CUREe-Kajima 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

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

' ............ ........ . , ..... ..... ...... . , ., ' ' ,.. ,. • .J

Report No. CK 92-03A February 1992

California Universities for Research in Earthquake Engineering ( CUREe)

Kajima Corporation

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 Angeles • University of California, San Diego • University of Southern California

• Kajima Institute of Construction Technology ( Kajima Corporation

• Information Processing Center • Structural Department, Architectural Design Division • Civil Engineering Design Division • Kobori Research Complex

(

SUMMARY REPORT

CUREe-Kajima Research Project

DESIGN GUIDELINES FOR DUCTILITY AND DRIFT LIMITS

James C. Anderson, University of Southern California Vitelmo V. Bertero, University of California, Berkeley

Gary C. Hart, University of California, Los Angeles, Team Leader Helmut Krawinkler, Stanford University

Jack P. Moehle, University of California, Berkeley and the Kajima Research Team

PROJECT OBJECTIVE AND SCOPE

This project was concerned with the development of approaches that can be utilized to determine the drift and ductility demands and capacities for high-rise buildings and to improve seismic design practice through the explicit incorporation of ductility and drift control in the preliminary design process. To achieve this objective, emphasis was placed on (a) a review and evaluation of the state-of-the-practice in ductility and drift based earthquake resistant design, (b) an evaluation of the damage potential of recorded ground motions, (c) in-depth studies of the seismic performance of three high-rise reinforced concrete frame buildings, including accurate analytical modeling, nonlinear time-history analysis, assessment of predicted and recorded responses, and evaluation of detailing, (d) a study of member detailing requirements, and (e) the development of a conceptual design approach.

PROJECT ACCOMPLISHMENTS

Evaluation of the State-of-the-Practice in Ductility and Drift Based Design

A thorough review was performed of seismic building codes of the U.S., Japan, New Zealand, and Europe (ECCS and CEB). It is concluded that most present codes are inconsistent in accounting for the basic parameters that control the seismic performance of structures, namely, member and structure strength, local and global ductility ratios, and interstory drift. Codes are usually based on seismic load levels that have little relation to the actual strength of the structure and, therefore, provide no consistent level of protection for damage control and collapse safety. Present codes correctly acknowledge the need for simple design procedures, but in emphasizing simplicity they often obscure the physical principles on which seismic protection needs to be based. Present codes are providing adequate protection for most simple and regular building structures, but they are not based on explicit considerations of seismic demands and structural capacities and, therefore, are not easily adaptable to special cases nor are they flexible enough to permit incorporation of much needed improvements.

This review and evaluation, which is discussed in detail in a recently published EERC report (Benero et al.), has led to the following major conclusions: • Although the advantages of using plastic deformations of the structural materials to

dissipate part of the seismic energy input and the need for limiting the interstory drift are

recognized by most codes, their implementation, and particularly their reliable quantification, has not been accomplished fully in present seismic codes.

• While most codes contain philosophical statements that acknowledge the need to consider three limit states (serviceability, damage control, and safety), design is typically carried out only for one limit state (usually safety), on the assumption that the other two will be satisfied automatically.

• The growing concern over the costs of earthquake damages (direct, functional, and indirect) points out the need to pay more attention to serviceability and functionality limit states, i.e., control of damage.

• The following three areas are in need for improvement in code formulations: (1) Establishment of critical earthquake input (design earthquakes), (2) prediction of the seismic demands imposed on the entire soil-foundation-superstructure and nonstructural components systems, and >(3) determination of the real capacities supplied by the building and its components.

Evaluation of Damage Potential of Recorded Ground Motions

The research performed in this task is intended to demonstrate that ductility and cumulative damage consideration can and should be incorporated explicitly in the design process. Protection against failure implies that available ductility capacities should exceed the demands imposed by ground motions with an adequate margin of safety. Available ductility capacities depend on the number and magnitudes of individual inelastic excursions and need to be weighted with respect to anticipated demands on these parameters. Cumulative damage models can be employed to accomplish this. Normalized hysteretic energy dissipation is used here as the basic cumulative damage parameter since it contains the number as well as the magnitudes of the inelastic excursions in a cumulative manner. Thus, demands on hysteretic energy dissipation have to be predicted. Once this is accomplished, ductility capacities are known quantities and the objective of design becomes the prediction of the strength required to assure that ductility demands will not exceed the available capacities. Basic information on the required strength (inelastic strength demand) and displacement demands can be obtained from SDOF studies, but modification must be employed to account for higher mode effects in real MDOF structures.

This task focused on the derivation of data that can be utilized to implement the steps outlined in the previous paragraph. The data show the sensitivity of hysteretic energy and inelastic strength demands to various structural response characteristics for SDOF systems, and the great importance of higher mode effects on the base shear strength required to limit the story ductility ratios in multi-story structures to specified target values. The effects of higher modes was found to be strongly dependent on the number of stories, the target ductility ratio, and the type of failure mechanism in the structure.

An evaluation of seismic demand parameters is performed for bilinear and stiffness degrading SDOF systems. In this study, the inelastic strength demands and cumulative damage demands are evaluated statistically for specified target ductility ratios. Such a statistical study can be attempted only for ground motions with similar frequency characteristics, such as rock and firm soil motions recorded not too close and not too far from the fault rupture. Strength demands are represented in terms of inelastic strength demand spectra or spectra of strength reduction factors. Expressions are developed that relate the strength reduction factor to period and target ductility ratio. Cumulative damage demands are expressed in terms of energy quantities, number of inelastic excursions, and a simple cumulative damage model. Displacement demand spectra are also developed on the basis of the normalized inelastic strength demand spectra. It was found that the present practice of estimating inelastic interstory displacement demands from elastic demands can

be far from the truth, particularly for short period structures and structures located on soft soils.

The effects of higher modes on inelastic strength demands for MDOF systems are evaluated for three types of multi-degree-of-freedom models. The three MDOF models studied are: (a) BH (beam hinge) models, in which plastic hinges will form in beams only (as well as supports), (b) CH (column hinge) models, in which plastic hinges will form in columns only, and (c) WS (weak story) model, in which plastic hinges will form in columns of the first story only. The main objective of the MDOF study is to estimate the modifications required to the inelastic strength demands obtained from bilinear SDOF systems, in order to limit the story ductility demands in the MDOF systems to a prescribed value. The main conclusions derived from the parametric study of these MDOF systems are as follows:

• MDOF story ductility demands differ significantly from those of the corresponding SDOF systems. The deviation of MDOF story ductility demands from the SDOF target ductility ratios increases with period (number of stories) and target ductility ratio, and decreases with strain hardening. MDOF systems that can develop story mechanisms tend to drift more.

• The required MDOF base shear capacity for specified target ductility ratios depends strongly on the type of failure mechanism that will develop in the structure during severe earthquakes. Quantitative information is developed on the relative strength requirements for three types of MDOF structures, illustrating the disadvantage of structures in which story mechanisms develop, and particularly the great strength capacities needed to control inelastic deformations in structures with weak stories.

• Extreme strength discontinuities, such as those in the WS structures, should be avoided whenever possible, as they lead to excessive ductility and overturning moment demands that may be greatly amplified by the elastic vibration of the upper portions of the structure.

Seismic Performance of Three High-Rise Reinforced Concrete Buildings

The work in this task focused on (1) evaluating the reliability of present system identification techniques for deriving dynamic characteristics from recorded responses of buildings, (2) assessing the accuracy of analytical models and methods that are available for conducting analyses of the seismic response of RC buildings, (3) evaluating the buildings' mechanical characteristics with particular emphasis on the strength, deformation and ductility capacities, and ( 4) analyzing the probable performance of the buildings under more demanding seismic motions than those recorded at their foundation.

Two RC frame buildings constructed in the U.S. (10 and 30 stories) and one constructed in Japan (30 stories) have been analyzed in detail. The results obtained have emphasized the importance of measuring the response of the buildings to ambient and forced vibrations and/or to real ground motions in order to obtain reliable estimates of the dynamic characteristics of the entire soil-foundation-superstructure system and to assess the difficulties in analytical modeling of RC buildings. The results have also confirmed the importance of the effects of higher modes in predicting the response of buildings. In addition, the results have provided valuable information on the overstrength of code designed building structures and on the relationship between global and local ductility ratios for these tall buildings.

Some of the important conclusions derived from this study are as follows: • Because of early concrete cracking and bond slip it is necessary for designers and

analysts to consider more than one analytical model when evaluating the dynamic

,}

response of an RC building. There is a need to consider a range of values for the fundamental period or at least the bounds of this range, and not just a single deterministic value.

• Those analyses that only took into account the fundamental mode failed to reproduce the recorded accelerations. The number of modes that need to be considered to achieve good agreement between predicted and measured response depends on the response parameter (e.g., acceleration, velocity, displacement).

• The predicted response depends strongly on an accurate description of the seismic demands. For elastic and lightly nonlinear response this implies elastic response spectra that reasonably represent the local soil effects. For the U.S. 30-story building the design site spectra were very different from the elastic spectra obtained from recorded ground motions and, as a consequence, the lateral forces and displacements used in design were not representative of the forces and displacements that can be attracted in a severe earthquake.

• The overstrength ratio (ratio of predicted structure strength to factored code design strength) varies widely, depending on the structural configuration and design process. For the U.S. 10-story building this ratio was between 4.2 and 5.0, whereas it was only about 2.1 for the U.S. 30-story building. This overstrength ratio will have a large effect on the ductility demands experienced by buildings in a major earthquake.

Member Detailing Requirements

This task focused on an examination of detailing requirements for RC structural elements in high-rise buildings. An evaluation was carried out on a great number of beam, column, and beam-column subassembly experiments performed at different universities. From the experimental results it was observed that beams and columns were generally capable of undergoing equivalent end rotations of 0.02 rad. or more, except for a few cases of columns having relatively high axial compression forces or relatively low aspect ratios. Beam-column subassembly tests exhibited drift capacities having a lower bound of nearly 0.04, even though many of the reviewed test specimens had structural details that did not satisfy minimum seismic requirements of current codes.

The review of experimental results was supplemented with an analytical parameter study to project the experimental results to more general conditions. A comparison between analytical predictions and measurements of rotation capacities showed significant scatter, but in most cases the measured capacities exceeded the analytical predictions, indicating that the predictions tend to represent a lower bound to expected behavior. The analytical model was used to perform a parameter study of the deformation capacity of beams and columns as a function of the reinforcement quantities and details. The results of this parameter study are represented in graphs relating the rotation capacities to reinforcement ratios and axial load ratios.

Development of a Conceptual Design Approach

This conceptual design approach is based on the premise that seismic design needs to be based on a transparent procedure that considers two or three levels of protection (damage control at the serviceability and/or the functionality level, and collapse safety) and accounts explicitly for the requirement that ductility and drift capacities should exceed the demands imposed by the design earthquakes. The work performed in this project focuses primarily on design for collapse safety. For this design level it is postulated that the ductility capacity of critical structural elements is the basic design parameter, and the objective of design is to provide the structure with sufficient strength so that the ductility demands in these elements are less than their allowable capacities. Target ductility capacities for structures are established by modifying (weighing) member ductility capacities for anticipated cumulative

damage effects and transforming these member ductility capacities into story ductility capacities which are used as measures of the structure ductility capacity. For the so derived target ductility capacity the required structure strength (inelastic strength demand) may be estimated from SDOF systems and appropriate modifications that account for MDOF effects. An additional criterion for design for collapse safety is the limitation on interstory drift, which again can be implemented by estimating displacement demands from inelastic SDOF systems and applying appropriate MDOF modifications.

Thus, implementation of this approach necessitates extensive information on system dependent SDOF seismic demand parameters, including cumulative damage parameters (in order to weigh ductility capacities), and system dependent MDOF modifications. In this project much of this information has been generated for structures located on rock or stiff soil sites, and a design approach has been formalized that can be applied for building structures that do not have significant strength or stiffness irregularities. There are many imponant aspects of this design approach that need to developed in more detail, and much more research needs to be performed to generalize this approach to structures located on soft soils and/or containing strength and stiffness irregularities.

CONCLUSIONS

The work performed in this project has pointed out specific strengths and weaknesses of currently employed seismic design and verification (analysis) procedures. It was found that current code design procedures provide seismic protection that varies significantly from country to country and depends strongly on the configuration of the structure to be designed. Differences in overstrength and detailing criteria, inflexibility of most codes to account for special conditions, and the empirical nature of basic code coefficients and approaches are the main reasons for these variations. The performed research has demonstrated that it is feasible to develop a transparent design approach that considers explicitly the basic quantities controlling seismic performance, i.e., ductility, story drift, and cumulative damage effects that can be represented by energy terms.

The analytical studies performed on three tall reinforced concrete buildings has demonstrated that presently available analytical tools are adequate to predict most of the important performance characteristics of regular structures, provided that the effects of nonlinearities (including concrete cracking) are properly accounted for in the analytical model. For structures in which three-dimensional behavior is an important issue, better analytical tools need to be developed to capture three-dimensional effects.

REFERENCES

Anderson, J.C., Bertero, V.V., Miranda, E., "Seismic Response Analysis of the Pacific Park Plaza Building," Proceedin~s of the Second Conference on Tall Buildin~s in Seismic Re~ons. Los Angeles, California, May 16-17 1991, pp. 21-31.

Anderson, J.C., Bertero, V.V., Miranda, E., (and the Kajima Research Team), "Evaluation of the Seismic Performance of a Thirty-Story RC Building," Earthquake Engineering Research Center Report No. EERC 91/16, University of California, Berkeley, to be published soon.

Bertero, V.V., and Miranda, E., "Evaluation of the Seismic Response of Two Reinforced Concrete Buildings," Proceeciin~s of the 1992 ASCE Structures Con~ess, San Antonio, Texas, Apri11992.

Bertero, V.V., Anderson, J.C., Krawinkler, H., and Miranda, E., "Design Guidelines for Ductility and Drift Limits," Eanhquake Engineering Research Center Report No. EERC 91/15, University of California, Berkeley, July 1991.

Bertero, V.V., and Miranda, E., "Evaluation of Damage Potential of Recorded Ground Motions and its Implications for Design of Structures," CUREe/Kajima Project Report, July 1991.

Benero, V.V., and Anderson, J.C., "Seismic Performance of an Instrumented Six­Story Steel Building," Earthquake Engineering Research Center Report No. EERC 91/11, University of California, Berkeley, ready to go to printer.

Hart, G.C., Anderson, J.C., Bertero, V.V., Krawinkler, H., and Moehle, J.P., "Design Guidelines for Ductility and Drift Limits," CUREe/Kajima Project Summary Report, July 1991.

Hart, G.C., Ekwuene, C.G., and Sabol, T.A., "Earthquake Response and Analytical Modelling of the Japanese S-K Building," CUREe/Kajima Project Report, July 1991.

Krawinkler, H., Rahnama, M., and Nassar, M., "Zonation Based on Inelastic Strength Demands," Proceedin~s of the Fourth International Conference on Seismic Zonation, Stanford, California, August 1991 Vol. II, pp. 703-710.

Krawinkler, H., Nassar, A., an~ Rahnama, M., "Damage Potential of Lorna Prieta Ground Motions," The 1 Q89 Lorna Prieta. California. EarthQuake and Its Effects, Bulletin of the Seismolo~cal Society of America, Vol. 81, No.5, October 1991, pp. 2048-2069.

Krawinkler, H., Nassar, A., and Rahnama, M., "Evaluation of Damage Potential of Recorded Ground Motions," CUREe/Kajima Project Report, June 1991.

Miranda, E., Anderson, J.C., and Bertero, V.V., "Seismic Response of a 30-Story Building During the Lorna Prieta Earthquake," Proceedin~s of the Second Conference on Tall B uildin~s in Seismic Re~ons, Los Angeles, California, May 16-17 1991, pp. 283-293.

Miranda, E., and Bertero, V.V., "Evaluation of Seismic Performance of a Ten-Story RC Building," Earthquake Engineering Research Center Report No. EERC 91/10, University of California, Berkeley, ready to go to printer.

Nassar, A.A., and Krawinkler, H., "Seismic Demands for SDOF and MDOF Systems," John A. Blume Earthquake Engineering Center Report No. 95, Department of Civil Engineering, Stanford University, June 1991.

Qi, X., and Mohle, J.P., "Displacement Design Approach for Reinforced Concrete Structures Subjected to Earthquakes," CUREe/Kajima Project Report, January 1991.

CUREe • KAJIMA PROJECT

TOPIC 5

DESIGN GUIDELINES FOR

DUCTILITY AND DRIFT LIMITS

by

Gary C. Hart, Team Leader James C. Anderson Vitelmo V. Bertero Helmut Krawinkler

Jack P .Moehle

ABSTRACT 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 supported by a grant provided by the Kajima

Corporation and administered by CUREe (California Universities for Research in Earthquake

Engineering). This fmancial support is gratefully acknowledged.

The report consists of seven chapters. The first six chapters summarize the six different

studies that have been conducted according to the agreed team research project plan. These

studies are described in detail in the seven CUREe-Kajima reports given below.

REPORTS

1. 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.

2. Krawinkler, H., Nassar, A., and Rahnama, M., "Evaluation of Damage Potential of

Recorded Ground Motions," June, 1991.

3. Bertero, V.V., and Miranda, E., "Evaluation of Damage Potential of Recorded Ground

Motions and its Implications for Design of Structures," July, 1991.

4. Miranda, E., and Bertero, V.V., "Evaluation of Seismic Performance of a Ten-Story

RC Building," July, 1991.

5. Anderson, J.C., Miranda, E., and Bertero, V.V., "Evaluation of Seismic Performance

of a Thirty-Story RC Building," July, 1991.

6. Hart, G., Ekwueme, C.G., and Sabol, T.A., "Earthquake Response and Analytical

Modelling of the Japanese S-K Building," July, 1991.

ii

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

v·alues 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 CUREe team. The valuable

contributions of the Kajima team to this joint research project are recognized and gratefully

acknowledged.

Chapter

1

2

3

4

5

6

7

iii

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

by Helmut Krawinkler, Aladdin Nassar, and Mohsen

Rahnama.

Evaluation of Damage Potential of Recorded

Page

1.1 - 1.17

2.1 - 2.19

3.1 - 3.19

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

Earthquake Response and Analytical

Modelling of the Japanese S-K Building

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

4.1 - 4.49

5.1 - 5.52

6.1 - 6.22

7.1 - 7.9

CHAPTER 1

REVIEW OF STATE-OF-THE-PRACTICE AND STATE-OF-THE-ART ON DUCTll..ITY

AND DRIFf -BASED EARTHQUAKE RESIST ANT DESIGN

by

Vitelmo V. Bertero James C. Anderson Helmut Krawinkler Eduardo Miranda

1.1 SUMMARY

In this project task, the state-of-the-practice and of-the-art in the use of the concepts of

deformation, ductility, ductility ratio, drift, and interstory drift indices for attaining

efficient Earthquake Resistant Design (EQRD) of buildings structures have been

reviewed.

The findings of this review are presented in detail in a separate report. After a

discussion of the advantages of an energy approach for the EQRD of structures, and

pointing out the differences between deformation, ductility and ductility ratio, the needs

for providing structures with the largest ductility economically feasible and for

controlling the interstory drift index are discussed in detail. The need for establishing

more reliable design criteria for EQRD of structures is also discussed.

The state-of-the-practice and of-the-art of EQRD of buildings are reviewed, beginning

with a review of the problems in design and construction of EQ-resistant structures,

followed by a review of present Building Seismic Codes, with emphasis on how the

concepts of Displacement Ductility Ratio, ~~.and Interstory Drift Index, IDI, are used,

and how they could be used, to improve the state-of-the-practice according to present

knowledge. The review covers the building seismic codes of the U.S., Japan, New

Zealand, and Europe (ECCS and CEB). The results plotted in Figs. 1.1 and 1.2 permit

a comparison of the required strength, stiffness and IDI by these different codes.

Based on a review of the problems encountered in the design and construction of EQ­

resistant buildings, research, development and educational needs to improve present

knowledge and particularly state-:of-the-practice are formulated.

1. 2 CONCLUSIONS

From the studies conducted and the results presented in the report on this task, the

following main observations can be made regarding the use of ductility and drift limits

in EQRD:

1.2

Although the advantages of using plastic deformations of the structural material

to dissipate part of the seismic Energy Input (EJ to the structure and the need

for limiting the lateral interstory drift have been recognized in the literature, their

implementation, particularly their reliable quantification, has not been

accomplished fully in present seismic design codes;

While it is possible to use the concept of ductility in a vague manner in discussing

the philosophy of ductility-based design, when such philosophy has to be applied

in the EQRD of structures the philosophy has to be quantified, and it is therefore

necessary to use unambiguous parameters;

Although displacement ductility factors, "'''provide good indications of structural

damage, they usually do not adequately reflect the damage to non-structural

components. To produce safe and economical structures, seismic design methods

must incorporate drift (damage) control, in addition to lateral displacement

ductility, as a design constraint;

Conventionally computed story drifts may not adequately reflect the potential

structural and non-structural damage to multistory buildings. A better index is

the tangential story drift index, RT ;

Although the general philosophy of EQRD is well established and is in complete

concordance with the concept of comprehensive design, current code design

methodologies fall short of realizing the objectives of the general philosophy.

While the statement of the general philosophy points out the need to consider

three different limit states (criteria for levels of earthquake, i.e.: service; damage

control or operational; and safety, or survival), in practice, design is typically only

carried out for one criterion (usually safety), on the assumption that the other

two would be satisfied automatically;

1.3

The growing concern over the costs of earthquake damages (direct, functional,

and indirect) points out the need that more attention be given to control of

serviceability and functionality, i.e., control of damage;

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. Strength, toughness, deformation control and repairability are

interrelated and hard to define;

The following three main problematical areas have been identified in the

earthquake-resistant design of structures: (1) Establishment of reliable critical

earthquake input (design earthquakes); (2) determination of the demands on the

entire soil-foundation-superstructure ·and non-structural components system; and

(3) prediction of the real capacities supplied (supplies) to the building at the

moment that an earthquake strikes;

While a sound preliminary design and reliable analysis of this design are

necessary, they do not ensure an efficient earthquake-resistant structure. The

seismic response of a structure depends not only on how it has been designed, but

also on how it has been constructed and maintained (monitored and preserved)

up to the moment that the earthquake occurs. There is a need to improve the

construction and maintenance practices of structures;

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

'estimation of demands, which can be grouped into two categories: (1) specified

seismic forces; and (2) methods used to estimate response to these seismic forces;

Strength Demands. For regular buildings up to a certain height (240 ft. in the

U.S.), most of the codes in the world recommend the use of equivalent (static),

lateral seismic forces, which are expressed as a base shear V =(C.,/R)W where:

C.., is the seismic coefficient equivalent to a SLEDRS (Smoothed Linear Elastic

1.4

Design Response Spectra) for acceleration, Sjg, and R is the reduction factor.

Although in most codes the value of R is given without any explicit reference to

global displacement ductility ratio, J..£ 6 , these values depend implicitly on J..£ 6 ;

Structural response is usually estimated using linear elastic analyses of the effects

induced by the equivalent static 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 Ooad and resistance factor) design

method;

There are few countries in which codes recommend the use of limit analysis and

limit design methods {plastic design methods);

Stiffness and Drift Demands. Most seismic codes address design for lateral

stiffness and for drift at service level. Only a few codes explicitly require that the

contributions 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

multicomponents of seismic excitations. Few codes give explicit requirements or

recommendations regarding how to estimate P-A effects. There is a need for

more rational code procedures for estimating the demands regarding the stability

effects at ultimate limit states;

Strength Supplies. Most of the Reinforced Concrete {RC) EQRD codes require

that the supplied strength be estimated using the strength method, in which the

required strength of critical sections are evaluated as a function of just the

minimum specified strength of the materials, and then reduced by a strength

(resistance) factor. There are a few codes in which the design and detailing of

the critical regions of the structure are based on the probable supplied strength

capacity of the members and of their connections and, therefore, of the entire

structure. The state-of-the-practice as reflected by most present EQRD codes for

1.5

RC buildings does not appear to include the use of the concept of energy

dissipation capacity in a rational and reliable way through the use of the J,£,;

Stiffness, Deformation and Stability Capacities. Most of the RC codes give only

empirical expressions to estimate the so-called "effective linear elastic stiffness";

they do not specify how to evaluate the change 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 will lead to

estimation of the global deformation capacity of the structure under not only

monotonically increasing deformation, but also under generalized (repeated

reversal) deformation. This should be done 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);

Present practice emphasizes the use of strength as the pnmary criterion for

preliminary EQRD. While preliminary design based on shear strength could be

justified where serviceability controls, it cannot be accepted in cases where the

design is controlled by the ultimate (safety) limit state where plastic deformation

. is accepted. At safety limit state (mechanism formation and mechanism

movement), base shear is insensitive to variation of deformation and, therefore,

to damage. Although there have been some proposals to base preliminary design

on only lateral stiffness, i.e., on only controlling the interstory drift, a practical

method of this type of design has yet to be developed. A more rational approach

is one which not only recognizes the importance of strength and stiffness (control

of deformation), but also recognizes that while these two factors are strongly

interrelated in the case of elastic response, they are less strongly interrelated in

the case of inelastic response. To control inelastic deformation, however, 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 ~-'•

(hysteretic energy); and the deformation, based on the limitation of IDI;

1.6

The future of EQRD is an energy approach in which the concept of ~' is used in

the derivation of IDRS through statistical and probabilistic analyses of the IRS

corresponding to all available recorded or expected critical ground motions at the

building site, and design is conducted using limit design methodology with proper

consideration of the possibility of shakedown phenomena;

For the immediate or very near future the following compromise solution is

recommended: Use design forces obtained from SLEDRS reduced by reliable

reduction factor R. The values of R must take into account the reductions due

to: hysteretic behavior (J..£ 6); changes in damping and in the fundamental period

of vibration of the whole building system; and the real overstrength. The R

should be period and site condition dependent;

Ideally, the use of either of the above methods should be complemented with

time history nonlinear dynamic analyses of the response of the preliminarily

designed building system to the predicted Maximum Credible Earthquake

(MCEQ), ground motions that can occur at the site. If this is not possible, the

least that should be conducted is a static nonlinear analysis of the building under

monotonically increasing lateral loads;

To control damage, it is necessary to control deformations. Control of Interstory

Drift Index, IDI, at Serviceability Level: Present seismic codes specify acceptable

limits of IDI that vary from 0.0006 to 0.006. Although the estimation of IDI at

the service level is usually based on linear elastic analyses, there are many

uncertainties regarding the effective stiffness of the structural . members, the

deformation of the foundation, and the contribution of the non-structural

components. Analysis of the deformations should be based on a realistic 3-D

model which considers properly the effect of torsion under multicomponents of

ground motions;

1.7

Control of IDI at the Safety Limit State. According to present seismic codes, the

acceptable maximum IDI to control damage varies with the type of structure and

its function, usually varying from 0.01 to 0.03. The IDI spectra demands can be

estimated based on the IDRS for strength for the adopted p.6 • The problem in

using these IDI spectra is in making a reliable estimate of the effective period,

T. This is so because of the difficulties in estimating the effective lateral

stiffness. The seismic design codes are not specific about how to estimate the

stiffness of members. In the case of RC structures, this is a difficult task.

Although some rules have been formulated for estimating the lateral stiffness of

buildings, the real lateral stiffness varies with the level of deformation;

Most of the practical methods that have been recommended for design

considering IDI have been based on the assumption that the nonlinear

displacement response is equal to the linear response spectral values provided

that the system has certain minimum yielding strength. Recent studies 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.

Empirical formula have been suggested to estimate the deflection amplification

factor Cd , defined as the ratio of absolute maximum interstory displacement to

the corresponding value from a linear time history analysis;

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;

Code Comparison (Figs 1.1 and 1.2). In judging the results obtained from the

comparison of different codes, it is necessary to keep in mind that it is not

enough just to analyze the code requirements ·of the seismic forces and minimum

1.8

stiffness or maximum acceptable IDI to be used in the design. The designed

structure and the seismic behavior of the actual structure are not solely the result

of specified seismic forces and IDI, but are governed by the overall design

philosophy and the complex combination of the forces and IDI with many other

factors such as: The satisfaction of code material requirements; the construction

technology; and the maintenance or preservation of the entire soil-foundation­

superstructure and nonstructural components system. Furthermore, the seismic

forces in the code of one country reflect the seismicity as well as the seismic risk

of that country, and these factors vary considerably not only from one country to

another, but even from one region to another within a country;

Except for UBC, all the codes reviewed herein consider that portions of the live

loads are seismically reactive and are included in the computation of the seismic

forces;

For strength (ultimate or capacity) design there are significant differences in the

values specified by the different codes for the load factors as well as in the ways

that the loads are combined;

The codes reviewed herein are strength-based rather than ductility and damage

control-based, and with the exception of the Japanese BSL, advocate a single

level design;

Although the UBC and New Zealand NZS code recognize in their material

specifications the possibility for overstrength, the only code that explicitly

recognizes and accounts for overall structural overstrength due to inelastic

redistribution of forces is the ECCS;

Although most of the seismic codes that have been reviewed permit damage that

will not jeopardize human life, none explicitly defines what constitutes acceptable

damage. Most of the codes recognize that the level of acceptable damage has to

1.9

be different for different types of facilities depending on its occupancy type or

function. Quantitatively, this is accomplished by increasing the seismic forces

. through an importance or risk-to-life factor. However, the values adopted for this

factor seem to be very low, and it appears to be incompatible with the fact that

essential facilities and those housing very hazardous materials should remain

practically elastic. The values for the occupancy factor, specified by the different

codes reviewed herein, varied from 1 to 2;

Code Specified SLEDRS (Fig.l.1). For buildings with a fundamental period of

T ~ 2 sees. and located on firm soil, the U.S. and Japan have similar required

SLEDRS which are somewhat smaller (up to 20% for T = 3.0 sees.) than the

NZS. For buildings with T > 2.0 sees. and up to T =4 sees. located on very soft

soil (soft clay, UBC type S4 or Zone III of Mexico City), the UBC specifies the

most severe SLEDRS, and the CEB has the least demanding SLEDRS;

Use of J16 to Reduce SLEDRS to SIDRS. All codes except the Mexico Code use

a constant reduction factor, i.e., independent of the T of the structure.

Site with Firm Soil (Fig.5.1 Soil Type 3): The largest reductions are those in the

UBC. The Japanese BSL uses the smallest reduction (3.3). The BSL reduction

is based on the energy dissipated only by cracking and local yielding since it does

not allow the yielding of the structure as a whole system (mechanism movement).

For tall buildings with T > 1.5 sees. and up to T = 3.0 sees., the SIDRS specified

by the Japanese BSL is more than 33% higher than any one of the other SIDRS.

Site with Soft Soils (Fig.5.1 Soil Type 3 ): The largest reduction is that

recommended by UBC which is 8.6, and the smallest is that specified by the

Japanese BSL (3.3). For tall buildings with a T > 1. 7 sees. and up to T = 3.0

sees., the yielding strength required by BSL exceeds by more than 30%, 82% and

121% those specified by the Mexican D.F., CEB and NZS codes respectively.

The yielding strength required by UBC for tall buildings having T > 2.0 sees. is

the lowest one of all the codes considered herein;

1.10

Use of IDI Limitations in EQRD. Although all of the seismic codes reviewed

herein have regulations limiting the maximum IDI for limit states, none of these

codes have recommendations regarding how the limitations should be directly

introduced into the preliminary EQRD of a building structure. The IDI limits

specified by codes are checked by analysis of the already finished preliminary

design of the structure;

Minimum Lateral Stiffness and Acceptable Limits on IDI at Serviceability Levels

(Fig.1.2). Short T (I' < 0.3 sees.): The NZS requires the largest lateral stiffness

and therefore, should result in better damage control under service EQs. This

is specifically true in cases when nonstructural elements can be damaged: IDI

::5 0.0006 which is 1/2, 1/4 and 116 of those specified by CEB, BSL and UBC

respectively. Long T (I' > 1.6 sees.): In the case of buildings located on firm

soils, the results regarding the maximum acceptable IDI limits are similar to

those for short T. For buildings located on soft soil, the Mexican D.F. code

requirements become as severe as the NZS;

Maximum Acceptable IDI at Ultimate Limit States (Safety) (Fig.l.2). The

Mexico D.F. explicitly specifies that the maximum IDI should not exceed the

values of 0.006and 0.012 depending upon whether the nonstructural components

can or cannot be damaged. The UBC implicitly specifies that the IDI shall not

exceed the values of 1.5% in the case of buildings less than 65 feet in height and

1.125% for buildings greater in height. Although the Japanese BSL does not

specify any limit for the IDI at the Safety Level, in practice the Japanese

designers limit the IDI to 0.01. These limits are a consensus judgment from

experience based on observations and analyses conducted during previous Eqs.

Compliance with these limits will ensure not only human safety, but also damage

control, provided that these limits are connected with a minimum required

yielding strength. The minimum UBC required yielding strength seems to be too

low. Thus, the design of tall buildings that attempts to provide only this

1.11

minimum strength will undergo significantly larger IDI than the maximum

acceptable by the code in case of severe EQ ground motions;

Efficient EQRD. Achieving an efficient EQRD requires an iterative process. It

is necessary to start with an efficient preliminary EQRD. To carry out this

preliminary design, it is necessary first to develop (establish) reliable design Eqs;

There is an urgent need to develop a reliable preliminary EQRD procedure

based on two-level design Eqs, in which the following two limit states are

considered: Functional continuation (serviceability) under frequent ground

motions; and then survivability and control of damage under a rare but possible

severe (extreme) EQ ground motion;

To enable development of reliable procedures for establishing a two-level EQRD,

it is necessary to conduct statistical and probabilistic analyses of available data

regarding what can be considered service and safety EQ ground motions, and

then to develop reliable SLEDRS and SIDRS that consider the LERS and IDRS,

respectively, of all available recorded or predicted motions at these two levels ,of

EQ ground shakings;

Because reliable measured data on EQ ground motions at different sites (soil

profile and topography) was scarce until 1987, design spectra are currently

formulated using inadequate statistical information.

SIDRS for Strength, C7• For any given site, the ideal solution is to derive the

SIDRS directly from statistical and probabilistic analyses of the IRS

corresponding to all recorded motions at the selected site or at similar sites

located in tectonically similar regions and even of records derived through the use

of theoretical considerations;

1.12

The shape of the IRS (i.e., the variation of Cy with T) varies significantly

depending on the predominant frequency (or period T,) of the reeorded ground

motion which in turn depends on the site conditions (soil profile and topography)

from which the record w~ obtained;

There is significant reduction (deamplification) of the LERS (i.e., for JJ. = 1)

produced by yielding (JJ. > 1) for structures with aT coinciding with or very close

to the predominant period (T J of the ground motion. The longer the T,, the

larger seems to be the deamplification;

The degree of reduction of the LERS due to JJ. > 1 decreases as T deviates from

T, and tends to zero as T tends to zero;

Because of the uncertainties in estimating the values ofT, and T, caution should

be taken in applying in practice the observed reduction of the LERS due to

JJ. > 1 when TIT, = 1;

For sites on firm or medium stiff soils (types S1 and S:z), there are already several

recorded ground motions whose IRS exceeds the SIDRS adopted by the codes

reviewed herein. This is true even in cases of JJ. = 6 which is not only very

difficult to achieve (supply), but also very difficult to justify its possible use

because of the damage that will be involved;

For soft soil sites (soil profile S3 or S4), particularly with soft clays whose depth

exceeds 40 ft., it appears that the SIDRS corresponding to the Cy adopted by all

codes will be exceeded even when a JJ. = 6 could be supplied and used. This

observation is based on the IRS corresponding to recorded ground motions which

can resist and transfer ground acceleration of 0.30 g to the structure foundation.

The only exception is the SIDRS specified by the Japanese BSL for low and

medium-rise buildings of perhaps up to 20 stories;

1.13

Code Procedures to Determine SIDRS for C7

• The SIDRS for Cy specified by

codes are obtained by deamplifying (reducing the LERDS) through the use of a

reduction or behavior factor. Although this factor depends on p., it is difficult to

judge the rationale for the values recommended in the codes;

The values recommended by the UBC (i.e., R,) appear too high, particularly for

structures with a T < T, if the designer attempts to design the structure with the

strength required by the code: The value for the reduction factor should be tied

to other requirements besides the value of p.. The values of the reduction factor

should be affected by the real strength capacity, i.e., the overstrength above the

yielding strength specified by the code;

For structures designed according to UBC, the required overstrength depends on

the p., T, soil conditions and design methodology;

In the case of structures located on rock or firm alluvium, the required

normalized overstrength has the largest values for T in the range of 0.1 to 0.5

sees. , and varies from 0.4 7 for p. = 2 to 0. 2 7 for p. = 6. The corresponding

required Reduction for Overstrength, R.,., varies from 3.6 to 2.1;

In the case of very soft soils, the longer the value of the predominant period of

the ground motions, T,, the larger is the range of the period of the structures, T,

for which significant overstrength is required. The normalized overstrength for

a T of 0.9 sees: can vary from 1.23 for p. = 2 to 0.58 for p. = 6. The

corresponding R'"" vary from 3.84 to 1.81. The R"" for aT of 2.0 sees. can vary

-from 6. 77 for p. = 2 to 1. 78 for p. = 6;

U.S.low-rise buildings usually have large seismic overstrength with respect to that

required by U.S. codes. The taller the building, the smaller the overstrength is.

Thus, it appears that the medium-rise buildings (particularly those located on

1.14

sites with very soft soils) are the ones that have to be suspected of becoming a

serious threat to life and/or incurring large economic loss in case of a major EQ.

1. 3 RECOMMENDATIONS

Recommendations for Improving Code SIDRS for Strength. C,

Develop more reliable SLEDRS;

Develop more reliable methods for estimating the values of the reduction factor;

This requires more precise definition of this factor. Although the values of the

reduction factor are affected by several parameters, the main two are the energy

dissipated through hysteretic behavior (damping ratio ~ and particularly JJ) and

the real overstrength.

The ideal solution is to attain reliable SIDRS directly from the recorded and/or

analytically derived ground motions. This will eliminate the need for specifying

R~. Therefore, for the proper use of these SIDRS, what remains is to calibrate

the real strength (overstrength) of structures that are designed according to

present code.

There is a need to consider in the inelastic design of structures the effects of the

duration of strong motions which include the cumulative ductility and number of

yielding reversals. This can be accomplished through the use of an energy

approach estimating the critical required Hysteretic Energy, Eu.

There is a need to find reliable factors that will permit the use of the computed

SIDRS for SDOF systems to design MDOF systems.

As it is very difficult to design MDOF structures that will develop uniform story

JJ6 throughout its height, there is a need to investigate a possible concentration

1.15

of required J.1. 6 at one or more stories and to establish the yielding overstrength

required to limit the maximum J.1. 6 to the target ductility used in the design based

on SDOF system.

Recommendations for Improving SDIRS for Lateral Dis.placement and IDI. Nonlinear

displacements are very sensitive to the dynamic characteristics of the ground motions

and of the structure, and they can be significantly different from those obtained based

on linear behavior.

For ground motions with long T,, the nonlinear displacement can be significantly

smaller (nearly 50% smaller) than the linear displacement for structures with T

= T,. On the other hand, for values T < 2/3T,, the nonlinear displacements are

significantly higher. The smaller the TIT, ratio, the larger the difference is, and

it tends to be proportional to the value of J.l..

Based on derived SIDRS for strength of SDOF systems, formulate SIDRS for

displacement of SDOF systems for different ~ and JJ..

Based on the derived SIDRS for the displacement of SDOF systems, obtain lower

and upper bounds for the IDI of MDOF systems.

As it is difficult to achieve a constant IDI throughout the entire height of a

MDOF structure, there is an urgent need to investigate (analytically and

experimentally) values of an amplification factor by which the SIDRS' lower

bound of SDOFS systems should be multiplied to obtain a reliable SIDRS for

MDOF systems.

c'f 1.:

La

a • J

a.'

0. I

a.:

o • a

(a) EL.ASiiC DESiGN S?EC:i<.A

I I I \ il98~ NZi-. ,.--·--···.'. i "\ ....

': ... ...... ·,:~ ... --- ---- -.. ---- --...... ·-

SOIL TYPE 1

1987 MEX OF ·-·-·-·-·-. .-,.,.---··--------------_,___·=-=~-=== a • ~ Q. J ! • 0 l.O 1.5

c'f 0. I

0 • J

0 • l

0 • l

Q • 0

PEl<lOD (sec)

(c) INEL.ASiiC DESIGN S?ECiRA

·· ...

................

·· ... 1987 c:: · .. ·-·-·, .. 19E3 uac·,. ··········· ...

SOIL TY?E 1

l '·... ····· ...

196 7 ~EX OF • -.-.-. ~ ·.~ :;:~~~~-~~~~~~~~~~~=~=·=::::! -·-·-··---·,·-·-·-·-·-·---·-·--·· I ---·-------·

Q • 2 0. J LO

PERIOD (sec)

1.16

c., l.l

l.'

0. I

Q. '

0, I

0. 2

0. 0

(b) ELASTiC CESiG~~ S?ECi~A

SOIL TYPE J 1988 uac S:

1987 CE3 r-·-·-· .... '196.<1 NZS \ ~--------.\ I •· i -~,

----'~~~~~-D_F------~~-,·,· ~! ..... --------------------------1 .· ,· '·

,·'· -·-.•. ···· ·-·-·-·-·-·-·-·-·-·-·

.•

o • a 0 • 5 1. 0 l. J l.O

PE:tiOD (sec)

c., (d) INELASTIC DES[GN SPECTRA 0. I

SOIL T':'P: 3

JA? AN·SSL ·-····-······ ·-·-··--········ O.l

0 .l

0 • 2 0 • s LO 1. s l. ~ J.o

PE:<lOD (sec)

Fig. 1.1- COMPARISON OF SLEDRS AND SIDRS

I • I

I • I

0. I

0, I

0. 0

(a) STIHIIESS AUD IDI REOIJIJ!EMUHS

SOli. TYPE 1 SIIOI!T I'EIIIOD

............... l~.!~~!:!:n~.\ .............. . / .·· (ho mu,l,nu•n Afllll)

.... .··' ...... . .... ··

..... •.···· ./ ,../ 1907 CEO r·r'!i-·-:r·-·-·-·-·---·-·-·---·-·-·-·-·-

1 i :i .. · ; · /- / 1900 unc . ! .:/ .. ! I :'I / 1 ?M NZS

:i/?~·,..r------- ---· :it·i/ 1907 MEX 01' ':!>;----........................... ..

D, D I, ODS 0 .... I'D U 0, 0 I D D.DH

•• I

D. I

D .I

D, I

...

INHRSTOIIY Dnll:r INDEX

(c) STIFFNESS AND IDI IIEQUinf:Mr:IHS

JAI'Al-1-0Sl

SOIL lYPE J SIIOIIf I'EiliOD

_,.. ................. :.>;.--·•·•·"'"'""j,;;;·~;~;I;;,IHfl lh~l)

....... .······· :' .. ··

_.././ _,.. ........... · 1?07 C[D

:· ,.{~~ . .-:~:~e!.:m~~~;.-~~~9oiofi~ --·- ·------ -·-·-·-·/F-' .·· :,/.> .. ·,v· I ... '·''' I, I I D • ... s 0. 0 J D '·'"

INTEUSJORY DlllfT INDEX

I, I I

D, II

0. II

D, I D

•••• I, D I

D, II

D,DI

0. 0

(h) STIHIHSS AND IDIIIEQUIREMHITS

JArAN-DSI.

SOil TYPE 1 LONG I'EniOD

_....!" ............ _::.:.::·----·· .. ····· .. ···i;,;;·,;;;;;i,;;;,;;;·"',4''

.... ..··· .. .· ...... . .....

,./ _../ 1?07 CEO rr .. :.-~_..,..),'-------·-·-·-·---·-·-·-·-·-·---, i :'.1 / 190~ NZS ; 1;·:·,--.--- ... ... .

:;1/i/ 19DOUOC : ,., ,. ... ", .. :·:_._,o40- ·-· ........ ·- .... -·- ·-· :i/ 1 .;/ IVO/ MEX Dr: ·,t/' ,]·'

D, 0 D.DOS D. 010 D, DIS

"INTEIISTOIIY DHIFT INDEX 0, DID I. DIS

Cy (d) STIFFNESS AND IDI IIEQUIIIEMENTS

D,H

D ,10

JAI'MI-DSl ,.f"'"""""":.:.:-................. j~~·;,:;;;i,;;;_;;;·~ .. "l

./· ....... ....

/ ......... .

a • IS _,1 ......... .... / ./.. 1907 CEO

{!·::-,,~;?_:-~ iitir\XiluT·-·- -- ·-·- ·-·-·-·-·-·-·-·-. /! l /' 1900 UIIC 54

f,l, ~ ...... _-__ -.. ------_-_-_-_-__ -:-. 19oo uoc s1

;.·1~_z" lVIII\ NZS S_Oil TYI'E 3 ,,, I lONG I'EI!IOD J IJ•

0. 10

D • IS

0. 0

a.o O,DOS D, DIG •• 01 s D. 010 0. Dl s

11-tHnsTOnY DlliFT INDEX

Fig. 1.2- CODE EXPECTED llASE SHEAn - JDJ DJAGUAMS

CHAPTER 2

·EVALUATION OF DAMAGE POTENTIAL OF RECORDED GROUND MOTIONS

by

Helmut Krawinlder Aladdin Nassar

Mohsen Rahnama

2.1

2.1 INTRODUCTION

Seismic design is an anempt to assure that strength and deformation capacities of

structures exceed the demands imposed by severe earthquakes with an adequate margin of

safety. This simple statement is difficult to implement because both demands and capacities are

inherently uncertain and dependent on a great number of variables. A desirable long-range

objective of research in earthquake engineering is to provide the basic kno~ledge needed to

permit an explicit yet simple incorporation of relevant demand and capacity parameters in the

design process. A demand parameter is defined here as a quantity that relates seismic input

(ground motion) to structural response. Relevant demand parameters include, but are not

limited to, ductility demand, inelastic strength demand, and cumulative damage parameters

such as energy demands.

Capacities of elements and structures need to be described in terms of the same

parameters as demands in order to accommodate a design process in which capacities and

, demands can be compared directly. In this respect a clear distinction needs to be made between

"brittle" elements and elements with ductility. For the former kind no reliance can be placed in

ductility and the design process becomes an anempt to assure that the strength demands on

these elements do not exceed the available strength capacities. This is usually accomplished by

nming the relative strength of ductile and brittle elements (e.g., the strong column- weak girder

concept). The presence of ductile elements provides the opponunity to design structures for

less strength capacity than the elastic strength demand imposed by ground motions by relying

on the ductility capacity of these elements. The permissible amount of strength reduction

depends on the ductility capacity, which in turn depends on the number, sequence, and

magnitudes of the inelastic excursions (or cycles) to which the elements are subjected in ar

eanhquake. This history dependence of ductility capacity, represented usually by cumulative

damage models, presents one of the biggest challenges in improving seismic design procedure:

since it requires refined modeling that considers all important ground motion as well a:

Sl!Ucrural response characteristics.

2.2

The term dama~e potential is used here to denote the potential of ground motions to

inflict damage to manmade structures. This potential depends on the "severity" of ground

shaking as well as the ability of the structure to resist this shaking. Thus, both demands and

capacities need to be considered in assessing the damage potential. In this summary repon the

emphasis is on demand evaluation; much more detailed discussions on demand as well as

:capacity issues can be found in Krawinkler et al., 1991, and Nassar and Krawinkler, 1991.

The shon-range objectives of the work summarized here are to illustrate the feasibility of

assessing seismic demands with simplified analytical models and to evaluate the sensitivity of

seismic response to ground motion and structure characteristics. The long-range objective is to

demonstrate that simple yet rational demand/capacity models can be used to replace the present

empirical code design approach with a more transparent approach based on fundamental

principles.

This summary repon addresses important issues in the context of seismic design for

ductility capacity, considering the effects of cumulative damage on the latter. A design

procedure is postulated and the components of knowledge needed to implement this procedure

are identified. The issue of cumulative damage is briefly discussed. quantitative information is

presented on important seismic demand parameters for SDOF systems, and selected data are

presented for multi-degree of freedom (MDOF) systems that can be viewed as conceptual

models of real multi-story buildings.

POSTULATED SEISMIC DESIGN PROCEDURE

The objective is to develop a design approach that permits better tuning of the design to

the ductility capacities of different structural systems and the elements that control seismic

behavior. Such an approach has to be simple to be adopted by design engineers and

transparent to the design process to permit the designer to explicitly consider demaods yersus

capacities. The approach must be equally applicable to the limit states of serviceability and

safety against collapse (i.e, a dual level design approach). Both limit states can be described by

damage control, with the serviceability limit state defined by drift control and small cumulative

damage, and the safety limit state defmed by an adequate margin of safety against the

cumulative damage approaching a limit value associated with collapse. This discussion is not

concerned with the issue of serviceability. It focuses on design for safety against collapse

during severe earthquakes.

2.3

In the design for safety against collapse it is postulated that element behavior can be

described by cumulative damage models of the type summarized in the next section. Since

these damage models are too complex to be incorporated directly into the design process, it is

suggested to use these models together with statistical information on seismic demand

parameters and experimental and analytical daf.a: on structural performance parameters to

: transform element cumulative damage capacity into element ductility capacity (ductility capacity

weighted with respect to anticipated cumulative damage demands such as hysteretic energy

dissipation). Thus, the ductility capacity of the critical structural elements becomes the starting

point for seismic design. This capacity will depend on the types of elements used in the

structural system, but it is assumed to be a known quantity. The strengths of elements and the

structW'e become now dependent quantities which need to be derived from the criterion that the

ductility demands should not exceed the given ductility capacities.

In order to derive structure strength requirements, the element ductility capacities have to

be transformed into story ductility capacities (sometimes a simple geometric transformation and

sometimes an elaborate process), which are then used to derive :.inelastic strength demands"

for design (discussed later). The so derived strength demands identify the required ultimate

strength of the structure. Recognizing that the design profession prefers to perform elastic

rather than plastic design, the structure strength level may be transformed to the member

strength level in order to perform conventional elastic strength design (by estimating the ratio of

the ultimate strength of the structure to the strength level associated with the end of elastic

response, shown as E8 and E1, respectively, in Figure 2.1). Pilot studies have shown that for

regular structures this transformation is usually not difficult but may require an iteration

(Osteraas and K.rawink.ler, 1990). After this preliminary design an important step is design

verification through a nonlinear static incremental load analysis (using a rational static load

pattern in a "push-over" loading) to verify that the required structure strength (Eg) is achieved

and that "brittle" elements are not overloaded (ductility demand < 1.0).

Figure 2.1 illustrates the step-by-step implementation of the proposed design approach.

As a basis the implementation requires a model to weigh ductility capacity for anticipated

cumulative damage effects. In the illustration equal nonnaliud hysteretic energy dissipation

(see next section) is assumed as the criterion for weighing ductility capacity. Using the

fundamental period of the structure, T, and its weighted ductility capacity, p., the strength

reduction factor, R, can be evaluated from R-~-t-T relationships discussed later, assuming the

structure can be modeled as an SDOF system. This strength reduction factor is used to scale

the elastic strength demand spectrum (i.e., the ground motion spectrum) to obtain inelastic

2.4

strength demands. System dependent modification factors are then applied to the SDOF

inelastic strength demands to account for higher mode effects in MDOF systems. This step

identifies the structure strength demand, £1, which defmes the strength capacity required in

order to limit the ductility demands on the structural elements to the target ductility capacities.

The local strength demand (associated with the end of elastic response), E1, is then estimated

:from the structure strength demand, the structure is designed employing conventional elastic

strength design, and a nonlinear incremental load analysis is carried out to verify required

structure strength.

Clearly, there are many issues in this design approach that have not been addressed and

that may complicate the process considerably. But the approach has been shown to work in

simple examples (Osteraas and K.rawinkler, 1990), and deserves further study to explore its

potential. The following list itemizes the basic information needed to implement this approach.

1. Experimental and analytical information on cumulative damage models for structural

elements.

2. Statistical data on anticipated cumulative damage demands needed to weigh ductility

capacities.

3. Statistical data on inelastic strength demands for prescribed ductility capacities,

using SDOF systems.

4. Statistical data on multi-mode effects on the inelastic strength demands derived from

SDOF systems.

The following sections provide discussions on specific aspects these four items. More

detailed information is presented in Krawinkler et al., 1991, and Nassar and K.rawinkler,

1991.

EXAMPLES OF CUMULATIVE DAMAGE MODELS

It is well established from experimental work and analytical studies that strength and

stiffness properties of elements and structures deteriorate during cyclic loading. Materials, and

therefore elements and structures, have a memory of past loading history, and the current

deformation state depends on the cumulative damage effect of all past states. In concept,' every

excursion causes damage, and damage accumulates as the number of excursions increases.

The damage caused by elastic excursions is usually small and negligible in the context of

seismic behavior. Thus, only inelastic excursions need to be considered, and from those the

2.5

large ones cause significantly more damage than smaller ones (however, smaller excursions are

much more frequent).

Many cumulative damage models have been proposed in the literature, each one of them

with specific materials, elements, and failure modes in mind. None of the proposed models is

:universilly applicable. A comprehensive summary of widely used model is provided by

Chung et al., 1987. Only two of these models are summarized here, the first one developed

specifically for elements of reinforced concrete structures, and the second one developed

primarily for elements of steel structures.

The damage index proposed by Park and Ang, 1985, for reinforced concrete elements is

expressed as a linear combination of the normaliud maximum deformation and the nonnalized

hysteretic energy as follows;

in which D = ~ = cSu =

~ = =

p =

D = 8,. +LfdE B., F, B.,

damage index (D > 1 indicates total damage or collapse) maximum deformation under earthquake ultimate deformation capacity under static loading calculated yield strength incremental hysteretic energy parameter accounting for cyclic loading effect

(2-1)

Park and Ang, 1985, tested this model on 403 specimens and found that the damage

capacity D is reasonably lognormal distributed but that the data show considerable scatter

(c.o.v. = 0.54), which is to be expected for reinforced concrete elements. This model is

simple to apply and has been used widely for damage evaluation of reinforced concrete

structures.

The cumulative damage model proposed by Krawinkler and Zohrei, 1983, takes on the

following form:

in which

N

D = c L (~Opi !8y)c i = 1

D = damage index (D > 1 indicates total damage or collapse) AS,; = plastic deformation range of excursion i (see Figure 2.2) 6.y = yield deformation N = number of inelastic excursions experienced in the eanhquake C ,c = structural performance parameters

(2-2)

2.6

This model was tested and found to give very good results for several failure modes in

elements of steel structures. In these tests the exponent c was found to be in the order of l.S to

2.0, whereas the coefficient C varies widely and depends strongly on the performance

characteristics of the structural element The model has not been tested on reinforced concrete

elements.

The two models appear to be very different but, in fact, they are rather similar under

specific conditions. Both contain two structural performance parameters, c\, and pin the

Park/ Ang model and C and c in the Krawinkler/Zohrei model. Both contain, explicitly or

implicitly, normalized hysteretic energy dissipation as the primary cumulative damage

parameter. This is evident in the Park/Ang model in which the hysteretic energy dissipated in

each cycle is normalized by the product F 1c\,. In the KrawinklerJZohrei model hysteretic

energy dissipation is contained in the term I(liCp/8,). which for elastic-plastic structural system

is exactly equal to the hysteretic energy dissipation normali:red by F~. It can be shown that

this relationship is almost exact also for bilinear strain hardening systems of the type illustrated

in Figure 2.2.

Thus, the hysteretic energy dissipation, HE, or its normalized value, NHE = HEtF,;. is

judged to be the most imponant cumulative damage parameter. It is evident that the hysteretic

energy demand depends strongly on the strong motion duration, frequency content of ground

motions, and the period and yield level of the structure, since they all affect the number and

magnitudes of inelastic excursions, which in tum determine the cumulative damage experienced

by a structure. Moreover, hysteretic energy dissipation is only one of the terms involved in the

energy equilibrium of a structure, and the hysteretic energy demand imposed by a ground

motion depends also on the other energy terms (Le., damping energy DE, kinetic energy KE, and recoverable strain energy RSE) that make up the input energy ,IE, imparted to the structure

by a ground motion.

This brief discussion on cumulative damage modeling was intended to show that damage

and energy demands are closely related. Evaluation of energy demands is important in seismic

design for two reasons. For one, input energy demand spectra, which include all energy

components (RSE, KE, DE, and HE), give a clear picture of the damage potential of ground

motions, much more so than elastic response spectra. Secondly, hysteretic energy demand

spectra, which form an imponant part of the input energy demand spectra, serve to provide the

information necessary to modify ductility capacities in accordance with appropriate cumulative

damage models of the type discussed in this section. Thus, there are good reasons to evaluate

energy demand spectra in addition to other demand spectra discussed in the next section.

2.7

SEISMIC DEMAND PARAMETERS NEEDED FOR DESIGN

Seismic demands represent the requirements imposed by ground motions on relevant

structural performance parameters. In a local domain this could be the demand on axial load of

a column or the rotation of a plastic hinge in a beam, etc. Thus, the localized demands depend

on many local and global response characteristics of structUres, which cannot be considered in

a study that is concerned with a global evaluation of seismic demands. In this study only

SDOF systems and simplified MDOF systems are used as structural models. Assuming that

these models have a reasonably well defmed yield strength, the following basic seismic

demand parameters play an important role in implementing the postulated design procedure.

Some of the terms used in these definitions are illustrated in Figure 2.2.

EIDstic Strength Demand, F 1,~· This parameter defmes the yield strength required

of the structural system in order to respond elastically to a ground motion. For SDOF systems

the elastic response spectra provide the needed information on this parameter.

Ductility Demand, p. This parameter is defmed as the ratio of maximum deformation

over yield deformation for a system with a yield strength smaller than the elastic strength

demand Fy.e·

Inelastic Strength Demand, F 1 (JJ). This parameter defines the yield strength

required of an inelastic system in order to limit the ductility demand to a value of J.l.

Strength Reduction Factor, R1 (JJ). This parameter defmes the reduction in elastic

strength that will result in a duc~ity demand of J.l. Thus, R1(JJ) = F1.JF1(JJ). This parameter

is often denoted as R.

Energy and Cumulative Damage Demands. From the cumulative damage

parameters discussed in the previous section only the following two are discussed here:

Hysteretic Energy, HE: The energy dissipated in the structure through inelastic

deformation.

Total Dissipated Energy, TDE: TDE =HE+ DE (FDE is usually equal to the maximum

input energy IE except for shon period structures and

structures with very large velocity pulses).

The list of seismic demand parameters enumerated here is by no means complete. But for

conceptual studies much can be learned from these parameters. In the following section these

parameters are evaluated for two types of SDOF systems for closely spaced periods in order to

2.8 .

permit a representation in terms of spectra, using a period range from 0.1 sec. to 4.0 sec. In

the subsequent section the strength and ductility demands are evaluated for three types of

MDOF systems, using six discrete periods covering a range from 0.22 to 2.05 seconds.

STATISTICAL DATA ON SDOF SEISMIC DEMANDS FOR ROCK AND STIFF SOIL GROUND MOTIONS

The results discussed here are derived from a statistical study that uses 15 Western US

ground motion records from earthquakes ranging in magnitude from 5.7 to 7.7. All records

are from sites corresponding to soil type S 1 (rock or stiff soils). Time history analysis was.

performed with each record, using bilinear (see Figure 2.2) and stiffness degrading (see Figure

2.3) SDOF systems in which the yield levels are adjusted so that discrete predefined target

ductility ratios of 2, 3, 4, 5, 6, and 8 are achieved. Damping of 5% of critical was used in all

analyses and strain hardening of a= 0, 2%, and 10% was investigated.

Since the problem of scaling records to a common severity level is an unresolved issue,

all results shown here are presented in a form that makes scaling unnecessary. This is

accomplished by computing for each record the demand parameters for constant ductility ratios

and normalizing the demand parameters by quantities that render the results dimensionless.

The normalized parameters are then evaluated statistically. Only sample mean values are

presented here.

Typical mean spectra of normalized hysteretic energy, NHE = HEIF18y, for bilinear

SDOF systems are shown in Figure 2.4. The graphs show the significant effect of system

period on this parameter, particularly for higher ductility ratios. Thus, if constant NHE were a

measure of equal damage, it would be prudent to limit the ductility capacity for short period

structures to significantly lower values than for long period structures. What is not shown in

these mean spectra is the effect of strong motion duration on NHE. It is recognized that this

effect is strong, but no success can be reponed in our attempts to correlate NHE and strong

motion duration, even when employing several of the presently used defmitions of strong

motion duration.

The effect of different hysteresis models (stiffness degrading versus bilinear) on NHE is

illustrated in Figure 2.5. In general, and particularly for short period systems, the stiffness

degrading model needs to dissipate more hysteretic energy than the bilinear modeL The reason

is simply that the bilinear model executes many more small inelastic excursions than the bilinear

model in which many excursions remain in the elastic range.

2.9

The contribution of hysteretic energy dissipation to the total dissipated energy TDE for

bilinear systems is illustrated in Figure 2.6. These graphs are valid only for systems with 5%

damping. It can be seen that the ratio HEriDE is not very sensitive to the ductility ratio except

for low ductilities. It was found that this ratio is very stable for all records used in this study.

Thus, the presented data can be used to evaluate the effectiveness of viscous damping

: compared to hysteretic energy dissipation in dissipating the energy imparted to a structure. As

Figure 2. 7 shows, in stiffness degrading systems a larger portion of TDE is dissipated through

inelastic deformations (hysteretic energy) than in bilinear systems, indicating that viscous

damping is less effective in stiffness degrading systems.

In the context of the postulated design procedure, the energy demands illustrated here

provide information to be used to modify ductility capacities by means of cumulative damage

models. In the design process, the need exists then to derive the strength required so that the

ductility demands are limited to the target ductility capacities. These strength demands can be

represented by inelastic strength demand spectra or, in dimensionless form, in terms of the

strength reduction factor R, which is the ratio of elastic strength demand. Fy.e• over inelastic

strength demand for a specified target ductility ratio, Fy(p.). A two-step nonlinear regression

analysis was performed on the R-factors, first regressing R versus J.l for constant periods T,

and then evaluating the effect of period in a second step. For reasons discussed in Nassar and

Krawinkler, 1991, the following form of an R-p.-Trelationship was employed:

R = (c (J.t- 1) + 1}1tc - ra .b.. where c(T,a) - 1 + Ta + T (2-3)

For different strain hardening ratios a the following values were obtained for the two

regression parameters a and b:

for a=O%: for a=2%: for a= 10%:

a=l.OO a=l.OO a= 0.80

b = 0.42 b = 0.37 b = 0.29

The regression curves for J.l = 2, 3, 4, 5, 6, and 8 for bilinear systems with 10% strain

hardening are shown in Figure 2.8 together with the mean values of the data points on which

the regression was based. It is evident that the R-p.-T relationships are nonlinear, particularly

in the shon period range. For all ductility ratios the R-factors approach 1.0 as T approaches

zero, and they approach p. as T approaches infinity.

Relationships of this type together with mean or smoothened elastic response spectra can

be employed in many cases to evaluate the inelastic strength demands. This can be done with

2.10

confidence for S1 soil types, on which these relationships are based, and probably also for s2 soil types since the average R-factms were found to be insensitive to relatively small variations

in average response spectra shapes. However, these R-p-T relationships cannot be applied to

motions in soft soils which contain a signature of the site soil column. If we use these R -p-T

·relationships to derive inelastic strength demand spectra from the ATC S1 ground motion

:spectrum, the results shown in Figure 2.9 are obtained. To no surprise, the inelastic strength

demands are anything but constant for periods below 0.5 sec., the range in which the

smoothened elastic response spectrum has a plateau.

The R-factors presented in Figure 2.8 can be used with good confidence also for stiffness

degrading systems of the type shown in Figure 2.3. From the statistical study it was found

that this type of stiffness degradation has only a small effect on the strength demands for all

periods and ductility ratios. The same cannot be said about the effect of stiffness degradation

on energy demands, as is evident from Figures 2.5 and 2. 7.

EFFECTS OF HIGHER MODES ON INELASTIC STRENGTH DEMANDS

The previous section provided information on seismic demands for inelastic SDOF

systems. This information is relevant as baseline data but needs to be modified to become of

direct use for design of real structures, which mostly are multi-degree-of-freedom (MD OF)

systems affected by several mcxies. For inelastic MDOF systems, modal superposition cannot

be applied with any degree of confidence and different techniques have to be employed in order

to predict strength or ductility demands that can be used for design.

The research summarized here is intended to provide some of the answers needed to

assess strength demands for inelastic MDOF systems. The focus is on a statistical evaluation

of systems that are regular from the perspective of elastic dynamic behavior. Thus, closely

spaced modes and torsional effects are neglected and structures are modeled two­

dimensionally. For convenience in computer analysis, all structures are mcxieled as single bay

frames even though they are intended to represent generic structures with three distinctly

different types of behavior patterns.

The three types of structures are illustrated in Figure 210. The first type is designated as

"beam hinge model" {strong column- weak beam model), from here on referred to as BH

model, and represents structures that develop under the 1988 UBC seismic load pattern a

complete mechanism with plastic hinges in all beams forming simultaneously as sho\\·11 in

Figure 2.10. The second type is designated as "column hinge mcxiel" (weak column- strong

2.11

beam iDOdel), or CH model It represents structures whose relative column strengths are tuned

in a manner such that all columns simultaneously develop plastic binges under lateral loads

corresponding to the 1988 UBC seismic load pattern, resulting in the "collapse" mechanism

shown in the second sketch of Figure 2.10. The third type is a "weak story model," or WS

model, which develops a story mechanism only in the first story under the 1988 UBC seismic

:load pattern, whereas all other stories are of sufficient strength to remain elastic in all

earthquakes. This type of structure has a strength discontinuity but no elastic stiffness

discontinuity in the first story.

Structures with 2, 5, 10, 20, 30, and 40 stories are considered, with the first mode

periods being 0.22, 0.43, 0.73, 1.22, 1.65, and 2.05 seconds, based on a constant story

height of 12ft and the code period equation T = 0.02h,.J14. The base shear strength, v,, is

varied for each structure and ground motion record in a manner so that it is identical to the

inelastic strength demand Fy()J.) of the corresponding first mode period SDOF system for target

ductilities of either 1, 2, 3, 4, 5, 6, or 8. Applying this strength criterion permits a direct

. evaluation of the differences between SDOF and MDOF responses for each ground motion.

A total of 5,670 nonlinear time history analyses were pelformed, using the 15 S1 ground

motion records, 3 types of structures (BH, CH, and WS), 6 different numbers of stories, 7

different yield levels (corresponding to SDOF yield strengths for p. = 1, 2, 3, 4, 5, 6, and 8),

and 3 strain hardening ratios (a = 0, 2%, and 10% ). Response parameters obtained from the

15 records were statistically evaluated using sample means and variations. The results of this

study are discussed in detail in Nassar and Krawinkler, 1991, and only a few pertinent data are

summarized below.

Figure 2.11 shows typical results of mean values of story ductility ratios for the three

types of structures. The graphs apply for structures· whose base shear strength is equal to the

SDOF inelastic strength demand for a target ductility ratio of 8. It is observed that the story

ductility demands for the MDOF systems are largest in the bottom story (this was found to be

true for most cases but not necessarily always for lower target ductility ratios) and in this story

are larger than the SDOF target ductility ratio of 8 because of higher mode effects. The

increase above the target ductility ratio is smallest for the BH structures and by far the highest

for the WS structures. Tills observation was found to hold true regardless of the number of

stories, the target ductility ratio, and the strain hardening ratio, which clearly illustrates the

importance of higher mode effects and of the type of "failure" mechanism inherent in the

structural system.

2.12

In the postulated design procedure the objective is to limit the story ductility ratios to

predetermined target values. The results illustrated in Figure 2.11 show clearly that the base

shear strength obtained from the cOITesponding SDOF system is insufficient to achieve this

objective. Thus, the inelastic strength demands obtained for SDOF systems must be modified

· to to be applicable to MDOF structures. The modification depends on the number of stories

:(first mode period), the Wget ductility ratio, the strain hardening ratio, and the type of "failure"

mechanism in the structure. For the three types of structure investigated here, data of the kind

presented in Figure 2.11 can be utilized to derive the necessary modifications (Nassar and

Krawinkler, 1991). Examples of derived modification factors are presented in Figure 2.12 for

target ductility ratios of 4 and 8. The modification factors define the required increase in base

shear strength v, of the MDOF structure over the inelastic strength demand F1 of the

corresponding first mode period SDOF system in order to limit the ductility ratio to the same

target value.· The dashed curves shown in the four graphs represent the modification factors

implied by the widely used procedure of raising the 1{[' tail of the ground motion spectrum to

1f1V3 in the elastic design spectrum. This procedure was first introduced in the ATC 3-06

document (ATC 3-06, 1978) and is presently adopted in the U.S. Uniform Building Code.

The following observations can be made from Figure 2.12 and similar but more

comprehensive graphs presented in Nassar and Krawinkler.

• The required strength modifications are Smallest for BH strucrures. For these structures the

modifications are m6stly in good agreement with the ATC-3 modification provided there is

considerable strain hardening (a= 10%). For shon period BH structures the base shear

strength demand is consistently lower than the corresponding SDOF strength demand,

indicating that MDOF effects are not important in this range.

• The MDOF strength demands for CH structures are higher than for BH structures. The

required increase in strength compared to BH structures is about the same regardless of

fundamental period.

• In general, the modification factor increases with target ductility ratios and decreases with

strain hardening. Systems without strain hardening (a= 0%) drift more, and larger strength

is required in order to limit the drift to a prescribed target ductility ratio.

• Figure 2.12 clearly illustrates that WS structures, ie., structures with a weak first story, are

indeed a great problem. Such structures require strength capacities that may be more than

2.13

twice those required for BH structures in order to limit the story drift to the same target

ductility ratio.

The foregoing discussion focused on a procedure that can be employed to derive design

strength demands for MDOF systems from inelastic strength demand spectra of SDOF

systems. The presented numerical results apply only within the constraints identified in this

section and cannot be generalized without a much more comprehensive parametric study. The

parameters that need to be considered include the frequency content of the ground motions

(which may be greatly affected by local site conditions), the hysteretic characteristics of the

structural models (stiffness degradation, strength deterioration, etc.), and the dynamic

characteristics of the MDOF structures (periods, mode shapes and modal masses of all

imponant modes, as well as stiffness and strength discontinuities).

SUMMARY

The research summarized here is intended to demonstrate that ductility and cumulative

damage consideration can and should be incorporated explicitly in the design process.

Protection against failure implies that available ductility capacities should exceed the demands

imposed by ground motions with an adequate margin of safety. Available ductility capacities

depend on the number and magnitudes of individual inelastic excursions and need to be

weighted with respect to anticipated demands on these parameters. Cumulative damage models

can be employed to accomplish this. Normalilf':.d hysteretic energy dissipation is used here as

the basic cumulative damage parameter since it contains the number as well as the magnitudes

of the inelastic excursions in a cumulative manner. Thus, demands on hysteretic energy

dissipation have to be predicted. Once this is accomplished. ductility capacities are known

quantities and the objective of design becomes the prediction of the strength required to assure

that ductility demands will not exceed the available capacities. Basic information on the

required strength (inelastic strength demand) can be obtained from SDOF studies, but

modification must be employed to account for higher mode effects in real structures.

This summary report presents data that can be utilized to implement the steps outlined in

the previous paragraph. The data show the sensitivity of hysteretic energy and inelastic

strength demands to various structural response characteristics for SDOF systems, and the

great imponance of higher mode effects on the base shear strength required to limit the story

ductility ratios in multi-story strucrures to specified target values. The effects of higher modes

was found to be strongly dependent on the number of stories, the target ductility ratio, and the

type of failure mechanism in the strucrure.

2.14

ACKNOWLEDGEMENTS

The work summarized here was in pan supponed by a grant given by Kajima

Corporation and administered by CUREe, the California Universities for Research in

Eanhquake Engineering. Additional suppon was provided by the John A. Blume Eanhquake

Engineering Center at Stanford University, and the Stanford/USGS Institute for Research in

Earthquake Engineering and Seismology. · The suppon from all these sources is gratefully

acknowledged. This summary repon, in a slightly modified format, has been submitted to

Elsevier Science Publishers L 1D and is expected to appear in the Elsevier publication

"Nonlinear Seismic Analysis of reinforced Concrete Buildings."

REFERENCES

ATC 3-06. (1978). "Tentative Provisions for the Development of Seismic Regulations for Buildings," Applied Iechnolo~ Council, June 1978.

Chung, Y.S., Meyer, C., and Shinozuka, M. (1987). "Seismic Damage Assessment of Reinforced Concrete Members," Repon NCEER-87-0022, National Center for EanhQuake En~neerin~ Research, State University of New York at Buffalo, October 1987.

Krawinkler, H., Nassar, A., and Rahnama, M., (1991). "Evaluation of Damage Potential of Recorded Ground Motions," CtlREe-Kajima Research Rewrt- June 1991.

Krawinkler, H., and Zohrei, M., (1983). "Cumulative Damage in Steel Structures Subjected to Earthquake Ground Motions," Journal on Computers and Strucrures. Vol. 16, No. 1-4, 1983.

Nassar, A., and Krawinkler, H. (1991). "Seismic Demands for SOOF and MDOF Systems," John A. Blume EanhQuake En~neerin~ Center Repon No. 95, Depanment of Civil Engineering, Stanford University, June 1991.

Osteraas, J.D., and Krawinkler, H. (1990). "Strength and Ductility Considerations in Seismic Design," John A. Blume EanhQuake En ~neerin ~ Center. Repon No. 90, Departtnent of Civil Engineering, Stanford University, August 1990.

Park, Y.-J., and Ang, A.H.-S., (1985). "Mechanistic Seismic Damage Model for Reinforced Concrete," Journal of Structural En~neerin~. ASCE, Vol.lll, No.4, April1985.

NHE • HE IF, 6,

V/W

V/W

T (eec:)

J

T (eec:)

Syw~H~ [)ependenl MadifiCIIIian Faden

"'M~OO--....--

T (eec:)

2.15

J

T (eec:)

~~~~I (few s ,lnd s pfNI'Id rnaticnl)

Deeign If E1 Level & Vetiy Ee Level by Noninear Incremental Load Ana ·

V/W~ Mechanism

E -----

T (eec:)

Fig. 2.1. Implementation of Postulated Seismic Design Procedure

Fig. 2.2. Basic Seismic Demand Parameters

~, Diaplacement

• FWo.dil~g a1 poinl A tolows path ABC. • RltloDng a1 poinl 0 toriDws path OBC

I .rape at DB ialargef ttan DC. else I tollows DC.

Fig. 2.3. Stiffness Degrading Model

80

-a. ~ 60

t:r I

.:t .. o ~ -w :X:

11 20 w :X: z

0

1.0

0.8

w 0.6 0 .... -w :X: 0.4

0.2

0.0

15s Records, Bilinear, a= 10%, Mean

~ I 11 = 2, J. 4, S. 6, 8 (lhln --+ thick llne5) ~

r:"\. ·-f-

"' ~~ r-----" -~rt ~ ---t---~ r--

~ r--- _j_ ""-,

'/'--1--.-~

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

T (sse)

Fig. 2.4. Mean Spectra of Normalized Hysteretic Energy, NHE (Bilinear, a= 10%)

15s Records, Bilinear, a= 10%, Mean

-

4.0

I 11 = 2, l. 4, S, 6, 8 (lhln --+ thick lines)}

-

-

00

----~

')V_ J - -1_,.-----

/'--./

0.5 1.0 1.5 2.0 2.5 3.0 3.5

T (sec)

Fig. 2.6. Contribution of HE to Total Dissipated Energy, TDE (Bilinear, a= 10%)

--

4.0

5

~4 :0 w :X: 3 z -~2 01 , w :X: z

0

15s Records, Degrading I Bilinear, a·= 0%, Mean

ll 11 "' 2, l, 4, S, 6, 8 (lhln --+ thick Ones) ~ - J

I

I

' t- l)..

~ ~ ~ - -

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

T(sec)

Fig. 2.5. Ratio of NHE for Stiffness Degrading to Bilinear Systems (a= 0)

15s Records, Degrading/Bilinear, a=O%, Mean 2.5 ,---r---.-----=-,....::::...._-=;---.:---T----"T---,

ij" ~ e 2.0 -t--...1r--+---t---+----t----11---t----+---f

~ 1.5 -~--:11::G~t-----~c..ll-f"'-.~----il---+------il----+---f----+---l - ~~-- ~-g -r~~~~~~~§~~~~~~~~-~~~~~~~~~~~~ ln 1.0 -

~

~ 0.5 -f---1----t---J~plll .. ~2.'='l.~<4."=s."=6~. B~(lh~ln~--+~lh~lc~k l~ln~es~) ,.1-t----l :X:

0.0 +---1---+--+---i--+---f---+----i

4.0

0.0 0.5 1.0 . 1.5 2.0

T(aec)

2.5 3.0 3.5 4.0

Fig. 2.7. Ratio of HEffDE for Stiffness Degrading to Bilinear Systems (a= 0)

N ...... 0'.

2.17

15s Records, Bilinear, a= 10%, Data (Mean), First & Final Regression

12 1 _ ~I

10 J_ ____ l-~~~~==::~/~~~--~~~~~==~-=-~!l~=-~~~~-~-~--~-~~~ I / ~~ ~-' ---=­~.d~

_ 8 ~-~~~Jpi"-::~=~~s.':-~"~o:,;.f,_=_-_-__ =f1_==_:! __ ==-~:;~--==~:=~:: __ ==.,~~-§_-_~-_-~_;:t~_::_:_: __ j

~64-~~~;;~~~~~~~=:==~==~;:===t~~ a: ~~ I ·1,-... ___ -----t------1------ f--

j_j~~~~,~r~-~-==~;1±:::=-J::::~~::~::::±:=--=-=-~ ... _ I

4 ~ ~ ~-- ,f---- f -'1--- I -----

~ -----l-----L-----1-----~----- ----- ____ _ :;;-" I I I r II • 2, 3, 4, 5, 6 and 6 (INn ... llidlliM&) I

duhed • C1a1L dan.d • 11rat. solid • 11na1 I o~----+---~-----+-1--~--~~====~.====~.====~

2

0.0 0.5 1.0 1.5 ~0 3.0 3.5 4.0

T {sec)

Fig. 2.8. Strength Reduction Factor Ry(J.tJ for Motions in S1 Soil Type

1.2 15s Records, Bilinear, a= 10%, Soil Type 51

I I I I ----- ATC-S1

I l\ I I I Fy(J-1) I W for J.1 = 2

I Fy(J-1) I W for J.1"" 3 I Fy<J.L> I W for J.L =4

I F v(J.L) I W for J.1 = 8

1.0 0.8

I - I I \\ I I i I :N ',I I

I I

I I g 0.6

>o 1.1..

0.4

0.2

0.0 '

0.0

1' ... I

~"L ...... ,I I , ...... ........ _ ....

. ---T---~~ I

0.5 1.0 1.5 2.0

T (sec)

I I I ------ '

I ----j-----2.5 3.0 3.5 4.0

Fig. 2.9. Inelastic Strength Demand Spectra Based on ATC S1 Spectrum

Beam Hinge (BH) Model

Column Hinge (CH) Model

Weak Story (WS) Model

Fig. 2.10. Types of Structures Used. in the MDOF Study

-= Cl

0.8

~ 0.6

CD > 76 0.4 Ci a:

0.2

2.18

2.5,10,20,30,40 IIDries (ltlick .... thin lines)

0.0 +----...-....._ .......... ,.....-~_=-....,.....---..,..---...,......----f

.E Cl Gi ::: G)

~ Cii Gi a:

-= Cl

1.0

0.8

0.6

0.4

0.2

0.0

1.0

0.8

~ 0.6

~ Iii 0.4 ;; :r:

0.2

0.0

0

0

0

5 10 15 20 25 30

Story Ductility Ratio, 1-4 = Sdyn,ll Oy,l

(a) BH Model

DYNAMIC STORY DUCTILITY DEMANDS,IJ.t • (15s.ch-8.10}

2.5,1 0,20,30,40 IIDrieS (ltlick .... lhin lines)

5 10 15 20 25 30

Story Ductility Ratio, 1-4 = Sdyn,ll Oy,l

(b) CHModel

DYNAMIC STORY DUCTILITY DEMANDS,IJ.t_• (15s.ws-8.10)

f I l I I 2.5,10,20,30.40 11Dries I

(ltlick .... lhin lines)

II I I I

10 20 30 .w 50 60 70 80

Story Ductility Ratio, 1-4 = Sdyn,J I Oy,l

(c) WS Model

Fig. 2.11. MDOF Story Ductility Demands for Base Shear Strengths Associated with SDOF Target Ductility Ratio of 8 (a= 10%)

BASE SHEAR MODIFICATION FOR MDOF EFFECTS V (MDOF) IF (SDOF) • (15s·4 00) ' 'y1 , y, 6

(L5 0 Q ~4

~ .._ 3 (L 0 Q 2

== --;.. >1

0 0.0

---- ATC-S1 --- MOOF • BH Model -o- MOOF • CH Model -t1- MDOF • WS Model

/" •

-~ ~ fo

~ ~ _,..._---

~ • a.-:::::::: ------... -0.5 1.0 1.5 2.0 2.5

T (sec)

(e) ~ = 4, a= 0%

BASES 8

HEAR MODIFICA110N FOR MDOF EFFECTS, Vy(_MDOF) I F1(SDOF) • (151·8.00

(L5 0 Q rn4 "'>. IL -3 (L 0 02 == --;.. >1

0 0.0

---- ATC-S1 l. _._.... MOOF • BH Model v -o- MOOF • CH Model

/ -t1- MDOF • WS Model

/ / 1-0

:-v'

p ~ !--"' ------- ------ ---------=- . - - -

0.5 1.0 1.5 2.0 2.5

T (sec)

(g) J.ll = 8, (l = 0%

BASE SHEAR MODIFICATION FOR MDOFEFFECTS V (MDOF) IF (SDOF) • (151·410) 6

' .,, ',, (L5 0 Q (/) 4 ........ ,., IL .._ 3 (L 0 Q 2

== ;_;., 0

0.0

---- ATC-S1 --- MOOF • BH Model -o- MDOF • CH Model -t1- MDOF • WS Model

-~

.....-

~ ~ I'"' ,. ------ ·------- -~---

0.5 1.0 1.5 2.0 2.5

T (sec)

(0 J.11 = 4, a= 10%

BASES 6

HEAR MODIACA110N FOR MDOF EFFECTS, V~MDOF) IF ~SDOF) • (151-8.10

(L5 0 Q rn 4 >. IL -3 (L 0 Q 2

== >. >1

0 0.0

---- ATC-S1 --- MOOF • BH Model -o- MOOF • CH Model • -t1- MOOF • WS Model

_... ~ _...........

,..---.,..........

~ ~ _,.. ::::;::::::::. fi _ _. ____ --------

0.5 1.0 1.5 2.0 2.5

T(sec)

(h) llt = 8, (l = 10%

Fig. 2.12. Modifications in Base Shear Strength Required to Account for MDOF Effects

CHAPTER 3

EVALUATION OF DAMAGE POTENTIAL OF RECORDED GROUND MOTIONS AND ITS IMPUCATION FOR DESIGN OF STRUCfURES

by

Vitelmo V. Bertero Eduardo Miranda

3.1

3. 1 INTRODUCTION

3. 1. 1 STATEMENT OF PROBLEM

One of the most effective ways to mitigate the destructive effects of earthquakes is to

improve existing methods of designing, constructing, monitoring and maintaining new

earthquake-resistant structures, and upgrading (retrofitting) and maintaining existing

seismic hazardous facilities. As discussed in detail in the reports on Task 1 [1] and Task

2 [2], the principal issues that remain to be solved in order to improve seismic design

of new structures and seismic upgrading of existing structures are related to the three

following basic elements: Earthquake Input to the Foundation of the Structure,

Demands Imposed by This Input on the Structure, and the Supplied Capacities to the

Structure, Which Should Exceed the Demands. Therefore, it is obvious that the

essential data needed to start any reliable design of a new structure or upgrading of an

existing facility is the reliable establishment of the earthquake input, or in other words

the establishment of design earthquakes.

Earthguake Input: Establishment of Reliable Design Earthguakes. Conceptually, the

~esign earthquake should be that ground motion which will drive the structure to its

critical response. In practice, the application of this simple concept meets with serious

difficulties, because, firstly, there are great uncertainties in predicting the dynamic

characteristics of ground motions that have yet to occur at the building site, and

secondly, even the critical response parameter of a specific structural system may vary

according to the various limit states that could control the design. Because in most cases

the design is controlled by the safety limit state which involves damage to the building

as a result of inelastic deformations, to establish the design earthquake at this level

(limit state), it is necessary to estimate the damage potential of the different earthquake

ground motions that can occur at any given site. One of the most promising ways, not

only for estimating the damage potential of earthquake ground motions, but in general

for improving the Earthquake-Resistant Design (EQRD) of structures and particularly

for improving establishment of design earthquakes for the limit states involving damage

3.2

(inelastic behavior), is the use of an energy approach. Reference 1 discusses in detail

such an approach based on the use of an energy balance equation.

As discussed in Ref. 1, a promising parameter for improving selection of proper design

earthquakes for safety limit states is the concept of Energy Input, ~ , and Associated

Parameters. In Refs. 3 and 4, it is shown that in order to define properly the Safety

(Survival) Level design earthquake it is necessary to consider the following spectra

simultaneously: the ~ ; the Inelastic Design Response Spectra (IDRS) for strength and

displacement; and the Energy Dissipation, Eo , particularly Hysteretic Energy, ~ ,

including the cumulative ductility I'~ , and Number of Yielding Reversals (NYR) spectra.

Examples of evaluation of the E1 and IDRS (particularly for strength, i.e., the yielding

strength spectra or its equivalent yielding seismic coefficient, CY , spectra) has been given

and discussed in Ref. 1. In Ref. 2, Professor Krawinkler and his associates address in

detail not only the problem of evaluation of the IDRS for strength, but also other

important issues of seismic design for ductility capacity, including the effects of

cumulative damage. Nonnalized Hysteretic Energy Dissipation is used as the basic

cumulative damage parameter. A total of 15 Western U.S. ground motion records were

considered in the statistical studies presented in Ref. 2. All of the records are from sites

corresponding to soil type S1 (rock or stiff soils). To complement the studies conducted

by Professor Krawinkler and his research associates, the authors decided to conduct

similar statistical studies of recorded ground motions, but considering also ground

motions recorded on soft soil, and obtaining not only the inelastic strength spectra but

also the inelastic deformation spectra. These studies were conducted with the following

main objectives.

3. 1. 2 OBJECTIVFS AND SCOPE

The ultimate goal of the studies which are being conducted at Berkeley on the

evaluation of the damage potential of ground motions has been to improve the

establishment of design earthquakes and, consequently, to improve the earthquake­

resistant design of new structures and the seismic upgrading of existing hazardous

3.3

facilities. To achieve this goal a statistical study of 124 earthquake ground motions

recorded on various soil conditions ranging from rock to very soft soil have been

evaluated, and the implications of the results obtained on the reliable establishment of

design earthquakes have been assessed [5].

The main objectives of this report are to summarize: First, the main results of the above

studies, focusing on the normalized elastic and inelastic strength spectra, as well as on

the displacement spectra; and secondly, the implications of these results regarding the

establishment of design earthquakes, particularly with reference to the use of present

values for the structural response factor, R or Rw· and the code methodology for

specifying limitation on interstory drift limits.

In the studies conducted, the main results of which are reported herein, the emphasis

is placed on the effects of soil, particularly of soft soils, on the seismic demands of

strength and deformation.

3.2 SUMMARY

Nonlinear response spectra for 124 earthquake ground motions recorded on various soil

conditions, ranging from rock to very soft soils, were computed and analyzed statistically

to provide engineers with improved tools to estimate strength and displacement demands

on new and existing buildings. For each record, responses were computed for 50

different periods between 0.05 and 3.0 seconds, and for 6 displacement ductility ratios,

1, 2, 3, 4, 5 and 6. The study was limited to computing the responses of SDOF bilinear

systems with post-elastic stiffness of 3% of the elastic stiffness and with a damping ratio

of 5% of critical. Average (mean), Figs. 3.1 to 3.6, and mean plus one standard

deviation, Figs. 3. 7 to 3.12, inelastic strength demand spectra were computed for rock

(38 records), alluvium (62 records) and soft soil sites (24 records). These spectra

provide adequate tools with which it is possible to estimate strength demands in a

deterministic framework.

3.4

Based on the results obtained for the strength demand spectra, a comprehensive

statistical study of the strength reduction factor, R,.,. due to the hysteretic energy

dissipation that occurs as a consequence of the developed displacement ductility ratio

J.£, was conducted. The main purpose of this study was to obtain reliable data on which

to judge the reliability of present code recommended values for the strength reduction

factors R and Rw , and particularly to improve understanding of the factors affecting

these values. Emphasis was given to studying how the values of RJJ are affected by soil

conditions, including the effects of very soft soils. Figures 3.13 to 3.18 show the mean

and the mean plus one standard deviation of RJJ for different soil conditions.

Displacement seismic demand spectra were obtained using the normalized strength

demand spectra. Present practice for checking against lateral displacement is based on

the assumption that the inelastic displacement demands for severe earthquake ground

motions can be based on estimation of the elastic demands and multiplication of such

elastic demands by an empirical coefficient which is independent of soil conditions. The

reliability of such a procedure was studied by computation of the ratio of inelastic to

elastic displacement demands for each of the 124 ground motions. Figures 3.19 to 3.24

show for different soil conditions the spectra for the mean of the ratio of inelastic to

elastic displacement demands and for the mean of displacement demands in elastic and

inelastic SDOFS.

3. 3 CONCLUSIONS

From analysis of the results obtained, the following observations can be made.

• Spectral shapes for inelastic strength demands (JJ > 1) differ significantly from

elastic (JJ = 1) spectral shapes (see Figs. 3.1 to 3.6).

• The largest dynamic amplification for elastic response (JJ = 1) is induced by soft

soil sites. However, these large amplifications are significantly reduced when

3.5

• For soft soil records and periods, T, smaller than the predominant period of the

site, Tg, (T/Tg < 1), there is little difference between the strength demand for

ductilities between 2 and 6 (see Figs. 3.5, 3.6, 3.11 and 3.12). This implies that

small changes in the yielding strength of structures with T > T g may produce

large changes in the ductility demands.

• Spectral amplifications between 0.1 and 0.5 seconds for ground motions recorded

on soft soil are usually much smaller than the 2.5 factor which is used to define

the Effective Peak Acceleration (EPA). For this type of soil condition, the use

of Peak Ground Acceleration, PGA, is probably more appropriate than the use

of EPA.

• Normalization of inelastic strength demands using peak acceleration parameters

increases in dispersion with increasing periods. However, this dispersion was

found to be independent of the ductility level.

• Strength reductions due to dissipation of energy induced by hysteretic behavior,

i.e., R~ , are by no means constant. These reductions (R~) are strongly affected

by the natural period of vibration, the level of displacement ductility, and the

local soil conditions (see Figs. 3.13 to 3.18).

• The dispersion of strength reduction factor R~ was observed to be nearly

independent of the period of vibration, and to increase with increasing ductility.

• For soft soil conditions, the values of R~ are characterized by small values for

T/Tg < 1 and by very large reductions for periods close to the Tg . The R~

values are approximately equal to J.L for T/Tg greater than 2.5. This means that

estimation of the predominant period, T g , of the site is of particular importance

when designing or upgrading structures on soft soil sites, where inelastic strength

demands are strongly influenced by the TIT g ratio.

• 3.6

Values of the reduction factor RJ.J which are based on the assumption that the

maximum displacement of an inelastic system is the same as that for an elastic

system, i.e. ,RJ.J = !J., are unconservative for structures with short T. Values of RJJ

which are based on the assumption that energy absorption in inelastic systems is

equal to energy absorption in elastic systems, i.e., RJ.J = [21J. - 1] 112, are also

unconservative for structures with short T.

• The mean values of the ratio of inelastic deformation due to elastic deformation

show that for structures with short T the inelastic displacement demands can be

considerable larger than the elastic demands (see Figs. 3.19 to 3.26).

• The range of the values of the structural period for which elastic analysis can be

used directly to estimate the inelastic displacement demand is dependent on the

ductility level and the soil conditions.

• For soft soil sites and for values of TIT g very near to 1, inelastic displacements

can be up to 40% smaller than the corresponding elastic displacements. For

values of T/Tg < 0.8, the inelastic displacement demands can be significantly

larger than the elastic demands, so that for sites with very long T g , the

displacement demands based on elastic analysis can significantly underestimate

inelastic displacement demands of structures having T as large as 1.5 seconds, or

even larger, depending on the value of T g •

From the above observations it is obvious that the studies reported herein clearly

indicate the importance of having a reliable estimation of the fundamental period of the

structure and of the predominant period of the site, particularly in case of soft soils.

3.7

3. 4 REFERENCES

[1] Bertero, V.V.,et al., "Design Guidelines for Ductility and Drift Limits: Review

of the State-of-the-Practice and of-the-Art on Ductility and Drift-Based

Earthquake-Resistant Design of Buildings," A CUREe-Kajima Report, July 1991.

[2] Krawinkler, H., et al., "Evaluation of Damage Potential of Recorded Ground

Motions," A CUREe-Kajima Research Report, June, 1991.

[3] Bertero, V.V.,and Uang, C.H., "Issues and Future Directions in the Use of an

Energy Approach for Seismic-Resistant Design of Structures," Proceedings of the

Workshop on Nonlinear Seismic Analysis of RC Buildings, to be published by

Elsevier Science Publishers, October 1991.

[4] Bertero, V.V.,"Structural Engineering Aspects ofSeismic Zonation," Proceedings,

Fourth International Conference on Seismic Zonation, Stanford University,

August 1991, Vol. 1, pp. 261-322, Earthquake Engineering Research Institute,

Oakland, California.

[5] Miranda, E., "Seismic Evaluation and Upgrading of Existing Buildings," Ph.D

Thesis, Civil Engineering Dept. of the University of California at Berkeley,

California, may, 1991. (To be published in two separate EERC reports).

3.8

11 3.0

ROCK SITES 2.5

= 1

2.0

, .5

1.0

0.5

0.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 PE:iiOD (sec)

Figure 3.1 Mean strength demands of ground motions recorded on rock when nor­malized using PGA (~=1 ,2,3,4,5,6).

Cy

E?Ng 3.0

2.5

2.0

1.5

1.0

0.5

0.0

0.0 0.5

ROCK SITES

1.0 1.5 2.0 2.5 3.0 PE:iiOD (sec)

Figure 3.2 Mean strength demands of ground motions recorded on rock when nor-!. '"' . -::lA ( :. 2 3 4 ::: 6' ma t:ze .... us1ng t::.. ~= 1, , , , ... , J·

1l 3.9

3.0

ALLUVIUM SITES 2.5 !l = 1

2.0

1.5

).0

0.5

0.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 PERIOD (sec)

Figure 3.3 Mean strength demands of ground motions recorded on alluvium when normalized using PGA (!J-=1 ,2,3,4,5,6).

Cy

E?Ng

3.0

2.5

2.0

1.5

1.0

0.5

0.0

0.0 0.5

ALLUVIUM SiT;S

1.0 1.5 2.0 2.5 3.0 PERIOD (sec)

Figure 3.4 Mean strength demands of ground motion recorded on alluvium when nor­malized using E?A (!J-=1,2,3,4,5,6).

11

5

4

3 =

2

1

0

0.0 0.5 1.0

3.10

1.5 T /Tg

SOFT SOIL SiTES

2.0 2.5 3.0

Figure 3.5 Mean strength dema.r1ds ot ground motions recorded on soft soil when normalized using PGA (~=1,2,3,4,5,6).

2 J.l. = 2

0

0.0 0.5 1.0 1.5

T /Tg 2.0

SOFT SOIL SITES

2.5

I 3.0

Fl·aure 3 6 Mean strena_th demands ot a_round motions recorded on soft soil when. 0 •

normalized using E?A (~=1,2,3,4,5,6).

!-1. = 1 3

2

1

0

0.0 0.5 . 1.0

3.11

1.5 PERIOD (sec)

z.o

ROC:-< SITES

2.5 3.0

Figure 3. 7 Mean plus one s~ar~d.a.rc deviation s~reng:h demands (normalized by PGA) tor rock shes.

E?AJg 4

ROCK SiTES

3

2

1

~ = 0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 PERIOD (sec)

Figure 3.8 Mean plus one stand.a.rd deviation Siiength demands (r:cmialized by E?A) tor roc!< sites. ·

3.12

ALLUVIUM SITES

!l = 1 3

2

1

. 0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 PE::\100 (sec)

Figure 3.9 Mean plus one stC!idc.rd deviation s~rength demands (normalized by PG.A) 1cr aliLNium sites.

Cy

E?Ng 4

....

....

2

1

0

0.0

ALLWIUM SIT::S

0.5 1.0 1.5 2.0 2.5 3.0 PERIOD (sec)

Figure 3.10 ~.ean plus one standard deviation strength demands (norr:;a.lized by E?A) for a.llLNium sites.

T1 8

6

4

2

0

0.0 0.5 1.0

3.13

1.5 T /Tg

2.0

SOFT SOIL SITES

2.5 3.0

Figure.. 3.11 Mean plus one standard deviation strength demands (normalized by PGA) fer soft soil sites.

Cy

E?AJg 8

6

4

2

0

0.0 0.5 1.0 1.5 T /Tg

2.0

SOFT SOIL sm:s

2.5 3.0

Figure 3.12 Mean plus one standard deviation strength demands (normalized by E?A) for sott soil sites.

R ).L

8

6

4

2

0

0.0 0.5 1.0

3.14

1.5

PE~!OD (sec) 2.0

RCCK SIT::.S

2.5 3.0

Figure 3.13 Mean of stiength reduc~ions due to nonlinear behavior fer rock sites.

6

2

0

0.0 0.5 1.0 1.5 PE:=\100 (sec)

2.0

ROCK SiTES

2.5 3.0

Figure 3.14 Mean minus one standard deviation of strength reduc:iens due to non­linear behavior fer rock sites.

R).t 8

6

4

2

0

0.0 0.5

3.15

ALLUVIUM SITES

Jl=S

Jl=S

Jl=4

J.L=3

Jl=2

1.0 1.5 2.0 2.5 3.0 PE?.IOD (sec)

Figure 3.15 Mean of strength reduc:ions due to nonlinear behavior for alluvium sites.

ALLWIUM SITES

6

2

0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 PERIOD (sec)

Figure 3.16 Mean minus one standard deviation of s~rength reduc!ions due to non­linear behavior for c.Jiuvium sites.

3.16

12 SOFi SOIL SiTES

10

8

6

4

2

0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 · T /Tg

Figure 3.17 Mean of strength reduc~ions due to noniinear behavior for soft soil sites.

RjJ. 14

12

10

8

6

4

2

0

0.0 0.5 1.0. 1.5

T /Tg 2.0

SOFi SOIL SiTES

2.5 3.0

Figure 3.18 Mean minus one s~ancard deviation of strength reduc:icns due to ncr.· linear behavior for scft soii sites.

3.17 ~:nelastic

.Q.elastic

4 ~. ----------------------------------------------~

3

2

'

\\ \\\ \\ I\\' I\\\ I'\, '

·. '.. ~""'-... \ ,--.......:......_..-,

ROCXS!TES

----j..l=1

---------····- 1-l = 2 -------j..l=3 -----j..l=4 ----j..l=5 -----J..L=6

· .... _ ..... --::::-. .........

··· ..... ::-.:---=~~;~ ~-"'?""'--:--~ -= ~ 1 -·- ................... -· -- I

0

0.0 0.5 1.0 1.5 PE~IOD (sec)

2.0 2.5 3.0

Figure 3.19 Mean of ratio of ine!as~ic to elastic displacement dema.I"Jc's for rock sites.

DIS?LA.CEMENT (in)

16

1<!. ---IJ-=1

-~ I G. ••••••••••••••• 1-L = 2 .

----~=4

10 ---- 1-L = 6

8

6

4

2

0

0.0 0.5

ROc:-\ srr:::s _,...__ ___ / --= . .....-

e:=..; = o.'-9

1.0 1.5 2.0 2.5 3.0 PERIOD (sac)

Figure 3.20 Mean of displacement demands in elastic and ine!a.stic systems for rack sites assuming an E?A of 0.4g.

3

2

1

0

0.0 0.5

3.19

SOFT SOIL SITES

----~=1

-----······- ~ = 2 ------- ~ = 3 ----- ~=4 ----!J-=5 ----- ~=6

·---,~t"-········st>=¥'.~---····.... : ....... ~ ..... ··-·· - ~

1.0 1.5 2.0 2.5 3.0 T /Tg

Figure 3.23 Mean of ratio cf inelastic to elastic displacement demands for soft soil sites.

DISPLA-CEMENT (in)

20

10

5

0

0.0

---!J.=1 SOFT SOIL Si'iES

••••••••••••••• 1.1 = 2 ----!J.=4

-- -~:::::;;:;:-::::--:::-.....,.4 .0 .:::.:: ......... :-:-:.:;.::-... ---.. .. ·······-.-~-/ .

----!J.=6

'..:....__ // ./) -:~-

_..,..- /:i ••• •· // .· ~~, .··

-~ _,..-; .... ~,--...­./.

~-::...-

0.5 1.0 1.5

PE~!OD (sec)

Tg = 1.: sec

PGA = 0.25g

2.0 2.5 3.0

Figure 3.24 Mean of displacement demands in eiastic and inelastic systems tor a soit soil site with a predominant site period of 1.5 sec and assuming a PGA of 0.25g.

t..:nelastic

t,.eias:ic 4

3

2

1 .........

0

0.0 0.5

3.18

ALLUVIUM SITES

----1.1.=1 -----------···- 1.1. = 2 ------- 1.1. = 3 ----- 1.1.=4 ----1.1.=5 ----- !.L=S

1.0 1.5 2.0 2.5 PERIOD (sec)

3.0

Figure 3.21 Mean of ratio of inelastic to elastic displacement demands for alluvium ;:;iies.

DISPLACEMENT (in)

16

14 ---!.1.=1

12 .•..•..•....... ll = 2

----!.1.=4 10

---- !.1. = 6

8

6

4.

2

0

0.0 0.5

ALLWIUM SiTES

E?A • 0.4g

1.0 1.5 2.0 2.5 3.0 PERIOD (sec)

Figure 3.22 Mean of displacement demands in elastic and ine!astic systems for allu­vium sites assuming 2I1 E?A of 0.4g.

CHAPTER 4

U.S. CONCRETE FRAME BUILDING RESPONSE

by

James Anderson Eduardo Miranda Vitelmo Bertero

4.1

4.1 INTRODUCfiON

This report summarizes the main results obtained in studies conducted to evaluate the

recorded seismic responses of two buildings. The main objectives of the studies are: (1)

To evaluate the reliability of present system identification techniques of inferring from

recorded responses of a building its dynamic characteristics; and (2) to assess the

reliability of analytical models and methods (computer programs) for conducting

analyses of the seismic response of a building.

To achieve these objectives, two seismically instrumented buildings that have survived

recent modest earthquake motions are reported herein. The first is a ten-story building;

the second is a thirty-story building. After collecting all of the necessary data regarding

design and construction of the buildings, how they were instrumented, and the records

of the ground motions at their foundations and of their response to ground motions that

had occurred in the past, the following studies were undertaken: (1) To analyze the

recorded responses of each of the buildings during the most demanding motions that

they had experienced and to attempt to identify from these records their dynamic

characteristics using system identification techniques; (2) to predict analytically the

behavior of the buildings when subjected to the recorded motions, and then to compare

these predictions with the recorded response, in order to evaluate the reliability of the

analytical motions used in the prediction; (3) to evaluate the buildings supplied

characteristics in order to determine its possible overstrength; (4) to analyze the

probable performances of the buildings under more demanding seismic motions than

those recorded; and (5) to study the possibility of using a simpler methodology than one

requiring nonlinear time-history analyses to attain reliable estimates of the magnitude

and distribution of local demands in the buildings. A summary of the results obtained

in the above studies for each of the buildings follows.

4.2

4.2 SEISMIC RESPONSE OF THE 10-STORY RC BUILDING

An existing instrumented ten-story RC building, shown in Fig. 4.1, which was subjected

to what can be considered as earthquake ground motions of moderate damage potential

during the 1987 Whittier Narrows earthquake, was selected for detailed analytical studies

to evaluate its seismic performance and to compare such performance with the observed

performance during that earthquake. This comparison has permitted an evaluation of

the reliability of the analytical models and methods presently used in the analyses

necessary for checking the preliminary designs of new structures and for the vulnerability

assessment of existing buildings. The structural system of the building consists of a

moment-resisting frame in the N-S direction and shear walls in the E-W direction. The

building was designed for a first yielding strength (member strength) seismic coefficient

of 0.052 in the longitudinal (N-S) direction and 0.073 in the transverse (E-W) direction.

The dynamic characteristics of the building were identified using system identification

techniques and acceleration time-histories recorded during the Whittier Narrows

earthquake. A small change in fundamental period was observed during the earthquake

for the transverse direction of the building. This would indicate that some damage

(cracking and perhaps some small amount of yielding) bad occurred. No changes were

observed in the longitudinal direction fundamental period, indicating that no significant

damage could have occurred in that direction.

A three-dimensional, linear-elastic model of the building, shown in Fig. 4.8, was

calibrated using the dynamic characteristics previously identified. Using this model,

time-history analyses were conducted using as input the acceleration time-histories

recorded in the basement. These analyses had the following objectives: i) to investigate

the effectiveness of linear-elastic analyses at capturing the response of the building under

moderate ground motions; and ii) to explain the absence of damage as a result of the

Whittier Narrows earthquake despite the apparent severity of the recorded ground

motions (i.e., the large peak ground accelerations in both directions: 0.60g and 0.40g

respectively in the transverse and longitudinal directions).

4.3

For both directions, very good correlations between the measured and computed

responses were obtained. Maximum computed interstory drifts of 0.34% in the

longitudinal direction and 0.21% in the transverse direction explain the absence of

damage in the building. These results confirm once more that Peak Ground

Accelerations are not a good (reliable) parameter by which to judge the damage

potential of an earthquake ground motion to a specific structure.

Non-linear analyses were conducted to investigate the strength and deformation

capacities of the building. Two lateral loading patterns, triangular and rectangular, were

used. Significant overstrengths were computed, particularly in the transverse direction.

For the longitudinal direction, the ratio between the base shear at first significant

yielding and the design base shear (0.052) was about 3.06 for the case of triangular

loading and 3.62 for the rectangular loading. Due to plastic redist:J:ibution it was

estimated that there was an additional overstrength: the ratio between the maximum

base shear and the base shear at first yielding was 1.38 for both lateral loading patterns.

Therefore, the ratios between the maximum resisting base shears (0.22W and 0.26W)

and the code design base shear (0.052W) were 4.23 and 5.0 for the triangular and

unifonn lateral loads respectively. These overstrengths were obtained assuming that the

structure would be able to develop a global displacement ductility ratio of about 2.4 with

a local ductility ratio of about 4, which it is doubtful that the existing detailing of the

reinforcing would allow to be developed. It should be noted that the above

overstrengths are static overstrengths and that they are a lower bound of the dynamic

overstrength.

For the transverse direction the overstrength ratios were higher than for the longitudinal

direction. Base shear strengths corresponding to the first significant yielding of the shear

walls were 0.32W and 0.43W respectively for the triangular and rectangular load

patterns. Considering that the structural system according to code requirements has to

be designed for 0.073W, the resulting strength ratios are 4.38 and 5.89. The maximum

base shear strengths were computed to be 0.42W and 0.51W respectively for the

triangular and rectangular load patterns, with the result that their ratio with the code

4.4

displacement ductility ratio larger than three and near 2.5 for the triangular and

rectangular patterns respectively. It is doubtful that the detailing of the reinforcement

in the coupling girders and walls could allow such a high global displacement ductility

ratio to develop.

Nonlinear time-history analyses were carried out for the longitudinal direction of the building

using the Hollister and James Road records. In spite of the fact that these two records have

peak ground accelerations smaller than those recorded at the basement of the building during

the Whittier Narrows earthquake, large inelastic deformations concentrated over the 3rd to

7th stories were computed. The maximum base shear demanded was about 0.24W. The

maximum displacement was 7.71 inches, and the maximum interstory drift was 0.016,

resulting in a maximum demanded story displacement ductility ratio of 3.15 in the 4th

story. The number of yielding reversals was small, only four.

An approximate method was proposed and used to estimate local displacement ductility ratio

demands. The method is based on the use of a relationship between global and local

deformations obtained from static loading, and the use of nonlinear (inelastic) spectra for

SDOFS. Simplified earthquake analysis using this method were conducted for this building

when subjected to the James Road and Hollister records. Results were then compared to the

those obtained using DRAIN-20. For both records, the simplified analysis method

produced very good estimates of story displacement ductility demands.

An attempt has also been made to estimate the maximum interstory drift index using the

above approximate method and other methods. The results obtained using the above

approximate method was in close agreement with those obtained from the nonlinear

time-history of the building.

4.3 SEISMIC RESPONSE ANALYSIS OF THE Y -BUILDING

4.5

4.3 SEISMIC RESPONSE ANALYSIS OF THEY-BUILDING

On October 17, 1989, a 7.1 surface wave magnitude earthquake struck northern

California. This earthquake, the largest magnitude earthquake in California since 1906,

caused 62 deaths, approximately 3750 injuries, and more than $8 billion in damages in

the San Francisco Bay area [1].

The Y -Building is a 30-story asymmetrical three-winged Y -shaped structure built in 1983.

It is located in the city of Emeryville next to San Francisco Bay. A typical plan of the

building is shown in Fig. 4.3. The structural system is a ductile (special) moment­

resistant space reinforced concrete frame. The site is underlain by a layer of soft silty

clay known locally as Bay Mud. The foundation of the building consists of a five feet

thick concrete mat and 900 prestressed concrete piles, 60 to 70 feet long. Non-structural

elements consist of precast lightweight concrete elements in all facades of the building

with interior partitions located at beam lines.

INSTRUMENTATION AND RECORDINGS

The building forms part of the strong-motion network operated by the United States

Geological Survey (USGS). The instrumentation consists of 21 CRA-1 analog

acceleration sensors distributed over the three wings and central core on the 13th, 21st,

and 31st (roof) levels, and at the ground level. Additionally, there is a 3-component

CRA-1 "free-field" analog accelerometer 40 meters north of the building and another 3-

component SMA-1 "free-field" analog accelerometer 100 meters south of the building.

Fig. 4.4 shows the location of instruments within the building.

The Y -Building is located approximately 97 km (60 miles) north of the epicenter of the

Lorna Prieta earthquake. Major damage occurred within 5 km (3 miles) of the building,

including the collapse of the Cypress Street Viaduct, the collapse of one segment of the

San Francisco-Oakland Bay Bridge, and damage to facilities at the Port of Oakland.

The building suffered no significant damage during the earthquake, structural or non-

4.6

structural. The parking structure next to the building experienced flexural cracks in the

floor system due to north-south motion of the structure, and also suffered shear cracking

and yielding of two columns in the first floor.

A total of 27 acclerograms were obtained in the Y -Building in the Lorna Prieta

Earthquake [2]. In general, the recorded motions are characterized by a strong phase

lasting approximately 9 seconds. Table 4.1 lists peak values of acceleration, relative

velocity and relative displacement for each instrument location.

OBJECfiVES .

A series of analytical studies were conducted on this building, with the following main

objectives: First, to obtain the dynamic characteristics of the building from the records

obtained during the earthquake using system identification techniques; and second, to

evaluate the effectiveness of simplified, linear-elastic, and time-history analyses for

capturing the response of tall buildings under moderate earthquake shaking.

SYSTEM IDENTIFICATION

The occurrence of an earthquake can be viewed as a full-scale, large-amplitude

experiment on a structure. If the structural motion is recorded, there is the opportunity

to make an quantitative study of the structure at dynamic force and reflection levels

directly relevant to earthquake-resistant design. In this study, three different frequency

domain system identification techniques were used. These were: i) non-parametric,

time-invariant; ii) non-parametric, time variant (moving window Fourier analysis); and

iii) parametric, time-invariant.

In the first technique the structure is idealized by a non-parametric (black box), time­

invariant linear model in which the dynamic properties are determined from the transfer

function H(i w), defined as the ratio of the Fourier transform of the input and output

signals. The second system identification technique (non-parametric, time-variant) is

essentially the same as the approach described above, except that in order to identify the

variation of structural parameters in time, a window smaller than the total duration of

4.7

the record, is "moved" in time. In this study, a window with a total duration of

approximately four times the fundamental period of the building is employed.

In the third identification technique the structure is idealized by a simple mathematical

model, which defines the input-output relation of the building. The parameters of the

model are adjusted through least square procedures to minimize the difference between

the smoothed Fourier transform of the recorded response (output) and the Fourier

transform of the computed response [3].

Figure 4.5A shows the Fourier amplitude spectra of input and output signals for the

260" component recorded ground motions. The input signal (dotted line) corresponds

to the motion recorded at ground level, and the output signals (solid lines) correspond

to the motions recorded in the central core at the 31st, 21st, and 13th levels. It can be

seen that the ground motion has its strongest input in a band between 0.6 Hz and

around 2.0 Hz. Transfer functions corresponding to motions recorded in the central core

in the 260" component are shown in Fig. 4.5B. From this figure, 1st, 2nd, and 3rd

modes were identified at 0.37 Hz, 0.94 Hz, and 1.81 Hz, respectively. Identified

translational periods and mode shapes for both directions of the building are

summarized in Table 4.2.

Estimation of the damping ratio in the first two translational modes in each direction

were found to vary depending on the resolution, filter, and smoothing used in the signal

processing. Their values range between 2.4 and 3.0%.

Ambient and forced-vibration measurements of the building were made in 1983, and

details of these measurements are given in Ref. 4. Table 4.3 compares the periods of

vibration obtained through ambient vibrations, small-amplitude forced vibrations, and

those obtained in the present study. As shown in this table, there is a very good

agreement between periods obtained through ambient and forced vibrations. However,

there exist very large differences between the small-amplitude measurements and the

records obtained in the Lorna Prieta earthquake. For 350" component the ratio of

4.8

fundamental period measured during the earthquake to that measured through ambient

vibration is 1.51. For the 260. component this ratio is 1.57. A comparison of mode

shapes obtained with the three methods is shown in Fig. 4.6, where it can be seen that,

unlike periods of vibration, mode shapes identified from earthquake records are very

similar to those obtained in small-amplitude vibrations.

Results from moving window Fourier analyses showed no change in dynamic

characteristics in the 350· component, and only small change in the 260. component.

SIMPLIFIED ANALYSES

Earthquake time history analyses were conducted using a simplified model of the

building consisting of two-dimensional models (one for each orthogonal direction) with

only one degree of freedom per floor. These models are an extension of those used in

the parametric system identification. The mechanical characteristics of these two­

dimensional models were prescribed such that their dynamic characteristics matched

those identified from earthquake records. The purpose of these simplified models was

to have a small model in which time history analyses could be performed relatively

quickly in order to calibrate a three-dimensional finite element model of the building,

and to evaluate the effectiveness of linear elastic, time-invariant models at capturing the

response of the building.

A time domain comparison of the recorded and calculated response is shown in Fig. 4. 7.

This comparison corresponds to absolute acceleration, relative velocity, and relative

displacement time histories of the west wing at the 31st level (350. component).

Relative motions correspond to the difference between the motion of the roof and the

recorded motion of the ground floor of the building (for this component). As shown in

the figure, correlation between the recorded and the calculated response is very good.

It was found that the relative importance of each mode in the total response depends

on the response function (acceleration, relative velocity, or relative displacement. For

relative displacement, the first mode response dominated the total response; for relative

4.9

velocity, the response was dominated by the first two modes; and for absolute

accelerations, at least three modes were needed to capture adequately the recorded

response. Fig. 4.6 shows how the calculated acceleration time-history is improved with

the incorporation of the higher modes.

Concluding Remarks Regarding the Use of Simplified Analysis

1. Periods of vibration identified from earthquake records are significantly longer

than those previously measured through ambient and small-amplitude forced

vibrations. Mode shapes inferred from small-amplitude vibrations are similar to

those identified in records from the Lorna Prieta.

2. Simplified, time-invariant, linear elastic two-dimensional models of the building

capture the recorded response relatively well.

3. Maximum interstory drifts computed for the building explain the absence of

damage during this earthquake.

4. Relative importance of each mode in the total response depends on the response

function.

THREE-DIMENSIONAL ANALYSES

Detailed three dimensional finite element models of the structure were developed in

order to evaluate the response of this irregular structure to the two horizontal

components of ground motion recorded at the base. These models will also be used to

evaluate the effect of the earthquake on the individual members of the structure and to

evaluate the developed inertia forces relative to the specified building code

requirements. In this phase of the study, critical comparisons will be made between

calculated accelerations and corresponding recorded values considering acceleration and

displacement time histories and floor response spectra.

4.10

Several computer programs are available on a commercial basis which can be used to

evaluate the elastic, dynamic response of the Y Building. The SAP90 [5] program was

selected for use in this phase of the study. The completed SAP90 model of the structure

consists of 2,362 nodes, 5,700 elements and 6,816 degrees of freedom. The analytical

model is shown in an isometric view in Fig. 4.9.

The deformed plan shape for the first three modes are shown in Figs. 4.10, 4.11, and

4.12. The translational mode in the north-south (Y) direction is shown in Fig. 4.10.

Here it can be seen that this is a translational mode that has some torsional component

due to the asymmetry of the geometry which is accentuated by the mezzanine slab in the

west wing. The translational mode in the east-west (X) direction is shown in Fig. 4.11.

Here the structure is almost symmetrical about the east-west (X) axis and the displaced

shape is almost pure tran~lation. The third mode, shown in Fig. 4.12 is a torsional mode

which is readily apparent from the displaced shape.

MODELING CONSIDERATIONS FOR REINFORCED CONCRETE

Reinforced concrete is a nonhomogeneous material which is normally placed

monolithically. This results in the following modeling considerations which need to be

considered when working with reinforced concrete structural systems:

1. Finite Width Joints. Due to the overall size of the beam and column members,

the clear span of the beams and columns can be reduced significantly thereby

stiffening the structure. This condition is considered in the program by the

inclusion of rigid offsets on the ends of the frame elements. There is no bending

or shear deformations within the rigid offset which extends from the joint to the

face of the support. It is possible that the use of rigid offsets which are equal to

the full dimension of the beam-column intersection may stiffen the structure too

much since deformations do occur in the joint region. This is accounted for in

the program by the inclusion of a rigid joint reduction factor which reduces the

length of the offset and thereby approximates the effect of the deformation that

4.11

occurs in the joint region. Analyses based on the centerline to centerline

dimensions are identified as having zero width joints.

2. Effective Beam Section. Initially, monolithic slab and beam construction results

in a tee section for the beams with the flange having the slab thickness and

extending a specified distance (nominally equal to eight times the slab thickness)

on either side of the web. Under service loads, microcracking occurs in the

concrete. This causes sections under negative moment to act as rectangular

sections and sections under positive moment to continue to act as tee sections.

Furthermore, as cracking occurs, the section properties are reduced from those

of the gross section to those of the cracked, transformed section used in working

stress analysis with the actual average section property along the cracked region

somewhere in between depending on the amount of cracking.

These modeling considerations are incorporated in seven different SAP90 models of the

Y Building which are identified in the following manner:

Model 1 - Finite width joints, tee beams, gross section properties.

Model 2 - Finite width joints, rectangular beams, gross section properties.

Model 3 - Finite width beam joints, rectangular beams, gross section properties.

Model 4 - Zero width joints, rectangular beams, gross section properties.

Model 5- Finite width joints with 50% reduction factor, rectangular beams, gross section

properties.

Model 6- Finite width joints average cracked, transformed section properties considering

tee section at center and rectangular section at supports.

Model 7 - Finite width joints with 50% reduction factor, average cracked transformed

section properties considering tee section at center and rectangular section at supports.

MODAL ANALYSES

The results of modal analyses of the vanous building models listed above are

summarized in Table 4.4. Here it can be seen that Model-l which uses finite width

4.12

joints and tee sections for the beams and girders gives the best approximation to the

results measured in the ambient and small amplitude forced vibration tests (Table 4.3).

The models which produce the best estimates of the recorded periods are Model-3,

Model-4 and model-5. Models 3 and 4 give a better estimate of the first mode (N-S) and

Model 5 gives a better estimate of the second mode (E-W). Model-3 represents the

effect of cracking by the convenient use of the rectangular section and the zero width

joint, however, it is recognized that the use of the zero width joint is an

oversimplification.

These results illustrate the complexity involved in developing an analytical model for the

analysis and design of a reinforced concrete structure. At force levels representative of

service loads, the actual stiffness of members, their connections and supports can vary

significantly and have a significant effect on the overall response of the system. This

indicates the importance of using recorded response data for evaluating the dynamic

characteristics of actual buildings.

DYNAMIC RESPONSE ANALYSIS

Using the accelerations recorded on the ground floor in the north wing as input, the

time history response of the model was evaluated. In this analysis, accelerations

recorded in the north-south and east-west directions were applied simultaneously to the

model and the dynamic response calculated using the modal time history approach

considering fifteen modes of vibration. Floor response spectra were also generated from

both the recorded and calculated motions in order to better compare the results. The

damping in the structure was assumed to be 5% in all modes. The roof spectra in the

east-west direction is shown in Fig. 4.13. Here it can be seen that there is a good match

between the periods of the recorded and calculated values. It is also of interest to note

that the peak response occurs at a period of approximately 0.9 seconds which is the

second mode of vibration. The peak due to the first mode occurs at about 2.6 seconds

but is much smaller. The corresponding acceleration time histories at the roof level are

shown in Fig. 4.14. Floor spectra at the 21st level are shown in Fig. 4.15 and the

corresponding time history response is shown in Fig. 4.16. In both cases the comparison

4.13

corresponding time history response is shown in Fig. 4.18. As in the previous cases the

comparisons are quite good.

INPUT ENERGY

In order to evaluate the relative importance of the recorded earthquake motions in the

N-S and E-W directions, the elastic seismic energy input to the structure in these two

directions was evaluated. The time histories of the input energy are shown in Fig. 4.19

which indicates that the input energy in the E-W (X) direction is almost 2.5 times that

in the N-S (Y) direction. This indicates that the main response of this structure due to

the Lorna Prieta earthquake will be in the E-W (X) direction although the fault rupture

occurred in the predominantly N-S (Y) direction.

DESIGN ANALYSIS

The design of the Y Building is based on the 1979 UBC supplemented by the use of site

specific design response spectra. Using the 1979 UBC with K=0.67, S=l.5, I=l.O,

Z=l.O, and C=0.038 results in a design seismic resistance coefficient of O.CJ8W. The

total dead load is estimated to be equal to 134,069 kips resulting in a seismic base shear

of 5120 kips.

The design response spectra were developed for a maximum credible earthquake having

a 10% probability of being exceeded in 100 years and a maximum probable earthquake

having a 50% probability of being exceeded in 50 years. Members were to remain elastic

for the maximum probable design spectrum (MPDS) and the structure was designed to

avoid major damage and collapse for the maximum credible design spectrum (MCDS).

These two spectra are compared to the 1979 UBC requirements in Fig. 4.20.

The design analysis was done using the ETABS program with a model that was almost

identical to the SAP90 model as shown by the isometric view of the ET ABS model in

Fig. 4.21. When performing a response spectrum analysis, the method of combining the

modal responses must be selected. A comparison of the SRSS and _CQC methods of

modal combination for this building is shown in Fig. 4.22. Here it can be seen that for

4.14

the MPDS the story shears obtained using the CQC combination are approximately 17%

greater than those obtained using the SRSS.

Linear elastic response spectra for four recent strong motion earthquakes are compared

with the design criteria which includes Code, MPDS, and MCDS in Fig. 4.23.

Considering the building period of 2. 7 seconds, it can be seen that the seismic coefficient

specified in the 1979 UBC is about half of the spectral acceleration recorded at the site.

This would imply that had the building been designed for the minimum lateral forces

specified in the code, there would have been considerably more damage. Considering

the second mode in the E-W direction which has a period of 0.96 seconds, it can be seen

that the spectrum from the recorded motion exceeds the design criteria by approximately

100%. This content of the recorded motion tends to excite the fourth and fifth mode

(2nd mode in Y and X directions respectively) responses of the building.

The envelopes of maximum interstory drift indices are shown in Fig. 4.24. These results

indicate that the interstory drift indices due to the recorded ground motion exceed both

those due to the code required forces and those due to the MPDS in the upper stories.

This might imply some damage to both structural elements and nonstructural

components. It can also be seen that there is a bulge in the interstory drift envelope just

above the 18th floor. A similar but more pronounced bulge appears in the same region

for the MCDS, and for the Hollister and James Road recorded motions. There are two

factors which contribute to this behavior: (a) there is a change in column section at the

19th floor and (b) this building has a high second mode response due to the input

ground motions. The other bulge in the interstory drift curves occurs at the top of the

second floor and this indicates the stiffening effect of the shear walls that extend from

the base to this level. The maximum interstory drift index of over 2.2% under the James

Road record is extremely high. Story drifts (story drift angle) of this order are getting

close to the maximum that can be expected to be available from well detailed beam to

column connections.

4.15

The envelope of maximum story shears is shown in Fig. 4.25. Here it can be seen that

the 1979 UBC requirement is clearly a minimum. The story shears due to the MPDS

tend to approximate those due to the motion recorded at the site. However, the strong

contribution of the second mode causes the values due to the recorded motion to be

higher in the upper floors where they exceed the MPDS values by a substantial amount

and approach those of the MCDS. This indicates that in the upper floors, critical

members may be close to yield or in fact may have experienced some yielding of the

reinforcing steel.

RELATIVE DAMAGE POTENTIAL

The relative damage potential of these earthquake ground motions with respect to this

building can be evaluated by considering the elastic input energy. The time history of

input energy for this structure is shown in Fig. 4.26 for an elastic system. Here the eff~t

of the James Road record on this building when applied in the E-W direction is readily

apparent, being four times that of Hollister and twenty two times that of Emeryville.

This clearly indicates that the ground motion due to the Lorna Prieta earthquake was

not a severe test for this building.

COMPARISON OF U.S. AND JAPANEsE DESIGN CRITERIA

The building code used in the design of the Y Building was the 1979 UBC, however, the

designers wisely decided to use a site specific design response spectrum and dynamic

spectral analysis procedures to determine the lateral force requirements. The minimum

lateral force requirements of the 1979 UBC have been discussed previously. The

Japanese requirements consider two levels of earthquake motion, one having a peak

velocity of 25 em/sec and the other having a maximum peak velocity of 50 em/sec.

These two levels are similar to the maximum probable earthquake and the maximum

credible earthquake used in the design of the Y building with the exception that the

structure is expected to have a displacement ductility of less than unity for both levels

of earthquake under the Japanese code. This requirement allows cracking of the

concrete but only limited yielding of the steel reinforcement. In the figures that follow,

the maximum probable and maximum credible spectra are the site spectra for the Y

4.16

Building. The UBC 1988 spectrum is the spectrum given in the code for soft to medium

clays and sand soil conditions and this spectrum scaled by 0.5 is arbitrarily taken as

representative of the maximum probable condition. Note that both spectra are not

reduced by the structural system coefficient, R,.. The two earthquake time histories

normalized to a maximum velocity of either 25 em/sec or 50 em/sec are representative

of current Japanese design practice.

The envelopes of maximum interstory drift are shown in Fig. 4.27. The results presented

here show that in the upper floors the interstory drifts due to the MPDS are less than

those of the time history records normalized to 25 em/sec. As mentioned previously,

this is due to the ·higher mode response which is not estimated accurately in the MPDS.

It is also of interest to note that the normalized El Centro motion results in the critical

IDI in the upper 9 story levels. It can also be seen that the scaled 1988 UBC spectrum

does a good job of enveloping the normalized time histories and the MPDS. Japanese

practice limits the IDI for the 25 em/sec earthquake to 1/200. Therefore, this figure

indicates that this building does not meet this requirement in story levels 18-26.

Similar results are obtained when considering the time history motions scaled to 50

em/sec and the MCDS. It can be seen that the MCDS results in a good estimate of

maximum interstory drift in the lower 15 floors but fails to capture the maximum

response in the upper floors. As before, the normalized El Centro motion becomes the

critical motion for interstory drift in the upper floors. It is also interesting to note that

the 1988 UBC spectrum envelopes the normalized time histories at all story levels with

the possible exception of floors 28-29 where the comparison is quite close.

The envelopes of maximum story shear are shown in Fig. 4.28. Here it can be seen that

the story shear due to the MPDS is exceeded in the lower six floors (normalized El

Centro) and in the upper half of the building (normalized El Centro and normalized

Hachinohe). The scaled 1988 UBC spectrum envelopes the normalized time history

records in the lower 21 stories and gives a reasonable estimate of the shears in the upper

stories. The MCDS results in a good estimate of the story shear in the lower half of the

4.17

building but is exceeded substantially by the shears due to the normalized El Centro

motion in the upper nine stories.

IMPORTANCE OF PREDICTING SEISMIC RESISTANCE CAPACITY

From the results obtained in the evaluation of the seismic performance of the Y

Building using the linear elastic analyses described in the previous section, the following

observations became apparent:

1. When the linear elastic analytical models of the building were subjected to what are

considered as moderate earthquake ground motions, service or functionality level, such

as the motions recorded at or near the building during the Lorna Prieta earthquake and

the five records (normalized to a peak velocity of 25 em/sec) considered by the Kajima

Team, the building may develop some yielding of the steel reinforcement. This

observation is arrived at by comparing the values of the response parameters, maximum

acceleration, displacement, interstory drift and story shear, obtained from these records

with those that resulted from the modal spectral analyses using the MPDS and the ACI

strength method, which were used in the design of the building.

2. When the linear elastic models of the building are subjected to earthquake ground

motions representative of the safety or survival limit state, the values obtained for the

primary response parameters exceed those obtained from the MPDS (first significant

yield) by more than 100%. These ground motions are either those which have already

been recorded on similar site conditions in the U. S.(Hollister and James Road) or

which are considered as typical for this level of ground motion in Japanese practice.

RESISTANCE CAPACITY

A lower bound . of the strength capacity can be obtained by computing the lateral

resistance at first yielding. To recognize when this occurs, it is convenient to compute

the capacity ratio which is defined as the ratio between the internal forces (flexural

moment for the beams and interaction of axial and flexural forces for the columns and

shear walls) that result from the MPDS at each critical section of a member and the

. 4.18

yielding capacity of such section. The maximum capacity ratios (positive and negative)

for the beams in column line Wl are summarized in Fig. 4.29a. Here it can be seen that

the largest value occurs in the fifth floor level with all of the floors above the 2nd

having values above or near the calculated capacity. The column capacity ratios for

column line Wl are shown in Fig. 4.29b where it can be seen that all values are less

than the capacity. This data is further summarized in Fig. 4.30 which shows the

distribution of the maximum beam and column capacity ratios over the height. Here the

increased demand of the beams at the fifth level can be clearly seen.

The capacity ratios for the beams of column line W2 are summarized in Fig. 4.3la. Here

it can be seen that in the lower floors, the ratios are either close to or just above unity.

In the upper floors, however, there is a significant increase in the capacity ratios in the

exterior beams. This is primarily due to the reduced clear span of these members which

causes them to attract larger bending moments. The capacity ratios for the columns

which are summarized in Fig. 4.31b indicate that the demand in all of these members

is below the nominal capacity. The distribution of the maximum capacity ratios over the

height of the frame is shown in Fig. 4.32 where the increased demand in the beams at

the 22nd level is readily apparent. Analysis of these results reveals that the structure,

as far as its strength is concerned, has a considerable increase in demands (demands

larger than the supplied strength) at the twenty second story level, particularly when it

is subjected to motions in the E-W (X) direction. The main reason for this increased

demand is the existence of a relatively short beam at each end of the interior frame

along column line 2 which for the west wing is denoted as W2. This beam which is

between column lines A'B and EF has clear spans of 12.5 feet and 14.3 feet respectively

while the interior ones have practically twice the clear span length (26'). Because all the

beams along column line 2 have the same cross section, it is obvious that the stiffness

of the two exterior beams will be practically twice that of the interior beams and

consequently will attract significantly larger moments when the frame is subjected to

lateral deformations. Furthermore, because there is a significant decrease in the

reinforcement provided to this beam at the 22nd story level, the ratio of demand to

capacity has its peak value at this location, 1.51. Because the beam is has a relatively

4.19

low longitudinal reinforcement index in flexure ( p = 1. 7%), is doubly reinforced and well

confined (#4 ties at 4" = d/5), and in addition the maximum nominal shear stress that

can be developed corresponds to approximately 2.5 vT'c, it is clear that this beam can

develop significant rotation ductility without any decrease in its flexural capacity. In

other words, although the observed large demand could result in yielding of the

reinforcement, this will not impair the lateral capacity of the frame and therefore of the

whole structure.

The capacity ratios for the beams of a transverse frame on column line C in the north

wing (NC) are summarized in Fig. 4.33a. Here it can be seen that all demands are less

than the nominal capacities, however, it is of interest to note that the maximum demands

occur at the 28th and 22nd floor levels. Values for the column capacity ratios for this

frame are summarized in Fig. 4.33b where it can be seen that all demands are less than

nominal capacity. Here it is also of interest to note that the maximum demands (0.98)

are in the columns just above the shear wall (3rd level) and at the 22nd level. This can

be readily seen from the distribution of maximum capacity ratio which is presented in

Fig. 4.34.

From the above discussion it is clear that the first yielding will occur at the 22nd story

level when the corresponding base shear reaches a value of 13,900/1.51 = 9205 kips

rather than at the design base shear of 13,900 kips determined from the MPDS. These

values correspond to seismic yield coefficients of 92051134,050 = 0.069 and

13,900/134,050 = 0.104.

Analysis of the results together with an approximate analysis of the shear strength of the

22nd story indicates that the yielding of the structure would not commence until the

seismic base shear coefficient reaches a value that can vary from 0.14 to 0.17 depending

on the type of ground motion or in other words on how the inertia forces are distributed

over the height of the structure during its dynamic response to each of the different

ground motions that can occur at the foundation. The development of these base shear

coefficients has been confirmed by the results obtained from the approximate method

4.20

used by the Kajima research team. It should be clearly noted that depending on the

type of ground motion, the local ductility that will be demanded in the exterior, short

length beams in the 22nd story of the frame can be very large, on the order of at least

twice that of the global ductility demand. It should also be noted that in order to obtain

reliable estimates of the local ductility it is necessary to conduct 3-D nonlinear analyses

on a 3-D finite element model. The authors are conducting this work at present. A direct

estimate of local ductility cannot be obtained from the use of a stick (cantilever) model,

such as the one used in the simplified elastic analysis or a combination of stick models

used in the simplified nonlinear analysis.

SUMMARY AND CONCLUSIONS

This study has performed a detailed analysis of a 30 story reinforced concrete moment

frame which in plan has three equally spaced wings in the shape of a Y. The building

contains 583 condominium units and was completed in 1983. The building code used

for the design was the 1979 UBC, however, the designers decided to supplement these

requirements with site specific response spectra representative of maximum probable

and maximum credible earthquakes. Ambient and forced vibration tests were conducted

on the structure in 1983 near the end of construction. The building was instrumented

with 21 strong motion accelerometers at the time of the 1989 Lorna Prieta earthquake

and recorded peak accelerations which ranged from 0.26g at the base to 0.47g at the

roof. This caused only limited damage to nonstructural components and no visible

damage to the structural system.

System identification techniques were used on the recorded data to identify the vibration

mode shapes and periods. Moving window Fourier analyses were performed to

investigate changes in the period of vibration during the earthquake. The response

effects of torsion, rocking and soil-structure interaction were also evaluated using the

recorded data. This information was then used to construct a simplified model of the

building which could be used for parametric studies and code evaluations. Expanding

on the identification studies and the response analyses conducted with the simplified

model, a detailed, elastic finite element model of the building was developed using the

SAP90 program which contained 6,816 degrees of freedom. Using this general model,

4.21

seven different mathematical models were developed to investigate various modeling

considerations for reinforced concrete structures. These models were evaluated by

making critical comparisons with the recorded earthquake response and with the results

of the earlier ambient and forced vibration tests. One of the models was selected for

detailed comparisons which included floor acceleration time history, floor displacement

time history and floor response spectra. This model was also used to investigate the

response of the building to other ground motions which have been recorded during

recent earthquakes.

For the design analysis phase of the study, a detailed finite element model similar to the

SAP90 model was developed for the ET ABS program and validated against the SAP90

model. This model was then used to make critical comparisons between lateral code

loads, site spectra and recorded ground motions considering design parameters such as

maximum lateral displacement, maximum interstory drift index (story drift angle) and

maximum story shear. Effects of modal combination, P-delta and 2-D versus 3-D

modeling were also investigated.

Working independently from the same database, the Kajima research team developed

a 3-D elastic model of the building and investigated the design relative to current

Japanese design practice. Critical comparisons were then made between U.S. and

Japanese seismic design requirements.

In order to evaluate the damage potential of the building, the authors performed a

detailed capacity check of the individual members of certain critical frames using the

maximum probable design spectrum. At the same time the Kajima researchers used the

results from their 3-D elastic model to develop a simplified 3-D inelastic model. The

damage potential of the building was then evaluated by analyzing the results obtained

from these two distinct approaches.

Based on these extensive studies, the following general conclusions are presented:

4.22

1. Comparison of the dynamic characteristics of the building identified following the

earthquake with those obtained from ambient and forced vibration tests at the end of

construction indicated that the fundamental period of vibration had increased by as

much as 59%, however, this change is not considered unreasonable based on changes

reported in other RC buildings.

2. Moving-window Fourier analyses indicated that there was no significant change in the

dynamic characteristics of the building during the earthquake.

3. Analyses of the recorded data indicate that there was very little torsional movement

in the building and that soil-structure interaction and rocking effects were not significant.

4. If the dynamic properties are available or if the results of a detailed analytical model

are available, a simplified model· can be constructed which will produce good estim.ates

of the response and can be used for parametric studies and overall response evaluations.

5. Detailed 3-D finite element models can be used to obtain an accurate estimate of the

dynamic response prior to yielding of the reinforcing steel, however, due to cracking, RC

structures actually become weakly nonlinear systems at low lateral force levels

representative of the service loads. For this reason, it may be necessary for the designer

to consider more than one analytical model when evaluating the dynamic response.

6. Calculation of the elastic energy input to the structure by the recorded base motions

indicates that the input in the East-West direction is 2.5 times that in the North-South

direction although the fault rupture was predominately in the N-S direction. A further

study of input energy indicates that the recorded motion at the base of the structure was

not a very severe test for this structural system. The ground motion recorded at

Hollister which is much closer to the epicenter of the Lorna Prieta earthquake resulted

in an input energy that was 5. 6 times that of the recorded base motion. Using the ground

motion recorded at James Road during the 1979 Imperial Valley earthquake resulted

in an input energy that was 22 times larger than the recorded base motion.

4.23

7. This building was designed to remain elastic (no yielding of the reinforcing steel) for

lateral forces obtained from the MPDS. These lateral forces resulted in a base shear

which was almost 2. 7 times the base shear due to the lateral force requirements of the

1979 UBC. Results of the analyses show that had the building been designed for these

minimal code loads, the damage resulting from this earthquake would have been much

more substantial.

8. Acceleration spectra for the recorded base motion and the motion recorded at

Hollister indicate that both records have a strong acceleration content in the period

range of 0.9 to 1.2 seconds which includes the 4th and 5th modes of the building (2nd

mode E-W and 2nd mode N-S). These spectral accelerations were not included in the

relatively narrow band site design spectra. This causes a higher second mode response

and results in lateral forces in the upper half of the building which are significantly

higher (as much as 50%) than those predicted by the MPDS.

9. For this structure, use of the CQC modal combination method with the MPDS

resulted in story shears that were more than 17% higher than those obtained using the

SRSS method. Even larger variation was obtained for the MCDS.

10. The interaction of axial load with the lateral frame displacement does not cause a

significant increase in the total lateral displacement even for the James Road ground

motions which produce interstory drift angles of more than 2% at certain levels.

11. The lateral base shear coefficient for this building based on the 1979 UBC

requirements is 0.04. The base shear coefficient obtained from the MPDS is 0.08,

whereas, the value specified in the Japanese code (BSL) is 0.10. Since the lateral force

requirements of the 1988 UBC are similar to the 1979 UBC, it can be concluded that

for a building of this type, the minimum Japanese lateral force requirements would be

2.5 times greater than those of the United States.

4.24

12. The two levels of earthquake ground motion (normalized to peak velocities of 25

em/sec and 50 em/sec) used in Japanese practice are similar to the concept of the

maximum probable and maximum credible spectra used in the design of this building.

However, due to the deficiencies in the site spectra discussed above, the normalized time

histories give a better estimation of the actual response. However, Japanese practice also

requires that the displacement ductility of the structure under both, motions be less than

1.0. Based on the results of their studies, the Kajima researchers conclude that the

upper stories of this building are not adequate when compared with Japanese practice.

13. Use of the 1988 UBC response spectrum for soft soil sites and with a structural

system factor, R..,, equal to unity results in response envelopes which are similar to those

obtained following Japanese design practice.

14. Capacity ratios calculated by the authors show a good correlation over the height of

the building when compared to the ductility ratios calculated by the Kajima researchers

using their simplified 3-D nonlinear model. However, evaluation of the capacity ratios

indicates that the ductility demand of certain critical members of the frame may be

considerably higher than the average ductility demand reported by the Kajima study.

Therefore the authors believe that to quantify this demand in a reliable manner it is

necessary to perform a detailed 3-D nonlinear analysis.

15. Evaluation of the capacity ratios and the nonlinear response analyses indicates that

the yielding seismic resistance coefficient for this structure is approximately 0.17

indicating that the building has an inherent overstrength of more than 100%.

4.25

L..EVE.. I Loc;.noN I COMP. I Fii.ENA.\tE I P:AKAC::. I PE.~VE!..' I P:AK OIS?.u 1

(~JS~ (c::n/Sa<:j [cmj I 31st Level West Wing 350 PL.A.ZA4 %.--=7.4 30.59 S.a:!

31st Level Soutn Wing osa PLAZAS 298.7 62..77 17.16

31st Level North Wutg 290 P!..AZA6 466.7 70.06 17~2

31st Level Cantral Core 3SO P!..AZA7 240.3 2.6.05 5.45

31st Level Cantral Core 250 PLAZAS :!SS.1 77.42 '19.45

21st Floor West Wing ~so PLAZA10 1S5.6 13.02 ~.77

21st Floor Sc:utn Wing 050 PUZA11 155.4 2.5.05 a.~

21st Fleer North Wing 290 P!..AZA12 2.:!5.9 30.06 s.eo 2'1st Floor Cantral Care 350 PLAZAS 179.4 15.00 s.sa 21st Fleer Central Core 2.60 P!..AZA1S 2~9.2 32.1 6.76

1 :itn Fioor West Wing 350 P!..AZAlS 206.3 19.21 2.77

13tn Floor Soutl'l Wing 050 PI..AZA17 2'1S.4 3~.42 7.SO

13th Floor NOt"w., Wing 290 Pt.AZA1S 303.0 40.64 6.1,

13tn Fieor Cantl'Gl C.:re ~.:a Pl.AZA13 2.SS.S 25.:;7 4.24

13th Fie:::r Cantl'Gl Core 250 PI..AZA14 253.7 40.13 9.10

Gtaund Fiocr Nel"w., Wing 350 PI..AZA24 173.!. 1S.S1 2.50

Ground Fleer North Wing 250 ?UZA.24 -208.:3 37.~0 s.es Ground Fioor NertnWing UP P~:l 41.6.8 .d..i7 0.94

Grouna Floor West Wing UP Pl.AZA19 ;s.s 4.:;6 0.5-:J

Ground Floor Soutl'l Wing UP P~O SS.4 4 .,. 0.87 --I G:cur::: Ficor Central Core UP P!..AZA21 37.3 4.24 O.i':

Ground Soutn Free Field 350 Pl.AZA1 210.:3 21.53 ~.75

Grcunc: Scutt! Free Fieid UP P!.AV-.2 sa.s 4.=4 O.i.:.

Ground South Free Fie!d 260 P!..AZA3 2.52.!! 40.S4 8.13

Ground Ncr-.. '1 Fr~ Field 350 PUZA.25 178.7 15.74 2.:7

Ground North Free Field UP Pl.AZ=.25 82.2 s.:;:z 1.01

Ground NoM Free Field 2.!:0 Pt.AZA27 225.1 37.94 6.0i

Table 4.1 Peak responses in the building during the Lema Prieta earthquake.

4.26

COMPONENI ~SO"' (NS) I COMPONENI2!0~ (EW) I PARAM.c.E::\ 1stMOOE 2nd MOOE ~td MOOE I 1st MOOS 2nd MOOE ~td MOOE I

Period (sec} z.:s 0.89 0.46 z.ss 1.07 o.:; FreQuenc'/ (Hz] 0.:39 1.12 Z.1S 0.:37 0.94 1.81

Camping Ratio (%} Z.~Z.9 2.5-3.0 - 2.5-2.9 2.5-3.0 .

3,st 1.00 1.00 1.00 ,.00 1.00 1.CO Mode Shape 2,St 0.69 -o.36 -1.02 0.63 -Q.29 . -o.79

13th 0.38 -Q.S2 o.eo 0 ~. ..J- -Q.84 0.:34

Table 4.2 Translational dynamic characteristics Identified from earthquake records.

. ::.ARTHOUAK- --::~aNc:J COMPONE.l'.,ll MOOS FO~CEJ VI BAA TlON AMBIENT VISRA'i'ION . c J-\C:.-r" --·

I 1 ... -· 1.sa 1.71 2.:9

:;:o" (NS) 2nd 0.60 o.:s o.es 3rd 0.:32 0.::32 0.4-6

1st 1.63 1.71 2.6S

2sa· (EW) 2nd 0.60 0.59 1.07

::3rd 0.:32 0.32 a--.::

Table 4.3 Comparison of translational periods of vlt:ratlon

4.27

Table 4.4 Comparison of Computed and Recorded Modal Periods

Model Mode 1 Mode 2 Mode 3 Mode 4 ModeS Mode 6 N-S E-W Torsion N-S E-W Torsion

AMBIENT 1.77 1.69 1.68 0.60 0.60 O.S9 TEST

Model-l 2.00 1.99 1.89 0.70 0.70 0.62

Model-2 2.34 2.34 2.16 0.82 0.82 0.72

Model-3 2.65 2.65 2.41 0.94 0.94 0.82

Model-4 2.74 2.73 2.49 0.97 0.97 0.85

Model-S 2.54 2.S4 2.32 0.90 0.90 0.78

Model-6 2.91 2.84 2.56 1.02 0.96 0.86

Model-7 3.15 3.08 2.76 1.12 l.OS 0.94

RECORDED 2.69 2.59 1.07 0.89

4.28

Figure 4.1 General view of the ten-story RC building.

Figure 4.2 Three-dimensional finite element model view of the building.

4.29

Figure 4.3 Typical floor plan of the thirty-story building.

4.30

NORTH WING SCUT'ri WING 31ST (ROOF), 21ST, & 13i'H FLOORS

___1'1--F==;:::_'--!.:~ 1 l RCCF LRrs'j : I ~-. I ~J--~--~1 '

J : : I I

~--~, ~,--~--~~' . ~--~: ~~--~:----~; l

f----l: l.t---: ___ :__,j l

I· • I.,__~=---------: F : i -~-~ _:_ ...... : _....;: ~--' I

~I ~ ~! I • 1 ~ ~ ~ ! E:3 '--',.__ ,-----i: -~s~ : = ' ,

- 1

1 ?t-:~:.:.:.: :_:_ ..... qj--;1

,__, _ _...j GnOUNO FLOOR GRCUND FLOOR

~.o---.... 1

SENSORS

-7 HORIZONTAL • VERTICAL

Figure 4.4 Instrument locations in the building.

FOIIOIEII AMruntOE (cmlu<)

lOr-----------------------------------------~

u so 40

]0

-- lltt noon. J60' •• ••• • GIIOlJIIO noon. uo•

:: .. }L -~Y~ o~~.~----~~~-~-~-~-u~~--~~~~~~-~~~~-~~~-~~1 0 l

FOEOUEIIGY 0 hl

fOUOIER AMrUWOE l<mlu<) J5r-----------------------------------------~

-- 2111 noon. 360'

JO •· ••• • GIIOUIIU flOOn. 310'

u

lO

5

1 l fllEOUEIICY Phi

fOll/liER Al.lruniDE (cmlucj 50r-------~----------------------------~

40

]0

JO

10

-- n•~> ft oon. 360' •••••• onou11o noon, uo•

1 FOEOUEIICY Phi

···~ ~~ l

A) FOURIER AMPLITUDE SPECTRA

111~1

JO

IS

10

s

ll(wJ

lO

• '

ll(wl

' s

l

J

lllllEVEl· CEIIIAAl cone. 160'

J fREQUEIICY Phi

2 hi lEVEL • CEIIJAAL cone . 260'

2 fRfOUEIICY llhl

lllh lEIIEL • CEIITAAl cone · 260'

J FOEOUEIICY flhl

D) TRANSFER FUNCTIONS

Figure 4.5 Fourier nmpllhtde spoctrn ond trnnsfor functions In the conlrnl core of tho hulldlno for lhc 260° component

~ w .......

4.32

r G ..._ ___ ...;.... ___ _

tstMOOE

:= r .. ' .. -Zl

IS

.V

~~:r \c

:[ ....__ ----~-1 Figure 4.6 Comparison of translational mode shapes ot the building (:;SQ0

) obtained through three dlt:erent procedures.

- ...:.,.su.-~:~ -~t£.:J

a~· .. ·5

·IC !__ _______ ___:~------------------.._;

a IC :o TIME (se:J

Figure 4. 7 Ccmoar:scr. ct measurec anc calc~lated res;:c:-:se at the root level ct c:ar:::al · • ·h .. ·· .. ( - ,.. • "c:0°' core o. , e ... ~uctn~ c:::rr.:"'cne ... .:.- J·

4.33

ROOF ASSOt..UTE .\C~~~ON (gzisl :CC - Mf.J'$U"t~

-~ ~~~~wr~'{'l'v-A/"'_;;::~~~ .. -~ r~~w -~~ ~----------------------------------------------------------~

:co 100

0

•I CO

.:c;, -~oo

::0 100

0 ·100

•ZCO -:co

Figure 4.8

0 10 TIME Csecl

lntluence ot higher modes In cafc:Jiatec ac:eleratlcn time hls:::ries at the root ct ~he builcir.g {component :l;Oj.

4.34

figure 4.91sollletric ..new of Y-Building, SAJ'90.

Figure 4.11 Plan ..new of 2nd vicration

roode shape sAP90.

Figure 4.10 Plan vieW of lst vioration

roode shape, sAP90.

Figure 4.12 Plan view of :lrd vibration

mode shape, sAP90. > I

; I

\ I

\ 1

\ I

4.35 ,.. ::-:: 1c-! 1c:Y

~=---------·~'--~·-·-·~"-"'~----~~--~--~ - - CR.a..um:~ ~_..

- -- -- P.EC:.O.oEO C: -YJ

--~~~~~~r-~~-~.~-~-~r-~~~~~--~.~.~.~ .. ~.~1 2

10-2 10-I toO 10L 102

PERIOD

Figure 4.13 Calculated vs. recorded roof spe~ra, .5% damping.

Figure 4.14 Calculated vs. recorded accelerations, roof, 5% damping.

4.36

-~.c.urrc:::~ !:·• ----- 1'£c:::I'IXQ (..;,j

=~·~~~~~~~~~~~~~~~~ - ;c-2 PERIOD

Figure 4.15 Calculated vs. recorded spectra, 21st floor.

~~~~-2~--~~~a-_'--~--~~~----~~~c_l._~~~:2 - --~Tt!l 0:-'1 C'!:

-----~£ .... ~

.. : ... , laW

PE:?.IOO

Figure 4.17 Calculated vs. recorded spectra, 13th floor.

:.oo 10.c:: 2c.cc ~oooo Oo!O .;.._ ;;...,_ ___ .;_:;,:;;...,_ ___ -:1-------~~ 0.!0

~ ~ ~ - 2isr ORE ~ ~ -·- 2 ,Si CORE REC. - '

• ~0 .. ~

z l r IL .. 3 ~:~ (t ~~ ~~ ~r

0 0.10 .10

'< c:: ~-cote w u u <-o.:lO

~ : • 3 ~ :: ~ j ~ '!

-o.!O o.co

~'-

• 0

~ ·:: "· I~ '1l.~.f~~L~1· :·..-.:; ~I" o:i on] ~~ .. i . 'I l!Y ~ U7 E

-o.10

1 l

0.

IOoOO 20o00

TIME (SECONDS)

I I

-o.:lo

-Q.!O JO.OO

Figure 4.16 Calculated vs. recorded

acceleration, 21st floor.

ooco to.oo zooo. o ~ooco ~:o~---~-~------~~~----~·o~o

" 1 - -

I . - d"TH CORE :.:.L... ~ . :;

0"" ·_,­~ ·--. c; . -z C ColO

'< c::: w _: -0.10 u u c.; <

-~o.!O

-.... -.... __

:: . . : -. . -. ..

-o.c:

..

1 •• •• 30th CORE RECo ----- • . t,l'\.,,.. ! I E ---

1 • ~ ':

~~~l~! ~ 0.10

• 0

,L~jll N\V oJ ., E • lo•o oo I o ), ol -~ 0 • · "?!r1\! ll I { r. ~yfw:=vY~~;..-"--1 rn it E r : 1 I' ~ il :::

-Oo10

I . E ..

.... ...... • ..,.. ""'0

ofi'M'E (sc:co'·N'os) ~

-0.!0 :lOoCO

Figure 4.18 Calcul:lted vs. recorded

acceleration, 13th floor.

0.00 6COOO

'

-- E-W ·•••••• N-S

z 40000 ......._...

>­C) e::: w z w 20000

1 1-:J 0... z

1

l ~ 0,

0.00

4.37

10.00 20.00 ~c co ~

A~~~ ~

-······-----··-----~ •A .•••• I

•' ... .- 1-. . 1-. .. ··-

. . . ~ ~

' 10.00 20.00 Jo.oo TIME (SC:CONDS)

-Figure 4.19 Comparison of elastic input energy, E-W vs N-S.

-- MAX. F'R08A8L£ ---- MAX. C~EDISL:: - - uec t9i9 t.O

~ 1

~ -..... -

[ --- t 0.5

------ ~ -- ·----------~

~ 0.0 .

0

----- I ..... ' .. ~ .~ .-. -:-.-:- .~ ~.-:- .-:--:- -:-.-:-.-: :-. ~ .;- 0.0

I 2 J 4

PERIOD (SEC.)

Figure 4.20 Site spec!ra vs. 1979 UBC spectrum.

>­a:: 0 I--

4.38

-..., .. ..., :­

~:-

~ :-: ~ -.-.:...::::~

-/ ~~~~:p=: ~~~~~y,

. ':!:;;

-;· . ~

J •

. UNOEF"Ortrt£0 SH .. P£.

iOP Jl eor 1

OPTIONS H !OOErl LINES

E. TABS

Figure 4.21 Isometric view of Y-Building, ETABS.

.30

0 10000 • • • • 0 ••• . ...

I~"'- I

j \'\~ j

l ~--

20000 .30000 • ' ' I

40000

~0

', • • ' • . ' I • ' ' • ' ... .. ! I I

--19i9 CODE -MAX. -MAX. ~~EJ. SRSS --

~R08ri<SOJ \\ ~ -MAX. ~Ros. cccj

~ \ \\ \~ -MAX. ~~E::l. CCC --J I I ' ' ' \ '

l \ ~ • I \l L l. ~

~ l l. • ~ l. ~ \ '\ l l. ~

J t ~ \ \ \. J l. \. '\. 1 t ~ ..

l. ..

20

U1 tO ~ ! \ '\ , ' I \

J I k \ \ \l I 10

I \ F

l L \ l. \ •. I ~ • .. t \ ~ \

~ • 1 + \

I l. I ~ • • l l ~ ~ l

l • ' l • 0 I ' • • • • • • o • . . . . . . . . ..... . . . . . . . I 0

4.QQCO 0 10000 20000 .:sc6ao STORY s;~E.:i.P. (KIPS)

Figure 4.22 M<J.x:imum smry she:J.r, SRSS vs. CQC.

4.39

0.0 1.0 2.0 f t • ' ' ' ' • I • ' r ' r • • r r l

1.50

3.0 4.0 5.0 I f f I t t t t t o f 1 t t I t t I f

Gl" a" II HACHINOHE (1968) A== 6 • EMERYVILLE (1989) a • • • o HOWSTER 1989)

MAX. PROS. (SITE) --- MAX. CRED. (SITE) --usc 1979 -- JAMES ROAlD (1979) ~ ..... usc 1988 -- usc 1988 0.5 .

i:l 0.00 I ••••• ' •• ' ~ •••••••• ' : ' •••• ' ••• : ' •••• ' ' • ' I '. ' •• I •• ' I

0.0 1.0 2.0 3.0 4.0 5.0

PERIOD

Figure 4.23 Response spectra vs. design spectra.

4.40

c.cco o.:o: 0.010 c.:z~ o.c:: c.c..:::·:

- ~979 coos tO

- ~AX. F'ROSt(C::C) - !,jAX. CRE:DI(CCC) - ~LAZA SASE: - ,OLUSiER(J'lS) •••••• .. :A-MES RO~O

I I . . ,0

o.oco 0.005 0.0 t 0 0.0 t 5 0.020 0.025 0.0.30

INTERSTORY DRIFT

Figure 4.24 Envelopes of maximum interstory drift.

0 10000 20000 JOOOO ~000 50000 I, , , , , , , . I., ! , , , o,,,, 1, •, • • •,, • I

- 0 I I

.,. ~ i'\~ .... ~ t9i9 boe: ....

~I \ ···-.. :=: ?t.A'~·r8Asc:-\ ··· .... +- 1-!0LUSC:;;(NS) t . '. '\. "l:---- JA.'w!ES I' ROAD _J J \ '. '-1 ··. 1.1 J l ~ \ ' ·. ~ 20 I I I 20 > I ~ ~ I ; \1 ~ L L.:.J J ~ ~I; •.1 t ~ 1 i \. \r ·.

j \ X v~ ·. ~ J t ( l\' \\ \. ~ 0 ~ I • \ •.

t/110-l ~ ~ \ •\ \ tO

j \ \~\ \ '""\ \l .. \ ~ ~ ; t! \ l ... t j i .l ~ ~ : ~ 1 r • 1 ~ ~ · l 0, ......... , ......... , ......... , ........ , ......... ,0 0 1 COCO 20000 JOCCO 40000 ~0000

STORY SHEAR (KIPS)

Figure 4.25 Envelopes of ma:"<imurn stary shear.

4.41

0.00 1 0.00 20.00 30.00 2000000~'~~~~~·~·~' ~·~·-·~~~·~· ~·~·~·~·~·~·~·~·~·~'

JAMES ROAD ,.--.... (f) CL

~1500000~----------~--~----~~~-------+ .

z

~1000000~-------+--+-----------~---------+ Q:: w z w ~ 500000~,~------~--~----------~----------~ ~ J 0... -1 z J

J. EME~YVILLE 1 r

t l t I I I I I '

0.00 10.00 20.00 30.00

TIME (SECONDS)

Figure 4.26 Elastic input energy, earthquake ground motions.

4.42 0.000

' 0.005 O.OZO 0.025 O.C:!O

•' • f •'.' I • ' ' '• •. '•

:;o~l--~~~~~~----~------~----7-----~: :;a

cj20~~------~~--~~~~------~----~----~20 ~ .,

~ ~ ~ MAX. P~08A8L:: 0 --;- MAX. ~EDIBLE

tn 10~----~~~~~~a----~'~HA~~~~!~~~E~~~~~~~.~~=~~~~~~=~~--~10 --!- EL CENTR0(25 e{n/s) - -j- EL CENTR0( 50 c:m/:s) --'! USC 1 !88 S?~CTRUM

1

_ o.sxu·r .. S?ECTRUM

0 1 •• Jii •.•. 1 tl, .. l,,l,,,,,j,Jiil'iliilll,,.!t.illil, .. ;t,,,jl 1 0 0.000 0.005 0.010 0.015 0.020 0.025 0.0.30

INTERSTORY DRIFT

Figure 4.27 Effect of design criteria on interstory drift.

- MAX. PROSAa:: - MAX. CREJISUE --- ~CHINOHE}25 c:m/sl - HACHINO~~~SO c:m/:s - EL C::NTRC 25 c:m/s --- EL CENTRO :0 c:m/s

- USC t 988 Sii'E:CiRUM - Ct5xUE!C ee p?ECTRUM

Figure 4.28 E:fect of desip criteria on story she:1r.

J./1 • 'i1 ,ql • 8 z. ·88 . 1L ·'19 ·81 .9~ .so --

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4.44

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Figure 4.30 Maximum capacity ratios, column line Wl, MPDS.

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4.46

0.0 0.5 1.0 I ' I I ' ' I ' I t I I ' I

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CAPACITY RATIO

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4.49

REFERENCES

1. Governor's Board of Inquiry on the 1989 Lorna Prieta Earthquake, "Competing

Against Time," State of California, May, 1990.

2. Maley, R., et al., "U.S~ Geological Survey Strong-Motion Records From the

Northern California (Lorna Prieta) Earthquake of October 17, 1989," Open-File

Report 89-568, Department of the Interior, United States Geological Survey,

October, 1989.

3. McVerry, G.H., "Frequency Domain Identification of Structural Models from

Earthquake Records," Report EERL 79-02, Earthquake Engineering Research

Laboratory, California Institute of Technology, Pasadena, California, 1979.

4. Stephen, R.M., Wilson, E.L., Stander, N., "Dynamic Properties of a Thirty-Story

Condominium Tower Building," Report No. UCB/EERC-85/03, Earthquake

Engineering Research Center, University of California, Berkeley, California,

April, 1985.

5. Wilson, E.L., and Habibillah, A., "SAP90 User's Manual," Computers and

Structures, Inc., Berkeley, California, July, 1989.

6. International Conference of Building Officials, "Uniform Building Code," 1979

Edition, Whittier, California, 1979.

CHAPTERS

EARTHQUAKE RESPONSE AND ANALYTICAL MODELLING OF THE JAPANESE S-K BUILDING

by

Chukwuma G. Ekwueme Gary C. Hart

and Thomas A. Sabol

Description of building.

Description of earthquakes.

Response of the building.

5.1

CONTENTS

Chiba To-Ho Earthquake.

Tokyo To-Bu Earthquake.

Computer Analysis.

Description of the model.

Mode shapes.

Time history Analyses and Response Spectra.

Inelastic Analysis of S-K Building

Conclusions.

5.2

DESCRIPTION OF E ING

The (S-K Building) is a 30 story concrete apartment building

located near Tokyo and constructed by the Kajima Corporation in

March 1987.

Figure 1 shows floor plans of the building. Figure 2 shows

sections through the building at grid lines A and c. The strength

of the concrete varies along the height of the building as shown.

The foundation of the building consists of 3m thick girders

along the column lines, piles beneath the interior columns and a

continuous bearing wall on the exterior of the building. The

bottom 1.3m of the piles and exterior bearing wall penetrate a

layer of alluvial sandy gavel at about 32m below ground level.

Instruments were placed at the roof, ground floor and 35m

below ground level (beneath the deep foundation).

DESCRIPTION OF EARTHQUAKES

Two earthquakes were considered in the study - the Chiba To­

He Oki earthquake and the Tokyo To-Bu earthquake.

The Chiba To-Ho Oki earthquake occurred on December 17, 1987

at 11:08 JST. It had a Magnitude of 6.7 and its hypocenter was at

35.2N, 140.29E at a depth of 58Krn. At the ground floor of the

building a peak acceleration of 0.04g was recorded during the

5.3

earthquake. Figure 3 shows the 5% damped response spectrum of the

ground motion at the base of the building in the x and y

directions compared to two popular California design earthquakes,

EQ-I and EQ-II [1]. EQ-I corresponds to an earthquake with a

fifty percent chance of being exceeded in fifty years or a chance

of occurring once every seventy two years. United States

buildings are designed to remain essentially elastic up to this

level of earthquake. EQ-II is the maximum credible earthquake and

has a ten percent chance of being exceeded in one hundred years

or a return period of nine hundred and fifty years.

The Tokyo To-Bu Earthquake occurred at 5:34 JST on March

18, 1988 and had a magnitude of 6.0. At the ground floor of the

S-K building peak acceleration of 0.064g was recorded during the

earthquake. The 5% response spectrum of the ground motion is also

compared with EQ-I and EQ-II in Figure 4.

Since ground motion at the base of the building during both

earthquakes was much smaller than EQ-I, no substantial inelastic

behavior of the building is expected to have occurred during the

earthquakes.

0 C). ••• ~,:.. .... ~-.-.s>·-o= .. ~--...:: I I

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@ 81 ..,,

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Figure 1

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Typical floor plans in the S-K building.

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Figure 2 section through frames in S-K building.

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ACCELERATION RESPONSE SPECTRA ~ 10-00 EQC£ IX-oornDHI. Eo-! ! Eo-1

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Figure 3 Response spectra for Chiba To-Ho Earthquake, EQ-I and EQ-II.

-J

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0.4

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5.7

ACCELERATION RESPONSE SPECTRA ::«'10 TO-tAl [QK[{X-OR[ClXlH). [~I&: [~I

I

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ACCELERATION RESPONSE SPECTRA iOO'O TO-&J [QI[(Y-OIRI:Cllli). [~I&: [~I

I

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(b)

Figure 4 Response spectra for Tokyo To-Bu Earthquake, EQ-I and EQ-II.

5.8

RESPONSE OF THE BUILDING

Chiba To-Ho Earthquake

Figure 5 shows the first 40 seconds of acceleration recorded

at the ground floor and roof of the building in the x-direction.

It can be seen that the strong ground motion starts about 20

seconds into the record, probably when the surface waves arrived

at the site. (The difference in arrival times between the s-waves

and P-waves is about 10 seconds). The frequency content of the

acceleration at the roof is different from that at the ground

indicating that the fundamental period of vibration of the

building is different from the of dominating periods in the

ground motion.

Figure 6 shows the acceleration recorded 35m below ground

level in the x-direction for the same time. Comparing this with

the acceleration at the ground floor of the building it is seen

that there 'is an increase in acceleration and change in frequency

content between the bedrock and the ground. This shows that the

32m deep layer of soft soil between the ground floor of the

building and the sandy gravel on which the deep foundation is

supported has a significant effect on the ground motion

experienced by the building.

Figure 7 shows the acceleration at the roof and ground floor

in the x-direction later in the record. In Figure 7(a) a

fundamental period of approximately 1.75 seconds dominates the

5.9

~CC£!.IFATION AT GROUND FLOOR X..f.ii!!J:IUj ICB ~ £N111W1l1987l

0.1 ,..-----------------------~

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Figure 5 Acceleration at ground floor and roof in x-direction (Chiba To-Ho Earthquake}.

~

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Figure 6

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5.10

ACCELERATION 35 MffiRS BELOW GROUND H~RI:ClXJI IOlB\ 10-1() fiR~ 19871

-·J.l l...---------'-------i--------~--------1 c :o 10

7a.!E (stCOIIJS) 30

Acceleration 35 meters below ground level in x-direction (Chiba To-He Earthquake).

40

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5.11

ACCElERATION AT ROOF &: FIRST FLOOR x-~Ctnl 1~ TO-Ill £Mil0lf4. 19871

T, ~1.75s. 7: :::!-0.47s

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ACCELERA.TON AT ROOF &: RRST FLOOR x-~m 10\FA TO-fO £M1lCWL 1987)

80

0.04 .-------------------------

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110 120

Figure 7 Acceleration at roof and ground floor in x-direction (Chiba To-Ho Earthquake).

5.12

response. A secondary period of vibration of about 0.47 seconds

is also observed. Later in the record, with a smaller ground

motion input, a period of vibration of about 1.8 seconds is

noticed.

The response of the building in the y-direction is similar

to that in the x-direction as seen in Figure 8. The higher ground

motion also starts about 20 seconds into the record. In Figure 9

the mode with a period of vibration of about o.s seconds

dominates the response and in Figure 10, with a smaller ground

motion input, the first mode of about 1.7 seconds governs.

5.13

ACCELERATION AT GROUND FLOOR Y-:ft£C'OON lot~ T(>-t«l ~ 19871 0.1 : ______ ___:.:_:.:....:.......=.:..:.:.....:...:::..:::....:.:.=..:.:.:::.:_ ______ __,

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(a)

ACCELERATION AT ROOF Y-DREC'OOH lot~ T(>-t«l ~[ 1987)

JO 40

i -ll --------'------....:.._ _________ __J

:o

(b)

Figure 8 Acceleration at ground floor and roof in y-direction (Chiba To-He Earthquake).

40

Figure 9

5.14

ACCELERATION AT ROOF ~ -~.Jl[Cik)j (~ To-~ ENffiQJI,'(f. 1987) 0.1 .---------:....:.:.....:.__ ____________ ---,

0.05

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Acceleration at roof in y-direction (Chiba To-He Earthquake) .

Figure 10

I '

5.15

ACCELERATION AT ROOF &: GROUND FlOOR Y -ORI:eoctl (01&\ T~HO fJJU!Mt 1987)

0.05 r------------------------~

-0.04 ,__ _____ ....;.._ _____ ............ ___________ __

50 iS

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iO TlA£ (S£COOS)

--+- QlOOI() n<X:fl

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Acceleration at roof and first floor in y-direction (Chiba To-Ho Earthquake).

80

5.16

A better understanding of the periods of vibration of the

building is obtained by the use of response spectra. The response

spectrum for a particular motion is a plot of the maximum

response that single degree of freedom oscillators of different

frequencies experience when excited by the given motion. A system

responds with significantly larger amplitudes when excited by a

motion close to its natural period of vibration (resonance). Thus

a response spectrum for a given acceleration record will would be

characterized by peaks at frequencies that dominate the response

of that part of the building.

Figure 11(a) and Figure ll(b) show the acceleration response

spectra in the x and y-directions, respectively of the roof,

ground floor and 35m below ground floor. Twenty seconds of the

record - the time between 20s and 40s was used in calculating the

spectra since it is during this time.that the highest

acceleration was experienced by the building. The response

spectra were calculated using the program SRS2 developed by

Professor Gerard Pardoen of the Department of Civil Engineering,

University of California, Irvine on the spreadsheet LOTUS 123

[ 2] 0

The x-direction, shown in Figure ll(a), shows peaks in the

roof response at frequencies of about 0.57Hz (1.75s), 1.3Hz

(0.79s) and 2.3Hz (0.44s). The response spectrum of the ground

floor shows a definite peak at 2.3Hz (0.44s) and this is probably

the fundamental period of the 32m deep layer of soil beneath the

building.

..:::;

~

~ '-' !;,!

..:::;

~

~ '-' !;,!

5.17

ACCELERATION RESPONSE SPECTRA X-OIR[CIKJI (~ TQ-ID fJI!l!W4. 1987)

0.4 r----,..----:-------::------:------:----.

OJ

01

0.1

0~~--~---~---~---~--~~--~ 0 0.5

-e- Reef

1.5 fR[QJ!NCY (Hz)

~ GlOUlll

(a)

~ 3511 ea.cw CRill.

ACCELERATION RESPONSE SPECTRA

2.5

Y -OR£CllON (~ TO-HO fJ.QJ!M£. 1987) 0.4 r----;-----.--__;_-r-__ _:_,....-....,--;; _ ____,,.....------.

OJ

01

0.1

0.5 1 5 fR£00!NCY (Hz)

~ GlOOlil

(b)

~J

2.5

Figure 11 Acceleration response spectra for S-K Building.

5.18

In the y-direction peaks are observed in the roof response

at frequencies of 0.6Hz (1.67s), 1.15Hz (0.87s), 1.75Hz (0.57s)

and 2.15Hz (0.47s).

By normalizing the response spectra calculated for the roof

with that calculated for the ground floor, the peaks in the roof

response which occur due to ground motion of that frequency are

filtered out. This spectral response ratio is shown in Figure 12

for both directions. From the figure the first mode in both

directions is seen to have a period of 1.67 seconds. The second

mode in the x-direction has a period of 0.5 seconds and the

second mode in the y-direction has a period of 0.48 seconds.

Tokyo To-Bu Earthquake

Figure 13 shows the first 40 seconds recorded at the ground

floor and roof of the S-K building during the Tokyo To-Bu

Earthquake in the x-direction. The highest acceleration is

observed 20 seconds into the record. The difference between the

response at the ground and the response 35m below the ground,

shown in Figure 14, indicates that once again soil between the

ground floor and the bedrock the magnifies the ground motion.

In Figure 15 the acceleration at the roof in the y-direction

is shown. A period of vibration of 0.52 seconds is observed.

A plot of the ratio of the spectral acceleration at the roof

and the spectral acceleration at the ground floor is shown in

Figure 16. A fundamental period of vibration of 1.75 seconds is

g 0:: .., 0

0 u ~

g u ls: ~ ...... = = 0::

0 ...... .... u u <

~ u e:;

Figure 12

5.19

SPECTRAL RESPONSE RATIO CIIPA TO..fr> [AAJIWIII. 1987

14

T•l.~7s I 12

10

T=l.&7sl

I I T=-O.SOs-....

0~------~------~------~------~------~------~ 0 . 0.5 2.5

= HlR£CDll

Ratio of spectral acceleration at roof an spectral acceleration at ground floor.

3

5.20

ACCELERATION AT GROUND FLOOR x-!mltlN crooo To-Ill FN!IlMt 19881

0.05

0 ~

i5 ~ ~ -0.05

~.1

-0.15 0 tO 20 30 40

lll.l[ (SECClflS)

{a)

ACCELERATION AT ROOF X-llilrnllH (TOK"lll TO-Ill fN111Mt 1988)

0.1

0.05

~.05

~.I

-0.15 0 10 20 30 40

M(SECOMJS)

{b)

Figure 13 Acceleration at ground floor and roof in x-direction {Tokyo To-Bu Earthquake) •

Figure 14

5.21

ACCELERATION AT 35M BELOW GROUND X-OO!ECIJJH (TOK'IO TO-BIJ ~ 19~)

0.05

-0.05

~.1

-0.15 L_ _____ ..__ _____ ..__ _____ ..__ ____ ___.

0 10 20 Tal (SECO!ilS)

30

Acceleration 35 meters below ground level in x-direction (ToKyo To-Bu Earthquake).

40

0.15

0.1 f-

~ 0.05 ~

5 ~ 6 ~ 0

-0.05 1-

0.06

0.04

0.02

~

~

~ 0

~ -J.02

-0.04

-0.06 zs

10

5.22

ACCELERATION AT ROOF Y -oolfCIXJf ITOK'IO TO..!RJ fAA~ 1988)

1 A , A 'l .JI ryvvvv '..,.,.\

20 ·ma: (S£COIIlS)

II

~

ACCELERATION AT ROOF & GROUND FLOOR Y -oolfCllOl (TOK'tO TO..!RJ fAA~ 1988)

\~ IIA " '~A A~ I ~~ 'V" qvv~nn

30

Figure 15 Acceleration at roof in y-direction (Tokyo Ta-Bu Earthquake) .

10

3

2

I

5.23

SPECTRAL RESPONSE RATIO TOOO TO-BU ~IHXJAI(E. 1988

'?, T=l.~

1~

:r ,......-Tr1.75sJ I I

I ~ ;) I 1 \ I ~

I \ I \ !

-::r I \ I I

? ~~ "'"""'"'· ....,..~

I 0 0.5

= X -Dil£CTDI

I I Td:Q.S:!6; I

\

AlrTco~~ I ~~ -~ ~-

~

1.5 fR[OOOCf (Hz)

. ~ Y-Oil£W

v

2.5

Figure 16 Ratio of spectral acceleration at roof and spectral acceleration at ground floor (tokyo To-Bu Earthquake)

5.24

observed in both directions. In the x-direction the second mode

is 0.5 seconds and in the y-direction the second mode is 0.53

seconds.

COMPUTER ANALYSIS

A three dimensional computer model of the S-K building was

developed using the finite element analysis program SAP90 (3].

Time history analyses were performed the Tokyo To-Bu and Chiba

To-He Earthquakes.

Description of the Model

The building was modelled using beam-column elements for the

columns and beams in the moment resisting frames. Figure 17 shows

the outline of the model.

Since the ground motion at the site during the earthquakes

was well below the EQ-I it was assumed that the forces the

building was subjected to were far less than the yield capacity

of the members and that cracking of the concrete was minimal.

Thus, the gross sectional properties of the beams and columns

were used in the properties of the elements.

The elastic modulus of the concrete was used and this varied

with the strength of the concrete with the equation [4]:

Ec - 57000{£; psi

5.25

Figure 17 outline of SAP90 computer model.

z y ~X

Sk3d

UNOEFORNED SHAPE

OPTIONS WIRE FRAME

SAP90

5.26

The floors were assumed to be rigid diaphragms and the mass

at each story was concentrated at the center of mass of the

floors.

The network of 3m deep beams and that connected the ground

floor to the piles and bearing wall was considered to be very

rigid and so the structure was modelled as being fixed at the

ground level.

In the time history analysis, the first ten modes of the

building were considered and a damping ratio of 5% was used for

all modes. This damping ratio of 5% corresponds to the value

reccommended in Table 4.1 of the "Seismic Guidelines for

Essential buildings" by the Joint Departments of the u.s Army,

Navy and Airforce [1] for structures that resist forces with

elastic or nearly elastic behavior. The peak acceleration levels

at the site of 0.04g and 0.064g for the Chiba To-Ho Oki

Earthquake and the Tokyo To-Bu Earthquake, respectively should

result in nearly elastic response of the building. The results of

systematic studies of buildings [11] also indicate that a damping

ratio of 5% is acceptable.

Mode Shapes

The first ten periods of vibration of the structure

calculated from the analysis are shown in Table 1.

The shapes of the first and second modes are illustrated in

Figure 18. The modes involve a translation along the "diagonals"

of the building but while the first mode also exhibits some

5.27

rotation, the rotation in the second mode is negligible. The

presence of rotation in the first mode explains the difference in

period of the two modes. (1.68s and 1.32s).

Figure 19 describes the third and fourth modes. Both shapes

are the second translation modes along the diagonals of the

building but the third mode exhibits some rotation. The effect of

the rotation is less in this secondary mode and thus the two

periods are closer. (0.67s and 0.66s).

The fifth mode is essentially a pure rotation mode.

Table 1 periods of vibration obtained from computer Analysis

FREQUENCY (CYCLES/SEC).

1 0. 59 2 0.75 3 1.50 4 1.52 5 1.74 6 2. 71 7 2.73 8 3. 75 9 3. 98 10 5. 34

PERIOD (SEC) 1. 68 1. 33 0.67 0.66 0.57 0.37 0.37 0.26 0.25 0.19

Figure 18

30

25

20

15

10

5

oL-------~------~------~------~ -0.01 -0.005 0 0.005

-e- 1st MODE (T=i.68s) ~2nd MODE (T=1J2s)

(a) Translation of center of mass

lr----_____

I:-~~- -r; I I ~ I: I I I I -L -_ --.J _j

r ------l I

y

L~ I 1-------

1st mode 2nd mode

(b) Plan view of mode shape at roof.

First and second modes obtained from computer analysiso

0.01

35 ,---------------------------------------5.29

30

25

20

15

10

5

0 ~------~---------*~------~--------~ -0.01 -0.005 0 0.005

~ 3rd MODE (T =0.67s} -4th MODE (T =0.66s)

(a) Translation of center of mass

I ----- -ll

~ II I I i I

I I I : - _,

Jrd mode

r-----, I I I I :

L__ _____ _J

4th mode

(b) Plan view of mode shape at roof.

Figure 19 Third and Fourth modes obtained from computer analysis.

0.01

5.30

The sixth and seventh modes are the third translational

modes and the eighth and ninth mode are the fourth translational

modes. As in the first and third mode, the sixth and eighth modes

exhibit some rotation. The tenth mode is the fifth translational

mode along a diagonal.

Time History Analyses and Response Spectra

Time history analyses were performed on the SAP90 computer

model using the acceleration recorded at the ground floor of the

building as the base excitation. This was done to validate the

accuracy of the model.

Figure 20 and Figure 21 compare the measured and calculated

response at the roof of the building in the x and y-directions

respectively, for the 20s - 40s period of the Chiba To-Ho

Earthquake. The comparison is favorable. The time history curve

for measured response is smoother and this is expected since the

elastic computer analysis cannot take into account the sligthtly

non linear response that results from cracking, rubbing of

nonstructural elements members and small amounts of yielding.

In Figure 22 the spectral response ratios obtained from the

computer analysis are compared with those from the measured

'records. The first mode compares favorably but the second

translational mode differs by about 0.15 seconds.

A similar result for the Tokyo Ta-Bu earthquake is shown in

Figure 23.

5.31

MEASURED RESPONSE x -ll!R[Cilal !OifA ro-m f.I.R1liXm 1987) 0.1 ______ ___::...::....:..__:__:_ ___ ..;__ _____ -,

0.05 t-

~'

-0.05 f-

-o.J L__ ___ __._ ____ __._ ____ ;_,_ ___ _....40

m ~ M ~ Ill£ (S£CONJS)

CALCUlATED RESPONSE x-ll!R[Cilal !Oi& ro-m fi.RIJWI.I([ 1987) 0.1 ..-------_____:_...;...___ _________ ,

-0.05 I"'"

-o.1 L_ ___ __._ ____ __._ ____ ;_,_ ___ __.40

20 25 ;o JS i1ME (SECOI{)Sl

Figure 20 Comparison of recorded and calculated response of building in x-directon.

~

1:5

~ '-' !01!

~ 1:5 ~ ~

0.1

1-

~ I~

0.05

A

w~ I

-0.05 1-

~.1

20 25

5.32

MEASURED RESPONSE Y -IJRECOOH ICIIBA T~ £JmiM£. 1987)

i

r~

I~

30 111£ (SfCO!IlS)

\

II ~

~ ~

\

~ v ~ ~~ ~ (\<

35

CALCULATED RESPONSE Y-!li!£C1klH (CifBA f()-HO ~[. 1987)

0.1 ..-----------~-----------~

0.05 t-'

" ~ M I\ (\ 0

·v Vv ~

-0.05 t-

~.1 L-----'-------........:....-----___.:.._-----20 25 30 35 40

00: (SfCONJS)

Figure 2~ Comparison of recorded and calculated response of building in y-directon.

5.33

SPECTRAL RESPONSE RATIO X-OO(CIXJI{OiB\ 10-fO F.lll!l~Xm. 1987)

... s 5~------~--~---+--------~------~-------+------~ ~

~ 4~------~~~---+--------~-----+~-------+------~ ~ ~ 3~----~~-+~~-+~--~--~--~~~~-----+------~ ~ ~ 2~~~~~--~~~~~--~~--~~ri-----~~------~ e;;

Figure 22

0.5 1.5 fREOOE!t'Y (Hz)

-+- CJUlJWID

SPECTRAL RESPONSE RATIO Y-tfl£Cn11 (C!IS\ IO-HO ~[. 1987)

2 2.5

15r-------,-------~-------,--------~-------.-------,

0.5

_WSIJ!ED

1.5 fR£0000 (Hz)

-+- CN.C!JIA!ED

2.5

comparison of ratio of spectral acceleration at roof and spectral acceleration at ground floor. (chiba To-Ho Earthquake).

10

0

8

0

. 5.34

SPECTRAL RESPONSE RATIO X-!liR£CI1lN ITOIOO TO-BU fJ,IliiMt 1988)

li\ I

1/ ' I I \ I

J \ I ~\

/ -~ ~ ! ;r \U jll ~"'.

I~ I

I 0 0.5

I ~

tt\" l

\~ h ft \\

K1 \'

~ I I

~

1.5 FR£00E!ICY (Hz)

?

- YfASLRED ~ DLOJlAIED

SPECTRAL RESPONSE RATIO Y -crR!:CWI [TOKYO TO-BU fNlllW\1(( 1988)

I I I I i I I I

lP- \\1 -.A~~/\

0 0.5

~1~\/ 1/\ '~

I I

- !loo.RED

~

15 fR£001:!1a (Hz)

-+- DLC1JtAJED

I I I I I I I I I I I i~_l

I I ! I

2.5

I I I I I I

I I

I I I

~ ~ I I

I 2.5

Figure 23 Comparison of ratio of spectral acceleration at roof and spectral acceleration at ground floor. (Tokyo To-Bu Earthquake).

535

INELASTIC ANALYSIS OF S-K BUILDING

In this section an inelastic analysis is performed on the s­

K building to determine the post yield capacity or ductility of

the building. This is important since large earthquakes subject

buildings to displacement beyond the elastic limit.

A two dimensional model of a typical moment resisting frame

in the building is used. This two dimensional model was developed

using the properties of the three dimensional model used in the

previous section.

The inelastic analysis of the structure was approximated by

using an elastic step-by-step superposition analysis. This

involved applying a steadily increasing static triangular load

(as shown in Figure 24, with a point load applied at each floor)

to the structure. When the moment on a member reaches its plastic

moment capacity, the structure is modified by inserting a hinge

at the point where the plastic moment was reached. The load is

then increased until another hinge forms. This process is

continued until enough hinges are formed to cause instability in

the structure.

A shell control program that performs this method of

inelastic analysis in conjunction with SAP90 has been developed

by Shimano (6] and is used in the study.

I I j

I I 1 i I i I I I l I I I I I I I I I I I I I I ! I i

. I

' ' I

I I I I I I

I I I I

I I I I I I I I I I I I I I

I I I

I I I I I I I I I I !

I I I I I I I I i I

I

I

I I I I

I I I

5.36

I

I

I

I I

I

I

I I I i I I I

I I I I

I

I

I I

Figure 24 Triangular lateral load applied to S-K Building.

5.37

capacity of Members

In the hinge zones of the column and beams of the s-K

building, closely spaced lateral reinforcement was used to

provide confinement of the concrete. This confinement affects the

behavior of the concrete significantly. Thus, in calculating the

capacity of a member (moment at which a hinge will form), a

stress-strain curve that adequately describes the behavior of the

confined concrete needs to be used. The stress-strain curve

developed by Mander, Priestley and Park (7] was used in this

analysis. This stress-strain curve is determined by the effective

confining pressure provided by the lateral reinforcement on the

concrete.

The stress-strain curve of the concrete and thus the

capacity of a member depends on four variables:

(a) The compressive.strength of the concrete.

(b) The dimensions of the cross section of the member.

(c) The amount, arrangement and strength of the

longitudinal reinforcement.

(d) The amount and strength of lateral reinforcement

The effect of the compressive strength and dimensions of the

cross section on the capacity of the members are obvious - higher

compressive strengths and larger sections result in greater

moment capacity.

The longitudinal reinforcement affects the capacity of the

member not only by determining the ultimate tensile force and

moment arm, but also by influencing the stress-strain curve used

5.38

for the concrete. The area of effectively confined concrete is

reduced by arching action between the longitudinal bars. This

decrease in effectively confined concrete area by arching reduces

the confined compressive strength of the concrete and thus

affects the stress-strain curve used in the analysis. When the

longitudinal bars are placed further apart the arching takes

place over a longer distance. The area of effectively confined

concrete is decreased and so the capacity of the member is lower.

The lateral reinforcement affects the strength of a member

in a similar manner since arching action also occurs between the

ties or spiral reinforcement. Therefore, a larger spacing or

pitch of the lateral reinforcement results in weaker members.

Also, the size and strength of the lateral reinforcement

determines the confining pressure provided.

These four variables change significantly in the s-K

building and so stress-strain curves were calculated for the

members with different properties. The moment capacities of the

members were then calculated using the computer program IMFLEX

(Hart, Sajjad and Basarkhah (8]). The program is capable of

calculating moment-curvature diagrams for concrete and masonry

beams with any arrangement of longitudinal steel and a specified

stress-strain curve for the concrete or masonry. A more detailed

explanation of the calculation of the stress-strain curve and

moment capacity of members in the S-K building has been provided

in a previous paper (9].

A typical moment-curvature diagram for a beam is shown in

5.39

Figure 25. Yielding of the longitudinal steel is seen to govern

the plastic moment capacity. The columns and beams of the S-K

building possess very high ductility and concrete strain did not

control the plastic moment in any of the members. This is

particularly so since confined concrete can endure strains of

about 0.03 [7]. The unconfined cover concrete was assumed to

spall at a strain of 0.005 as recommended by scott, Park and

Priestley [10].

No strain hardening is accounted for in the analysis. The

members were assumed to be perfectly plastic. The floor slab was

assumed to be infinitely rigid and so the beams did not carry any

axial load. The moment-curvature diagrams for the columns were

calculated for the axial load that they were subjected to from

dead loads and lateral loads.

Results of Analysis

Figure 26 shows the load-deflection curve calculated from

the analysis. The graph is normalized by plotting the total drift

ratio against the base shear coefficient. The total drift ratio

is the displacement at the roof divided by the total height of

the building. This gives an idea of the average story drift in

the building.

The first hinge occurred at a base shear coefficient of 0.11

and a total drift ratio of 0.23 percent. This indicates a

relatively stiff building since the allowable inter-story drift

ratio at yield is about 0.5 percent for u.s. buildings. The

ultimate total drift ratio when the structure becomes unstable

5.40

MOMtNT -cURYAfURE D~CIWJ FOR BEAM 2~~------------------------------------------~

c: I

c..

g !OC() -.3 :::E c :::E

:oo

I

- - - - - - - - ~ - - - - ::J

\

\-Steel yields

o~------~----~------~------~----~-------

0 0.5 1.5 ThOUSillldths

OJM.lUR£

L5

Figure 25 Typical Moment~curvature diagram for member

5.41

lOMJ-OEFlECTION CUfM OF S-K FRAME OISPIJ£[J,(Mf AI ROCf

u~----------------------------------------~

0.15

First yield~

;J.J

0.05

0~------~--------~------~--------~------~ 0 0.1 01 OJ OJ 05

row lllliT (PfR!IIIf)

Figure 26 Load-deflection curve for typical S-K building frame. (Gross section properties).

5.42

was 0.46 percent. Thus, the displacement ductility of the

building is

0. 46 - 2. 0 0.23

This means that the building can endure displacements twice those

for which first yield occurs. It should be noted that this is

the ductility of the bUilding as a whole. Components of the

building may possess greater or less ductility.

To account for the reduction in the moment of inertia in the

members caused by cracking of the concrete, the analysis was

repeated using eighty percent of the gross moment of inertia in

the columns and 40 percent of the gross moment of inertia in the

beams - a common approximation. The load-displacement curve is

shown in Figure 27. The total drift ratio at yield was 0.44

percent and the total drift ratio at instability was 0.87

percent. This gives a ductility of 1.97 or approximately 2.0 -

the same value calculated previously. Also the shape of the load

deflection curve in Figure 27 is similar to that in Figure 26.

This suggests that even though the deflection depends on the

moments of inertia selected, the calculated ductility does not.

In reality, it is expected that during the loading process

the moments of inertia would decrease gradually as more cracking

takes place in the members with the increasing load. Hence, the

deflections at and instability would be somewhere between the

values calculated for the two cases. Thus 2.0 serves as a lower

z ...... u ..: ...... ...... 0 u 0:: < '=! Vi ..... VI

~

5.43

LONJ-DEFlECTION CUlM OF S-K FRAME cmmNr AT ROCf

01~--------------------------------------,

0.15

0.1 / -,

.·-"--First yield

O.o5

0.1 01 OJ OJ 05 0.6 TOTN. 1m (Pffillllf)

OJ OB 0.9

Figure 27 Load-deflection curve for typical S-K building frame. (Eicol = 0.8EI9 ... 055 ; Eibeam = 0.4EI

9 ... 055

).

5.44

bound for the ductility. An upper bound can be obtained by taking

the ratio of the ultimate deflection for the second case and the

deflection at first yield for the first case (gross moments of

inertia). This would give a value of

1-Luppper -au(reduced)

ay(gross)

0. 87 - 3. 78 0.23

The S-K building can then be said to have a ductility of between

2.0 and 3.8.

Figure 28(a) and Figure 28(b) show the sequence of formation

of the 246 hinges that were calculated in sets of 40. The

building is seen to obey the "strong column weak beam" concept

with all the hinges forming in the beams. This ensures that

premature instability does not develop. Plastic hinges are seen

to form first around the eighteenth floor and then around the

seventh floor. This is because the nominal strength of the

concrete is reduced at these floors causing a· sudden drop in the

moment capacities of the beams on these.floors relative to the

floor below.

5.45

i ' I I i I I I I ! I I I ! I I I I I l I I I I ' ! I I !

I ' I ! I : I i I ' I I ;

I I ' I I i I i ! I I I I I I ;

i ' ' I I I ; I I I I I i I !

I I I I I I I I I I I j I I I ! I : : I I I I I I ; : : ; I !

I I I I I l : ! ! i I ' : i : I ' I I I I ; I I I I '

I I ; I I ! I I : I ' :

! I i I I

!

' I ' ' I

; I ; i I I I I '

1: :: : I :; I

i ' I : i I I I I I I i ! I ' I

i ! ! I I I ! I I I I I ! I I I

' i i : i : I '

I. I : !

I .I I I I I I I

I~ I I ! I '

I I I I I I I I I I I I I I :1 I : I I I I I I I I I I I I I

I I I I I : I r I I I I I I I I i I ! I I I I ! I I : I: ' ! I ;

! I I i I I i I i i 'I I I I I 1: :1 I ; I ' I I I ! I i I : : I i '

I

i : ' ; I I I I ' I ! I

i ; I : i j

I I I I I I

I I i I I i i

I ! ' i I ! I I I I I I I : I ! I i ! i ! I i I !

I I I I I I i I i I I I ' ; I ' ' ' I ' ' i i I ' ' ' '

40 hinges 80 hinges 120 hinges

Figure 28(a) Sequence of hinge formation in inelastic analysis.

5.46

I I ; I I I I I ! I I I I i i I I j I I ! I I I I i I I I i I I I ! I I I I I I I I i I I I I I I i i I I I i I I I I I I I I I I I I i I I I I I T I I I I I I I I l

I I I I I ! I I I

i i I I : ! I I ! ! I

; ; ;

I ! \ -, i I

I I I -I I I i I I I I I ; ! I i I I : I i I I

I I I I I

.L I I I I ! I I I_ I I ! I I I

i I I I I I I I I I I I I I I

I I i I I

1: I I

1: :i :! I

I I I

I_

I ! ! I I i I I I I

I ' I ! I l

: I I I I

! ·r I I I i I I I I I

i: I

1: ::: : : :~: : i: :l ! ! I I : I I I

I I I I I : I I I I ;

I I I T I I ! I I I I I I I i i I I i ! i

I I ! ~ I I ! I I I I

160 hinges 200 hinges 246 hinges

Figure 28(b) Sequence of hinge formation in inelastic analysis.

5.47

CONCLUSIONS

1. The first and second translational periods of the building in

are approximately 1.7s and o.ss.

2. The computer model describes the building reasonably well with

translational modes of 1.68s and 0.66s respectively. Further

adjustment of the parameters of the building by a more

rigorous calculation of the building properties would make

the comparison to the real structure even more accurate.

3. The outline of the building in plan is approximately square

and thus the principal axis are along the diagonals of the

building. The translational modes of vibration thus involve

motion along these diagonals. This explains the similarity in

recorded response in the x and y-directions.

The position of elevator shafts and the shape of the

floor plans in the building leads to a slightly non

-symmetrical arrangement of mass on the floors. This

eccentricity is the reason for the coupling of rotation and

translation in some modes of vibration of the building. Figure

29 shows the approximate positions of the center of mass for

some floors. In all cases the eccentricity from the x-axis is

greater than that for the y-axis. The eccentricity from one

diagonal is also greater. Thus the results from the analyses

showing significant coupling of translation and rotation in

5.48

one direction and negligible coupling in the other are

expected.

The measured response also show similar behavior. Figure

7 shows a first mode period of about 1.8 seconds in the x -

direction and igure 10 shows a period of about 1.67 in the

y-direction. Figure 12 and Figure 16 also show that there is

a slight difference in period for the first two modes in the

y- direction and the first two modes in the x-direction.

4. The building exhibits reasonably strong ductile behavior. It

adheres to the "strong column weak beam" concept with plastic

hinges forming in the beams and not in the columns. The

building can be said to possess an overall ductility of

between 2 and 4.

! I

II"'Jl .1/\..1

I

5.49 y

~ ~ .3'i_~ ~

ll

I

lc+OH

SECOND FLOOR PLAN

I I ;

tiASS

Agure 29(a) Posttlon of center of mass on floor plan.

X

I

I I

I I

I

5.50 y

~ ~

I

1.6 mi .II'!

~ ....

1\

lCEN~ OF~

T I I I

3RD - 13TH FLOOR PLAN

I I

1 I I I

I

tiASS

I

Rgure 29(b) PosHion of center of mass on floor plan.

X

5.51

REFERENCES

1. Joint Departments of Army Navy and Air Force, "Seismic Guidelines for Essential Buildings", us Technical Manual, TM-809-10-1, February 1986.

2. Lotus Reference Manual, Version 3.0, Lotus Development Corporation, Cambridge.

3. Wilson, E.L. and Habibullah, A., "SAP90- A Series of Computer Programs for the static and Dynamic Analysis of Structures", User's Manual, Computers and Structures Inc., Berkeley, California, 1988.

4. Park, Rand Paulay, T., Reinforced concrete Structures John Wiley and Sons, Inc.,New York, 1975.

5. Fukuzawa, E., "Earthquake Resistant Design and Analysis of a 30 Story Reinforced Concrete Building", International Institute of Seismology and Earthquake Engineering, Building Research Institute, Ministry of Construction, Japan, 1985.

6. Shimano, R.T., "Limit Analysis of Frame Structures Using Shell Control Program", Masters Thesis, University of California, Los Angeles, 1990.

7. Mander, J.B., Priestley, M.J.N., Park, R., "Theoretical Stress-Strain Models for Confined Concrete", Journal of Structural Engineering, Vol. 114,No.8 August 1988.

8. Hart, G.C., Sajjad, N.A., Basharkhah, M.A., Inelastic Masonry Shear Wall Analysis Computer Program (IMFLEX; Version 1.01), January 1989.

9. Ekwueme, C.G., Hart, G.C., Sabol, T.A., "Behavior of Japanese S-K Building Reinforced Concrete Columns with Core Reinforcement"

10. Scott, B.D., Park, R., Priestley, M.J.N., "Stress-Strain Behavior of Concrete Confined by overlapping Hoops at Low and High Strain Rates", ACI Journal. Vol. 79, No. 2, January 1982.

11. Mcverry, G.H., Frequency Dormain Identification of Structural Models from Earthquake Records,Report No. 79-02, Earthquake Engineering Research Lab,. California Institute of Technology, Pasadena, 1979

CHAPTER 6

MEMBER DErAILS AND RESPONSE REDUCTION

by

Jack P. Moehle

6.1

6.1 - Object and Scope

The object of the present study is to examine detailing requirements for reinforced concrete structural elements in highrise buildings constructed in seismically active regions. Detail requirements in a building will be dependent on the seismic input and building proportions and configuration. For lowrise construction, economical considerations do not permit setting building specific detailing requirements; for these buildings code established minimum detailing requirements are generally accepted as being satisfactory. For highrise buildings, the large scale of the design and construction activity may in many cases make it feasible to develop building specific details. Analytical approaches to determining those details are desirable.

The present study descnbes a numerical model that can be used to assess the performance of reinforced concrete beams and columns. Numerical models of several experimental specimens are prepared and compared with available experimental data. Results of the comparison suggest a level of confidence to be assigned to the analytical method. A series of parameter studies to describe expected performance as a function of details and loadings is presented. All results are presented using displacement capacity rather than a ductility capacity as a basis. The former approach is believed to be the more desirable for highrise frames in which strict drift control limits are generally applied and checked as part of the design. The present study is limited to flexural response of line elements. Behavioral modes associated with shear, anchorage, and connections (beam­column joints) are not addressed.

This chapter contains a summary of experimental data for beams, columns, and beam-column joints. Observed deformation capacities as a function of details, configuration, and loading are presented to provide a frame of reference on expected behavior given a variety of details. A simple and well established analytical model of deformability of reinforced concrete beams and columns is descnbed, and results of the model are compared with the experimental data. Finally, projections of expected deformability of beams and colum..'"ls are made using the model.

6.2 - Review of Experimental Studies of Reinforced Concrete Elements

Results of laboratory experiments provide a frame of reference for deformability of structural elements and a benchmark for analytical procedures. In the present study, a series of experimental data generated at a variety of locations was gathered and analyzed. The data are limited to beam, column, and beam-column joint specimens constructed at no less than half of full scale.

The experiments carried out at different institutions had fairly consistent test configurations and loading programs. Loading programs were one of two different types.

6.2

In the first type, loads were applied that· resulted in at least two cycles of constant displacement amplitude followed by successive pairs of cycles at increased displacement amplitude. In the second type, loads were applied that resulted in constant displacement amplitude. The loadings were increased until failure occurred, except that for some of the tests having incrementally increasing displacement amplitude the test was terminated by equipment limitations before specimen failure.

Tables 6.1, 6.2, and 6.3 summarize principal test results from the studies. In the tables, the deformation capacity of a test specimen was normalized as the measured peak deflection at loading point divided by the length of the element for beams and columns, and that quantity was designated the equivalent end rotation ee, which may be viewed as the equivalent drift angle corresponding to deformation of the element. For beam-column specimens, the drift index obtained during the test is reported directly. The maximum deformation capacity during a test is defined as the deformation sustained without loss in resistance exceeding 15% of maximum strength. Additional details may be found in the report by Qi and Moehle (1991).

Figures 6.1 and 6.2 present variations of measured equivalent end rotation for beams and columns. Drift capacities of beam-column joints are summarized directly in Table 6.3. In summary, it was observed that beams and columns were generally capable of undergoing equivalent end rotations of 0.02 rad or more, except for a few cases of columns having relatively high axial compression forces or relatively low aspect rations (and resulting predominant shear failure modes). Because beams and columns together contnbute to the total drift capacity of a frame~ the quantities observed can be viewed as representing lower bounds to frame drift capacity. Beam-column joint tests exhibited drift capacities having a lower bound of nearly 0.04. It is noteworthy that many of the test specimens for which data have been reviewed had structural details not satisfying minimum seismic requirements of current codes.

6.3 - Parametric Study of Plastic Hinge Rotation Capacity of Reinforced Concrete Beams and Columns

Tne experimental data are insufficiently numerous to define clearly and uniquely the performance and detailing requirements of framing elements in buildings. Analytical study was undertaken to develop a gage for determining detailing requirements. Comparison of the gage with experimental data was undertaken to provide a confidence indicator for the gage. A parametric study was also undertaken to project the experimental results to the more general conditions.

The analytical model used for all calculations is depicted in Figure 6.3. The model idealizes the structural element as having a fixed base with deformations occurring solely along the length and being solely flexural. Elastic and plastic curvature distnbutions along the length are idealized as shown. To simplify the presentation of results, only the plastic component is presented in the results that follow. The plastic rotation is defined by Equation 6.1.

6.3

(6.1)

in which ¢u and ¢u represent the ultimate and yielding curvatures, respectively, and IP is the equivalent plastic hinge length. Curvatures were calculated for monotonic loading considering plane sections to remain plane, with confined concrete properties and typical reinforcing steel properties including strain-hardening characteristics. The plastic hinge length was assumed to be equal to 0.65d, where d is the section effective depth. Details of the calculation procedure are descnoed and rationalized in the report by Qi and Moehle (1991).

Tables 6.4 and 6.5 compare measured equivalent end rotations with calculated plastic hinge rotations for several of the experiments reported in Tables 6.1 and 6.2. The experiments are limited to those for which both of the following were satisfied: (a) the load history resulted in incrementally increasing displacement amplitudes, and (b) the test was terminated by capacity of the test specimen rather than capacity of the loading equipment.

The results in Tables 6.4 and 6.5 indicate a relatively wide range of scatter between experimental and analytical results. The scatter arises from several sources, including (a) the analytical model includes only plastic hinge rotations, whereas the experiments include elastic deformations, shear deformations, and connection deformations, (b) the analytical model is based on monotonic properties and an assumed linear strain distribution across the section, whereas the tests were conducted under cyclic loading histories, and (c) though all the tests were cyclic with increasing displacement amplitudes, the details of each loading program varied. The scatter suggests that development of improvements in the analytical model would be a reasonable goal for continued research. The degree of improvement sought should be consistent with the considerable uncertainty that is known to be associated with defining the design earthquake and overall building response.

Despite the scatter in the data (Tables 6.4 and 6.5), it is noteworthy that the measured rotation capacity exceeds the calculated capacity in most cases, with the implication that the calculated result tends to represent a lower bound to expected behavior. Considering all the data, it is concluded that the actual deformation capacity under severe cyclic loading is likely to be at least equal to half the calculated value.

A parameter study of deformation capacities of beams and columns as a function of the reinforcement quantities and details was carried out. In the study, beams were assumed to be rectangular (and without slab) having cross-sectional dimensions of 12 in. by 24 in., and columns were assumed to have cross section of 20 in. by 20 in. These are considered to be lower bound sizes for multi-story building construction. A range of longitudinal reinforcement ratios was studied for beams. A total longitudinal steel ratio (equal to 0.03) was selected for columns; effects of varying this quantity for columns were not deemed to be worthy of study given that the reinforcement is symmetrically placed and given the accuracy that can be expected for the analytical procedure. Transverse reinforcement ratios were selected to cover the likely range permitted by codes (as represented by the ACI Building Code) and encountered in practice. Column axial loads were varied over the common range.

6.4 . .

Calculated results are summarized in Figures 6.4 and 6.5. General trends of the calculated results are as follows:

(a) For beams having longitudinal ratios less than 0.01 deformation capacities were calculated to be limited by fracture of the longitudinal reinforcement. The ability of the analytical model to represent this phenomenon is not clear. Nonetheless, calculated deformation capacities associated with this phenomenon were generally relatively large.

(b) Calculated beam deformation capacities increased with increasing transverse reinforcement, a trend that is consistent with the observed behavior. Calculated deformation capacities decreased at a moderate rate with increases in the longitudinal reinforcement ratio. This trend, though expected, was not clear in the experimental data.

(c) Calculated column plastic hinge rotations increase with increasing transverse reinforcement ratio, and decrease with increasing axial load ratio. Deformability was very low for axial load ratio exceeding 0.5. Similar results are evident in the experimental data.

The overall results of Figure 6.4 and 6.5 suggest practical ranges of reinforcement quantities to achieve desired deformation capacities in reinforced concrete beams and columns. In viewing these data, it should be recalled that actual capacities observed during experiments were as low as half the calculated quantity. It should also be noted that deformation and failure modes associated with shear, anchorage, and connections were not included in the analyses. ·

6.5

6.4 REFERENCES

1. Ma, S. M., V. V. Bertero and E. P. Popov, "Experimental and Analytical Studies on the Hysteretic Behavior of Reinforced Concrete Rectangular and T-Beams," Reuort No. UCB/EERC-76/2, Earthquake Engineering Research Center, University of California at Berkeley, May 1976.

2. Popov, E. P., V. V. Bertero and H. Krawinkler, "Cyclic Behavior of Three R.C. · Flexural Members with High Shear," Report No. UCB/EERC-72/5. Earthquake Engineering Research Center, University of California at Berkeley, October 1972.

3. Fenwick, R. C. and A Fang, ''The Behavior of Reinforced Concrete Beams under Cyclic Loading," Reuort No. 176, Department of Civil Engineering, University of Auckland, Auckland, New Zealand, 1979.

4. Brown, R. H., "Reinforced Concrete Cantilever Beams under Slow Cyclic Loadings," Ph.D. Dissertation submitted to Rice University, Houston, Texas, 1970.

5. Brown, N. H. and C. P. Seiss, "Repeated and Reversed Loading in Reinforced Concrete," Journal of the Structural Division, ASCE, Vol. 92, No. 5, October 1966.

6. Saatcioglu, M. and G. Ozcebe, "Response of Reinforced Concrete Columns to Simulated Seismic Loading," ACT Structural Journal. Vol. 86~ NO. 1, January­February 1989.

7. Ramirez, H. and J. 0. Jirsa, "Effect of Axial Load on Shear Behavior of Short RC Columns under Cyclic Lateral Deformations, PMFSEL Reuort No. 80-1, Department of Civil Engineering, The University of Texas at Austin, Texas, 1980.

8. Gill, W. D., "Ductility of Rectangular Reinforced Concrete Columns with Axial Load," Research Reuort 79-1, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, 1979.

9. Ghee, A. B., ''Ductility of Reinforced Concrete Bridge Piers under Seismic Loading," Research Reuort 81-3, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, 1981.

10. Zahn, F. A., "Design of Reinforced Concrete Bridge Columns for Strength and Ductility," Research Report 86-7. Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, 1986.

11. Durrani, A J. and J. K. Wight, "Experimental and Analytical Study of Interior Beam to Column Connection Subjected to Reversed Cyclic Loading," Report No. UMEE 82R3, Department of Civil Engineering, The University of Michigan, Ann Arbor, Michigan, 1982.

6.6

12. Ehsani, M. R. and J. K. Wight, "Behavior of Exterior Reinforced Concrete Beam to Column Connections Subjected to Earthquake Type Loading," Renort No. UMEE 82R5, Department of Civil Engineering, The University of Michigan, Ann Arbor, Michigan, 1982.

13. Kurose, Y., G. N. Guimaraes, Z. Liu, M. E. Kreger and J. 0. Jirsa, "Study of Reinforced Concrete Beam-Column Joints under Uniaxial and Biaxial Loading," PMFSEL Renort No. 88-2, Department of Civil Engineering, The University of Texas at Austin, Texas, 1988.

14. Kurose, Y., "Recent Studies on Reinforced Concrete Beam-Column Joints in Japan," PMFSEL Renort No. 80-1. Department of Civil Engineering, The University of Texas at Austin, Texas, 1980.

15. Boroojerd, A and C. E. French, ''T-Beam Effect in Reinforced Concrete Structures Subjected to Lateral Load," Structural Engineering Renort No. 87-04, Department of Civil and Mineral Engineering, Institute of Technology, University of Minnesota, 1987.

16. Zerbe, H. E. and A. J. Durrani, "Effect of a Slab on the Behavior of Exterior Beam to Column Connections," Structural Research at Rice. No. 30. Department of Civil Engineering, Rice University, Houston, Texas, 1985.

17. Cheung, P. C. T. Paulay and R. Park, "Interior and Exterior Reinforced Concrete Beam-Column Joints of a Prototype Two-way Frame with Floor Slab Designed for Earthquake Resistance/' Research Renort 89-2, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, 1989.

6.7

Table 6.1 Properties a!'..d Deformation Capacities of RC Beax::::.s

Beam Reinforcing Bot./Top Transverse Shear Span Loacilng Beam End

ID Inde."C Steel Ratio S tee! Index Ratio History1 Rotation

r· t P1 fp p3.jb[; Z/d Be

university of California. at Berkeley, California. (23]

Beam R-1 0~1832 0.53 0.0085 4.50 Cyclic-I 0.0417

Beam R-2 0.2217 n2 " ,

" 0.0276

Beam R-3 0.2028 " 0.0160t " " 0.0497

Beam R-4 0.2121 " " ~ ,

Cyclic-C 0.0704 I

Beam R-5 0.2028 1.00 " ... 2.30 Cyclic-I 0.0382 I

Beam R-6 0.2140 " " ~ 4.50 " 0.0459 I

Beam T-1 0.1939 0.53 " ... , " 0.0475 I

Beam T-2 0.2015 " " ~ " Cyclic-C 0.0660 I

Beam T-3 0.2078 1.00 " ~ " Cyclic-! 0.0503 I

university of Cal.ifor.:.ia. at Berkeley, Califor..Ja (44]

Beam 35 0.2142 1.00 0.0110 3.09 Cy~c-I 0.0320

Beam 46 0.2653 " 0.0123 , ,

0.0320

Beam 43 0.1885 " 0.0339 ,

" 0.0480

University of Auckland, New Zealand (15}

1A 0.1691 1.00 0.0313t 2.09 Cyclic-! 0.0429

1B 0.1691 " 0.0231 t 3.01 " 0.0458

2A 0.1441 " 0.01SOt 3.93 " 0.0481

2B 0.1441 " " ~ 4.85 " 0.0447 I

3A. 0.1168 0.64 0.0231 t 3.01 " 0.0437

SA 0.0913 1.00 " ... 2.99 " 0.0439 I

SB 0.0913 " 0.0313t 2.08 " 0.0440

6.8

Table 6.1 P;oper;:ies and Defor~ation Capacities of RC Bear::.s (Cone 'd)

Beam Reinforcing Bot./Top Transverse Shear Span Loading Beam End

ID Inde."C Steel Ratio Steel Inde."C Ratio His;:ory Rotation

r; p' I P P:~.JbTS z I a. Be

Rice University, Houston, Te."Cas (6]

66-35-RV 5 0.1261 1.00 0.0215 6.00 Cyclic-I 0.0720

66-35-RV10 0.1301 " " " Cyclic-C 0.0952

66-32-RV 5 0.1301 " 0.0847t " Cyclic-I 0.1112

66-32-RV10 0.1406 " " t " Cyclic-C 0.1009

66-35-RV 5 0.1269 " 0.0215 3.00 " ·o.o673

66-35-RV10 0.1277 " " " " 0.1000

88-35-RV 5 0.2081 " " 6.00 Cyciic-I 0.0855

88-35-RV10 0.2278 " " " Cyclic-C 0.1137

88-32-RV 5 0.1927 " 0.0847t " Cyclic-I 0.0785

88-32-RV10 0.2096 " " .:. " Cycllc-C 0.1057 I

88-34-RV 5 0.2443 " 0.0299 3.00 " 0.0507

88-34-RV10 0.2191 " " " " 0.1055

86-35-RV 5 0.2443 0.56 0.0215 6.00 Cyclic-! O.OS42

86-35-RV10 0.2<;43 " " " Cycllc-C 0.1026

University oi Tilinois at Urbana, Tilinois [8]

J3 0.1947 1.00 0.0132 6.60 Cyclic3 -C 0.1424

J7 0.1146 " 0.0110 3.70 " 0.1061

Jl2 0.1088 0.56 " " " 0.1061 '

1 Cyclic-! = Cyclic loading with increased displacement mag!litude;

Cyclic-C = Cyclic loading with constant dispalcement magnitude.

2 " sign iudicates the same value as the above.

3 Combined cyclic and repeated loading history.

t Beams satisfying the current ACI code [2] detailing requirements.

6.9

Table 6.2 P:-operties a.nd Deformation Capacities of RC Columns

Colum..'"l Reinforcing A.:cial Load Transverse Shear Span Loading Column End

ID Index Index1 Steel Index Ratio Direction2 Rotation3

Tj P/A1f~ p3-fi/S lfd Be

University of Tornoto, Canada (48]

U1 0.3162 0.0 0.0130 3.28 u 0.0461

U2 0.4809 0.162 0.0130 114 " 0.0422

U3 0.3961 0.141 0.0365t " " 0.0510

U4 0.4388 0.153 0.0672t " " 0.0869

us 0.2796 -0.08-0.08 0.0130 " " 0.0442

U6 0.3765 0.131 0.04S2t , ,

0.0895

U7 0.3952 0.125 0.0452t , ,

0.0882

D1 0.3603 0.0 0.0130 " D 0.0414

D2 0.4809 0.162 0.0130 " " 0.0211

D3 0.3961 0.141 0.0365t " " 0.0288

D4 0.3162 0.112 0.0672t ,

" 0.0462

Ds 0.2796 -0.08-0.08 0.0130 " " 0.0247

B1 0.4388 0.153 0.0672t " B 0.0563

B2 0.3547 0.124 0.0365t " " 0.0533

The University of Texas at Austin, Texas (46]

00-U 0.261 0.0 0.0165t 1.73 u 0.0186

120C-U 0.355 0.187 n.:. " " 0.0167 I

120C-B 0.219 0.140 "t ,

B 0.0173

00-B 0.218 0.0 n.;. " " 0.0174 I

SOT-U 0.256 -0.068 n.:. ,., u 0.0226 I

100T-U 0.233 -0.124 n.:. , , 0.0225 I

200T-U 0.225 -0.239 lt.:. " ,.,

0.0233 I

SOT-B 0.340 -0.075 "t ,.,

B 0.0217

ATC-U 0.337 -0.15-0.18 ,.

" u 0.0112 I

ATC-B 0.316 -0.07-0.17 ,. ,

B 0.0173 I

6.10

Table 6.2 P:operties a.nd Deformation Capacities of RC Columns ( Cont'd)

Column Reinforcing Axial Load Transverse Shear Span Loading Column End

ID In de."'< Index Steel Inde.x Ratio Direction Rotation

r· I P/A..g/~ p$.fi/s lfd Be

University of Canterbury, New Zealand [18]

ONE 0.299 0.26 0.0391t 2.46 u 0.0283

TWO 0.167 0.214 0.0620t " " 0.0213

THREE 0.322 0.42 O.OS04t " " 0.0176

FOUR 0.293 0.76 0.0966t " " 0.0129

University of Canterbury, New Zealand (17]

Unit3 0.273 0.38 0.0567 .:i A-•• -:I u 0.0253

Unit 4 0.258 0.21 0.0463 n " 0.0367

University of Canterbury, New Zealand (70]

Unit 1 0.176 0.23 0.04S9t 4.47 D 0.0265

Unit 2 0.222 0.43 0.0660t n n 0.0248

Unit 3 0.198 0.23 o.oso.;t " ,

0.0291

Unit 4 0.237 0.42 o.o7sst " ,

0.0250

Unit7 0.235 0.23 0.0288 " ti 0.0375

Unit 8 0.166 0.39 0.0415 " " 0.0233

i Compression loadir.gs a.re defined a.s positive.

2 U = Cyclic la.te.:-alloading along one principal a."'<is of the column;

D = Cyclic lateralloa.ding along one diagonal of the column;

B = Cyclic lateral loading along both principal axes of the column.

3 The larger value iu a. principal direction when subjected to bia:cia.lloadings.

" " sign indicates th.e same value a.s the above.

t Columns satisfying the current ACI code [2} detailing requirements.

6.11

Table 6.3 P:-operties and Deformation Capacities of RC Beam-Column. Assemblages

Assemblag'!! Span to Height Specime:!l Loading Joint Drift Index5

ID Ratios1 •2 T:rpe3 Direction4 Location

Lt!HI Lz/H I 0

The University of ~Iicillga.n, Ann Arbor, Michigan [13}

Xl 1.02 _6 1 u Interior 0.0463

X2 "; - n n n 0.0551

X3 n - n n n 0.0568

Sl n 0.41 3 n n 0.0619

S2 , , n n ,

0.0616

53 , n , n n 0.0611

The University of Michigan, Ann Arbor, Michigan [14]

1 1.57 - 1 u Exterior 0.0372

2 n - n " n 0.0425

3 , - "

, " 0.0429

4 " - , , , 0.0580

5 l.:!.O 0.46 3 " " 0.0520

6 , , ,

" ,.,

0.0623

7 " " ,

" n 0.0596

9 1.12 - 1 " ,.,

0.0414

10 " 0.46 3 " " 0.0436

11 " 1 " " 0.0460 -12 " 0.46 3 "

, 0.0527

The University of Te.'Ca.s, Austin, Te.'Ca.s [221·

J1 1.22 1.22 4 u Interior 0.0408

J2 " ,

3 ,

" 0.0402

J3 ,

" , ,

Exterior 0.0406

6.12

Table 6.3 Properties and Deforrr.ation Capacities of RC Beam-Column Asse.I:lblages

Assemblage Span to Height Specimen Loading Joint Drift Indi:.."C

ID Ratios Type Direction Location

LdHI L2 /H c University of Tokyo, Tokyo, Japan [21]

S1 1.84 - 2 u Interior 0.0431

S2 " - " " " 0.0432

J1 " - 1 " " 0.0429

J2 " - " n " 0.0429

C1 " - " n " O.Oi15

C2 " - " " " 0.0685

C3 " - " n " O.OiOS

University of )l!i:J.D.esota, Minnesota [5]

E'\V2 2.50 2.50 3 B Interior 0.0565

EW3 , " "

,., " 0.1257

Rice Ur.iversity,Houston, Texas [71]

Jl 1.50 - 1 u Exterior 0.0555

J2 " 0.73 2 ,.,

" 0.0555

J3 " - 1 " " 0.0556

J4 " 0.35 3 " " 0.0555

J5 " 0.48 ,

" " 0.0.556

JG " 0.60 , " , 0.0556

Ji " O.i3 , ,

" 0.0556

University of Canterbury, Christchurch., New Zealand [9]

2D-I 1.16 1.16 3 B Interior 0.0383

2D-E n " , n Exterior 0.0451

1D-I ,

1.06 4 u Interior 0.0459

1 L 1 = The beam length in the longitudinal direction,

£.! = The beam length in the transverse direction.

6.13

1 The ratio is 2Ld H iu cases of exte::ior joint.

3 Type 1 = Beams and columns only in the longitudinal direction.

4

Type 2 = Type 1 plus transve::se beams.

Type 3 = Type 2 plus floor slabs.

Type 4 = Type 1 plus floor slabs.

U = Unia."cial cyclic loading in the longitudinal direction.

B = Bia.-cial cyclic loadings in both longitudinal and transve::se directions.

5 The larger value in a principal direction when subjected to bia."cialloadings.

6 - sign means not ava.llable or not applicable.

7 " sign indicates the same ':alue as the above.

6.14

Table 6.4 Rados of Calculated and ).Ieasured Colu:cn End Rotations

Column Reporter Measured Calculated Ratio of

ID Rotation Rotation Rotations

[Reference] Be B' e B~/Bc

U1 Saatcioglu [48] 0.0461 0.0285 0.62

U2 nl 0.0422 0.0177 0.42

U3 " 0.0510 0.0393 0.77

tT4 " 0.0869 0.0587 0.67

us " 0.0442 0.0224 0.51

U6 " 0.0895 0.0450 0.50

U7 " 0.0882 0.0453 0.51

Unit 7 Za.hn (70] 0.0533 0.0456 0.78

UnitS " 0.0611 0.0414 0.68

).;fea!l value of B~/Be = 0.607

Standard. derivation (o-n-1) = 0.123

1 " sig:>. indicates the sa!:l.e repor: as the above.

6.15

Table 6. 5 Summary of Parameters and Their Values

Parameters I Beam Sections I Column Sections

Pt (%) _1 3.00

p (%) 0.61- 2.50 -p'fp 0.25- 1.00 1.00

PJ (%) 0.50- 2.00 0.80- 2.80

P/A,f~ - 0.10- 0.60

h (in) 24 20

bjh 0.5 1.0

Ljd 3.0 3.0

f~ (ksi) 4.0 4.0

fv (ksi) 69.0 69.0

1 - sig!l indicates not applicable.

,........_ 0.16 ,........_ 0.16 "U (a) lJ _(c) 0 : lncrco3ing Cyclic Loading 0 A ·o A L L 4 : Comtont Cyclic Loading

............. .............

c 0.12 c 0.12 0 0 A 0 t :;::; AA

~A A II. A ~~ A

0 0 ..... ..... 0 0.08

n 0 0 0.08 0 0 ~ 0 rr.: 0

~ A A a 2 'U 'U c

8 oo oaa A c

~ w 8 llJ f) 0.04 0 on o 0.0-4 - u 0

E 0 n a E 0

n 0 0 v v m m I l I I I I I 0.00 0.00

0.08 0.12 0.16 0.20 0.2-4 0.20 0.4 0.6 0.8 1.0 1.2 0\

Long. Reinforcing Index Bottom to Top Steel Ratio ....... 0\

..-... 0.16 ..-... 0.16 'U _(b) A

u _(d) 0 0 A L L

............. .......,.

c 0.12 c 0.12 0 A

~ 0 6 :;; A

~ A :;::; A A i A

0 0 A ...... .>J

0 0.08 a 0 0.08 D

~ n ~ - n ~ 2 A a 0

'U u c

f8 A c

fp H w 0 ld 0 0.0-4 a H c 0.0-4 ~- 0

a 0 E a 00 E 0

0 0 0 v Ql

m l_t__l_t_l_l m I I J i 0.00 0.00 0.00 0.02 0.04 0.06 0.08 0.10 2.0 -4.0 6.0 6.0

Trans. Reinforcing Index Sheor Span Ratio

Fig. 6.1 Mcasurccl Dcnm End llotalion Capacities versus Dirfcrent Parameters

0.10 0.10

,....... -(a) n o ,....... e-(c) a: Uniaxial Loading 'U [] 'U o: Diagonal Loading ~ O.OB 1- ~ 0.06 o: Bi-uxiol Loodinq ...._.,. .......__..

c c 0 0.06 1-

0 0.06 -:;:; 0 :6J r{} 0 0 0 0 ~ +' 0 0 0 0 0 oO o L~ 0.0-4 1- 0 n lr 0.0-4 0

[] 0 (j]

'U 0 QJ 0 'U

0 0 Sa ra~ c Bo 011) [] c

Ll.J 0.02 0 0 ld 0.02

_o 0(} ~[] 1- 0 u (J1 0 H 0 - 0 [] - 0 0 0 0

0 I I I I I 1__1 0 I I I I I 0.00 0.00 0.1 0.2 O.J 0.4 0.5 -0.4 0.0 0.4 0.8

Long. Reinforcing Index Axial Load Index 0'1 ...... -...)

0.10 0.10

......... -(b) ,-..... -(d) 'U 0 u ~ 0.08 ~ 0.08 ...._.,. .......__..

f-c c 0 0.06 0 0.06 ·.;:; 0 :;:;

~ 0 8 0 +' +' 0 0 0 0 8 n::: 0.04 n::: 0.04 [] [] 1:1

'U Oo <P 0 'U t-

~ l c 8g [] 0 c []

td 0.02

[] 0 l.LI

0.02 0 [] n [] . [] .

0 0 0 0 0

0 u I I .

I I I I I 0.00 0.00 0.00 0.02 0.04 0.06 0.06 0.10 2 J .. 5

Trans. Reinforcing lndox Shear Span Ratio

Fig. 6.2 Meil.!lured Column End notation Capacities versus Different Parameters

(a) Beam or Column

Joint face

(b) Moment distribution

6.18

Mu My

_I I (c) Idealized cur.;ature distribution

Inflection point

Fig. 6. 3 Idealized Curvature Dis,ribution in a Can:ileve:-

6.19

Typ cc I Rect Beams, p -0.67%

0.250 0.020

0.015 0 --0 c:

v r:n ..... " ~ 0.010 c 0 .....

1-

o.ocs 0.250

0.500 0.750

0.500 0.750

Compression/Tension Steel Retia

0.005 1.000

Fig. 6. 4 Calculated Plastic Hinge Ror:ations for Beams, (a) p = 0.67%

iyp eel Rect

-.... (l

~

ctO r::l • 0~

(.)

. 0 0 - . < 0

Q::o

0

0 c:::

~ ~

(./)

~ c:: ... ~ > 111 c: 0 ...

1-

. oa

0.250 C.02C

0.015

0.010

o.ocs 0.2!0 0.500

6.20

Becr.-S, p -1.33s:e;

0 . 01.()

0 . -o<s

0.750

0.750

1.000 0.020

0.055 _j l· l

o.oso ~

l o. 0 ., I

s'j I

O.o -1, "'o ~

I

o.o.Js ~

O.o.Jo l

0.015

O.OiO

0.005 1.000

Compression/Tension Steel Ratio

Fig. 6 A Ca.k:.riateci Pla..scic Hinge Roca::cns for Be2-r:1s, (b) p = l.ZZ%

0

c e:::.

~ ~ --(/j .. c:n '-~ > c:n c 0 '-

1-

6.21

Typ eel Rect Becr.:s, p - 2. 00%

0.250 C.02C

C.Oi5

0.010

0.005 C • .Z!:O

0 . .500

0.500 0.750

Compression/Tension Steel Ratio

0.005 1.000

Fig. 6.4 Ca!c~laced Plastic Hinge ?..ocac:ons for Bear..s, (c) p = 2.00%

Ty p c c

0 0 ~ . 0".

~ Q

• Q~ ~

0

0: Q Q . Q

0. 100 0.028

0

c 0.020 e:::

~ ~ --V1

~ c. 0 1 6 Ctl .... ~

> Ctl c 0 ,_ r-

0.012

6.22

Square Columns, p- 3. 0%

0. 200 O.JOO 0. LOO 0. 500 0. 600 . I

I 0.028

c;-~.a a"":: a·

-----------0· - ~a/l c- 1 0. 024 a·~ a""'=' a. -

0~~ ~ a· 0. 020

~o I a')" l

o. a 1 s

c'~1 o.a'lo OJ

0.012

a':: c'o l C· 0· _,

0. 008~----~----~~--------~----~--~--------~--~--~~~ 0.008 0. 600 0.100 0.200 o. 3oo a. +oo o. soo

Axial Load Ratio, ·pj~f'c

Fig. 6.5 Caicula.ted P!a.stic Hing~ Rotations for Colur:1ns

CHAPTER 7

SUMMARY, CONCLUSIONS, AND IMPLICATIONS FOR DESIGN

by

H. Krawinkler and

V.V. Bertero

7.1

7.1 SUMMARY

The research summarized in this report and discussed in more detail in Refs. 7. 1-7.7 has

been directed to attempt to improve seismic design practice.

Chapters 1-3 provide a discussion on presently employed code design procedures,

recommendations for improvement of code procedures, and basic information needed to

assess seismic demands and the damage potential of ground motions. Chapters 4-6 focus

on the behavior of reinforced concrete frame structures and their components. This chapter

provides a summary of the most important conclusions derived from this study and their

implications for seismic design practice.

In regard to present code design procedures, it must be said that present codes are very

inconsistent in accounting for the most basic parameters that govern the seismic

performance of structures, namely, member yielding strength, yielding strength of the

structure, local and global ductility ratio (~1 , ~g), and interstory drift (IDI). Codes are

usually based on a seismic load level that has little relation to the actual yielding strength

of the structure and, therefore, provides no consistent level of protection for damage control

and collapse safety. Present codes correctly acknowledge the need for simple design

procedures, but in emphasizing simplicity they often obscure the physical principles on which

seismic protection needs to be based. Even though present codes are providing adequate

protection in most cases, for simple, regular building structures, they are not based on

explicit considerations of seismic demands and structural capacities and, therefore, are not

easily adaptable to special cases nor are they flexible enough to incorporate much needed

improvements.

The work summarized in Chapters 1-3 is based on the premise that seismic design needs to

be based on a transparent procedure that considers at least two levels of protection -­

damage control and collapse safety and accounts explicitly for the requirement that ductility

capacities should exceed the demands imposed by the design earthquakes, and that the

7.2

resulting demanded drift should not exceed acceptable values. Focusing first on the design

for collapse safety, it is postulated that the ductility capacity of critical structural elements

(expressed as local ductility ratio) is the basic design parameter, and the objective of design

is to provide the structure with sufficient yielding strength capacity so that the ductility

demands on these elements are less than their allowable capacities. Target ductility ratio

capacities for structures are established by modifying (weighing) member ductility capacities

for anticipated cumulative damage effects and transforming these member ductility ratio

capacities into story ductility ratio capacities which are used as measures of the structure

ductility capacity. For target ductility ratio capacity derived in this manner, the required

yielding strength (inelastic strength demand) of the structure may be estimated from SDOF

systems and appropriate modifications that account for MDOF system effects. Thus,

implementation of this approach necessitates extensive information on system dependent

SDOF seismic demand parameters (in order to weigh ductility capacities) and system

dependent MDOF modifications.

An evaluation of seismic demand parameters is performed for bilinear and stiffness

degrading SDOF systems. In this study, the inelastic strength demands and cumulative

damage demands are evaluated statistically for specified ductility ratios, utilizing ground

motions with similar frequency characteristics, such as rock and firm soil motions recorded

not too close and not too far from the fault rupture. Some efforts have also been devoted

to the evaluation of demand parameters for motions recorded on soft soils. Strength

demands are represented in terms of inelastic strength demand spectra or in terms of elastic

strength demand spectra together with a spectra of strength reduction factors. Expressions

are developed that relate the strength reduction factor to period and target ductility ratio.

Cumulative damage demands are expressed in terms of energy quantities, number of

inelastic excursions, and a simple cumulative damage model.

In Chapter 3 displacement seismic demand spectra are developed on the basis of the

normalized strength demand spectra. The reliability of the present practice of checking IDI

demands from severe EQ ground motions by just estimating the elastic demands has been

7.3

analyzed by computing the spectra of the ratios of inelastic to elastic displacement for each

of 124 ground motions. The work summarized in Chapters 4 and 5 has been devoted mainly

to : (1) Evaluating the reliability of present system identification techniques of inferring

from recorded responses of a building its dynamic characteristics; (2) assessing the reliability

of analytical models and methods that are available for conducting analyses of the seismic

response of RC buildings; (3) evaluating the building's supplied mechanical characteristics

with particular emphasis on the strength, deformation and ductility capacities; and (4)

analyzing the probable performance of the buildings under more demanding seismic motions

than those recorded at their foundations. Two constructed U.S. RC frame buildings and

one Japanese RC frame building have been analyzed in detail. The results obtained have

emphasized the importance of measuring the response of the structures to ambient and

forced vibrations and/or to real earthquake ground motions in order to have reliable

estimations of the main dynamic characteristics of the entire (soil-foundation-superstructure­

and-nonstructural components) system and the difficulties of modeling analytically real RC

buildings. The results have also confirmed the importance of the effects of higher modes

in predicting the response of real buildings. In addition, the results have supplied valuable

information regarding the overstrength of real MDOF buildings and the relationship

between global ductility ratio and local ductility ratio for these tall buildings.

The research described in Chapter 6 examined the detailing requirement for RC structural

elements in high-rise buildings. A summary of experimental data for beams, columns and

beam-column joints is presented. A simple and well-established analytical model of

deformability ofRC beams and columns is described, and results ofthe model are compared

with experimental data. Plots suggest practical ranges of reinforcements required to achieve

desired deformation capacities in beams and columns.

7.2 CONCLUSIONS

From the studies on SDOF systems that are summarized in Chapters 1, 2 and 3 the

following conclusions have been drawn.

7.4

• The strength reduction factors depend strongly on the target ductility ratio and the

period of the SDOF system and to a much lesser extent on the deformation

hardening and hysteresis model. The reduction factors are not sensitive to epicentral

distance. The peaks and valleys of the spectra of the reduction factors usually

coincide with those of the elastic demand spectra, which explains why the inelastic

strength demand spectra are much smoother than the elastic ones.

• Smooth R-J..L-T relationships are developed for typical S1 ground motions through a

regression analysis based on a database of 39,000 points. The R-J..L-T relationships

are highly nonlinear in the short period and the relationship R = (2J..L-1) 112 will give

poor predictions for all but one specific short period. The relationship R = J..L is a

conservative approximation for long period systems.

• The R-J..L-T relationships can be used together with smooth ground motion spectra,

such as those proposed in the A TC-3-06 for soil types S 1 and S2 , to obtain inelastic

strength demand spectra. Because of the high nonlinearity of the reduction factor

in the short period range, the inelastic strength demand spectra, derived from

utilizing the A TC-3-06 ground motion spectra and the developed R -J..L-T relationships,

do not exhibit a plateau in the short period range.

• The peaks in the elastic response spectra give a distorted view of the inelastic

strength demands as they tend to disappear with increasing ductility ratios.

• Systems without deformation hardening tend to drift more, thus requiring higher

strength capacities than deformation hardening systems. The difference between

strength demands for 0 and 10% deformation hardening is in the order of 10-20%

for bilinear systems. The difference between strength demands for 0 and 2%

deformation hardening is in the order of 5-10%, i.e., small deformation hardening

can be very effective.

7.5

• The differences in strength demands between bilinear and stiffness degrading peak­

oriented models are usually small and in many cases the degrading model gives more

favorable results (smaller strength demands). Much effort is often devoted to refined

hysteresis modeling for elements and structures. With regards to assessment of

ductility or strength demands, this effort may not be warranted provided that stiffness

degradation is of a type similar to that described by the peak oriented model.

• Hysteretic and input energy spectra (per unit mass) are not very sensitive to the

target ductility ratio and are quite similar in shape.

• Stiffness degrading models tend to dissipate more hysteretic energy, because they

execute many more small inelastic excursions.

• The contribution of hysteretic energy to total dissipated energy (HE I TDE) is not

very sensitive to period and increases only moderately with the target ductility ratio.

• Normalized hysteretic energy, NHE, is a good index for comparing relative

cumulative damage for systems with the same target ductility ratio.

• Strong motion duration has an important effect on cumulative damage. The

"effective" strong motion duration experienced by the system is a function of the

frequency characteristics of the ground motion as well as of the structural response

characteristics (period and target ductility ratio). Presently used definitions of strong

motion duration, which do not consider structural response characteristics, cannot be

used as general indicators of cumulative damage. More research needs to be

directed towards formalizing a system dependent on strong motion duration

descriptions.

It has to be emphasized that the above conclusions were derived primarily from the studies

conducted on rock or firm soil ground motions and summarized in Chapter 2. From the

7.6

results obtained in the studies conducted on soft soil motions and summarized in Chapter

3, it can be concluded that most of the above qualitative conclusions are also valid for

motions in soft soils, but the specific values of the R-J..L-T relationships are very different

from those obtained on firm soils.

The importance of the effects of higher modes on elastic strength demands are well known

and have been clearly brought out again in the studies of the RC frame buildings

summarized in Chapters 4 and 5. The effects of higher modes on inelastic strength demands

for MDOF systems are evaluated in Chapter 2 for three types of MDOF models. The three

model studies are: (a) BH (beam hinge) models, in which plastic hinges will form in beams

only (as well as supports); (b) CH (column hinge) models, in which plastic hinges will form

in columns story only; and (c) WS (weak story) models, in which plastic hinges will form in

columns of the first story only. The main objective of the MDOF study is to estimate the

modifications required to the inelastic strength demands obtained from bilinear SDOF

systems, in order to limit the story ductility ratio demand to a prescribed value. For the

three models considered in Chapter 2, the controlling story, i.e., the story with the largest

ductility ratio demand, was the first one. The main conclusions derived from the parametric

study of these MDOF systems are summarized as follows.

• MDOF story ductility demands differ significantly from those of the corresponding

SDOF systems. The maximum ductility demands occur usually in the first story and

are usually higher than those of the SDOF systems. The deviation of MDOF story

ductility demands from the SDOF target ductility ratios increases with period

(number of stories) and target ductility ratio, and decreases with deformation

hardening. MDOF systems that can develop story mechanisms tend to drift more.

• The required MDOF base shear capacity for specified target ductility ratios depends

strongly on the type of failure mechanism that will develop in the structure during

severe earthquakes. Quantitative information is developed on the relative strength

requirements for three types of MDOF structures, illustrating the disadvantage of

7.7

structures in. which story mechanisms develop, and particularly the great strength

capacities needed to control inelastic deformations in structures with weak stories.

• The strength modification factor, which relates the required base shear strength of

MDOF structures to the strength demand predicted from SDOF systems for the same

target ductility ratio, is smallest for BH structures. For these structures it is usually

in good agreement with the A TC-3-06 modification (raising . of the liT spectral

ordinates to l!T213), provided that there is significant deformation hardening

(a= 10%). For short period BH structures the base shear strength demand is slightly

lower than the corresponding SDOF strength demand, indicating that MDOF effects

are not important for this range. Larger modifications are required for CH

structures. The WS structures require much greater strengths due to the problems

inherent in this weak story system.

• For the regular structures studied here, elastic MDOF systems attract lower base

shears than those predicted from the equivalent SDOF systems.

• Extreme strength discontinuities, such as those in the WS structures, should be

avoided whenever possible, as they lead to excessive ductility and overturning

moment demands that may be greatly amplified by the elastic vibration of the upper

portions of the structure.

• The results of the MDOF study indicate that overturning moments in inelastic

structures can be very large. If the story strengths are tuned to the code required

strength levels, it is likely that all the stories will yield simultaneously and, therefore,

the maximum overturning moments should be based on the shear strengths of all

stories above with due consideration given to deformation hardening. No overturning

moment reduction factors should be applied. In most real designs, the story strengths

cannot be tuned precisely to the code strength levels and individual stories may have

a shear strength larger than required. In such cases the overturning moments will

7.8

increase further. This study provides no information on the magnitude of this

increase, as it depends on the relative strength of each story and cannot be

generalized.

Regarding the problem of estimation of drift demands, seismic displacement demand

spectra were obtained using the normalized strength demand spectra. Present practice for

checking against lateral displacement demands for severe earthquake ground motions is

based on estimation of the elastic demands and multiplication of such demands by an

empirical coefficient which is independent of soil conditions. As is already mentioned in the

summary, the reliability of such a procedure was studied by computing the spectra of the

ratio of inelastic to elastic displacement demands. From the analyses of the values obtained

for this ratio spectra, which have been summarized in Chapter 3, the following conclusions

are drawn.

• The mean values of the ratio of inelastic deformation to elastic deformation show

that for structures with short T the inelastic displacement demands can be

considerably larger than the elastic demands.

• The range of the values of the structural period for which elastic analysis can be used

directly to estimate the inelastic displacement demand is dependent on the ductility

ratio level and the soil conditions.

• For soft soil sites and for values of TIT g very near to 1, inelastic displacements are

up to 40% smaller than the corresponding elastic displacements. For values of

TIT g < 0. 8, the im!lastic demands can be significantly larger than the elastic demands,

so that for sites with very long T g the displacement demands based on elastic

analysis can significantly underestimate inelastic displacement demands of structures

having T as large as 1.5 seconds, or even larger, depending on the value ofT g • Only

for values ofT IT g > 1.5 are the inelastic displacement demands approximately equal

to the elastic displacement demands.

7.9

The main dynamic characteristics of a given building during its response to earthquake

ground motions can be successfully identified by using different system identification

techniques. Comparison of the dynamic characteristics of the 30-story RC building

(reported in Chapter 4) with those obtained from ambient and forced vibrations tests

conducted at the end of construction indicates that the fundamental period of vibration of

RC structures varies (increases) considerably during its service life. From these

identification studies, it can be concluded that:

• To identify in a reliable manner the importance of the effects of torsion, foundation

movements, and soil-structure interaction, it is necessary to improve present

instrumentation of buildings, foundations, and surrounding soil. Insufficient number

(particularly of vertical sensors) and inadequate arrangement of sensors made it

difficult to reliably identify the above effects on the two buildings analyzed.

• Use of identifi_cation techniques to attain the dynamic characteristics from measured

response to any ground motions, forced vibrations, or even ambient vibrations is

important and greatly needed because it not only permits monitoring of the changes

of these dynamic characteristics during the service life of the building, but also allows

calibration of the analytical models that could be formulated and, particularly, makes

possible the formulation of reliable simplified models (one degree of freedom per

story or even an equivalent SDOFS), which make it possible to conduct parametric

sensitivity studies and overall response evaluations.

From the results obtained in the analyses conducted of the two U.S. RC buildings using

detailed finite element models, the following main conclusions have been drawn.

• Due to early concrete cracking of RC structures and bond slip, it is very difficult to

formulate an analytical model that will reliably simulate the actual main dynamic

characteristics (particularly the periods of vibration) at any given time in the service

life of a building. It is necessary for designers and analysts to consider more than

7.10

one analytical model when evaluating the dynamic response of a building. There is

a need to consider a range of values for the fundamental period or at least the

bounds of this range, and not just a single deterministic value.

• Detailed 3-D finite element models and existing computer programs, when properly

calibrated, can be used to obtain reliable estimation of the dynamic response of RC

structures in the so-called linear-elastic range.

• Those analyses which only took into account the fundamental mode failed to

reproduce recorded accelerations. The number of modes that need to be considered

in order to have reliable agreement between predicted and measured response

depends on the response parameter (accelerations, velocities or displacement).

• Despite the apparent severity of the recorded motion at the foundation of the 10-

story building (PGA of 0.60g and 0.40g), the maximum interstory drift indexes, IDI,

were small (0.21% and 0.34%). These IDI not only explain the absence of significant

damage in the building, but also confirm once more that the PGA of recorded

ground motions is not a reliable parameter by which to judge the damage potential

of an earthquake ground motion to a specific structure.

• Use of CQC modal combinations for the 30-story building resulted in story shears

that were 17% higher than those obtained using the SRSS method.

• The site design spectra for the two design earthquake levels (MPDS and MCDS)

were apparently based on a T g of approximately 0.25 seconds, and these two spectra

were very narrow band in their frequency content. These specified spectra

characteristics differ significantly from those of the spectra obtained for the recorded

ground motion obtained during the Lorna Prieta earthquake (T g =1.2 seconds with a

strong acceleration content in the period range of 0.6 to 1.5 seconds. As a

consequence of these differences, the lateral forces and displacements used in the

7.11

design of the building did underestimate the real forces and displacement that can

occur, particularly at the upper stories, during moderate and severe earthquake

ground shakings.

• Site design spectra should not be very narrow band in period (frequency content).

They should reflect the uncertainties in the estimation of the T g and T.

Regarding the observed overstrength and ductility ratio demands of the real buildings that

have been studied, it is concluded that:

• U.S. Buildings. The ten-story building has a structural yielding . strength capacity

(formation of a mechanism) that can vary from 4.2 to 5.0times the factored specified

code strength (i.e., factored to first significant yielding of the critical region of a

member). For the thirty-story building, such yielding strength capacity was about 2.1

times that used in its design. The maximum demanded global ductility ratio for the

thirty-story building was estimated to be 3.41 (this was demanded by the Tokyo 101

record normalized to a PGV of 50 em/sec). The maximum IDI was estimated at

1.5%, and it occurred under El Centro and Hachinohe records normalized to a PGV

of 50 em/sec. For the ten-story building, the structure's yielding strength capacity in

the transverse direction (dual structural system) was estimated to be between 5.75

and 6. 99 times that used in its design. In the longitudinal direction the ratio between

the structure's yielding strength capacity and the factored code design strength was

estimated to be between 4.23 and 5.0. When subjected to the Hollister and James

Road records (which are considered to be the most critical ground motions of all the

earthquake ground motions recorded in the U.S.), the maximum IDI in the

longitudinal direction is 0.016, resulting in a maximum global story displacement of

J.L = 3.15. It is doubtful that the existing detailing of the structure would allow such

a story ductility ratio to develop.

7.12

• Based on results obtained in the nonlinear analyses conducted on the ten-story

building, an approximate method is proposed for estimating story displacement

ductility ratio demands directly from the computed global ductility demands. The

method is based on first computing the relationship between global and story ductility

of the structure based on static lateral loading of the structure, and then determining

the required global ductility by conducting a nonlinear analysis of an equivalent

SDOFS when subjected to the expected critical ground motions.

• Japanese Thirty-Story S-K Building. The first mode period, T1 , of this thirty-story

building has been estimated to be 1.68 seconds. The first plastic hinge occurred at

a base shear seismic coefficient of 0.11 and an IDI that can vary between 0.23% to

0.44%, depending on how the effects of cracking on the member stiffness are

considered. The structure's yielding strength capacity was evaluated to correspond

to a base shear seismic coefficient of 0.15. Therefore the ratio between the

structure's yielding capacity (at mechanism formation) and the first significant

yielding of the critical story for which the structure has been designed is about 1 ,36.

The maximum IDI at instability was 0.87%, which corresponds to a story

displacement of J.£ =2.

From the results obtained in the parameter study of deformation capacities of beams and

columns as a function of the reinforcement quantities which has been summarized in

Chapter 6, the plots given in Figs. 6.4 and 6.5 can be used to determine the practical ranges

of longitudinal and transverse reinforcement needed to achieve desired deformation (plastic

rotation) capacities in reinforced concrete beams and columns. In using these plots, it

should be carefully noted that: First, the actual deformation capacity under severe cyclic

loading is likely to be at least equal to one-half the calculated values shown in these figures;

and, secondly, the values of these plots were obtained using a model in which only flexural

behavior was considered, i.e., that deformations and failure modes associated with shear,

bondslip and anchorage in the members and their connections were not included.

7.13

7. 3 IMPliCATIONS FOR DESIGN

The ultimate goal of the original proposed research project on topic 5 was to develop a

rational methodology for calculating the values of response reduction factors (R or DJ

which incorporates the present existing uncertainties in establishing reliable design ground

motions and in predicting the building responses to such ground motions. From the

problems encountered during the studies conducted and from the results of these studies

summarized in the previous six chapters, it was recognized that, rather than only

concentrating efforts to find an improved method for estimating the values of R or D8

, it

would be better to attempt to formulate an overall rational (conceptual) methodology for

seismic design that could be used to replace the present empirical code design approach.

This methodology should be a transparent approach based on well-established fundamental

principles and in compliance with the worldwide-accepted Earthquake-Resistant Design

(EQRD) philosophy. The advantage of this conceptual approach is that, notwithstanding

the great uncertainties in the quantification of some of the concepts involved in its

codification, the numerical quantification of the concepts can be improved without changing

the format (concept) of this codified approach as new and more reliable data is acquired.

Based on the studies conducted in the project, the EQRD problem can be formulated and

solved as follows [7 .1]:

GIVEN:

REQUIRED:

1.

2.

3.

Function of building;

Site of building;

General configuration of building, structural layout and

structural system.

To attain an efficient {optimum) EQRD of the building.

SOLliTION:

7.14

To achieve an efficient final solution requires an iterative

procedure starting with an efficient preliminary EQRD. The

first step in carrying out such a preliminary design is to

establish reliable design Eqs.

Therefore, in order to formulate a rational, transparent design procedure, it is convenient

to divide the formulation of such a procedure into two phases: The first phase covers the

acquisition and processing of the data needed to establish reliable design Eqs; the second

,phase is devoted to developing the conceptual design methodology based on the established

design EQs. Although it would be ideal for the designer to be involved in these two phases,

in general it will not be necessary since the design EQs can be established for different site

types by a group of experts.

7.3.1 FIRST PHASE: Acquisition and Processing ofData Needed to Establish Design EQs.

7.3.1.1 Acquisition of Data. For any given specific site (or region or zone), it is necessary

to: (1) Conduct an analysis of the selected site (soil profile and topography); _(2) identify

the sources from which EQs can originate; (3) define the seismic activity at the site due to

all possible sources and events at these sources in the form of time-histories of ground

motions and their recurrence period; and (4) establish the range of EQ ground motions

(time-histories) for the different limit states to be considered in the design of the building.

In the general case of a region, zone or urban area, it will be necessary to formulate EQ

ground motions (EQGM's) at service, continuous operation, and safety levels with their

corresponding recurrence period, TR. For each of these levels the EQGM's should be

specified for different site conditions. The soil conditions to be considered are: (1) Rock

or firm soils; (2) medium firm soils (alluvium); and (3) very soft soils. Possible effects of

topography such as buildings located on hills or in a valley surrounded by hills, etc., should

also be considered.

7.15

7 .3.1.2 Processing of Data. The recorded acceleration time-history should be processed

to obtain:

(1) The time-history of the velocity, incremental velocity, displacement and incremental

displacement;

(2) For the serviceability limit state, the LERS for strength (C5) and IDI for each of the

possible EQGM's that can be originat~ from the different EQ sources. From

statistical studies of these LERS, find the average or the average plus one standard

deviation serviceability spectra. Considering the uncertainties in predicting future

ground motions and in estimating the fundamental period of the structure, modify

the above statistically derived LERS and formulate the SLEDRS for strength, C5 and

IDI.

(3) For continuous operation and safety levels of design EQs, the LERS and the IRS (for

different values of IJ) for each of the possible EQGM's that can be originated from

the different EQ sources. From statistical studies of the LERS, find the average and

average plus one standard deviation LERS. Modify these LERS to include the

uncertainties in estimating T. In the case of sites with soft soils, it is convenient at

present to plot the spectra in Function of Tff g· Therefore, in modifying the

statistically-derived LERS to obtain the SLEDRS and SIDRS, careful consideration

should be given to the uncertainties in estimating T and T g· To obtain the critical

ground motions to be considered for continuation of OPERATION AND SAFETY

LEVEL in cases where some degree of damage is tolerated (i.e., 1J. > 1), it is

necessary to compute for each EQGM's the following spectra: E1, EH, IJ., and NYR.

Once the critical ground motions have been selected, then it is necessary to plot the

IRS for strength (Cy) and for IDI of each of the probable critical GM's considering

different resistance functions, i.e., hysteretic behavior. From statistical analysis of

these inelastic spectra, it will be possible to develop the SIDRS for Cy and IDI. The

shape of these smoothed spectra should consider the uncertainties involved in the

estimation ofT and T g .

7.16

7 .3.2 SECOND PHASE: Design Procedure

Two procedures are proposed. They are based on the use of the same basic concepts and

data, but differ in the way these data and concepts are used. The first procedure is

illustrated in Fig. 2.1 of Chapter 2 of this report, and it is discussed in more detail in Ref.

2. The second procedure consists of a series of steps that can be grouped as illustrated in

the flow chart shown in Fig. 7.1. The detailed discussion of this second procedure as well

as its application to a specific tall building will be the subject of a separate report that is in

preparation under the new research project, "Design of High-Rise RC Buildings".

REF. CHAPTER

[7.1] 1.

[7.2] 2.

[7.3] 3.

[7.4] 4.

[7.5] 5.

[7.6] 6.

[7.7] 7.

7.17

7.4 REFERENCES

REPORTS

Bertero, V.V.,Anderson, J.C.,Krawinkler, H.,and Miranda, M.,

"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.

Krawinkler, H., Nasser, A., and Rahnama, M., "Evaluation od

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 Bertero, V. V., "Evaluation of Seismic

Performance of a Ten-Story RC Building," July, 1991.

Anderson, J.C.,Miranda, E., and Bertero, V.V., "Evaluation of

Seismic Performance of a Thirty-Story RC Building," July, 1991.

Hart, G., Ekwueme, C.G., and Sabol, T.A., "Earthquake

Response and Analytical Modelling of the Japanese S-K

Building," July, 1991.

Qi, X., and Moehle, J.P., "Displacement Design Approach for

Reinforced Concrete Structures Subjected to Earthquakes,"

January, 1991.

7.18

(

PRELIMINARY DESIGN PHASE! _!

I. PRELIMINARY ANALYSIS 112. PRELIMINARY ~

3.ANALYSIS OF PRELIM-DESIGN !NARY DESIGN

OBJECTIVE: I OBJECTIVE: OBJECTIVE: ESTABLISH DESIGN CRITERIA 6 I DETERMINE MEMBER SIZES, DETERMINE ACCEPTABILITY

, DETERMNE i:lESIGN FORCES 1- ! AND REINFORCEMENT ~ OF DESIGN J

J IF UNACCEPTABLE I ACCEPTABILITY i

CHECK I

IF ACCEPTABLE

FINAL DESIGN PHASE

4. FINAL DESIGN ~5. RELIABILITY CHECK OBJECTIVE:

I OBJECTIVE:

DETERMINE FINAL REINFORCE- EVALUATE RELIABILITY OF MENT DISTRIBUTION I FINAL DESIGN AND OBTAIN

I r-

I GUIDELINES FOR MEMBER DETAILING TO ENSURE A

l DUCTILE STRUCTURE AND BUILDING

Fig. 7.1 Flow Chart of Design Procedure