MacGregor and Rage (32) recommend using 40% of the gross section moment of inertia for beams and 80% of the gross section moment of inertia for columns.

3. 5. 4 Recommended Practical Methods for Designing Considering IDI. A simplified method to estimate lateral drift of RC structures has been suggested by Sozen in Ref. 33.

The method is intended to be used for interpreting experience and evaluating relative merits of different structural schemes and member sizes on the basis of tolerable damage criterion. The method is conveniently. used in preliminary evaluation by simple estimates of the base shear capacity coefficient.

In Ref. 34 and 35 the effects of strength and stiffness and of the type of ground motion on

nonlinear displacement response of SDOF systems is investigated. The results obtained

show that nonlinear displacement response is equal to the linear response spectral values if the system has certain strength which is determined by dimensionless parameters for strength, initial period, and type of ground motion.

Recent results obtained by some of the authors (36) have' shown that the nonlinear displacements are very sensitive to the dynamic characteristics of the ground motions and

in some cases the displacement can be significantly higher than those computed from a

linear elastic response, particularly if high JJ. 6 are used in the derivation of the yielding

-39-

strength (see Fig. 3.5 for the case of Corralitos and Hollister ground motions recorded during the 1989 Lorna Prieta EQ). This observation agrees with the results obtained by Kappos in Ref. 37. These observations also agree with results reported in Ref. 38, which, based on results obtained, recommend the use of the following empirical formula for

estimating the deflection amplification factor Cd (defined as the ratio of absolute maximum interstory displacement to the corresponding value from a linear time history analysis).

In cd = 0.414 (1, J.L.J (3. 7) where J.l.m is the maximum story ductility.

In Ref. 39, Hatamoto et al. propose a newly automated seismic design method for RC

frames which aims at a uniform energy dissipation throughout the building frame, so that

the resulting damage is uniformly distributed as much as possible over all elements.

3. 5. 5 Need to Consider the Effect of Multicomponent Seismic Excitation and Direction

in Estimating Structural Response @D. At present most seismic code procedures as well as traditional dynamic analyses of 3-D buildings assume that the applied excitations are in

the direction of the structure's reference axes. For a real complex 3-D structure, it is

difficult to find the structural principal axes, and the centers of structural mass, stiffness and

resistance may not be coincident. Thus, the direction of structural reference axes chosen

may not coincide with the structural principal axes. Therefore, when applied excitations are

in the direction of structural reference axes, the structural response may not be maximum.

This has been clearly illustrated and discussed in Ref. 15. In this reference it is shown that the seismic components and their input direction can significantly affect the response of a

torsionally sensitive structural system. Ground components applied at the structural

reference axes may remarkably underestimate the response, because the structural maximum

response is dependent on the seismic input direction and its magnitude.

h

._ -- m

k

(n) SIJOFS

vglllliX

---- --- ____ ..

... t

(b) RECJ'ANGULAit ACCELERATION PULSE

\i gmax

/ \ / '\ tt .. 7'\

l :__--~----~ ' J.. --- ..

(c) TRIANGULAR ACCELERATION PULSE

Fig. 3.1 SINGLE DEGREE OF FREEDOM SYSTEM SUUJECfED TO GROUND-ACCELERATION PULSES I. 6

2.0 l v ! :---I v / l I v : 1.6

1/v 0 E

1.2 I ,~i b r.b_ 'V /? ~ ~ .... ..J 0

-0.8

0.4

0

v I--

~ ...... ,o

1/ v y VI

I 0.05 0.10 0.2

lrt

'L I . lrt

~ 0.5 1.0 2.0

'r~lr

---

5 10

. 0 E

I. 4

I. 2

1.0

s 0.8 0

0.6

0.4

0.2 I 0

0

I " 1/

I I

! I ;J

I I

1.0

Fig. 3.2 LINEAR ELASTIC RESPONSE SPECTRA [22]

\ 1\

\ v f-

\ '/ / 1"-

"lli_ '''" '"

3.0

r--.... "" ~

4.0

J,.. ....

c

-42-

7 '

'/// /Y/ I I 7z;r/f I ".:I I I

WI I I I I I

I 0. I I I I

0.1 1..0 10 40

Fig. 3.3 RESPONSE SPECTRA FOR Al~ ELASTO-PLASTIC SDOF SYSTEM: DUE TO RECTANGULAR PULSE [22]

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I I I I I 'II I /, 17' I I . \/1 I I 1/ 1 ~0 ; . I I I I I I VI I I I : : 1/ ., 1 I 111 I

I I ; I I II 17 :7 lA Ill I I/ l I . 'I I I I I u .l /J I l I 1/ !

r-:-- .f-ll_ ~ L -L _y_ l.E Tl. _/..{ 1f-+ V-4 -tT _j- - -1-20 ' I I I /1 I VI' / . . . v I I I 0.8 _l_

.__H itfTitftV:~J-r-Jtr+-0 I 1 t I r l 1 1 I I I : I I I

~~~~~+1-4~~~~1 ~~~~/~-~~-~~~~~~~--~~ 8 1 I 1 I I I / I /1 I 1 / I I I I I I I I I I I I . I I I y I ;r I (A I~ I I Tl I I I I I I 5 ~~~~~~~~+-Y*V~+.Y_I~Y~T~~~~~~~~~~~~~41~1~14-~~~ !/1 ~I II VI/ I~ I I; II I I I 09~ 1 l!i v v 1 /n ~ i t ' 1 1 1 vr ,

f-lf- _j -Y- ~/-~y 7 r4' L...-1-~ L J _JJL1_Ll_-i _l 2 ~/l /: ~ I "' I I .--I 011 II ' l

;m~~~~,t~~:~llf u.~ai~ 1.0 I I . I I I I ~ I I I I I 0.8 //> /1 /-;7 7 r I : : :: '-~"': I I~ ~: 'Y'Ii; 1.20-+--

/ Y Y A I/ 1....-(' I I I I I ~ '-i A I "!/I~ 1.60~ o.s /'/ Y L/1 /1 I I I I I I 1 ""-.1 ?1'""'-1 _...;......_ -:;( I ,.!___ ~;~y:~'Yl\ p' r- ~tziQO:

v~r--~ ~ u_ 1 F 0.2~-l-LL ~ t.J ! . ( )',{ l (111 ( L-

'

P.esislonce Oisclacement I l irianqulor culse function function l 0.1 1.._~1 ~~~ -l..' ----l.'__,.!-,1 ~~p_odl....,l .!...1 !-J' I'--_:_' -l-1 7-' --'-..!...' .-..:..' ~...J......J:......;'W'....!',..--~1---:i

0.1 . 0.2 0.5 0.8 1 2 5 8 10 20

Fig. 3.4 - RESPONSE SPECTRA FOR AN ELASTO-PLASTIC SDOF SYSTEM DUE TO A TRIANGULAR LOAD PULSE [22]

DISP.(in] -44-

CORRALITOS 90 DEG 14 ~----------------------------~~~

--j.J.=l ~=5% --- J1. = 2 ---- J1. = 4 12

10 ----- J1. = 6

~ --------8

6

4

2

0 0.0 0.5 1.0 1.5 2.0 2.5 3. 0

PERIOD (sec)

DISP.(inJ 14

HOLLISTER

12

10

8

6

4

2

0

--J.l.=l --- J1. = 2 -- - - J1. = 4 ----- J1. = 6

0. 0 0.5 1.0 1.5

90 DEG

~=5%/ I

.,. ,..--, ' .

I '---' / "' , ,

,

2. 0 2.5 3. 0 PERIOD (sec)

Fig. 3.5 NONLINEAR DISPLACEMENT RESPONSE SPECTRA [36]

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4. STATE-OF-TilE-PRACTICE: REVIEW OF CODES

4.1 COMPARISON OF TilE BASIC SLEDRS: UNITED STATES' UBC AND JAPAN'S BUilDING STANDARD LAW (BSL) Comparison of the Basic SLEDRS adopted by UBC and BSL for the static lateral load

procedures, which are illustrated in Fig. 4.1, shows that:

4. 1. 1 Shape of the SLEDRS The two above codes assume that, for low values ofT, there is a constant value for the amplified acceleration (or response pseudo-acceleration) which neglects the decrease in the amplification of the acceleration to one as the period of the

structure tends to zero. While UBC adopts a sharp transition from the constant value of

the pseudo-acceleration to the decreasing values, the BSL adopts a smooth decreasing curve

which seems a more rational transition.

4. 1. 2 SLEDRS Values Comparing the values for the three standard type of soils (soil profile types) S1, S2, and S3 , it is clear that except for low values of the Fundamental Natural Period (T ~ 0.6 sec.) and values ofT > 2 sees. ,the spectral values specified by BSL are higher than those required by UBC. The differences in the case of soil profile type S3 (soft soil) reach significant values. For example, in case ofT = 1.6 sec., the value of the BSL is 1.28/1.6 = 0.80. This is 1.46 times the value specified by UBC, which is 0. 75/(1.6)213 = 0.55. Only the special soil profile S4 introduced by UBC compares well with the values of the S3 given by the BSL (see Fig. 4.1).

4. 2 COMPARISON OF TilE DESIGN SPECTRA

4. 2. 1 Japan's BSL. This is the only code of those analyzed herein that explicitly specifies

two-level design earthquakes: moderate earthquake ground motions, which may occur several times during the use of the buildings and should be resisted with almost no damage; and severe earthquake ground motions, with a low probability of occurrence during the use

of the buildings and which should not cause collapse or harm human lives.

-46-

4. 2. 1 (a) Service-Level Design Earthquake. The stresses caused by moderate earthquake ground motions shall not exceed the allowable stresses for temporary loads. These

allowable stresses are: for concrete, two-thirds of the specified concrete strength; for steel,

the yield stress. The lateral seismic shear coefficient Q; of the ith story above ground level shall be determined in accordance with the following formula.

(4. 1) where C; and w; are the lateral seismic shear coefficient of the ith story as determined in accordance with the formula in Eq. 4.3, and the weight of the reactive mass above the ith

story.

For base shear at service level:

(Qs). = (V s), = (Cs).(W J, (4. 2) (WJ. =The weight of the building, which shall be the sum of dead load and the applicable portion of live load, and

(C.), = Z.R,.A; Co = Z.R.(1)(0.2) (4. 3) where

Z = the seismic hazard zoning coefficient, which for Zone A (the zone of highest seismic risk in Japan) is ~ 1.0.

R = the design spectral coefficient (see Fig. 4.1) which is similar to the C factor = C of UBC.

A; = the lateral shear distribution factor (equal one at the base).

Co = the standard shear coefficient assumed to be 0.2 for moderate earthquake motions. This defines the SLEDRS at service level.

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Based on above Eqs. 4.1 to 4.3, the base shear for the zone of highest seismic risk is:

(Qs). = (Vs). = (C.),(WJ. = R.(0.2)(WJ. (4. 4)

(C.). = 0, 2 R. defines the SLEDRS at the service limit state and is shown in Fig. 4.2.

4. 2. 1 (b) Ultimate or Safety Level Design Earthguake. Japan's BSL specifies that limit analysis design procedures be used to ensure the minimum resistance against severe

earthquake motions.

For this level earthquake, the ultimate lateral shear stren