3D Contribution to Frame Wall

8/3/2019 3D Contribution to Frame Wall

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UILU-ENG-87 2001

'ACIVIL ENGINEERING STUDIESSTRUCTURAL RESEARCH SERIES NO. 531

10129A531

ISSN: 0069-4274

3-DIMENSIONAL CONTRIBUTION TOFRAME-WALL LATERAL BEHAVIOR

ByCLAUDIO CHESIandw. C. SCHNOBRICH

A Report on a Research ProjectSponsored byTHE NATIONAL SCIENCE FOUNDATIONResearch Grant CEE 83-12041

DEPARTMENT OF CIVIL ENGINEERINGUNIVERSITY OF ILLINOISAT URBANA-CHAMPAIGNURBANA, ILLINOISFEBRUARY 1987


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S0272 -J OJREPORT DOCU MEIfT AnON14,REPORT NO.PAGE

4. Title en d S4Jbtltle3-Dimensiona l Contr ibut ion to Frame-Wall Late ra l Behavior

7. Authori.)Claudio Ches i and Will iam C. Schnobrich9. Performlna Ors.nlz.t lon N.me .n d Addr...

Univer s i ty o f I l l i n o i s208 North Romine St ree tUrbana, IL 61801

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14 .

Behavior o f the f i r s t f l o o r of the U.S . -Japan seven s to ry re inforced concre te t e s ts t r u c tu r e was modeled by a f i n i t e element model. The c o n s t i t u t i v e matr ix descr ib ingmater i a l behav io r i s a normal concre te model which inc luded a smeared crackingcapab i l i ty . The computed response of the system was shown to have a dependence on thel e v e l of t ens ion s t i f f en i ng presen t in the concre te . The se lec t ion too I o w a va lued i s to r t e d th e behavior observed in the model. Th e 3-d imens ional e f f e c t s presented inthe t e s t s t r uc t u r e wa s a l so observed in the computa t ional model. Motion of the t ens ioncolumn was t r ansmi t ted through the s lab and beams to the oute r f rames. This mechanismprovided a s i gn i f i can t con t r ibu t ion to the l a t e r a l load r es i s t ance .

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Earthquake Response, Ful l -Sea l Tes t , I ne l a s t i c Behavior , Fin i te Element Analys is

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3-DIMENSIONAL CONTRIBUTION TOFRAME-WALL LATERAL BEHAVIOR

by

Claudio Chesiand

W. C. Schnobrich

A Report on a Research ProjectSponsored by theNational Science FoundationResearch Grant CEE 83-12041

University of I l l inois a t Urbana-ChampaignUrbana, I l l inois

February 1987


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TABLE OF CONTENTS

PageINTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1NUMERICAL MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2NON-LINEAR STATIC ANALYSIS - MAIN RESULTS . . . . . . . . . . . . . . . . . . . . . . . . 8CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41


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3-DIMENSIONAL CONTRIBUTION TO FRAME-WALL LATERAL BEHAVIORby Claudio Chesi and Will iam Schnobrich

INTRODUCTION

The sub jec t o f the research was suggested by the U.S. -JapanCooperative Research Program, which consis ted of the construct ion andpseudo-dynamic t e s t i ng of a model bui ld ing. In t ha t program, the t e s tspecimen was a fu l l - sca le seven-s tory re inforced concre te frame-walls t r uc t u r e . Figs . I and 2 show schematic views o f t ha t s t ruc ture .Resis tance to l a t e r a l loads wa s provided by three pa ra l l e l frames: twomoment r e s i s t i ng space frames ( the ou te r ones, frames A and C) and acoupled frame-wall (frame B). The connection among frames was r ea l i zedby f loor s l abs with t r ansversa l beams.

Severa l i n t e r e s t i ng aspects of the seismic behavior of concreteframes have been c la r i f i ed by the experimental work and subsequentana l y t i ca l s tudies assoc ia t ed with the NSF supported research beingperformed within t ha t program. In th i s inves t iga t ion , in te r e s t has beendevoted to a speci f i c exper imenta l resu l t , showing the so r t ofin terac t ion occurr ing among pa ra l l e l frames, due to the coupling act ionof t r ansversa l beams.

In the ea r ly s tages of loading, the response is con t ro l led mainly byshear wall deformation. As loading proceeds, bending in the plane o f thewal l , indeed. causes extremely large elongat ion a t the tension s ide ofthe wal l , so tha t t r ansversa l beams framing into t ha t wall undergo larger e l a t i ve ve r t i ca l displacements between t he i r ends. Th e shear forcesthus genera ted have a s t ab i l i z ing e f f ec t on the shear wal l , increasing,


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a t the same t ime, the overturning moment in the ou te r frames.the so-ca l l ed "3-dimensional e f f ec t . "

This is

Th e contr ibut ion of the 3-dimensional ef fec t s to the bu i l d i ng ' su l t ima te re s i s tance has a simple but meaningful in te rpre ta t ion in aco l lapse ana lys i s , assuming t ha t in the col lapse mechanism p la s t i chinges develop a t a l l the t r ansversa l beam ends (Yoshimura and Kurose,1985). More complete s tudies have been developed by Otani e t a l . (1985)and by Charney and Bertero (1982). These authors have incorporated the3-dimensional e f f ec t in to computer codes fo r frame ana lys i s , by simplyin t roducing spr ing connections between the shear wal l tension s ide andthe corresponding columns in the oute r frames. The spr ing s t i f fnes s i staken as close as possib le to the t ransversa l beam s t i f f ne s s .

In the presen t work, a f i n i t e element non-l inear model i sdeveloped, represent ing a s ingle f loor of the t e s t s t ruc ture . The loadhas been progress ively increased through a s t a t i c monotonic process .Atten t ion has been focused on the mechanisms generat ing the 3-dimensionale f f ec t . An est imat ion is also given o f the contr ibut ion of th i s l a s tmechanism to the t o t a l bui ld ing res is tance a t d i f f e r en t load l eve l s .

NUMERICAL MODEL

Th e por t ion of the bui ld ing included in the numerical modelconsis ted of the f i r s t s to ry plus a port ion of the nex t s to ry , up tomid-height between the f i r s t and second f loo r . Due to symmetry o f thes t r uc t u r e about the plane conta in ing the shear wall , only on e s ide , i . e . ,one-half of the bui ld ing, was analyzed. A schematic view of the


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s t r uc t u r e as modelled is shown in Fig. 3; the f in i t e element modell ing ofit r e su l t ed in the grid of Fig . 4.

The fol lowing two kinds of elements have been used fo r thed i sc re t i za t ion of the d i f f e r en t s t r uc t u r a l components:

1) For the shear wal l : a 9-node Lagrangian she l l element (Milfordand Schnobrich, 1984); the wal l i s subjected to in-plane forces only , sothe element i s used mainly to descr ibe a membrane behavior .

2) For the s l ab : the same kind of she l l element but here it is

sub jec ted to both in-plane and out-of -p lane forces .3) For the T-beams, r esu l t ing from an e f fec t ive s lab width plus

eccen t r ic web: the webs have been represented by the eccen t r ic she l ls t i f f ene r beam element (Milford an d Schnobrich, 1984), which i s in theform of a 3-node Lagrangian beam element . This l a s t element , if used inconj unct ion with the 9-node Lagrangian she l l element , i s expected toprovide an accurate desc r ip t ion of the T-beam behavior . This fea ture wasof specia l i n t e r e s t fo r the present ana lys i s , as there was experimentalevidence of a beam-slab in terac t ion having a much more pronounced e f f ec tthan convent ional ly assumed.

4) For the columns: the same elements as in 3) , which can simplywork as beam column elements, if not coupled to she l l elements.

5) For the shear wal l ' s eccentr ic columns: again , the same beamelements as in 4 ), but now with a zero bending s t i f fnes s .

Non-linear mater ia l behavior was spec i f ied fo r a l l the elements butthe columns. In the Milford and Schnobrich formulation, the beam i shandled as a layered system, thus, the non- l inear beam elements havenon-zero bending s t i f fness in one di rec t ion only. For the purpose of


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analyzing the 3-dimensional e f f ec t , however, b i - ax ia l column bending hadto be considered fo r the columns in the outer frames. These columnswere, thus , cons idered to remain e la s t i c . This assumption of e la s t i cbehavior fo r columns i s supported by experimental resu l ts , those resu l t sshowing p las t i c hinges occurr ing in beams much e a r l i e r than in columns.

Th e RCSHELL and RCBEAM mater ia l models (Milford and Schnobrich,1984) present in F in i t e fo r the analys is of non- l inear analys is ofconcrete behavior have been used in th i s study. Although these models

r ep r e s en t exac t ly the same m a t e r i a l , tw o d i s t i nc t mater ia lspeci f i ca t ions are required fo r she l l and beam elements respect ively .The concre te proper t ies which are requi red as input to the mater ia lmodels a re l i s t ed in Table 1 (see also Fig. 5). A reduced in tegra t ionorder (2x2 fo r she l l elements and 2 for beam elements) has been used, soas to reduce poss ib le problems from membrane and/or shear locking, thephenomena often observed with th i s class of element. With th i simplementat ion, no problems were encountered re la t ive to the poss ib leac t iva t ion of zero-energy modes.

The unloading capabi l i t i es , as incorporated in the two mater ia lmode I s , have been proven to be very important even fo r a monotonicloading process. As cracking i s occurr ing a t some in tegra t ion po in ts ,indeed, temporary unloading and/or reloading may be tak ing p lace a t someo the r poin t s . A typ ica l a- E:. relat ionship as it wi l l ex i s t followingsevera l subsequent load s teps is shown in Fig. 6 fo r a gener icin tegra t ion point . The tension s t i f fen ing parameter ( fi) , governing thepost-cracking behavior of concrete , has shown a remarkable ef fec t on theglobal s t ruc tu ra l response. Figure 7 shows the crack dis t r ibu t ion


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5recorded in the shear wal l a t col lapse fo r the cases computed while using/3-5 and t ha t fo r {3=20. Th e corresponding ( 7 - re la t ionsh ips fo r there in fo rced concre te in the shear wall and tha t in the end columns areshown in Fig. 8. In both cases ( i . e . , fo r the tw o {3 values) a shearco l lapse occurs, al though the two mechanisms are qu i te d i f f e r en t . Notet ha t i n the second case ({3=S) , the horizonta l crack a t the wal l base haspropagated to a l l the in tegra t ion points along the lowest l eve l , and thewal l bending s t i f fnes s was consequently sensib ly reduced.

In car ry ing out th i s inves t iga t ion while using a model whichincludes only the f i r s t one and one-hal f s to r i e s , the following loadshave been appl ied to the model:

- ve r t i ca l load , including s lab weight and axia l loads oncolumns and shear wal l ; these r ep resen t the ef fec t s o fthe upper s t o r i e s i n the response;

- l a t e r a l load , including horizonta l i ne r t i a force a tthe s lab l eve l , shear force and moment a t the topof the wal l .

Th e l a t e r a l load was a f fec ted by a mul t ip l i e r , represent ing ther a t io between the t o t a l hor izon ta l force and the t o t a l bui ld ing weight( r e f e r ~ n c e d in the following as the " l a t e r a l load i n t ens i t y f ac t o r " ).

The cons t ra in t s imposed on the model are:- .symmetry condi t ions on the symmetry plane;- f ixed condi t ions a t the colWUTI ends and shear wal l bases ;- hinges a t the column's mid-heights ;- the same horizonta l displacement fo r the columns and the shear

wal l a t the top of the model.


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6Moreover, the same z ro ta t ion (see Fig. 4) i s imposed a t a l l of the nodesa t the s l ab -wal l in te r sec t ion ; th i s s t ipu la t ion i s requi red as aconsequence of the absence o f a dr i l l ing mode fo r the planar wallelements . The theory which forms the bas i s fo r the development does notinclude a s t i f fnes s for ro ta t ions around the normal. This is a typ ica lproblem fo r she l l elements in ter sec t ing a t r i gh t angles .

Several di f ferent models ( ten) had to be t r i ed , before the properone cou ld be def ined. Major d i f f i cu l t i e s orig inated from two problems:1) In the ear ly attempts to solve the problem, the model included a

gener ic f loor , with the shear wal l and columns spanning one-hal f ofth e in ter s tory he igh t above and below the s lab . In th i s way, themodelled port ion of the wall was 5 m (16' 5") wide and 3 m (10 ' )h igh. The cons t ra in t s associa ted with the model make it impossiblefo r the expected bending behavior to develop. By analyzing a modelwhich included the ent i r e f i r s t s to ry , ins tead , ( i . e . , from the baseo f the columns to mid-height between the f i r s t and second s tor ies )allowed the inc lus ion in the model o f a l a rger port ion of the wal l .Th e expected behavior was then observed.

2) Specia l care had to be used in the def in i t ion of the normal and theshear s t r esses appl ied a t the top of the shear wal l . Theserep resen t the shear load and moment coming from the uppers t r uc t u r e . Improper s t ress dis t r ibut ions caused a loca l f a i lurebefore a global col lapse of the model could take place . Theso lu t ion shown in Fig. 9 was then adopted: an ex t ra por t ion of thewal l was included in the model and the loads appl ied a t the top oftha t wal l . In th i s way, the same moment a t the base of wall could


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be developed by lower i n t ens i ty fo rces . Stresses , moreover, werenot imposed in the whole region o f i n t e r e s t bu t , r a t he r , wereal lowed to r ed i s t r i bu t e .

Note also t ha t a s impl i f ied model was used in most o f the prel iminaryana lyses , with non- l inear i ty r e s t r i c t ed to only the wal l . This l a s t ,indeed, due to the extremely high l a t e r a l s t i f fnes s j u s t of the wal li t s e l f , governs to ta l ly the model 's global response.

A fe w remarks about the model:1) Th e r ea l s t ruc tu ra l behavior cannot be reproduced by a numerical

model t ha t inc ludes only one f loor :- not only external forces , but i n t e r na l forces as wel l have

to be specif ied , in order to r ep resen t cont inui ty withupper f loo rs . In terna l forces , however, are not knowna pr io r i ;

- a s ingle load pat t e rn must be used throughout the ana lys i s ,while the in terna l force d i s t r i bu t i on depends on the loadl eve l ;

- due to the absence of the upper f loor s , column and walla x i a l loads represent ing those upper f loors do not inc ludethe e f f ec t of the shear forces assoc ia t ed with the t ransverse beam bending of the upper l eve l s .

2) As a consequence, the l a t e r a l load systems in the model and in thet e s t s t ruc ture are d i f f e r en t . Equivalence between the two has beenimposed so t ha t y ie ld ing o f the wal l ' s main re inforcement occurs fo rthe same l a t e r a l load fac to r in both cases .


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3) It is worth under l ining, however, tha t the model does not have, asi t s purpose, the reproduct ion o f the global s t ruc tu ra l behavior;r a the r , it aims a t reproducing the three-dimensional re s i s tancecont r ibut ion developed by the slab and t ransverse beams. This is al oca l phenomenon, requi r ing the analys is of a s ing le f loo r only.

NON-LINEAR STATIC ANALYSIS - MAIN RESULTSThe non-l inear analysis was ca r r ied out by progress ively increasing

the l a t e r a l load in tens i ty fac to r through 136 load s teps . Major ef for t s(see Appendix) were required to fol low the crack opening and propagat ionthroughout the shear wall , which governed the whole s t ruc tu ra l response.On the one s ide , indeed, the non- l inear problem connected with wallcracking i s a hard one. The wal l i s subjected to in-plane or membraneforces only. The s t i f fnes s contr ibut ion associa ted with an in teg ra t ionpo in t suddenly drops to zero a t tha t in tegra t ion point as crackingoccurs, then l a rge amounts of load are re leased and have to ber ed i s t r i bu t ed . On the other end, the shear wal l i s by fa r the s t i f f e s telement in the model, so tha t most of the l a t e r a l load is car r i ed by i t ,and the re s i s tance contr ibut ion from the o ther elements is very smal l .

The following i s a b r i e f his tory o f the wall cracking ands t r uc tu r a l behavior .

The l inear e la s t i c range extends up to a l a t e r a l load in tens i tyfac to r o f 0.113 (note tha t , according to Wight e t ale (1984), the designvalue was 0.112). Non- l inear i ty occurs because of cracking a t the baseo f the wall with the end column in tension (see Fig. 10). As aconsequence of t h i s , cracking soon extends to the adjacent points along


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the wall base. During the next load s teps , other points on the wall endcolumn crack, followed immediately by the adjacent wall points . At thesame t ime, the crack a t the wal l base propagates towards the compressedend, causing a "neutra l axis migration" to take place. Note t ha t ,because of th i s l a s t phenomenon, the increase in the moment i s car r i edmore by a l eve r ar m act ion than by an increase in tension s t r e s se s .Figure 11 gives a c lear picture of this ef fec t ; the increase of ax i a lload in the column does not counterbalance tha t in the wal l moment. Atload s tep no. 84, the wall base and the end column are completely cracked(26 cracks opened or integrat ion points cracked, see Fig. 10); then, theax i a l load in the l e f t end column s ta r t s increasing again, un t i lre inforcement y ie ld ing occurs in the end column a t load step no. 119.This s tep corresponds to a l a t e r a l load fac tor of 0.244. Thecorresponding crack dis t r ibu t ion i s given in Fig. 10. The s t ra in prof i leover a cross sec t ion a t the base of the wall i s shown in Fig. 12.Agreement with the experimental prof i le i s sa t i s f ac tory ; note , moreover,tha t a fe w wall bars had al ready yielded a t previous load s teps .

The analys is was then car r i ed on fo r a few more load s teps , andterminated a t load s tep no. 136, before the model had reached a completecol lapse (n o p la s t i c hinges had formed yet in beams). The reason fo rs topping the analys is was due to the very low convergence r a te of themodel. The l a t e ra l load carrying capaci ty of the system, indeed, wasextremely reduced, so tha t the load s tep s ize was necessar i ly verysmal l . Most of the expected behavior had al ready developed.

A global descr ip t ion of the s t ruc tu ra l response is given inFig. 13, in terms of the l a t e r a l load-hor izonta l def lect ion curve.


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10Sudden, b u t temporary decreases in s t i f f ness can be observed a t thecrack ing o f each o f the in teg ra t ion po in t s o f the wal l end column int e n s i o n . The f igure a l so shows the high degradat ion o f the wal l ' sl a t e r a l s t i f fnes s , re su l t ing in the t r a n s f e r o f the addi t i ona l shearfo rces from going in to the wal l to going in to the adj acen t columns, asthe l a t e r a l load increases .

In order to i nves t iga te the 3 -dimensional e f f ec t , a t t en t ion hasbeen focused on the elongat ion o f the t ens ion s ide o f the wal l , which i s

the key parameter con t ro l l ing the bending of the t r ansver se beams. Withthe cracks opening to near ly the compression column, the wal l tends top i v o t around t h a t compression column. Thus, movement on the t ens ion s idei s q u i t e s i gn i f i can t , while on the compression s ide the movements arenominal . Figure 14 shows the load def l ec t ion curve, r e l a t i ng the l a t e r a lload f a c to r to the v e r t i c a l disp lacements a t the j o i n t where the beamsframe in to the wal l ' s tens ion s ide .Fig . 13 i s re f lec ted in th i s f igu re .

The same behavior observed inA comparison i s also given with

t e s t r e s u l t s . Th e model appears a little s t i f f e r than the t e s ts t r uc t u r e , mainly a t the lo w load l eve l s (where the model assumesconcre te to be uncracked) .

The magni tude o f ver t i ca l displacements sugges ts t h a t bending oft r a n s v e r s a l beams has been ac t iva ted . This i s d iscus sed in thefollowing.

Figure 15 shows the ax ia l loads presen t a t the base o f both thecolumns and the shear wal l fo r a l a t e r a l load fac to r of 0.244 . Thee f f ec t of g rav i ty is not inc luded in the va lues given in Fig. 15.Columns A and C, connected by beams to the wal l ' s t ens ion s id e , undergo


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11much higher loads than the corresponding columns connected to the wal l ' scompression side (as expected based on the observed displacementsdescr ibed in the previous paragraph). The e f f ec t is most pronounced incolumn c the increase in ax ia l load which comes from thet ransversa l beam shear , gives a measure of the 3-dimensional e f f ec t .Figure 16 shows t ha t , as expected, the axia l load increase in the columnand the shear in the t r ansver sa l beam are about the same and growpropor t ional ly to wal l elongat ions. Note tha t the ve r t i ca l equil ibrium

i s s a t i s f i ed by ax i a l forces in columns A, B, C, D, E, and F. A port ionof the boundary column's ax i a l load has been t r ansfer red to thesurrounding columns as a consequence of the wal l ' s tension s ideelongat ion . The wal l moment r es i s t ance i s thus enhanced by the formationo f a moment r e s i s t i ng mechanism, including both the wall and the columns.

A measure of the contr ibut ion developed by the 3-dimensional e f f ec tto the t o t a l res is tance can be def ined by comparing the moment developedby to the to ta l over turning moment. The r e su l t of th is comparison isshown in Fig. 17 , where the beams a t a l l the f loors are supposed todevelop the same contr ibut ion a t col lapse . Again, the dependence on theend column elongation i s evident . Af ter th i s member has en t i r e lycracked, the percent contr ibut ion becomes almost constant . Note tha t ameaningful value of this is reached with the wall main reinforcementstill e la s t i c : the deformations act ivat ing the 3-dimensional e f f ec t comemore from the concrete cracking than from column bar yie ld ing .

Th e 3-D contr ibut ion to r es i s t the over turning moment reached avalue of 6.12% a t load step no. 136, a t which point the analys is wasterminated. I t i s not d i f f i cu l t to give an approximate evaluat ion of


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12the maximum value fo r th i s 3-D contr ibut ion . A fu r the r increase of thel a t e r a l load would produce p la s t i c elongat ion o f the reinforcement in thewal l ' s end column and formation of p la s t i c hinges a t both ends of thet ransverse beams ( th i s was observed in the experimental analys i s aswel l ) . In such a s i tua t ion , the l imi t value fo r shear in t r ansve rsa lbeams has been es t imated as T = 6 t (metric tons) , or 13.2 kips ,corresponding to a value of 6.87% fo r the above percentage contr ibut ion .(The average value o f the shear s t ress in the t ransverse beam is about5 kg/cm2, or 70 ps i . ) This re su l t i s not fa r from the on e given byYoshimura (1985), who es t imated the contr ibut ion of the t ransverse beamsto bu i ld ing moment re s i s tance a t a value o f 8%.

I t i s worth mentioning also t ha t a meaningful contr ibut ion to thebending re s i s tance o f the t ransverse beams i s provided by the s lab .Clear evidence of th i s was given, among others , by Yoshimura (1985),through an ana lys i s o f the s ta tus of bar yie ld ing in the t e s t s t ruc ture ,and by Joglekar e t a l . (1985), who t es t ed beam-column-slab assemblies .I t i s a common conclusion t ha t the s lab width which i s ef fec t ive with thebeam in car ry ing moment i s s igni f i cant ly larger than tha t prescr ibed bydesign codes (ACI 318-83 included) . In the present analys is , eccentr icshe l l s t i f f ene r beam elements have been used to model the t ransversebeams. This modelling al lows a good representa t ion of the beam-slabin te rac t ion phenomenon, and the same conclus ion has been achieved.

Figure 18 shows bending moments in the t ransverse beams and bothmoments and tension s t ra ins in the s lab , a t load s tep no. 136. The s labcon t r ibu tes to the moment car ry ing capaci ty mainly by providing the beamwith addi t ional tension bars ( the moment car r i ed by the s lab i t s e l f i s


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13only a smal l percentage of t o t a l moment). In Fig . 18, a reasonable valuefo r the ef fec t ive s lab width (w) i s suggested (w i s the ra t io of t o t a lt ens ion force car r i ed by bars in the beam inf luence area and the t ens ionper u n i t length a t the beam axi s ) . A value of w = 21 5 cm (7 ' ) i s sofound, while a value w = 150 cm (4 ' 11") would be prescr ibed by the ACI318-83 Code. When computing the l imi t value fo r the shear force ,w - 21 5 cm was used. Note, however, t ha t w i s a function of the l a t e r a lload in tens i ty (as also remarked by Joglekar e t a l . (1985)) , in the sense

t ha t a higher value should be expected fo r higher load in tens i t i e s .

CONCLUSIONS

The behavior of the f i r s t f loo r of the U.S.-Japan seven-s tory t e s ts t ruc ture was modelled by a f in i t e element model, which used as i t smater ia l , those proper t ies of re inforced concrete . Nine-noded she l l andthree-noded beam elements were se lec ted fo r the model.

The computed response of the system was shown to have a dependenceon the level of tension s t i f fen ing assumed to be present in theconcre te . Se l ec t ion of too lo w a value fo r the s t i f fen ing parameter f3d is to r t s the behavior observed in the model.used in th i s study.

Values o f 5 and 20 were

The three -dimensional ef fec ts presen t in the t e s t s t ruc ture werealso present in the model. With increased def lec t ions the wall tended topivot about the compression columns. The motion a t the tension columnwa s t ransmit ted through the t ransverse beams to the columns in the ou tframes. Computed response was s imi la r to the experiment.


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14The computed e f fec t ive s lab width was found to be in excess of tha t

presc r ibed by ACI 318-83.

ACKNOWLEDGEMENTS

The work summarized in th i s report was performed by C. Chesi whilehe was on sabbat ica l from the Pol i tecnico Di Milano. Support for th i ss tudy was provided under the National Science Foundation GrantNo. CEE 83-12041.


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15

Concrete in i t ia l tangent modulus (Eo)Concrete cylinder strength (f ' ). cConcrete tensile strength ( ft ) *Strain at maximum concrete stress (s )cuUltimate stress factor (FCU)Ultimate strain factor (ECU)Linear elastic optionFixed crack direction optionConcrete tension stiffeningConcrete tension stiffening factor (S)Number of concrete layersNumber of reinforcement layersReinforcement tangent modulusReinforcement plastic modulusReinforcement tension stiffeningYield stress of reinforcement

237000 kg/cm 2290 "22

0.00210.891.42

"FALSE""F ALSE""TRUE"

5

84

"

1710000 kg/cm 2o"F ALSE"

3650 kg/cm 2Then, fo r each reinforcement layer at each integrationpoint:- depth of reinforcement layer "i"- area of reinforcement for layer "i"- direction of reinforcement layer "i"

(*) Concrete tensile strength computed as:f t = 5 /4200 = 324 psi = 22 kg/cm 2

TABLE 1


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Luadingdirectiun

16

I II II I----,-----..0- ---,- ---0-----.----- II I I II I I II I J II I I I: I I II II II I II I I

_____ .1_ -----C :J-----!...----I I II I IIiIII

IIIi II I I II I I I

- - - - - - - - - -{ ]- -- _L - - -0---- -'-- --I II I

Frame A

Frame 8

Frame C

Figure I Test specimen ( f u l l - sca l e seven-s torybu i ld ing) : t y p i c a l f loor p lan


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17

- I - - liiiI J :... ..., I' " ....c ;.;;;1

I. - ... ,..oi .11\ ,..

- , ... .. I'" .. ; ... .. J - I ...

22.75 mii i :...1 .. ...J ;.::i

w ,....l ...I ;::1 .;.:1

I- l::;lr - 1m ;.JI -=:III l

Sectiun 8-8 uf fig. 1

Figure 2 Test specimen: e leva t ion


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[u_ lIr-----'----11 /

'l 1/ 1 // I'I / / I /r; / /: /

r; / / : /'I l / I /'I / / / /'I / / L - - l - - - - - - - 7- --- -, -

'I / / / /'I / / / /

SItf. TRY PLANE -IIIIIII_-1

'l .I / / /'I / I / / ----- BEAMS-- - -- ..L___ -.- --1'-- - - - --'- - ._- -(- - - ----- ---

/1 / .I I/ I / I

Figure 3 Tes t specimen: a schematic view of th e por t ion of th e bui ld ingincluded in th e numerical model


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>-

..-!Q)

'"0oS


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e:

f't

f'cFCU f'c

a

//h

//

/ELJ 0

/1

20

E: ECU E:CU CU

e:

Figure 5 Stress s t r a in r e l a t ionsh ip for concrete (a) andbehavior of concre te in tens ion (b ) with theTENse opt ion

a)

b)


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a

//

/

21

//

Figure 6 Typical unloading-and-reloading behavior ofconcrete in the softening range


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000000

oo0000000

22

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 B = 20

cracked cuncreteo uncracked concrete

oo000000000

oo00000000

0000000

oo00000

B = 5

0

00000000

000

00000000000

000

000000000000

o-00000

Figure 7 Crack d i s t r i bu t ion i n the shear wa l l fo rd i f f e ren t values of the S parameter


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,aI

a

1;

23

e:

wall - 6 = 20 wall - B = 5

cr

II II II

end culumn - B = 20 end culumn - B = 5

Figure 8 St r e ss s t r a i n r e l a t i o n s h i p s f o r r e in f o r ced conc r e t e fo rd i f f e r e n t values of th e S p ar amete r

e:

e:


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24

Figure 9 The modified scheme fo r the f i n i t e element ana ly s i s ,inc luding an ex t r a -por t ion of the shear wal l


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25

23 - ~ ~ o

~ ~ 7 28- ---1812 22 25 \33.....6

- 31 " ,\0-----.0 8 13 26 \9 \27- -----.. ----..2 3 4 5 6 9 14 \\ - - - ---- - - --- ---

Figure 10 Crack dis t r ibut ion an d or ien ta t ion in the shear wal l a tyield ing of re inforcement in the t ens ion end column( load s tep n. 119) . Numbers give the cracking sequence.


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M

600

400

200

26luad step n. 84ItmJ , N [ tJ/ I

/ I , /",/ I ." . // i /,/// -- / M /r-,/'/ ". // ) // ---/ /1 / ""// v~ ; > r : r ~ I / - V ~ i

// II I I-1\/ N

80

60

I- 40

-l- 20

IIII

I I 115 . 15 .20 .25Lateral luad factur

Figure 11 Varia t ion of moment in the shear wal l ( ~ 1 ) and of ax i a l loadin the tens ion end column (N) during the load process


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27

--;- '

3

numeriC8lX experiment8l._--- \4/ / \

/ yield level2 ~ - - - 1 ~ ' ~ - ~ ~ - - - - ~ - - - - ~ - - - - - _ ~ / ~ - - ~ \ ' - - ~ - - ~ - - ~ ~ ~ 1 II

-.

....

.......

I II I~ . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - .

Figure 12 Ver t j ca l s t r a in prof i l e on the cross sec t ion a tthe wal l base (load s tep n . 119)


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0.25 -

:J 0.20 -Cd IcolI -"'0co:J.....co 0.15; -C!J

0.115-

28

b)

I0.2 0.4 0.6 0.8slab hurizuntal displacement [em]

Figure 13 Late ra l load f ac to r versus the s lab hor izon ta l disp lacement :a) t o t a l base shear , b) wal l base shear


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0.25:J.....,;Umuct1:J

0.20ct1OJ.:..;ct1

o. 15 -

o. 115

29

a)I- ' .....-

. / / b),/ //// 'l

- - z ~

/, // /

/ '/ /-/ // // /// ' //

/// v/ It/ I "A/I'"

V [em], I I ,0.2 0.4 0.6 0.8

Figure 14 Late ra l l o ~ d fac to r versus the slab ve r t i c a l displacementa t point A. Numerical (a) and experimental (b ) r e su l t s .


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I,"

30

1/\ Vi /1: : /: /: :0 E F

.. - - - - - - - - - - - - - - I- - - -- - -- -- - - - - ..,,, !/;'[, "B;'"., J----

+

..QZ

CJCD

+0"\NNII

coZ

t---_l/',"! ,,/- - - - - - - - - -*""r---. r---.r---. CD 1"'"\\.0 CJ

f'o"'\ \.0 .;:j"r---. f'o"'\+ II IIN "0 Q.).;:j"NII uz

Z Z

i /G--- '"l

N.;:j"NIIenz

\.0CJ\.0U"'\

III

!.ze.-

1I

/Ht

1"""\N.;:j"

II..cz

I t

II......z

Figure 15 Axial loads a t th e base of columns and shear wall a tload step n. 119 ( la tera l load factor = 0.244)


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[kg]

4000 -

3000 -

2000 -

1000 -

31

vr--..A

I I0.2 0.4 0.6 0.8 V [em]

Figure 16 Var ia t ion of shear in the t r an sve r sa l beam (a) and ax i a lload increase in column C (b) as a func t ion of theve r t i c a l displacement a t poin t A


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32

load step n. 84

l imit value6 . 8 7 % ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - ~ - - - - -

"--"/" ~ " VI0.115 O. 15

b) a)

\ - - - - - : l ~ \ "~ I o - ~ ' /""..---VJ ~ ";

0.20 0.25la tera l load factur

Figure 17 Percentage o f the global over turning moment ca r r iedas 3-d imens ional e f f ec t versus the l a t e r a l loadf ac to r . (a) Transversal beam shear ; (b) ax i a l loadincrease in column C.


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e:

H

33

II II II II II II

----- ---Figure 18 Bending moments fo r beams (a) and s lab (b) and s labs t r a ins a t the l e v e l of top re inforcement along al ong i tud ina l sec t ion . Th e beam moments have beend is t r ibu ted on the beam in f luence widths .


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34APPENDIX

The RCSHELL and RCBEAM Mater ia l ModelsTwo opt ions ex i s t fo r handl ing the tens ion s t i f fen ing ef fec t

pr esen t in a f in i t e element desc r ip t ion o f the behavior of a reg ion ofre in fo rced concre te : TENSC and TENSS. With TENSC the s t i f fen ing i sassigned to the concrete model, while with TENSS the s t e e l modelr e f l ec t s the s t i f fen ing ef fec t .

1) I f the TENSC opt ion ( tension s t i f fen ing appl ied to concre te) isused, the response of the mater ia l models to increasing tension s t ra insi s governed by the following ru les :a) A l i nea r e la s t i c behavior i s assumed fo r o


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35+the 0- diagram. In Fig . A .l a t s t ep 3, i s increased to 3 andthe corresponding s t r e s s i s 03 . Due to the assumption E=Eo,however, the re s idua l load is propor t ional to 110=3-3 Thisre s idua l load i s now i t e r a t ed ou t of the system. At the nexts t i f fnes s update the t angen t modulus wi l l be se t to zero ( inFig. a . l , s t ep 4, =4 produced 0=4) .

The above behavior i s contro l led , in the mater i a l models, by the crackf lags CFlAG and CCFlAG , wi th CFLAG o corresponding to uncrackedconcre te , i . e . , o


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36cracking to t r i gge r i t e ra t ions on the unbalanced excess tension, s t r e s sdi f ference in f ina l resu l t s are s i gn i f i can t .

Due to the above problems, updating the tangent s t i f fnes s matrix a tthe second i t e r a t ion , r a ther than a t the f i r s t one, has been proven ane f f i c i en t procedure.

2) I f the TENSS opt ion ( tension s t i f fnes s lumped to s t ee l ) i sused , the behavior of concrete i s the same as with the TENse opt ion,while th e s tee l s t ress i s always given the correc ted value , i . e . , themost updated one. The global behavior a t f i r s t cracking r esu l t s to be asshown in Fig . A.3:a) l e t the s t a r t i ng po in t be A, corresponding to a s t r a in value 1 ;b) if the s t r a in i s increased from 1 to 2, the new solu t ion is not in

B ', as it might be expected, but , r a ther , in B, as the s tee l e la s t i cmodulus has been updated to the new value 4Es;

c) i f no i t e r a t ion is done, the so lu t ion a t the nex t load s tep wi l l beon the OD branch of the diagram, but ,

d) i f i t e r a t ions are done, the negat ive re s idua l load Rl causes thes t r a in to be reduced to a value ~ . This la s t corresponds to aposi t ive res idual load R2. At the next i t e r a t ions , the so lu t ionw i l l always osc i l l a t e between s t r a in values l ess than and grea te rthan t, respect ively . No convergence can be found.


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37Choosing a su i t ab le so lu t ion procedure

Th e above problems suggest tha t spec ia l care should be used inmembrane app l ica t ions , if one or both the mater ia l models are employed,and the TENSC opt ion act ivated . Using a very small load s tep s ize could,genera l ly , lead to a good solu t ion , provided t ha t a reduced number ofi t e r a t ions per step i s done. While i te ra t ing , indeed, overshooting mayoccur a t new in tegra t ion points , and unloading w i l l s t a r t a t the nextstep only.

A more ra t iona l approach would require to s ize the load s teps so asto minimize overshooting. This i s what was t r ied in the presen t work;d e t a i l s about the solut ion procedure are given in the fol lowing. Theprocedure was appl ied to the shear wall elements, which undergo membranes t r e s se s only.

For the purpose of checking whether overshooting occurred a t anin tegra t ion point , the tension pr inc ipa l s t ress has to be compared tothe t ens i l e concre te s t rength (a t ) . The output s t resses come from thesuperposi t ion of both concrete and s tee l s t resses ; so the concretes t r e s se s have to be separated as:

ax-conc. ax- to t . - ax-s tee l ax- to t . E S Xin each of the X and Y direc t ions o f the reference system. Thepr i nc i pa l s t r a in direct ions have then to be found, which are assumed, inMilfo rd ' s and Schnobrich's mater ia l model, to coincide with thepr i nc i pa l s t r e s s di rec t ions . Final ly , ro ta t ing the concrete s t resses tothe pr inc ipa l d i rec t ions gives the "pr incipal s t resses" . From thesevalues , the a- theore t i ca l curve can be reproduced and crackingchecked. The a values for the current load step and the previous one are


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38now compared. I f overshoot ing occurred a t an in teg ra t ion po in t a t a tool a rge e x t e n t , comparing the tw o solu t ions suggests a b e t t e r s ize fo r theload s t ep , so as to reduce overshoot ing . If no new crack has opened, thes ize fo r the next load s tep i s governed by the h ighes t tension s t r e s s .Af te r at has been exceeded a t an in teg ra t ion po in t , a smal l load s tep i sused in order to al low a s t i f fnes s update .

A b e t t e r so lu t ion to the problem, however, would requi re changes inthe mate r ia l model such tha t :

1) the computed solu t ion i s always on th e a- curve;2) if cracking occurred , th e tangent modulus i s immediately s e t

to zero ( e l im ina te the need o f wai t ing fo r a new load s tep) .


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a

a)

,

1---

///

39

Figure A.I

a'3

The RCSHELL and RCBEM1mater i a l models: t yp ica lbehavior with increas ingtens ion s t r a i ns TENSCopt ion

b) ,

~ ~ - - - - - - - - - - ~ ~ ~ - - - + - - - - - - -

1_- J--- 0 'abcr a

Figure A.2 Dif fe ren t responses due to d i f f e r en t loadingprocedures


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1. Charney, F.Analyt ica lFrame-WallCal i fo rn ia

41REFERENCES

A. and Bertero , V. V., "An Evaluation of the Design andSeismic Response o f a Seven- Story Reinforced ConcreteStructure ," Report no. UCB/EERC-82/08, Univers i ty of

a t Berkeley, Cal i fo rn ia , August 1982.2. Jog1ekar , M., Murry, P ., J i r s a , J . , and Klingner , R. , "Fu l l Scale

Tes t s on Beam-Column Jo in ts , " in "Earthquake Effects on ReinforcedConcrete Structures U.S.-Japan Research," edi ted by JamesK. Wight, A.C.I . Special Publ icat ion no. SP-84, Detro i t , 1985,pp. 271-304.

3. Milford , R. V. and Schnobrich, W. C ., "Nonlinear Behavior ofReinforced Concrete Cooling Towers," Civ i l Engineering Studies , SRSC::1' . T T ~ . ; ~ ~ ~ ......... . ; + - ~ ... "...4= T11.;.,..,."....; ..... TT .... h..,.,..,..., T 1 1 ' ; . , . . , . , , ' ; ~ M.." u 1QQ/ ,l1U. - ' i . ' - + , Ul.l. .1.Vf;;4':;:' .J. . . '- 'y VoL. ~ . . L . J . . . . L I . I V . L . w , V.LIJQ.I.LCI., . .L-L .. . . . L . l . 1V .Lw , J...I.o.J ..L""v-t".

4. Otani , S., Kabeyasawa, T ., Shiohara, H., and Aoyama, H., "Analysisof the Ful l Scale Seven Story Reinforced Concrete Test Struc tu re , "in "Earthquake Effects on Reinforced Concrete StructuresU.S.-Japan Research," edi ted by James K. Wight, A.C.I . SpecialPubl icat ion no. SP-84, Detro i t , 1985, pp. 203-240.

5. Wight, J . , Bertero , V., and Aoyama, H., "Comparison Between theReinforced Concrete Test Structure and Design Requirements fromU.S. and Japanese Building Codes," in "Earthquake Effects onReinforced Concrete Structures U.S.-Japan Research," ed i ted byJames K. Wight, A.C.I . Spec ia l Publ icat ion no. SP-84, Detro i t , 1985,pp. 73-104.

6. Yoshimura, M. and Kurose, Y., " Ine l a s t i c Behavior ofin "Earthquake Effects on Reinforced ConcreteU. S. -J apan Research," edi ted by James K. Wight,Publ icat ion no. SP-84, Detro i t , 1985, pp. 163-202.

the Bui ld ing ,"Structures

A.C.I . Specia l


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