Kajima - CUREe Research Project

Design of High-Rise Reinforced Concrete Building

LM

-4

Dr. Norio Inoue

Dr. Norio Suzuki

Mr. Hiroshi Morikawa

Mr. Masaaki Okano

Mr. Takaharu Fukuda

Mr. Hitoshi Hatamoto

Mr. Motomi Takahashi

Mr. Satoshi Orui

Mr. Makoto Maruta

Prof. Vitelmo V. Bertero

Prof. Helmut Krawinkler

Prof. James C. Anderson Prof. Graham H. Powell

Prof. Filip C. Filippou

Mr. Hatem Y. Goucha

Mr. Pasan Seneviratna Mr. Mohsen Rahnama

Mr. Amador Teran-Gjlm ore Mr. Raul D. Bertero

CUREe

Kajima Corporation CUREe;

California Universities for Research

in Earthquake Engineering

* Kajima Institute of Construction Technology * The California Institute of Technology

* Information Processing Center * Stanford University

* Structual Department, Architectual * The University of California, Berkeley

Design Division * The University of California, Davis * Civil Engineering Design Division * The University of California, Irvine * Kobori Research Complex * The University of California, Los Angeles

* The University of California, San Diego

* The University of SOuthern California

SUMMARY REPORT

CUREe—Kajima Research Project University of California, Berkeley

High-Rise Reinforced Concrete Buildings

Vitelmo Bertero, Team Leader

OBJECTIVES

The ultimate goal was to advance, through evaluation of present knowledge and of the results of new coordinated research, the states of the art and the practice in the earthquake-resistant design of high-rise reinforced concrete (RC) buildings. To achieve this goal, particular emphasis was placed on:

identification of RC buildings systems which are particularly suitable for high-rise con-struction in seismic regions with soft-soil sites;

evaluation of seismic response characteristics of these systems, considering linear and non-linear responses;

development of new computer programs for computer analysis of 3-D nonlinear responses;

evaluation of recent developments in energy dissipation mechanisms for possible integra-tion into these systems;

use of high strength concrete (500 to 670 kg/cm2); and

00 -

• development of improved methods of preliminaiy design to enhance seismic performance of these systems.

MAJOR ACCOMPLISHMENTS

To achieve the above objectives, a series of studies were planned, grouped under five main tasks. The major accomplishments in each of these five tasks are the following.

Review of the State of the Art and the State of the Practice

The maln results of this review are described in two reports.

Structural Systems. In spite of the fact that the use of dual structure systems Consisting of shear walls (particularly coupled walls) and special moment-resisting space frames (SMRSF) and other systems, such as outrigger structures and tubes, are very promising for earthquake resistant design, up to now most of the tall RC buildings in zones of high seismic risk have been built using just SMRSFs. The main reason for this is that the practicing engineers have more confidence in their ability to predict the behavior of SMRSF than for other systems and relatively reliable com-puter programs are available to analyze the linear and nonlinear responses of SHRSF buildings. This points out the need for investigating the nonlinear seismic response behavior of the other sys-tems such as tube (framed and braced), outrigger, and dual (SMRSF and shear walls).

Foundation. The use of encasement walls with drilled piles (as used by Kajima in the S-K building) is technically the most effective type of foundation for tall buildings on soft soils, how-ever, its use is expensive. U.S. seismic codes do not address the design of foundations in ade-quate detail and as the foundation may constitute a weak link in the entire soil-foundation-super-structure-and-nonstructural components systems, better code regulations for earthquake-resistant design are needed. The practice of Kajima of including the soil and foundation mechanical char-acteristics in the model of the tall building at the start of the design should be adopted in the U.S.

Review of Seismic Performance of High-Rise RC Buildings

The reviews conducted are described in three separate reports, which concentrate on the response of this type of building in Japan, the U.S., Mexico and Chile. Site soil effects, which proved to have a predominant effect on the performance of structures located on soft soil, need to be accounted for more realistically in earthquake resistant design than at present. Soil-structure interaction is not always beneficial in reducing response demands, and therefore needs to be con-sidered in the design process. More reliable methods for estimating damping of soil materials and radiation damping are needed. There is a need for improved methods to estimate the effective structural period (7), and the predominant period of the soil. Site spectra for earthquake resistant design should account for the uncertainties in computing the T and Tg. Initial tilting, due to dif-ferential settlement, when an earthquake occurs has been shown to be detrimental for seismic response of the building. Overstrength with respect to the ultimate (maximum) strength expected from seismic code requirements depends upon the T (height) and the design method that is used. The taller the building, the smaller the overstrength. Design methods based on elastic force distri-bution result in larger overstrength than those based on plastic redistribution. The lowest over-strength results from use of optimal plastic methods.

Dynamic Response Analysis of Promising Systems

This task covered two main groups of studies. One is the development of computer pro-grams for nonlinear dynamic analysis of RC buildings. User guides for the DRAIN-2DX, DRAIN-3DX and DRAIN-31) BUILDING have been released. This, together with the develop-ment of a "Nonlinear Analysis Method by the Fiber Model for Applications to RC Columns, Beams and Beam-Column Subassemblages," conducted and reported by the Kajima Team, will enable conducting more reliable analyses of the real nonlinear responses of RC structures, and will

therefore improve earthquake resistant design of new RC structures and the vulnerability assessment of existing RC buildings. The second main group of studies were conducted to evalu-ate the effectiveness of present U.S. seismic code design procedures, which were applied to different structural systems; SMRSF, Framed Tube and Braced Tube. Two reports discussed in detail the results obtained for SMRSF. Another report in prepaation describes the results obtained for tube systems. In all these designs, problems in complying with serviceability requirements have been detected. Tall buildings designed according to U.S. seismic code regula-tions while they can be safe are not serviceable. Analysis of seismic response demands using the static push-over technique can detect the weaknesses of the design but cannot give reliable esti-mations of several important response parameters. In this type of analysis, P—E effects are usually overestimated (however time-history analyses show that these effects are very sensitive to the dynamic characteristics of the earthquake ground motions), the maximum strength is underesti-mated, and the inelastic deformations are underestimated. Time-history analysis of the response of buildings using available nonlinear 2-13 computer pmgrams (such as DRAIN-2DX), although giving more reliable predictions of the demands than the static push-over analysis, still has serious limitations, such as that it cannot give estimations of the effects of bi-directional earthquake ground motions and of torsion. Therefore there is a need for a reliable and effective 3-D non-linear computer program. Although Kajima has a 3-13 program based on concentrated plasticity, it uses supercomputers and is expensive.

Feasibility of the Use of Energy Dissipation Devices and High-Strength Concrete

Due to the lack of necessary funds and time, only preliminary studies have been conducted. Preliminary redesign of the S-K building using high-strength concrete (500 to 670 kg/cm2) has been completed and the results are encouraging. The use of high-strength concrete results in reduction of 12% in the total weight of concrete without any significant increase in the deforma-tion demands. A report describing the design of the S-K building using high-strength concrete has been prepared. The use of passive control of the seismic response of SMRSF buildings has been considered through preliminary analysis. The results of this analysis are encouraging, particularly when energy dissipation devices are used. The use of additional viscous dampers over the use of devices based on yielding of metals or friction is favored.

Development of Preliminary Design Methods

Two reports discuss the development of a "Conceptual Methodology for Numerical Earthquake Resistant Design," Results from the analyses of the linear and nonlinear responses of one 30-story building (of similar layout to the S-K building) designed according to this new con-ceptual methodology to service and safety levels of design earthquake ground motions are very encouraging. The overall conceptual approach to earthquake resistant design consists of two main parts. The first part covers guidelines for conceptual design of the entire facility system including building configuration, structural layout, structural system, structural material, nonstruc-tural elements and their materials, as well as type of foundation. The second part is the concep-tual methodology for numerical earthquake resistant design of the entire building system. It complies with the worldwide accepted philosophy of earthquake-resistant construction and is based on fundamental principles of structural dynamics, mechanical behavior of the entire building

system (soil under and surrounding the building, foundation, superstructure, nonstructuraj com-ponents and contents) and comprehensive design (which is a probabilistic approach to design which includes not only the reliability of the design at each limit state, but also the cost/benefit analysis of reaching each of these limit states. The main advantage of this conceptual methodol-ogy is that notwithstanding the great uncertainties in the quantification of some of the concepts involved in its codification, such numerical quantification can be improved without changing the format of the codified methodology as new and more reliable data are acquired.

IMPL&CT OF THE RESEARCH RESULTS

It is well recognized that one of the most effective ways to improve seismic risk reduction in urban areas is through improving the earthquake resistant design of new facilities and the upgrad-ing (rçtrofitting) of existing hazardous constructions. In the past two decades there has been an increaM in the construction of high-rise RC buildings in regions of high seismic risk. There is a lack of reliable data on the performance of these tall RC buildings, particularly those built on soft soils, and there is doubt about the adequacy of the methods that have been used and are presently used in their design. This has been dramatically illustrated by the failure of many tall buildings during the 1985 Mexico earthquake.

The methods of analysis and particularly the conceptual design methodology in this research project will lead to better earthquake resistant design of tall buildings, as well as improved reliabil-ity of the vulnerability assessment of existing buildings which is so much in need for deciding the demolition or upgrading of these buildings.

RECOMMENDATIONS REGARDING ADDiTIONAL RESEARCH

Study of the seismic behavior of dual systems, tubes (framed and braced), an outrigger structural system, particularly their nonlinear response (yielding mechanisms)

Search for more effective (technical and economic) foundations (design and construction)

Development of more reliable methodology to estimate the effect of soil-structure interac-tion and the damping values for soil materials and radiation

Improve methods for estimating the period of RC structures considering the effects on the stiffness of cracking, aging, etc.

Develop more efficient 3-D computer programs

Investigate through integrated analytical and experimental studies the use of energy dis-sipation devices to control the seismic response of tall RC (as well as steel) buildings

Apply conceptual methodology to the design of typical buildings and then to analyze their response tocritical earthquake ground motions

Based on the results obtained in the application of the conceptual methodology, develop seismic code regulations that are simple, practical and reliable.

CUREe-KAJIMA RESEARCH PROJECT

REVIEW OF THE STATE OF THE ART AND THE STATE OF THE PRACTICE OF

EARTHQUAKE-RESISTANF DESIGN OF HIGH-RISE REINFORCED CONCRETE

BUILDINGS ON SOFT SOILS IN HIGH SEISMIC RISK AREAS

Hatem Y. Goucha and Vitelmo V. Bertero

Earthquake Engineering Research Center

University of California at Berkeley

July 15, 1991 - January 14, 1993

ABSTRACT

The objectives of this study are the following: First, to review the different super-

structure and foundation systems that have been used or could be considered for high-rise

reinforced concrete buildings on soft soils; then, to evaluate the limitations and advantages

of each system in resisting earthquake effects; and finally, to investigate analysis methods

and design procedures that have been used or proposed recently. Different definitions can

be found for tall buildings, but it was found that the slenderness ratio is key to determining

whether a building should be considered a high-rise building. A slenderness ratio greater

than 4 in a building will generally cause problems that are specific to high-rise structures.

Ten structural systems have been examined: moment resistant space frames; single

shear walls; coupled shear walls; wall-frames; suspended structures; outrigger structures;

tubes; tube-in-tubes; bundled tubes; and braced tubes. Their advantages and disadvantages

in resisting earthquake effects were examined and discussed. One important observation is

that outrigger structures, tubes, tube-in-tubes, bundled tubes and braced tubes all share one

main disadvantage: the lack of understanding of their non-linear behavior and therefore,

the lack of 3-D non-linear analysis tools. One disadvantage of tubular structures, in the

non-linear range, is that they usually rely on axial resistance of the columns, which is not a

desirable means of energy dissipation. Regarding the use of innovative techniques such as

base isolation and energy dissipation, it was found that base isolation is not effective in

reducing the earthquake effect on buildings with more than 12 to 15 stories. Some energy

dissipation devices have been tested and have been used in buildings in high seismic risk

areas. Their use for mitigation of earthquake hazards is recommended for tall reinforced

concrete buildings.

The seismic behavior of different foundation systems (piles, mat foundation, embedded

foundation and control piles) was reviewed. From this investigation, it was concluded that

the embedded foundation is a good solution in case of soil with low strength capacity and

when excessive settlements can occur such as in case of soft soil. However, this method can

be uneconomical if excavation needs to be carried much lower than the water table. Tall

buildings on soft soils can undergo significant tilting, which can be a direct cause of pro-

gressive collapse during ground motion. Rocking can also cause impact forces on the

foundation and the superstructures, and will also affect the period of vibration of the building

and therefore change its response to the earthquake ground motions.

11

The design aspects of the problem were illustrated by the study of six reinforced

concrete high-rise buildings in high seismic risk regions: two instrumented 30 story MRSFs;

one 23 story shear wall; one 30 story tube-in-tube; one 18 story tube-in-tube and one 32

story perimeter frame. All except the perimeter frame have experienced moderate earth-

quakes. The two instrumented buildings (MRSF) responded satisfactorily to service ground

motions. The 23 story shear wall suffered minor damage under a ground motion that could

be considered more than "moderate". The 30 story tube-in-tube suffered no damage during

a service ground motion. The 18 story tube-in-tube experienced a strong ground motion and

suffered some structural damage.

The analysis methods for reinforced concrete tall buildings have been reviewed. It was

found that non-linear analysis programs for 3-D buildings were available, but they do not

have elements that capture the important non-linear behavior of reinforced concrete

beam-column elements. Some methods for 2-D simplifications are suggested for reinforced

concrete shear walls, coupled shear walls, wall-frames, tubes and braced tubes.

Finally, after discussion of the seismic behavior of existing tall reinforced concrete

buildings and analysis of the advantages and limitations of possible structural systems

keeping in mind the state-of-the-art in analysis methods, some recommendations on

promising systems are made. Reinforced concrete MRSFs have been built in seismic regions

for up to 37 stories (precast MRSF recently built in Tokyo, Japan), and have performed well

when subjected to ground motion. The methods of analysis for 3-D linear systems are very

reliable and widely used. However, non-linear analysis of reinforced concrete frames can

only be used reliably with 2-D programs. Shear walls are believed to be adequate systems

for buildings with less than 30 stories, as proved by existing structures, and are believed to

have good capabilities for ultimate-level seismic response as well. However, more

sophisticated and "modelling-intensive" computer analysis is required. For heights greater

than 40 stories, outrigger structures, tubes, tube-in-tube bundled tubes and braced tubes need

to be used for deflection limitation. No explicit cut-off heights can be drawn for any one of

the five systems, but they each have advantages and disadvantages. The non-linear behavior

under safety earthquake ground motions (some features of which are mentioned in the study)

needs to be examined in a case-by-case manner.

111

REVIEW OF SEISMIC PERFORMANCE OF TALL REINFORCED CONCRETE BUILDINGS

Report on Task 2 of the CUREe/Kajima Project on

DESIGN OF HIGH-RISE REINFORCED CONCRETE BUILDINGS ON SOFT SOILS

by

Pasan Seneviratna

Helmut Krawinkler

and

and the Kajima Project Research Team

A CUREe-Kajima Research Report

February 1993

1. INTRODUCTION

During the last two decades taller and more slender reinforced concrete buildings are

being designed and constructed in areas of high seismic risk. Developments in high strength

concrete and concrete pumping technology has contributed to this popularity of reinforced

concrete for high-rise buildings. Current seismic code regulations, however, do not adequately

address specific problems encountered in seismic resistant design and construction of tall

concrete buildings. The goals of the research project that led to the writing of this report is to

advance the state-of-the-art and the-state-of-the-practice in seismic design of high-rise

reinforced concrete buildings. The main objectives are

Identification of reinforced concrete building systems particularly suitable for

high-rise construction at soft soil sites.

Evaluation of the seismic response characteristics of these systems

considering both linear and non-linear response.

Development of improved methods of preliminary design that will enhance

the seismic performance of these systems.

As part of this study a review has been carried out on the performance of reinforced

concrete building structures during past earthquakes. The objectives are to evaluate and

document the observed performance of various reinforced concrete tall building systems and to

summarize the salient findings in a format that can serve as a background for the research work

to be performed in this project. Emphasis is placed on instrumented buildings for which

ground motion and building response records are available and have been evaluated in past studies.

1971 San Fernando, 1979 Imperial Valley, 1984 Morgan Hill, 1987 Whittier Narrows,

and 1989 Loma Prieta earthquakes are used in this study. Research results which have been

obtained from shaking table tests of structural systems suitable for tall buildings are also

incorporated wherever pertinent.

This report summarizes the findings from a review of reports and papers that discuss

the performance of R/C buildings in the following U.S. earthquakes: 1971 San Fernando,

1979 Imperial Valley, 1984 Morgan Hill, 1987 Whittier Narrows, and 1989 Loma Prieta. The

data from the U.S earthquakes is supplemented with data from several R/C frame buildings in

Japan for which vibration test results, earthquake response measurements, and analytical

predictions were provided by members of the Kajima research team. Pertinent data of the

reviewed U.S. and Japanese buildings are summarized in Table 1(a) and Table 1(b),

respectively.. Qualitative and quantitative information extracted from this review and related to

1

dynamic characteristics of buildings, structural and non-structural damage, site soil effects, and

soil-structure interaction is presented in the Appendices to this report.

The performance review focused on the dynamic characteristics of buildings, soil-

struèture interaction effects, and site soil effects. In the assessment of performance it must be

considered that none of the reviewed earthquakes was very severe and that only few of the R/C

buildings included in this review exhibited noticeable structural damage. But all earthquakes

were of sufficient severity to cause various degrees of cracking in structural elements. Moment

resisting frame as well as shear wall buildings from 5 to 30 stories high were included in the

performance review.

2

BUILDING 8 Of LEN. .1 LOAD RESISTING SYSi TYPE TYPE YEAR OF CSMIP EARThQUAKE EN. [NSTRUMENI STRUCTURE REFERENCE VERTICAL LAT ERAL DESCRIPTION WIDTh OF OF DESIGN [USGS] SUBJECTED CENT. LOCATIONS PERFORMANCE

LONGiTUDINAL TRANSVERSE STOR. (ft) SOIL FOUNDATION Stn# 3D DIST.

Mmin.Building 8 154 RCSIab/Beam R.C.ShearWalls R.CShearWaila NotOiven Speadfootlngs 1967 24468 WhinIer 91m Basement Expectedsoftstoay Luletal. 1990

CSUIA 63 Floor above 2nd Floor above 2nd Floor & Cone. Caisso. Narrows '87 2nd ,Roof behavici not semtHlgfrr

node effects significant

BenkofCalifornia 12 161 LWtRthiforced M.R.Conrrete M.R.Concxete Sift/Silty Drilled and 1969 San Fernando 17m1 OroundFlr., StructnraljNonStructunl Blumel9l3

Sherman Oaks 60 Conc. Slab/Beam FramejS.WalI Frame Sand Can In Situ (1968 EQuake 71 7th & Roof Damage observed. Reparable

Lo.Angeles - - Structure Below 3rd Floor Pile Fdn. LA.Code)

Breotwood Square 9/12 141 RC Slab/Beam Non-ductile Non-ductile Pile Foundation San Fernando Building sustaIned no structur- Bettero Ct. al. 1988

San Vlncentc 86 Floor Moment Resisting Moment Realutl. 1971 al damage and Insignificant

Frame Frame - - on-structural damage

Burbank PacifIc 10 215 R. C. Slab/Bearing Precast Concrete Precast Coner. Alluvlam Cone. Calssons 1974 24381 WhIttier 26km tat 4th • No structural or non-atnictural Pardoen 1989

Manor 75 Wall System Shear Walls Shear Walls wider Walls UBCI3 - Narrowa'87 - 81h,Roof damagerepoited. Moehleet.al. 1990

CanuryClty 18 105 RCSlab/Beam/Wafl DuctlleRCMom. DuctlleRCMwn. 1967 San Fernando Building suataInednostnrctur- Berteroet.al. 1988

Medical Plaza 105 Floor Resisting Concrete Resisting Concrete 1971 al damage and Insignificant I

Frame Frame - non-structural damage

Certified Life 14 180 R.C. Flat Slab on R.C. Shear R.C. Shear Loose Fill on Raymond Piles 1966 San Fernando 17ml Ground FIr, Hairline Cracka on Shear Conrad Aasocltea

Building 120 Columns & Walls Walls Walls FInn Under- Both Vert. & EQuake 11 6th FIr & Walls Observed. 1973

Los Angeles - - lying soils Battered - - Roof

Ccsnmerclal 10 190 RCSIab/Framc MomautReslst R.C. Shear Alluviam MatFcxindatlon 1964 57355 MorganHill'84 Basement RlgldbodyrocklngofShear Mahlnetal. 1989

Building 82 Concrete Frame Walls Mt Lewis '86 2nd, 5th Wall bases In E-W diem Sederit Ct.al. 1991

San j - - - Iowa Prleta '89 33km Roof

HiltonHotel 13 249 RCSIab/Beam RCMomwit RCMoment 1968 San Fernando Building sustalnednostructur- Berlaoetal. 1988

Ventura Blvd. 165 Floor Resisting Resisting 1971 ii damage and Insignificant

Frame Frame - - non-structural damage

Holiday Inn 7 160 R.C. Flat Slab on PcrlmeterM.R.P. Perimeter M.R.F. Recent Alluvi. Can In situ 1965 San Fernando IlmI Ground Fir., Extensive non-structural Blume 1973

OrlonStreet 62 Columns &IntColumn &Int.Colunin am (Finesan- PlleFoundat- EQuakell 4th&Roof Damage&mlnorStrucnrral

LcsAngelea I I SlabFramea jSlibFrames I dyallis) lion - Damage

Table 1(a) Summary of Instrumented Buildings - U.S. Buildings

BUILDING #01 LEN.& WAD RESISTING SYSTEM TYPE TYPE YEAR OF CSMIP EARThQUAKE EPL INSTRUMENT STRUCFURE REFERENCE VERTICAL LAT ERAL DESCRIPTION WIDTh OF OF DESIGN [USGS] . SUBJECTED CF. LOCATIONS PERFORMANCE

LONGITUDINAL TRANSVERSE STOR. (ft) SOIL FOUNDATION Stn# TO DIST.

Sears Warehouse 5 360 Rat Slab on Perimeter Perimeter Not Given Spread 1970 24463 WhittIer 14km Basement No atrueteral or ncat-gnactural Filhippou 1990

Los Angeles 280 Ciroular Columns Moment Resist Moment Resist. Footings (1970 Narrows 87 243rel damage reported.

Cone. Frame Conc. Frame ?..A.Code) I - - Roof

Sheraton-UnIversal 20 184 RCSIab/BeamFlr. Moment Resist Moment Resist. Beddedsoft SpresdFootlngs 1967 24464 SanFernan.11 19m1 Basement, Minornon.strueturaldamage Blumel9l3

Hotel 58 LWt R.C. used Cone. Frame Cone. Frame Sandstone/ B. C. - 6ksf (1966 WhinIer 28km 3rd .9th • Significant Torsional Filuippou 1990

Hollywood - above Basement (L. Wt. Cone.) (L Wt. Cone.) Shale L.A. Code) - Narrows 87 - 16th ,Roof response observed.

lslmtan Airport 14111 200 RCflat Slab on RC Moment RC Moment RCCalssms 1967 San Fernando Building suatalnednoatructur. Bestaroetal. 1988

Center 200 Frame Resisting Frame Resisting Prime & Footings 1971 at damage and insignificant

nn.structoraldamage

UnlonBank 13/2 193 RC.Slab/Beam Moment Resist. Moment Resist Ailuviam Pile Foundation 1964 24322 SanFernandoll I7mi Basement San FerstEquake..Sw.& 8lume 1973

Building 75 Floor on Columns R.C. Frame R.C. Frame WhIttier 17 38km Ground Fir. on-struc. damage. Whiflier U. Y. 1991

heiman Oaks - - - - 2nd,8th,Roof UIkst-Non4tr. damage

Vslley Pesbitar1an 7//I 841 L.WL Concrete Slab RC Moment RC Moment Pile Foundation 1968 San Fernando Building sustained no stiuctur- Beticro et al. 1988

Hospital dii. on Steel Deck supp- Resisting Frame & Resisting Frame & 1971 al damage and Insignificant

Van Owen - - ,ited on RC Frame Partial. Rigid Core Partial. Rigid Core - on-structwal damage

Warehouse 14 217 RC Flat Slab Moment Resist Moment Resist. 100 ft. deep RC Footings on 1925 24236 WhittIer 25km Free Reid Soil Sna1czure intairtlon Fenves Ct. aL 1989

Building 51 Cone. Frame Cone. Frame Sandy-Clay Raymond Piles Narrows 17 Basan.,Bth observed In longitidInal dim.

.os Angeles - - Vp2400ft - - 12th,Roof I

Wilshire 16//I 166 PSC Slab onRC RCMoment RC Moment Cast-in-sItu 1969 San Fernando Buildingsustsinednostructur. Berteroetal. 1988

CuaistlanTowem 60 Frame Resisting Frame Resisting Frame Pile Foundation 1971 al damage and Insignificant

on-struetwil damage

WilahireCoraredo 13111 239 RC Slab on RCMontcstt RC Moment RC Pile 1970 San Fernando Buildlngaustainednoatnicsur. Berteroetal. 1988

Wilshire 142 Frame Resisting Frame Resisting Frame Foundation 1971 al damagearef insignificant

non-structural damage

Table 1(a) Summary of Instrumented Buildings - U.S. Buildings.(Contd.)

BUILDING 4 Of LEN. .1 LOAD RESISTING SYSTEM TYPE TYPE YEAR OF CSMIP EARThQUAXE EPL INSMUMENI STRUCTURE REFERENCE

DESCRIPTION WIDTh OF OF DESIGN [USGS SUBJECFED CENT. LOCATIONS PERFORMANCE VERTICAL LAT ERAL STOR. (ft) SOIL FOUNDATION 5us$ TO DISt LONGiTUDINAL TRANSVERSE

Holidaylms 7 160 R.C. Flat Slab on PerimeterM.R.F. PerlmcterM.R.F. RecentAlluvi- Cast Insitu 1965 San Fernando 26m1 Ground Fir., SurealmilartoVanNuya Blume 1973

larengo Snees 62 Columns & list. Column & mt Column am (Fine ian- Pile Foundat- EQuake 11 4 th&Roof Building. Similar damage

cs Angeles - - Slab Frames Slab Frames dyailts) Ion - - utlesseatensive

Holidaylnn 22 196 RCSIabBeam RCMomcnt RCMoment 1970 San Fernando Building sustalnednostnictur- Betteroet.al. 1988

North Orchid 97 Floor Resisting Resisting EQuakell al and

Frame Frame - - non-suisural damage

ImpaialCmsnty 6 137x86 R.C.Slab/Frame MomcntResistlng R.C.Shesr Alluviam TaperedPile 1971 ImperlalVailey 29km FreeFleld FoundatlonandFlrzt Floor wu Pausclskect.al. 1981

Services Building Concrete Frame Walls (Sar4tlay) Foundation (UBC'67) EQuake 19 Ground Floor Irrepaably damaged.

2rd,Rocf

L*sthain WhIttier 10 183 R.CSlab/Frame MomastRealsi. R.C.Slwar Alluviam Spread 1972 (804) Whittier 13km Basement HlgserModeEffecta Miranda 1991

'ow - 53 Concrete Frame Walls Footings - Narrows 17 - Sth,Roof Observed MohnOlymplc 10 212 PanjoinFloor RCMomad RCMoment SpreadFootlngs 1969 San Fernando Bufldingsustalnednoatnactur- Betteroet.al. 1988

OlymplcBlvd. 98 onRCFrame Resisting Resisting &GradeBcama 1971 al damageandlnslgniflcant

Frame Frame - - 'on-souemral damage

MuirMedical 11 144 R.C.FlatSlabon PerlmetcrM.R.F. PertmcicrM.R.F. SofttoMed. CastlnPlace 1966 San Fernando 2ImI Basement. Onlymlnornrn-atruclwii ConradAssocites

Caster 89 Columns & Intl. Column & Intl. Column Firm Silty PileiCalssons EQuake 11 6 thFlr & damage was observed 1973

Los Angeles - - $lab Frames 'iab Frames Sandt B.C.- 12hf - - Roof

Office Building 6 2DO R.C. Slab/Beam Moment Resist Moment Resist IndIvidual 1977 58490 Loma Prleta 89 811cm Ground Fir. No souctural or nas-struct. Celebi Ct. al.

San Bruno 90 Floor on Columns R.C. Frame R.C. Frame Spread FootIngs 2 nd,S th & damage was observed.

Roof

PacillcPlaza 30 110 RCSlabIFrame Moment Resist. MomentResiat. SoftSllty S'tkmaton 1983 LomaPrieta89 97km PreeField Buildlngauatalnednostnictur- AndemonI991

Building 56 Concrete Frame Concrete Frame CIay(Bay P.S.CpIle Ground .lIth aldamage&lruigniflcant Miranda 1991

Emayville - 00 Mud) Foundation - - 21 at, Roof non-auuctural damage

ResIdential 10 210 R.C.Slsb/Bearing R.C.Shear R.C.Shcar Alluvium Pre.Stressed 1971/72 57356 Morganliilll4 Ground Torsionaleffectahigber than Mahlnetal. 1989

Building 64 WaIl System WaIls Walls Coner. Piles Mt. Lewls86 6th,Roof predlctedbyUBC.88 Sedarat et. al. 1991

San Jose - - underwalls I - LomaThicta'89 133km . Moehiectal. 1990

Table 1(a) Summary of Instrumented Buildings - U.S. Buildings (Contd.)

BUILDING DESCRIPTION

#01

STOR.

LEN..1 WIDTH

(It)

LOAD RESISTING SYSTEM TYPE OF

SOIL

TYPE OF

FOUNDATION

EARTHQUAKES SUBIECFED

TO

EN. CENT.

INSTRUMENT LOCATIONS

DIS'I'.

STRUCfURE PERFORMANCE

REFERENCE

VERTICAL LAT ERAL LONGITUDINAL TRANSVERSE

Shinamachi 18 80 R.C. Slab Beam R.C. Moment R.C. Moment Clay I Pile Ize-Peninsula Coastal '74 150 kin Under Pile Fdn. No structural or Non-structural Kajima

Apartment 45 Floor Resisting Resisting SandyGravet Foundation lbaragi-kenCoastall4 190krn Base.,9th& damage reported. Team

Building - - Frame Frame Eastern Saitama 14 40km 18th Floor

S-K Building 30 99 R.C. Slab Beam R.C. Moment R.C. Moment Soft B.Wall under perip- Chiba To-Ho Oki '87 63km But, of pile Fdn. No structural or Non-structural Kajima

99 Floor Resisting Resisting Soil feral columns. Piles TokyoTo-Bu'88 13km 1 st Floor & damage reported. Team

Frame Frame -mder interior column - Roof

Sun-City 25 138 R.C. Slab Beam R.C. Moment R.C. Moment Not Pile Chiba-ken-Central '80 50km 1 St Floor, No structural or Non-structural Kajima

0-Tower 93 Floor Resisting Resisting Known Foundation II th Floor & damage reported. Team

Frame Frame Roof

Tohoku 9 123

_________

Conerete Encased Steel Structure Not Pile Miyagi-ken Old '70 115km 1 at Floor & No structural or Non-structural Kajima

University 57 Known Foundation Miyagi-ken Oki 18 128km 9th Floor damage reported. Team

Building - - ________________ Miyagi-ken Oki '78 1211m

Table 1(b) Summary of Instrumented Buildings - Japanese Buildings

CUREe-KAJIMA RESEARCH PROJECT

NON-LINEAR BEHAVIOR OF A TUBULAR STRUCTURE

Hatem Y. Goucha and Vitelmo V. Bertero

Earthquake Engineering Research Center

University of California at Berkeley

July 15, 1991 - January 14, 1993

ACKNOWLEDGEMES

The work presented herein is a follow-up on the report on Task 1 of the CUREe-Kajima research project on the design of high-rise buildings. The previous report is entitled, "Review of the State of the Art and the State of the Practice of Earthquake Engineering Design of High-Rise Reinforced Concrete Buildings on Soft Soils in Regions of High Seismic Risk."

I wish to thank Professor Vitelmo V. Bertero for his constant support and advice. I would like also to th ik Amador Terán and Raul Bertero for the support they provided, as well for some very fruitrul conversations on the subject of this report.

Finally I wish to thank my family in Tunisia, who have continuously supported me and encouraged me throughout the length of the research project.

11

1 INTRODUCTION

1.1 STATEMENT OF THE PROBLEM

Since it was first introduced by F.R. Khan [1974], the concept of tubular structures has been

used mainly in regions of low seismic risk or regions of no seismic risk at all. Recently, taller

and taller buildings are being designed in high seismic risk regions. In some cases, conventional

structural systems such as space frames or shear walls can not be used due to their insufficient

lateral stiffness and development of significant tensile forces in the columns at high slenderness

ratios. The use of tubular structures, because of the optimal location (at the perimeter) of the

lateral structural system offers a possibility for a better solution. In the elastic range, a tube can

provide a system stiff enough to satisfy serviceability constraints otherwise harder to achieve with

the more conventional MRSF structural systems (e.g., a 30-story RC MRSF has a fundamental

period of vibration of 2.5 secs., while a 30-story RC bundled tube has a period of 0.90 secs. The

overall higher stiffness is obtained by approaching as closely as possible the cantilever behavior

of a perfect tube: the columns are closely spaced and the spandrel girders are very deep, and

therefore very stiff, resulting in what can be considered a perforated tube. However, the post-

yielding range is not well understood. In this study, which is a continuation of a previous study

by the authors [Goucha and Bertero, 1992], an attempt is made to have a better understanding

of the behavior of tubular structure in the non-linear (inelastic) range when subjected to severe

seismic loading. Halabieh [1990] concentrated mostly on the method of analysis, and proved that

the 2D simplification he used (similar to the one used in this paper) gave good results. He

obtained a plastic hinge distribution during the static pushover that suggests a soft-story

mechanism at the 21st story. No specific conclusion was made regarding the collapse mechanism.

1.2 OBJECTIVE

The main objective of this work is to achieve a better understanding of how RC tubular

structures can dissipate large amounts of the EQ energy input by studying their non-linear

behavior of reinforced concrete tubular structures through mathematical modelling and non-linear

analysis. The analysis includes static pushover and a dynamic time history ground motion

analysis of a 2D model.

To achieve the main objective, it was necessary to accomplish the following secondary

1

objectives: first, the development of a reliable 2D model of the tubular structure, and second, the

establishment .f the importance of including the internal gravity frames in the modelling process

of a tube building for the purposes of design. This last objective was motivated by the fact that

previous works on the subject by Anderson [1975], Grossman [1986] and Halabieh [1990] did

lateral load analytical studies on tube buildings without including the internal gravity frames.

Anderson and Halabieh considered ground motions, and Grossman only-considered wind (due

to low seismicity at the site).

1.3 SCOPE

In order to achieve the above-mentioned objectives, the following steps were taken:

Identification of an existing reinforced concrete tubular structure.

Creation of a 2D model of the structure for use in the 2D non-linear program DRAIN-2DX

[Allahabadi,1988]. Use of a 2D program was selected for two reasons: first, the available 3D

non-linear programs are still inadequate for use with large structures having many degrees of

freedom (59 bays, 11 stories) due to the still inadequate and slow hardware freely available.

Second, the beam column elements available in FACTS [SSD, 1987] and the ANSR series

[Mondkar, 1975; Mondkar, 1979; Oughourlian, 1982] have element libraries more geared

toward steel elements than reinforced concrete elements.

Creation of a 3D model of the structure for use in the 3D linear program SAP90

[Wilson, 1992].

Static analysis of the 3D model. Two load patterns were used: LOAD 1 is an inverted triangle

shape; LOAD 2 is a rectangular shape. LOAD 1 is the expected lateral load distribution

caused by ground motion for the case of a building that stays elastic and behaves in a first

mode of vibration approaching a straight line. LOAD 2 is the expected lateral load distribution

if a soft story develops in the first story.

Determination of whether the internal frames in the model can be neglected or not by

comparing the results from the model with internal frames with the results from the model

without internal frames. One criterion is the following: is it always conservative to ignore the

contribution of the internal frames?

Checking the accuracy of the 2D model in the elastic range by comparing the results with the

3D analysis.

2

Non-linear static monotonic analysis (static pushover) of the 2D model.

Linear elastic static analysis on the 31) model to obtain moment demand and supply ratios.

Determination of the reliability of the 2D model by comparing the sequence of plastic hinge

formation with respect to the stress ratios obtained in the 3D elastic analysis.

Dynamic linear elastic analysis on the 3D model to obtain simultaneous stress ratios at the

critical time during the ground motion.

Dynamic non-linear analysis of the 2D model.

Evaluation and comparison of the results of the analyses, drawing the appropriate conclusions

from the non-linear behavior.

Removal of the weakness of the selected tubular structure and repeat the non-linear analysis.

This is done by having the closely spaced columns in the perimeter extend to the foundation.

Design of an ideal tubular structure for a 30-story RC building and repetition of the non-linear

analysis to study its non-linear behavior.

3

EFFECTS OF SOFT SOILIS AND HYSTERESIS MODELS ON SEISMIC DESIGN SPECTRA

Report on Task 5 of the CUREe/Kajima Project on

DESIGN OF HIGH-RISE REINFORCED CONCRETE BUILDINGS ON SOFT SOILS

by

Mohsen Rahnama

and

- Helmut Krawinkler

A CUREe-Kajima Research Report

February 1993

ABSTRACT

The main objective of this research is to develop procedures that will permit an

explicit incorporation of the effects of deterioration of structural properties and site surface

geology on the seismic demands imposed on structures by strong ground motions. This

implies consideration of both the influence of stiffness degradation and strength

deterioration of structures and the effects of source-site distance and site soil conditions on

those demand parameters that can be used directly for design of structures. Thus, the

research combines ground motion and structure response issues, with an emphasis on

response parameters that incorporate both relevant ground motion as well as structural response characteristics.

The seismic behavior of a structure subjected to a strong earthquake needs to be

evaluated with due consideration to the fact that the mechanical properties of the structure

(i.e., stiffness, strength) are being modified during each inelastic excursions. In order to

consider this effect on the seismic demands, a general hysteresis model is developed.

During dynamic loading the dissipated hysteretic energy of SDOF systems is describe to define the deterioration of strength and stiffness by means of a deterioration parameters.

This deterioration parameter is also used to develop a damage index for damage evaluation of SDOF structures. In order to investigate the effects of deterioration of structural properties on seismic demands, a parametric study on SDOF systems was conducted using different hysteresis models. The seismic demands are evaluated statistically for a specified

target ductility ratio and the results are presented in terms of the spectral ratio between the

deteriorated structures and the non-deteriorated systems.

The research related to the study of soft soil effects on seismic demands is carried out

in two parts. In the first part advantage is taken of the extensive set of ground motions

recorded during the Loma Prieta earthquake and the availability of data on local soil

conditions at recording stations. These data sets are utilized to improve the basic

understanding of the phenomena involved, identify the most relevant parameters, develop

analytical models, and calibrate these models. In the second part of the study simplified

models of soil columns are employed for an extensive parameter study on the effects of site

soil conditions on seismic demands. The properties of the soil columns are varied to cover soil periods ranging from 0.5 to 4.0 seconds. The study has shown that the soft soil effects cannot and should not be lumped into a constant soil factor. Rather, it appears to be

Abstract

feasible to relate the strength demand for a soft soil motion to that of the motion in the

underlying rock by a modification factor which is a function of soil period and ductility

demand of the system. It was found that the amplification in the vicinity of the soil period

is approximately 5 for elastic strength demands and between 3 and 4 for inelastic strength

demands. This amplification of strength demands is approximately the same for soil

columns of all periods and for near-source and far-source motion, whereas the

amplification of PGA is strongly period dependent on soil period and source-to-site distance.

Abstract

-

CUREe-KAJIMA RESEARCH PROJECT

SEISMIC PERFORMANCE OF A 30-STORY BUILDING

LOCATED ON SOFT SOIL AND DESIGNED ACCORDING TO UBC 1991

Amador Terán-Gilmore and Vitelmo V. Bertero

Earthquake Engineering Research Center

University of California at Berkeley

July 15, 1991 - January 14, 1993

ABSTRACT

Researchers and practitioners interested in the seismic design of buildings have expressed

serious concerns about the reliability and rationality of present building code methodology for

the Earthquake-Resistant Design (EQRD) of tall buildings, particularly those to be built on deep

soft soil. Therefore it was decided to conduct the studies reported herein, which have the

following main objective: to assess the adequacy of the U.S. Uniform Building Code (UBC)

methodology for tall buildings on soft soil.

To achieve the above main objective, it was decided to design a tall building on soft soil

using the UBC methodology, and then to analyze its performance under the critical Earthquake

Ground Motions (EQGMs) that could occur at the building site. First, a 30-story RC building

with identical configuration, structural system and structural layout as those of a building that

has been designed and built in Japan was selected. The 30-story building, assumed to be

located in the San Francisco Bay Area, is constituted by a three-dimensional assemblage of

Reinforced Concrete (RC) special moment-resisting frames. The following studies that were

conducted are reported herein.

In Chapter 2, a description of the function, configuration, structural system, and structural

layout of the selected building is given. In this chapter, some of the general requirements for

the design of the 30-story building according to UBC are presented, together with the methods

used for the preliminary design of the 30-story building.

A detailed discussion and interpretation of some UBC design guidelines is presented in

Chapter 3. In this chapter, the design procedure for obtaining the final design from the

preliminary design is presented, as well as a summary of the member sizes and reinforcement

for the final design of the 30-story building. Some considerations about the way acóidental

torsion is accounted for in the UBC specifications are presented.

In Chapter 4, the studies conducted on the behavior of the designed 30-story building when

subjected to different levels of EQGM was studied. A summary of the results obtained from

the several analyses that were carried out on this building are presented: elastic response

spectra analyses (RSA) and elastic time-history analyses (THA) for service and safety limit

states; nonlinear pushover analyses, and nonlinear THA for service and safety. It should be

noted that the nonlinear THA were limited to plane (2D) models. The results obtained from the

elastic and nonlinear analyses, which include floor displacements, Interstory Drift Indices (IDI),

maximum and cumulative plastic rotations at the ends of the members (O and O), global 1

displacement ductility demands (Ii), story displacement ducthhity demands (t), local

rotational ductility demands (ib), and finally, an estimate of local damage index to the

members of the building (DM1), provide information on which the assessment of the adequacy

of UBC specifications and design methodology in the design of the 30-story building can be

based for the service and safety limit states. In Chapter 4, only the performance of the 30-story

building is discussed; while the discussion of the possible reasons for its behavior are

presented in Chapter 5.

Chapter 5 provides information that complements that presented in Chapter 4. Additional

analyses of the 30-story building were carried out to complete the information on which the

assessment of the behavior of the building can be based: elastic analyses were carried out

to assess the adequacy of a 2D model of the building has for predicting the global three-

dimensional (3D) behavior of the building; an extra nonlinear 2D ThA was carried out to

assess the effect of P-is on the dynamic nonlinear behavior of the building; and finally, the

nonlinear response of single-degree-of-freedom systems (SDOFS) is computed to study the

reliability of estimating nonlinear response from the linear elastic response of systems

subjected to EQGMs recorded in soft soils. Once the information regarding the behavior of the

building is completed, an assesment of the seismic performance of the building is made.

Finally, Chapter 6 presents a comparison of the seismic performance of three 30-story

buildings with exactiy the same structural layout, but designed according to three different

design philosophies: American practice, Japanese practice, and a newly developed Conceptual

Design Methodology. Based on the results obtained from this comparison and from those

discussed in Chapters 3 to 5, conclusions are drawn and recommendations are formulated for

improving present EQRD Code procedures and for the needed research to achieve such

improvements.

CUREe-KAJIMA RESEARCH PROJECT

TALL BUILDING BEHAVIOR

DURING THE 3 MARCH 1985 CHILEAN EARTHQUAKE

Raul D. Bertero and Vitelmo V. Bertero

Earthquake Engineering Research Center

University of California at Berkeley

July 15, 1991 - January 14, 1993

1

1. INTRODUCTION

On 3 March, 1985, a major earthquake of magnitude Ms=7.8 occurred off the coast of central Chile. The affected area included the most populated area of Chile and the cities of Santiago and Viña del Mar, where many tall buildings exist. The Chilean earthquake of 3 March, 1985, was particularly significant in that the ground motion was well recorded, was of strong motion and long duration, and modem structures performed extremely well (Wyllie 1986). Although the design forces for buildings in Chile are comparable to those in the U.S., the Chilean engineers developed a structural design philosophy that is unlike those in the U.S., Japan, or other regions of high seismicity. Most moderate-rise residential buildings in Chile rely on reinforced concrete structural walls to resist lateral and gravity loading. In general, the walls have moderate amounts of reinforcement without special detailing for producing a ductile structure (Wood 1991).

The main objective of this report is to review and evaluate the performance of tall buildings during the 3 March, 1985, Chilean earthquake in order to improve the seismic design of high-rise reinforced concrete buildings, particularly when they have to be built on soft soil.

This report is divided into seven chapters. The Introduction describes the general goal of the report as well as the partial objectives of each chapter.

The second chapter, Seismic Characteristics of the Region, has two objectives: a) to evaluate the return period of a ground motion with the severity of the 3 March 1985 earthquake at Vifla del Mar, intending to classify it as a serviceability, damageability, or survivability ground motion for the city; and b) to evaluate ground motion characteristics (peak instrumental values. Arias intensity, linear elastic response spectra, effective peak acceleration and velocity. Housner intensity, and strong motion duration) and to compare their severity with those corresponding to El Centro, which is traditionally considered as a severe ground motion.

The third chapter, Structural Engineering Practice in Chile, studies different aspects of Chilean practice that affect the design and behavior of tall buildings in Vina del Mar. Seismic code, design concepts, construction materials with nominal and real properties, structural and nonstrüctural details are summarized with a view to emphasizing the most peculiar aspects of Chilean practice.

The fourth chapter, Tall Buildings in Viña del Mar, studies specific aspects of the tall buildings in Viña del Mar: configuration, structural lay-out, structural systems and foundations. Also summarized are: the tall building inventory; analysis of its periods and damping, periods comparison with Mexico, Japan and US; and geotechnical characteristics of soil in Viña del Mar (soil profile, standard penetration tests, depth of the soil deposit to bedrock and the characteristic period site).

The fifth chapter, Effects of the 3 March 1985 Earthquake in Viña del Mar, has three objectives.

I a-

2

To evaluate the accuracy of the recorded ground motion in Viña del Mar as input for the studied tall buildings.

To evaluate the damage potential of the ground motion in Villa del Mar, computing linear elastic and elasto-plastic strength demand, linear elastic and elasto-plastic displacement demand, cumulative ductility demand, and hysteretic energy demand spectra. Also, interstory drift, accelerations, and damage indices of buildings designed according to Chilean practice are evaluated and compared with observed structural and nonstructural damage of tall buildings. Using these data, an estimation of the average overstrength of tall buildings in Viña del Mar is obtained.

To evaluate the effect of the soil-structure interaction on the response of tall buildings in Viña del Mar.

In the sixth chapter, Evaluation of Four Buildings in Vina del Mar, studies of design. analysis, and performance during the 3 March 1985 earthquake [mainly based on a report by Wallace and Moehle (1989)] are presented for four buildings in Villa del Mar. Both damaged and undamaged buildings of similar construction were selected to determine the differences between the buildings, and to correlate the differences with observed damage.

Finally, in the last chapter, Implications of the March 3 1985 Chilean Earthquake on Tall Building Design, the lessons of the behavior of tall buildings during the 1985 Chilean earthquake are summarized and the main conclusions for tall building design are stressed.

TALL REINFORCED CONCRETE BUILDINGS:

CONCEPTUAL EARTHQUAKE-RESISTANT

DESIGN METHODOLOGY

by

R. D. Bertero and V. V. Bertero

Report to Sponsor: CUREe Kajima

Report No. UCB/EERC-92/16 Earthquake Engineering Research Center

College of Engineering University of California at Berkeley

December 1992

ABSTRACT

The ultimate goal of the studies reported herein is to formulate a methodology for preliminary Earthquake-Resistant Design (EQRD) of high-rise reinforced concrete buildings that is more reliable than those that are presently available. This improved methodology should be a conceptual one, i.e., one based on well-established fundamental principles of structural dynamics, mechanical behavior of actual buildings, and comprehensive design; it should also also be in compliance with the worldwide accepted EQRD philosophy. The studies undertaken and conducted to achieve this goal are presented and discussed in this report, which contains eight chapters.

The first chapter briefly states the need for formulating an overall rational conceptual methodology for EQRD and describes the main objectives of the report. The EQRD problem is summarized and a solution is presented. A flow chart summarizes the main steps and tasks to be conducted. This is followed by remarks clarifying that the conceptual methodology for numerical design presented herein should not be confused with what has been defined previously as "conceptual design." These are two different phases of the EQRD process. The "conceptual methodology" phase (numerical design) formulated herein should follow after the "conceptual design" phase of the overall EQRD and Earthquake-Resistant Construction (EQRC) has already been conducted.

Chapter 2 describes the acquisition and processing of the data needed to establish reliable design earthquakes, which is the first and perhaps the most important step in carrying out a conceptual preliminary EQRD. The different spectra needed to determine the critical earthquake ground motions (EQOMs) at service and safety levels are discussed, with emphasis on the advantages of introducing the concept of a Damage Index (DM) and the parameter 'y to define the critical EQGM at the safety level. The acquisition and processing of the data necessary for the establishment of the design EQs for a 30-story building to be built on a site with soft soil conditions are presented.

.Chapter 3 describes the different steps involved in the preliminary analysis of the preliminary EQRD procedure, and contains a flow chart summarizing these steps. It is noted that, although the main purpose of this preliminary analysis is analysis of the problems involved (i.e., what is given, what is known, and what is needed) in establishing the design criteria and finding the maximum fundamental period (T1), the seismic forces, and the critical load combinations that control the design, preliminary design of member sizes is in fact necessary in order to obtain from the displacement design equation the T1 that satisfies the design criteria to be used for estimating the seismic forces. After selecting the design criteria, which is based on satisfying the requirements of the two main limit states of serviceability and survival (safety) and the critical load combinations, the necessary design equations to obtain the maximum acceptable T1 for these two limit states are developed.

The theoretical aspects of the solution of the problems involved in the preliminary analysis step are discussed in detail in Chapter 4, where it is clearly shown that the design criteria adopted in Chapter 3 are in compliance with the world-wide accepted EQRD philosophy. The importance of simultaneously considering the Energy Input, E1, the Inelastic Design Response Spectra, IDRS (for strength and displacement), and the Energy

I

Dissipation, ED (which can be obtained through Damping Energy, E, and plastic Hysteretic Energy, EH), is discussed. In the studies reported herein, design for safety is based on developing large ED through structural damage, i.e., EH. Thus, the use of equivalent ductility ratios based on different damage models is emphasized. The Park-Ang model is then adopted, as is the use of the dimensionless parameter y introduced by Fajfar. This parameter permits the derivation of a simple equation for the equivalent ductility ratio where the reduction due to low cycle fatigue is controlled by two parameters, f3 and 'y; and by the permissible Damage Index, DM. The need to reduce the established equivalent Single-Degree-of-Freedom (SDOF) ductility ratio considering Multi-degree-of-Freedom (MDOF) effects is also discussed, and the use of a factor 12 is recommended. The potential sources of overstrength with respect to the strength used in the design observed in real structures are also discussed. Finally, the detrimental effects of torsion in the elastic and inelastic range of the behavior of the structure are analyzed, and simplified equations are developed to introduce these effects from the beginning of the design procedure. The formula that is presented for the reduction of the accidental eccentricity with increase in the number of stories of a building was derived based on a probabilistic analysis.

In Chapter 5, the theoretical aspects of the preliminary design step are discussed. A strong column-weak beam concept, together with a "capacity design" approach, is used. The need for amplification of column bending moment demands is discussed in detail, and the need to modify the axial forces according to the number of stories above the column under consideration is also discussed.

Application of the developed conceptual methodology to the preliminary EQRD of a building is discussed in Chapter 6. A 30-story RC building designed and built in Japan, whose structural system is a special moment-resisting space frame, was selected for the application of the developed methodology.

Chapter 7 describes the analyses that were conducted to evaluate the preliminary design of the 30-story RC building. These analyses were the following: a) linear elastic dynamic analysis (3-D linear elastic response spectrum using serviceability response spectra and 3-1) linear elastic time-history analysis for the EQGM component N90W recorded at SCT station during the 1985 Mexico EQ, but with a b) nonlinear static analysis using a 2-1) nonlinear "pushover" technique with a lateral force pattern obtained from the safety spectra modal analysis; and c) nonlinear dynamic analysis using as EQGM the N90W component recorded at SCT station during the 1985 Mexico EQ, but with a PGA y=0.30g.

The final chapter summarizes the main results obtained and observations made during the studies reported herein. Based on these results and observations, specific recommendations for improving the present EQRD of tall buildings are offered. Recommendations for needed research are also formulated. The chapter's concluding remarks point out that the main advantage of this proposed conceptual methodology is that, notwithstanding the great uncertainties in the quantification of some of the concepts involved in its codification, the numerical quantification of these concepts can be improved without changing the format of this codified methodology as new and more reliable data are acquired. It is also pointed out that it is not the intention of the authors

H

to propose that such a detailed methodology as has been presented be implemented in the code for all kinds of facilities. What has been proposed is that such a conceptual methodology for numerical EQRD be used for design of irregular buildings, tall buildings, and particularly buildings on abnormal sites. For short, regular buildings located on standard sites and using known, simple and reliable structural systems, this methodology can be used to formulate and calibrate seismic code regulations that are as simple or simpler, but still more reliable and transparent, than present ones.

Ill

ACKNOWLEDGEMENTS

The studies reported herein were conducted as Task #5, "Development of Preliminary Design Methods," of a research project entitled "Design of High-Rise Reinforced Concrete Buildings on Soft Soils." This project is part of a research program supported by a grant by Kajima Corporation and administered by CUREe, the California Universities for Research in Earthquake Engineering. The financial support from Kajima is gratefully acknowledged. Any opinions, discussions, fmdings, conclusions and recommendations are solely those of the authors and do not necessarily represent those of the sponsor.

The authors of this research report wish to thank Dr. Norio Inoue, Group Manager of the Kajima Research Team, and the members of his team for supplying all the information needed regarding the 30-story building used in this report, and for their valuable comments during the meetings that we had to discuss this research project.

The authors are also indebted to Profs. J. Anderson, P. Filippou, H. Krawinlder and G. Powell for the fruitful discussions held during the studies. Thanks are also extended to research assistants H. Goucha and A. Terán for their assistance during the project and to Brad Young for editing this report.

iv

PERFORMANCE OF TALL BUILDINGS DURING THE 1985 MEXICO EARTHQUAKES

by

Ainador Terán-Gi imore

Vitelmo V. Bertero

fr,

Report to CUREe-Kajima

Report No. UCB/EERC-92/17 Earthquake Engineering Research Center

College of Engineering University of California at Berkeley

December 1992

ABSTRACT

In the studies reported herein, the behavior of tall buildings during the 1985 Mexico earthquakes (EQ5) is investigated, with the main objectives of: (1) identifying and formulating seismic design guidelines for tall buildings built on soft soils, and (2) assessing which types of structural systems had acceptable performances.

To accomplish the above objectives, an extensive literature survey on the 1985 Mexico earthquakes has been carried out. The information gathered from the survey was analyzed, and the main results from such analyses are reported here in six chapters (Chapters 2-7).

Chapter 2 gives, firstly, a summarized overview of how the Earthquake Ground Motions (EQGM5) that were recorded in Mexico City were generated. Secondly, special attention is paid to the dynamic characteristics of the EQGM recorded at the SCT station. Linear Elastic and Inelastic Response Spectra (LERS and IRS, respectively) for strength and deformation are given, as well as the IRS for the Energy Input (E1) and the Energy Dissipation (ED). What can be called a nominal Drift Index [equal to tip displacement divided by the height of a Generalized Single-Degree-of-Freedom System (GSDOFS)}, or an average Interstory Drift Index (IDI) spectra, i.e., the average IDI vs. period, T, of the structure for the EQGM recorded at SCT, assuming a constant damping ratio, 4, and different values of the ductility ratio, t, have been plotted considering the relationships between the T and the height, H, (or number of stories, N) of typical Mexican, Japanese and U.S. moment-resisting frame buildings. From analyses of these spectra, it is concluded that Mexican waffle slab buildings having seven to 15 stories should be expected to suffer significant damage under the EQGMs recorded at SCT station. On the other hand, Japanese moment-resisting space frames subjected to the SCT recorded ground motions seem to limit the IDI adequately, and therefore to limit the damage. The advantages and disadvantages of present design practice for tall buildings in Japan are drawn from analyses of the Number of Equivalent Yielding Cycles at maximum j.t (NEYC ax), and the resulting Damage Index (DM) as defined by Park and Ang.

Chapter 3 deals with the statistics of damaged buildings in Mexico City during the 1985 EQs, providing an idea of the type of structural systems that were most vulnerable during the 1985 EQ5, as well as their dominant modes of failure.

The performance of tall buildings in Mexico City during the 1985 Mexican EQS is discussed in Chapter 4, where such performance is related back to the different seismic codes that were used in their design and construction. Special attention is paid to waffle slab framed buildings: results of case-history studies are presented and

1

discussed. This chapter ends with discussions of: (1) the different foundation systems used in Mexico City, and (2) the types and effects of nonstructural components.

Special aspects of the observed seismic behavior of tall buildings during the 1985 Mexican earthquakes are discussed in Chapter 5. Some of these aspects have been identified as direct consequences of the soft sites on which the buildings were built: these cases involve: (1) buildings that were already tilted before the EQs, and (2) soil-foundation flexibility effects on the seismic responses of tall RC buildings, tilted or not. Other special aspects discussed are the large number of observed collapses of upper stories, and the damage caused by pounding of adjacent buildings.

Chapter 6 is devoted to the discussion of what has been learned from the evaluation of the performance of buildings in Mexico City during the 1985 EQs. One of the main sources used for identifying the lessons learned was a review of the studies, discussions and comments that were carried out and offered as background after the EQs for the development and formulation of the new 1987 building code for the Federal District of Mexico. The main lessons learned are identified by comparisons between the 1976 and the 1987 building codes. The rationality of the changes introduced is discussed at the end of this chapter.

The main results obtained in the studies reported herein are summarized in Chapter 7, where general conclusions regarding the EQGM5, damage, Mexican RC building design practice, foundation systems used, special aspects, and the rationality and reliability of the new 1987 Mexican building code are offered. The important lessons learned from the studies conducted on single-degree-of-. freedom systems are also summarized. Finally, the special issues that need to be considered in the design of tall buildings on soft soils are identified, and recommendations for their proper seismic design, in the form of design guidelines, are offered.

ii

ACKNOWLEDGEMENTS

The studies reported herein have been conducted as Task #2, "Review of Seismic Performance of High-Rise Reinforced Concrete Buildings, of a research project entitled "Design of High-Rise Reinforced Concrete Buildings on Soft Soils." This project is part of a program of research which is financially supported by Kajima Corporation and administered by CUREe, the California Universities for Research in Earthquake Engineering. This financial support from Kajima is gratefully acknowledged. The findings, observations, conclusions and recommendations of this report are those of the authors alone.

The authors would like to express their gratitude to Professors J. Anderson, F. Filippou, H. Krawinkler and G. Powell for their valuable comments and fruitful discussions during the meetings that we had to discuss the studies reported herein.

Special thanks are due to Dr. Norio Inoue, Group Manager of the Kajima Team, and the members of his team for their valuable comments during the meetings that we had to discuss this work.

Thanks are also extended to Brad Young for editing this manuscript.

iii

Kajima—CUREe Project

Design of High—rise Reinforced Concrete Buildings

Final Project Report

Norio Inoue Norio Suzuki Hiroshi Morikawa Masaaki OkanO Takaharu Fukuda Hitoshi Hatamoto Motonii Takahasbi Satoshi Ohrui Makoto Maruta

(Kajima Corporation)

Vitelmo V. Bertero Helmut Krawinkler James C. Anderson Graham H. Powell Filip C. Filippou

(CUREe Team)

March 1993

ABSTRACT

The goal of this study is to develop a method to predict the nonlinear behavior of a rein-

forced concrete frame structure. The commonly used method based on the empirical formulae

can not be applied to the structures of the new type. The structure made of high strength

materials is an example of such a structure. Furthermore, the effect of shear deformation can

not be neglected in a short member such as the columns in Japanese building, and the rotation

due to the slippage of longitudinal reinforcements should be taken into account.

Therefore, a nonlinear member model for a reinforced concrete column and/or beam which

can consider the effect of shear deformation and the slippage of longitudinal reinforcements

was newly developed. In this model deformation was assumed to be the total of fexural

deformation, shear deformation and rotation due to the slippage of reinforcements. Flexural

deformation was calculated by the fiber model in which the hinge zones with constant curva-

ture were assumed. Shear deformation was taken into account by inserting a nonlinear spring

which expressed the relationship between shear stress and shear strain. The method to predict

the characteristics of this spring was developed using a truss analogy model. The rotation due

to the slippage of longitudinal reinforcements was calculated by setting up fiber slices in

which stress-strain relationship similar to the relationship between the stress and slippage was

used for a reinforcement. The relationship between the stress and slippage of a reinforcement

was estimated using nonlinear finite element analysis.

The developed model was verified through the simulation analyses of reinforced concrete

short columns. The objects of the analyses were two columns subjected to constant axial

force and shear force and other two columns subjected to shear force under fluctuating axial

force. The relationships between deformation and shear force obtained from the analyses

agreed with those obtained from experiments.

The member model was included into a computer program for the nonlinear analysis of a

frame structure and the program was verified through the simulation analysis of a beam-

column-joint subassemblage. The slippage of the longitudinal reinforcements of a beam and

the deformation of a beam including the rotation due to the slippage obtained from the analy-

sis agreed with those obtained from the experiment. The analytical envelope curve of the

relationship between the shear force and total deformation agreed with experimental one, too.

Although the shape of hysteresis loops obtained from the analysis were different from those

obtained from the experiment when the inter story deformation exceeded 1/50, they agreed

well with the experimental results when the inter story deformation was less than 1/50. These

results means that the developed computer program is of practical use enough because a

reinforced concrete frame is usually designed so that the maximum inter story deformation

does not exceed about 1/100 during any strong earthquake.

TABLE OF CONTENTS

1. Introduction

Page

1

* 2. Member Model

2.1 Calculation of Flexural Defonnation

2.2 Calculation of Shear Deformation

2.3 Calculation of Rotation due to Slippage of Reinforcements

Analysis of Reinforced concrete Short Columns

3.1 Objectives

3.2 Object of Analysis

3.3 Analytical Model

3.4 Results of Analysis

Analysis of Beam-Column-Joint Subassemblage

4.1 Objectives

4.2 Object of Analysis

4.3 Analytical Model

4.4 Results of Analysis

Conclusions

3

.7

13

23

23

23

24

31

31

31

32

40

0

1. INTRODUCTION

In the nonlinear analysis of a reinforced concrete frame subjected to lateral loads, the one

component model proposed by Giberson' has been adopted widely for a member model in

Japan. This model consists of two rigid-plastic springs at both ends of a member and an elas-

tic beam element between these springs. The advantage of this model is that it can incorpo-

rate arbitrary moment-rotation relationships in the end springs. For example, Takeda et al

proposed a complicated nonlinear characteristic rule for cyclic bending behavior of a rein-

forced concrete member including cracking, yielding and stiffness degradation.2

But, there remains a problem how to predict the in1astic characteritics of the member. One

of the popular method in Japan is to use "Sugano's formulae "3 . These formulae are empirical

ones reduced from the statistical analyses of a lot of experimental results of reinforced con-

crete members, and they have been accepted as reliable formulae to predict initial stiffness,

cracking point and yielding point of a member made of normal strength concrete and rein-

forcements.

However, it has not been verified that this method can apply to a member made of high

strength materials. One report4 suggests that the deflection at the yielding point predicted by

this method is different from the value obtained from experiments, but the experimental data

of the members made of high strength materials are not so much to modify these formulae

through some statistic analysis.

Thus, another member model which can predict the nonlinear behavior of a reinforced

concrete beam and/or a column without any empirical methods should be developed. Fiber

model is considered to be suitable because it can predict the bending behavior of a member

when the dimensions, the arrangement of reinforcements and the stress-strain relationships of

concrete and reinforcements are given.

However, the fiber model is apt to overestimate the stiffness of a short member in which

shear deformation can not be neglected. Because the columns in the reinforced concrete

frames in Japan usually have small shear-span ratio, it is important to take this effect into

account. Furthermore, it is so difficult to prevent the slippage of longitudinal reinforcements

-1-

from beam-column joint that the additional rotation of the beams and/or columns due to these

slippage become large at high stress levels.

In this study, a new member model in which the effect of shear deformation and slippage of

longitudinal reinforcements are taken into account was developed based on the fiber model.

As this model is developed to be included into a computer program for frame analysis, it is

desirable that the methods to consider these effects are simple in order to save computing time

and the memory of a computer.

The objective of this report is to show the newly developed member model and its applica-

tion to the analyses of reinforced concrete short columns and a beam-column-joint subassem-

blage.

-2-

2. MEMBER MODEL

2.1 CALCULATION OF FLEXURAL DEFORMATION

(1) BASIC THEORY

In order to calculate curvature some sections were divided into finite number of segments as

shown in Fig.2.1. Such a section will be referred as a "slice", hereinafter. If assuming that

plane remains plane after being deformed, strain of each segment is calculated when curvature

and strain at the center of the section is obtained. Moment and axial force of the section were

calculated by integration of the Stress of each segment which was obtained from the stress-

strain relationships of materials.

Rotation due to the flexural deformation can be calculated by the integration of the curvature

in the longitudinal direction of the member.

In the computer program, step-by-step calculation process was adopted. Basic equations are

as follows.

In the k-th slice, curvature around y and z axis(4 k' zk) and axial strain(20k) at the center of

the section are related to moment around y and z axis (MYk, MZk) and axial force(Nk) by the

following equation.

(Nk MYk M T = Dk ] (Eok 4yk T

(2. 1)

If some shape function was assumed in the longitudinal direction, the rotation angle at both

ends of an element('r ., ti., 't, r Zi ) can be calculated from the curvatures and strains at the

slices as follows.

)T [N I ( 801 4 Y1 z......80 c1i )T yn Zn

The moments, axial forces, curvatures and strains are related as following.

-3-

(N I Myl Mzi . N n M yn M Zn _. )T[D](cp e04 yn )T

The moments and axial forces at each slice are calculated from the moments and axial forces

at both ends as following.

(N1MIM z ......N n )'fl M MZn

)T_[A][N1 Myi MZi

N J M

yj M

zj )T

When the element is subjected to the axial force(N., N.) and moments (M. M ., N., M ., M., 1 J yl z1 1 yJ Zj

N) and shear forces (Q, Q2 , Q, Q2 ) at the ends, there exists following relations.

(N.Q.Q.M.M.N.Q.Q.M.M.)T [T]T(NMMNMM)T 1 1 ZI 1 11 J yJ ZJ XI 1.1 1 yl ZI J yJ ZJ

Furthennore, those forces can be related to the displacement at both ends as follows.

(N.I Q.)'l Q. ZI M yi MZI .NJ .Q.Q.M J .M zi .)T

= [TJT([ N ][ D ]'{A ])'[ T}f UI V)l w Z1. 8 yi 0Zi

uJ. V yj w zj 0

yj 0zj

1T

[T ]T([ N ][ D ][ A ]'[ T] is the 3-D stiffness matrix of the element and it can be used to

make a stiffness matrix of a total structure.

(2) STRESS-STRAIN RELATIONSHIPS OF MATERIALS

(a) CONCRETE

Fig.2.2 shows the assumed stress-strain relationship of concrete. Backbone curve was calcu-

lated based on the Noguchi's model in which the effect of confinement due to lateral rein-

forcements was taken into account. The stress-strain curve in compression was expressed by

the Fafitis-Shah's formula6 up to the compressive strength, and strain softening region was

-4-

expressed by a parabola curve. The compressive strength of concrete confined by rectangular

hoops was estimated by using the failure criteria for biaxially confined concrete proposed by

Kupfer7 , and the strength of concrete confined by circular hoops was estimated using the

criteria for triaxially low confined concrete proposed by Ottosen8 .

Ductility was estimated by a method similar to Park's mode19 .

The stress-strain relationship in tension was assumed to be linear up to the tensile strength,

and tension stiffening effect was considered in the tensile strain softening region.

The rule for cyclic loading was very simple. The modulus of unloading and reloading

branch was assumed to be equal to the initial stiffness when the experienóed maximum strain

was less than the strain at the compressive strength, and it was reduced according to the expe-

rienced maximum strain when it was larger than the strain at the compressive strength.

(b) REINFORCEMENTS

Fig.2.3 shows the stress-strain relationship of longitudinal reinforcements. The Filippou 's

model10 which can express the effect of strain hardening and Baushinger effect was adopted.

(3) ASSUMPTION OF CURVATURE DISTRIBUTION

If the distribution of moment are given, the distribution of curvature in the longitudinal

direction of a member is able to be calculated from the moment-curvature relationship of a

section. But, it is generally known that such a theoretical distribution of curvature is apt to

underestimate the flexural deformation. It is also suggested that there appear hinge zones in

which curvature can be regarded to be constant near the critical section of a member.

Therefore, the distribution of curvature in the longitudinal direction of a member was as-

sumed as shown in Fig.2.4 in this model. Curvatures at both ends of the member were calcu-

lated at the slices called "slices to calculate flexural deformation". It was assumed that there

appear hinge zones in which curvature distribute uniformly near the ends of the member. The

values of curvature were assumed to be equal to the calculated ones at the slices, and the

length of a hinge zone was assumed to grow according to the maximum strain of the longitu-

dinal reinforcements at the slice and to reach its upper limit when one of the longitudinal

-5-

reinforcements yielded as shown by the following equation. The upper limit was assumed to

be equal to the height of the member.

L =Da La H maxy (2.7)

Where, L1 : the length of a hinge zone, D: the height of the section, emax: the maximum

strain of the longitudinal reinforcements at the slice, c:strain at yielding of a longitudinal

reinforcements. Curvature was assumed to distribute linearly between the both hinge zones at

the ends of the member.

-6-

2.2 CALCULATION OF SHEAR DEFORMATION

(1) BASIC ASSUMPTIONS

A simple way to consider the effect of shear deformation is to introduce a spring which

expresses the relationship between shear force (stress) and shear deformation (strain). Here-

inafter, such a spring will be referred as a "shear spring". As one of the features of a fiber

model is that it needs only the dimensions of the member and the uniaxial stress-strain rela-

tionships of materials to predict the restoring force characteristics for flexural deformation,

the restoring force characteristics of the shear spring should be predicted by using the same

kind of information used for the fiber model. A truss analogy model was proposed here to

predict the characteristics of a shear spring. Hereinafter, this model will be called as a "shear

model". The basic assumptions for this shear model were as following.

No interaction is considered between bending and shear in the restoring force

characteristics.

The volume of longitudinal reinforcements are infinitely large.

Lateral reinforcement distributes uniformly.

Stress and strain of lateral reinforcements and concrete are uniform.

Shear cracks distribute uniformly.

(2) BACKBONE CURVE OF SHEAR STRESS-SHEAR STRAIN RELATIONSHIP

The backbone curve of the relationship between shear stress and shear strain was assumed to

be as shown in Fig.2.5. This curve contained three characteristic points which are expressed

as "Cl", "C2", and "Y". These points and curves between them were defined as following.

(a)Point "Cl"

This point represents where the first shear crack occurs. It is assumed that the shear crack

occurs when the principle tensile stress reaches at the tensile strength of concrete. Shear

-7-

stress does not distribute uniformly in a section as like shown in Fig.2.6. In a rectangular

section, the maximum shear stress is 1.5 times the average shear stress. Thus, the stress at

point "Cl" is defined as follows.

(/ 1 o) =

1.5 (2.8)

'Yci = - G (2.9)

f : Tensile Strengh of Concrete

Average Axial Stress

between the origin and the point "Cl"

This is a linear region. Thus, the stiffness is equal to the elastic shear stiffness "G".

Point "C2"

At this point, a truss mechanism is assumed to be completed. The stress of this point is

assumed to be the average shear stress when the tensile principal stress reached to the

tensile strength of concrete.

VC2 =

0 =tan-' (Z'CC2

2

(2. 10)

(2.11)

Curve between points "C2" and "Y"

A truss mechanism is assumed to be completed at point "C2". This mechanism consists

of lateral reinforcements, concrete struts with the angle of 0 and longitudinal reinforce-

ments as shown in Fig.2.7. 0 is the angle of the crack calculated by (Eq.2.19). The

concrete strut is assumed to resist the compressive stress parallel to the crack and the shear

stress transferred across the crack but not to transmit the tensile stress across the crack

(Fig.2.8). The equilibrium conditions are represented as follows.

= d 1 sin2O - v' sin28

(2.12)

v = fci i sinze - v' cos20

(2. 13)

In order to deduce the compatibility conditions, deformation is separated into two

modes(Fig.2.9). In one mode, called "Mode A", only the concrete struts are deformed. In

the other mode, called "Mode B", only the lateral reinforcements are deformed. The

compatibility conditions can be expressed as follows.

I = 7ASlfl26 (2.14)

= r8cotO (2. 15) 7' = 7ACOSZ8 + TB (2. 16) 7 = T+ TB (2.17)

The uniaxial stress-strain relationships of materials are assumed as follows.

Concrete strut: stress-strain relationship in compression up to the compression

strength is assumed to be equal to that used for the fiber model. After reaching

compressive strength, stress is reduced to zero rapidly (Fig.2.10).

= Fjl_(l_i~aja (&<€o) (2.18) 1. CO

Er

a = (2.19) (F / & o)

Lateral reinforcement: stress-strain curve is expressed as a bilinear type.

= pwEg& (&<e) (2.20)

Shear transfer across the crack:

= (0/31) (2.21)

From (Eq.2.12) to (Eq.2.21), the relationship between shear stress and shear strain between

point "C2" and point "Y" can be calculated as follows.

B+AC t

l+A T

A (E ,sin26+2GcosZO)sjn2O = pE+2Gsin2O

B = Eisin22O+Gcos22O

C = —GcosZO

E dc1

1— dc1

G = $Go, atic

a Normal Stress of the Concrete Struts

Normal Stress due to the Lateral Reinforcements Shear Stress

Shear Stress transfered across the Crack e Normal Strain of the Concrete Struts

: Normal Strain of the Lateral Reinforcements Shear Strain

Shear Strain transfered across the Crack

Compressive Strength of the Concrete Struts

Strain of the Concrete Struts at the Compressive Strength Young's Modulus of Concrete Struts

Pw Ratio of Lateral Reinforcements

Yield Strength of the Lateral Reinforcements

Young's Modulus of the Lateral Reinforcements

(2.22)

(2.23)

(2.24)

(2.25)

(2.26)

(2.27)

(e) Point "Y"

At this point, the yielding of lateral reinforcements or the crash of concrete struts occurs.

The force at this point can be calculated as follows.

ry = inin{v(wherz t=d ),), 'c(when c1Fj} (2.28)

-10-

(f) After point "Y"

After the yielding of lateral reinforcements, equilibrium conditions and compatibility

conditions are almost same as those between point "C2" and point "Y". Only the tangent

moduli of materials are different.

= pE8c (2.29) = pw{cy+a sE g(c&y)} (cc) (0a1) (2.30)

From these equations, the following relationship can be obtained.

B+AC Liv

= 1+A (2.31)

A (E isin2O+2Gcos26)sjn2O

pE+ZGsjn2O (2. 32)

B = .Eisln22O+Gcos22O (2.33)

C = —GcosZO (2.34)

B1 = d & 1 (2.35)

1 dcii Ewe = - P. d c t (2.36)

C = f3Giate (2.37)

When the crush of concrete strut occurs at point "Y", it is regarded that the member

failed in shear and calculation is ended.

(3) HYSTERESIS RULE

It was not easy to evolve the truss model for cyclic loading, because shear cracks do not

intersect each other at a right angle. Furthermore, derived hysteresis curve would not be real-

istic because some phenomena such as the slip of reinforcement etc. were not considered.

Therefore, the hysteresis rule was derived empirically. One feature of the hysteresis curve of

the relationship between shear stress and shear strain is that the area of the loop is small.

-11-

Thus, the hysteresis rule was assumed to be an origin-oriented-type as shown in Fig.2.5.

-12-

2.3 CALCULATION OF ROTATION DUE TO SLIPPAGE OF REINFORCEMENTS

Hysteretic response of the anchorage of a longitudinal reinforcement under cyclic forces was

analyzed using FEM. Bond between concrete and a reinforcement was idealized as a set of

link elements connecting the reinforcement and concrete element. For the relationship be-

tween bond stress and relative displacement between a reinforcement and concrete, a slip-type

hysteresis loop was assumed. The relationship of the stress and slippage of a reinforcement

was idealized as a tn-linear hysteresis loop.

ANALYSIS OF SLIPPAGE OF REINFORCEMENT BY FEM ANALYSIS

Analytical model was considered to be composed of concrete, a reinforcement and bond

between concrete and the reinforcement as shown in Fig.2. 11. Concrete elements were ideal-

ized as elastic material in order to simplify the analysis. A slip-type tn-linear loop proposed

by Morita and Kaku11 was adopted for the local bond-slippage model, and the deterioration of

bond stress under cyclic excitations was assumed where the value of 90% of the maximum

value(Fig.2.12) was assumed when reloaded. A reinforcement was represented by a rod

element possessing axial stiffness only and its stress-strain relationship was assumed to be bi-

linear type.

A beam-column joint was idealized as a. FEM model (Fig.2.13) and bending moments were

applied to, both ends to obtain the stress and slippage of a reinforcement.

Fig.2. 14 shows an example of the calculated relationship.

MODELING OF HYSTERESIS LOOP

In order to include the effect of the slippage of reinforcements into the fiber model, it was

necessary to clearly define the hysteresis model between the slippage and stress of a rein-

forcement. Fig.2.15 shows the model proposed by idealizing the results of FEM analysis.

Point "A" corresponds to the appearance of bond inelasticity. Point "B" represents the yield

-13-

point which corresponds to the occurrence of the inelasticity of bond at all part of a rein-

forcement. The stiffness in unloading from the skeleton curve is assumed to be equal to the

elastic stiffness at all times. When the experienced maximum stress of the reinforcement is

lower than c,, the reloading from point "C" has a stiffness terminating at the maximum

deformation. When the experienced maximum stress of the reinforcement is higher than

and the slippage is lower than 5j4, the stiffness is usually zero. When reloading from point

"D" the curve moves towards point "E" which is 90% of the experienced maximum stress.

(3) CALCULATION OF ROTATION DUE TO SLIPPAGE IN FIBER MODEL

Fig.2.16 shows a model when a beam is the object of the analysis. It is usually observed that

the cover concrete of columns (Part B & B') suffer injury. Therefore, the length of the beam

was regarded as "L", which stands for the distance between the location of the longitudinal

reinforcements of both side columns. One slice to calculate the flexural deformation has

already been set up at this front of the column. Furthermore, it was assumed that a longitudi-

nal reinforcement was elongated uniformly in the part B and B' and the value of elongation

was equal to the value of slippage obtained from FEM analysis. Therefore, one additional

slice was set up at the location of the longitudinal reinforcements of the columns. These

slices are referred as "slices to calculate slippage", hereinafter. Stress-strain relationship of the

reinforcements used in these slices were assumed to have a characteristics similar to the

idealized relationship between the stress and slippage obtained from FEM analysis. As unit

representing the slippage was length, it had to be Iransfonned to strain when using the stress-

strain relationship. Thus, the slippage "s" was divided by "Li", the distance between the loca-

tion of longitudinal reinforcements and front of a column. Furthermore, it was assumed that

curvature is distributed uniformly between the slice to calculate slippage and the slice to

calculate flexural deformation( Fig.2.16).

These explanations are for the case when the object of analysis is a beam. When the object

is a column, the word "beam" should be exchanged for "column".

-14-

Division of a Slice Strain Stress

7.\ RA Ri

Concrete Steel

Fig. 2. 1 Fiber Model

-15-

Confined by Rectangular Hoop

J Confined by Circular Hoop

Eel

C = Fcmax{1_(1_ k )a} (0ek&0 ) eo

)'IFcmax{l_(—kk 0 J (Ico<&)

E. a

(Fcm3x/kCü)

F cmax k= F

(2.38)

(2.39)

(2.40)

(2.41)

F

Confined by Rectangular Hoop Kupfer

Confined by Circular Hoop : Ottosen

Femax = Fc exp f3.3 (fe )"'1 (2.42) F c. plane

1. : Lateral Pressure due to the Hoop

= u. piane+l.Ep s /B/S (2.43)

u.pIane = 93

(2.44) Fc

I + 3.6$

( j+a )

Fig.2.2 Model of Stress-Strain Relationship of Concrete

-16-

train Hardening

a—b exp)

(2.45)

Fig. 2.3 Mode! of Stress-Strain Relationship of Steel

Slice to Calcu Flexural Defor

LH( Hinge Zone)

Moment Curvature

Fig. 2.4 Assumption of Distribution of Curvature

-17-

Truss mechanism is completed

mi tial V V) V VJ

Shear Cracks occur

Yield of Shear Reinforcements

. \ or •Crush of Concrete Struts

Fig. 2.5 Model of Relationship between Shear Stress and Shear Strain

- max.

Fig. 2.6 Distribution of Shear Stress in Rectangular Section

-18-

SHEAR REINFORCEMENT

N

_Q :; ftt1I I " -

'CONCRETE STRUT

Fig. 2.7 Truss Mechansni

Fig. 2.8 Equilibrium Condition

e m/sfnO

=L~ Mode A

+

e

Mode B

Fig. 2.9 Mode of Shear Defoemation

Fig. 2. 10 Model of Stress-Strain Relationship of Concrete Strut

-19-

Reinforcing bar Bond

Concrete

01 x

Fig.2.11 Element used in FEA

Fig. 2. 12 Model of Realtionship between Local Bond Stress and Slip

-20-

I I No

_

A

SIIJL.4(l

MEN 0 ) M

L

-,

" 80cm H

Fig.2.13 Model of Beam-Column Joint

Fig.2.14 Relationship between Stress and Slippage

-21-

(1)

Fig.2.15 Model of Realtionship between Stress and Slippage

B B

II I

Longitudinal

Reinforcement

Beam

ICo I um

I F_ - I I

n oIum

Ls Ls Slice to CIculate

Slippage Slice to Calculate

Slippage

Slice to Calculate

Flexural Deformatio1 Slice to Calculate

Flexural Deformation

Fig.2.16 Model Considering Flexural Deformation and Rotation due to Slippage

-22-

3. ANALYSIS OF REINFORCED CONCRETE SHORT COLUMNS

3.1 OBJECTIVES

In this chapter, columns with small shear span ratio were analyzed and the developed model

described in chapter 2 was verified.

3.2 OBJECT OF ANALYSIS

Fig.3. 1 and Table 3.1 shows the experimental test specimens of reinforced concrete column

performed by Kajima Technical Research Institute12 . These specimens were 1/3 scaled

models of columns in a 45 storied reinforced concrete building using high strength materials.

Their shear span ratio was 1.5. Two specimens NC1 and NC2 were subjected to shear force

and constant axial force, and other two specimens NV1 and NV2 were subjected to shear

force and fluctuating axial force. Specimen NC2 had twice reinforcements of other three

columns. Two columns subjected to fluctuating axial force had additional eight longitudinal

reinforcements at the center of section. The properties of materials were as shown in Table

3.2.

The specimens were subjected to axial force and point symmetrical shear forces. Constant

axial force subjected to NC1 and NC2 was 190tonf, which corresponded to about 1/3 of the

maximum compressive axial strength of the columns. When the axial force "N" was varied, it

was varied in relation to the shear force "Q" as "N = 20Q + 110 tonf". The upper limit of the

varying axial force was set up 520tonf in compression and 210tonf in tension. In the last

loading stage up to failure, specimen NV1 was subjected to a constant axial force correspond-

ing to the upper limit in tension, and specimen NV2 was subjected to a constant axial force

corresponding to the upper limit in compression.

3.3 ANALYTICAL MODEL

-23-

Fig.3.2 shows the fiber model idealization of the section of these specimens. The specimens

were modeled as cantilever columns with two slices at the front and location of the reinforce-

ment of the beam. The stress-strain relationships of materials were assumed based on the

material tests shown in Table 3.2 and Table 3.3. The restoring force characteristics of shear

spring was defined using the method mentioned in Chapter 2. The stiffness of the shear trans-

fer across a crack was assumed to be 20% of the elastic value when the axial force was in

compression, and 5% when it was in tension. Table 3.4 shows the characteristic values of the

relationship between the stress and slippage of a reinforcement.

The analyses of NC1 and NC2 were controlled by deformation and the analyses of NV1 and

NV2 were controlled by shear force.

3.4 RESULTS OF ANALYSIS

Fig.3.3 to Fig.3.6 show the comparison between the calculated and observed load-displace-

ment relationship. From the experiments with constant axial force, it was observed that the

maximum strength of specimen NC1 was almost equal to that of specimen NC2 but the ductil-

ity of specimen NC1 was not so good as specimen NC2. It was due to the difference of the

volume of lateral reinforcements between two specimens.

-

Although the analytical results are different a little from the experimental results in the shape

of hysteresis loops before yielding, they show good agreement with experimental results in

envelope curve and the shape of hysteresis loops after yielding.

In the comparison between the results of analysis and experiment of specimens NV1 and

NW, a little difference is also observed in the area of hysteresis loops but good agreement in

the envelope curve is obtained.

The reasons why the area of hysteresis loops of the analytical result was small before yield-

ing might be that the origin-oriented model was adopted for the shear spring and/or unloading

and reloading branch in the stress-strain relationship of concrete was simply modeled.

-24-

-p

y 111__ Beam

Column

i 450k H 300 900 300 450

r-300 i i

c

Li 4

NC1&NC2 NV1 &NV2

Fig.3.1 Object of Analysis (Short Column)

Table 3.1 Object of Analysis (Short Column)

Reinforcement Name Longitudinal Lateral

Outer Inner Rectangular Circular NC1 16-D16 - D6@7lmin D6@71inni NC2 16-D16 - D6@36mm D6@36mm NV1 16-D16 8-D16 D6@71mm D6@71nun NV2 16-D16 f 8-D16 D6@71mm D6@71mni

Concrete Confined by Rectabgular Hooj

Concrete Confined by Circular Hoor

Cover Concrete

Fig. 3.2 Division of Slice

-25-

y cry Ke 2.10X105 (kgf/cni2/cm)

Kp 1.60X105 (kgf/cin 2/cm)

Ky 1.33X 10 (kgf/cm 2/cm) op 2.00X103 (kgf/cm 2)

oy 2.40X103 (kgf/cm 2)

Table 3.2 Properties of Concrete

Compressive Strength Young's Modulus Name (kgf/cm 2 ) (kgf/cm 2 )

NC1 616 3.27x105 NC2 584 3.40X105 NV1 628 3.25x 10 NV2 1 652 1 3.27x i0

Tensile strength was assumed as fFc in analysis, where Fe stands for the compressive strength

Table 3.3 Properties of Reinforcements -

Yield Strength Young's Modulus Reinforcement (kgf/cm 2) (kgf/cin 2)

D160nner Longitudinal) 5840 2.1X106 D16(Outer Longitudinal) 7700 2.1X106

D6 (Lateral) - 8630 2.1X106

Table 3.4 Characteristics of Relationship between Stress and Slippage

-26-

[;] Analysis

Experiment

-46 -36 -26 -16016263646 50 Ueformation (min)

Fig. 3.3 Relationship between Shear force and Deformation (Nd)

-27-

-2C

-4-0

-60

-80

-100 -5

WO

Analysis -----Experinent

20 30 4-0 50 Uetormaton (mm)

Fig. 3.4 Relationship between Shear force and Deformation (NC2)

-28-

Deformation (mm)

50

4-0

C 0

30 a) C)

0 u. 20

a, C)

Cr) 10

0.

- —10

-30

Fig. 3.5 Relationship between Shear force and Deforffiatjon (NYl)

-29-

7 C D

L

Cd

cn2

C

-2

-50

- Analysis -----Experiment

I I 0 -5 0

I 5 10 15 20 Deformation (mm)

Fig. 3.6 Relationship between Shear force and Deformation (NV2)

-30-

4. ANALYSIS OF BEAM-COLUMN-JOINT SUBASSEMBLAGE

4.1 OBJECTIVES

As the developed member model was verified through the simulation analyses of short

columns, it was installed into a computer program for nonlinear analysis of a frame structure.

This chapter describes a simulation analysis of a beam-column-joint subassemblage executed

for the verification of the program.

4.2 OBJECT OF ANALYSIS

The object of the analysis was a beam-column-joint subassemblage'3 shown in Fig.4. 1 and

Table 4.1. It was a half scale model of the beam, column and joint of a 45 storied building

using high strength materials. Fig.4.2 shows the loading apparatus. It was supported at the

ends of columns with pin supporting systems and cyclic shear forces were applied to the ends

of beams. The axial force of column was kept constant at 100tonf during the experiment.

The properties of materials were as shown in Table 4.2. Not only total deformation but also

the deformation of each member and the strains of reinforcements were measured. From

these measurement, it was observed that the deformation of beams including the rotation due

to the slippage of longitudinal reinforcements from the joint occupied from about 80% to 50%

of total deformation. In columns, some flexural and shear cracks occurred, but yielding of

reinforcements was not observed. The proportion of the deformation of joint was small when

the total deformation was small, but it grew during cyclic loading to occupy about 40% of

total deformation at the maximum deformation.

4.3 ANALYTICAL MODEL

Columns and beams were modeled as cantilever members which have two slices, of which

one was considered to calculate curvature and another was to calculate slippage, at the front

-31-

and the location of the longitudinal reinforcements of perpendicular members. The properties

of materials were assumed based on the results of material tests. The stiffness of the shear

transfer across a crack was assumed to be 20% of the elastic value for columns and 5% for

beams.

Joint was modeled as a panel which was subjected to shear deformation only. As there was

no reliable method to predict the relationship between shear stress and shear strain of a joint,

the relationship was set up based on the relationship obtained from the experiment as shown

in Fig.4.3.

4.4 RESULTS OF ANALYSIS

SLIPPAGE OF LONGITUDINAL REINFORCEMENTS OF BEAMS

Fig.4.4 shows the comparison between the slippage of the reinforcement of a beam from

joint obtained from analysis and that obtained from experiment. The experimental results

were obtained by the integration of the observed strain along the reinforcement in the joint.

This comparison shows that the relationship between stress and slippage of a reinforcement

assumed in the analysis was appropriate.

DEFORMATION OF BEAM

Fig.4.5 shows the relationships between the shear force applied to a beam and deformation

of the beam obtained from experiment and analysis. In this figure, two curves are shown as

experimental results. One of the two curves represents the deformation excluding the effect of

rotation due to the slippage of longitudinal reinforcements and another represents the total

deformations of the beam including the effect of slippage. The other two curves represent the

results obtained from the analysis.

Analytical results agreed with experimental ones very much.

-32-

(3) TOTAL DEFORMATION

Fig.4.6 shows the relationship between the shear force applied to a beam and the vertical

'displacement of the end of the beam. Envelope curves obtained from analysis agreed with the

result of experiment very well. The shape of hysteresis loops also agreed well when the

maximum deformation was less than 28mm, which corresponded to the inter story deforma-

tion angle of 1/50. When the maximum deformation was larger than that value, pinching

effect was observed in the experimental result while the analytical result showed spindle-

shape. However, the developed computer program is considered to be of practical use enough,

because a reinforced concrete building is usually designed so that the maximum inter story

deformation does not exceed about 1/100.

The difference between analysis and experiment in the shape of loops during large deforma-

tion is considered to be from the imperfect modeling of the nonlinear behavior of joint. While

it was observed in the experiment that the shear deformation of joint grew during cyclic

loading, such a behavior could not be expressed by the model of joint assumed in the analysis.

The nonlinear behavior of a joint under cyclic loading is just under study and some appro-

priate model is expected to be developed in future.

-33-

400

Joint 0—HOOP 4fi D8(S080)

cD c'J

300

451_70 70145

ti-i i ti 6-019 4-08 (S080) I @60 6-019

B—B'

1200 200

12—D19

4-08 - (sD8o)

@60

A—A.

2001 1200 400

U) 14)

1 3:0 1 400

Fig.4.1 Object of Analysis (Beam-Column-Joint Aubassemblage)

Table 4.1 Object of Analysis (Beam-Column-Joint Subassemblage)

Reinforcement Member

Longitudinal Lateral

Rectangular Circular Column

Beam

Joint

12-D19

6-D19

16-D16

2-D8@60nim

4-D8@60mm

2-D8,4set

D8@60mm - -

-34-

Fig. 4.2 Loading Apparatus

-35-

y cry

me

Ke 1.33X 10 (kgf/crn 2/cin) Kp 6.25X104 (kgf/cm 2/cm) Ky 3.51X104 (kgf/cm 2/cm) op 2.00X103 (kgf/cm 2) oy 4.50X103 (kgf/cin 2)

Table 4.2 Properties of Concrete

Compressive Strength

(kgf/cm2) Young's Modulus

(kgf/cm2) 677 3.52x105

Tensile strength was assumed as fFc in analysis, where Fc stands for the compressive strength

Table 4.3 Properties of Reinforcements

Yield Strength Young's Modulus Reinforcement (kgf/cm2) (kgf/cm2)

D19(Longitudjnal Column) 8000 2.1X136 D19(Longitudinal Beam) 5930 2.1X106 D8(Lateral) 8970 2.1X106

Table 4.4 Characteristics of Relationship between Stress and Slippage

-36-

'r (kgf/cin2)

1501------ 0.OlGe

47. 51 0.2Ge.

Ge Ge 2(l+v)

Fig.4.3 Model of Relationship between Shear Stress and Shear Starin of Joint

4

- Analysis

Experiment

J20

10

UI I I I I

0 0.5 1.0 1.5 2.0

I Slippage (mm)

Fig. 4.4 Relationship between Shear force and Slippage of Reinforcement

-37-

40i Analysis

- Experiment

Excluding Effect of Slippage

34 ,1

/

0 I

/ I

20--

C-) - I

I//

,

I ,- ,,I/, I

i I

I / Ia)

I / -Including Effect of Slippage - I

10

0 5 10 15

Deformation (mm)

Fig.4.5 Relationship between Shear force and Deformation of Beam

40

2(

-20

-40 -80

- Analysis -----Experiment

IMOO I 1400_j

6=(o1 +o2)/2

I I

R=ó/1400

I

-40 0 40

80

Deformation (mm)

Fig.4.6 Relationship between Shear force and Total Deformation

11

10

-39-

5. CONCLUSIONS

A nonlinear member model for a reinforced concrete column and/or beam which can con-

sider the effect of shear deformation and the slippage of longitudinal reinforcements was

newly developed.

The developed model was verified through the simulation analyses of reinforced concrete

short columns which were subjected to cyclic shear force under constant or varying axial

force. The relationship between deformation and shear force obtained from the analyses

agreed with those obtained from experiments.

This member model was included into a computer program for the nonlinear analysis of a

frame structure and the program was verified through the simulation analysis of a beam-

column-joint subassemblage. The analytical envelope curve of the relationship between the

shear force and total deformation agreed with experimental one. Although the shape of hys-

teresis loops obtained from the analysis were different from those obtained from the experi-

ment when the inter story deformation exceeded 1/50, they agreed well with the experimental

results when the inter story deformation was less than 1/50. These results shows that the

developed computer program is of practical use enough because a reinforced concrete frame

is usually designed so that the maximum inter story deformation does not exceed about 1/100

during any strong earthquake.

One of the reasons of the difference in the shape of loops during large deformation is con-

sidered to be lack of the knowledge how to predict the nonlinear behavior of a joint, and the

progress of the study on this problem is expected

-40-

REFERENCES

Giberson, M.F : Two Nonlinear Beams with Definition of Ductility, Proceedings of

ASCE, V61.95, No.ST2, pp.137-157, 1969.2

Takeda, T., Sozen, M.A. and Nielsen, N.N. : Reinforced Concrete Response to Simulated

Earthquakes, Proceedings of ASCE, V61.96, No.ST12, pp.2557-2573, 1970.12

Sugano, S : Study on Restoring Characteristics of Reinforced Concrete Members (in

Japanese), Concrete Journal, Vol.11, No.2, pp.1-9, 1973.2

Nagai, 5, Otani, S. and Aoyama, H.: Study on Hysteresis Characteristics of Reinforced

Concrete Column Using High-Strength Concrete (in Japanese), Summaries of Technical

Papers of Annual Meeting of AIJ, VoI.C, pp.583-585, 1992.8

lizuka, T. and Noguchi, H. : Modeling of Compressive Behavior of Normal and High

Strength Concrete, Journal of Structural Engineering, Vol.37B, pp.329-338, 1991.3

Fafitis, A. and Shah, S.P. : Lateral Reinforcement for High Strength Concrete Columns,

Journal of ACI, Pub. ACI, No.SP-87, pp.213-232, 1985

Kupfer, H., Hilsdorf, H. and Rush, H. : Behavior of Concrete under Biaxial Stresses,

Journal of ACI, Vol.66, No.8, pp.656-666, 1969.8

Ottosen, N.S. : A Failure Criterion for Concrete, Proceedings of ASCE, Vol.103, EM4,

pp.527-535, 1977.8

Park, R. : Ductility of Square-Confined Concrete, Proceedings of ASCE, Vol.108, ST4,

pp.929-950, 1982.4

Filippou, F.C.: Effects of Bond Deterioration on Hysteretic Behavior of Reinforced

Concrete Joints, EBRC Report, UCBJEERC-83/1 9, 1983.8

Morita, S. and Kaku, S. : Local Bond Stress Slip Relationship under Repeated Loading

(in Japanese), Transactions of AIJ, No.229, pp.15-24, 1975.3

Maruta, M. and Bessho, S : Elastoplastic Behavior of R/C Columns of High-rised Build-

ing used High Strength Materials (in Japanese), Proceedings of JCI, Vol.14, No.2,

pp.523-528, 1992

Nakamura, M., Bessho, S., Usami, S. and Kato, T. : Experimental Study on Interior

-41-

Beam-Column Joint using High Strength Concrete and Rebars (in Japanese), Summaries

of Technical Papers of Annual Meeting of AIJ, Vol.C, pp.583-588, 1991.9

-42-

L SCHEDULE FOR PRESENTATION IN 1992 AND 1993

Domestic Conference

Summaries of Technical Papers of Annual Meeting of the Architectural Institute of

Japan (1992.8)

Proceedings of the Japan Concrete Institute (1993.6)

Summaries of Technical Papers of Annual Meeting of the Architectural Institute of

Japan (1993.8)