Analysis of Reinforced Concrete Shear Wall

7/29/2019 Analysis of Reinforced Concrete Shear Wall

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Compurers & Srrucrures Vol. 56, No. 2;3, pp. 48S504. 1995Pergamon 00457949(95)00039-9 Elsewer Science LtdPrinted in Great Britam

0045-J949/95 $9.50 + 0 00

ANALYSIS OF REINFORCED CONCRETE SHEAR WALLCOMPO NENTS USING THE ADINA NONLINEAR

CONCRETE MODELD. Khatri and J . C. Anderson

Department of Structural Engineering, University of Southern California, Los Angeles, CA, U.S.AAbstract-Two shear wall specimens loaded for experimental testing at the University of California,Berkelev. were modeled using the ADINA Nonlinear Finite Element Concrete Material Model withplane s&ess isoparametric fir&e elements. Force vs displacement results show good correlation withthe experimental data. The models were loaded with monotonically increasing static loads. Theanalyses give an estimate of the displacement ductility available in shear walls. Using this technique, finiteelement modeling can be used for future structural applications to design for greater displacementductility.

INTRODUCTION

There has been extensive experimental research onpredicting the in-plane response of shear walls sub-jected to both static monotonic loads and hysterisisloads. Research performed by the Portland CementAssociation (PCA) [1,2,3] has contributed signifi-cantly to the progress of knowledge in the experimen-tal domain. Experimental research has been thefoundation of empirical design methods which definethe standard of the industry by PCA and theAmerican Concrete Institute (ACI). Tests to deter-mine the ultimate capacity of shear walls are used todefine acceptable detailing requirements and formu-late simple empirical design methods.

The shear design parameters formulated by AC1 [4]are based on the balance of shear resistance providedby concrete and steel

where:VU= design ultimate shear forceV, = nominal concrete shear capacity

= 2zbdV, = nominal steel shear capacity

AVfYds24 = 0.85(strength reduction factor).Equation (1) was developed for shear stirrup design

in beams. It is applied to shear wall and deep shearbeams. The intent of eqn (1) is to provide an upperbound capacity on a reinforced concrete shear wall.

A design engineer can determine the extent of rein-forcing steel required to satisfy load requirements.

PCA [3] has an empirically based equation forflexure capacity

M,=O.SAB;I,(l+$)(l-9 (2)

where:MU = ultimate design resisting momentA, = total vertical reinforcingf , = yield strength of steel1, = horizonal length of shear wallc = distance of extreme compression fiber with

neutral axisd = distance of extreme compression fiber with

resultant tension forceh = wall thicknessN, = design axial load (+ compression).

This equation (2) was developed from empiricaldata [1,3] and provides an upper bound momentcapacity to assist the design engineer in selecting thereinforcing schedule for the wall.

Both eqns (1) and (2) define the ultimate designshear and moment that a shear wall can accept. Theultimate design force is the maximum static loadcapacity of a shear wall, as defined by AC1 and PCA.

Prior to designing a shear wall building, a struc-tural analysis is performed to assess moments, shearsand axial forces. This usually is done by modeling theshear walls using either beam elements or elastic plateelements to calculate the static and/or dynamic re-sponse.

After completing the finite element analysis, thedesign process utilizes AC1 eqn (1) and PCA eqn (2)

485


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486 D. Khatri and J. C. Andersonto size and detail the individual shear wall com-ponent. AC1 provides one method for design of shearwalls: Ultimate Strength Design (USD). Equations(1) and (2) are from the USD method. The USDmethodology considers the composite action of rein-forcing steel with concrete. Composite behaviorallows tension stresses to be taken by the steel andconcrete to accept compression forces.

Ironically, composite action of the steel and con-crete is not considered in the analysis stage. Forexample, a reinforced concrete wall is modeled withelastic plate elements using a linear E C, and the effectof steel reinforcing is neglected. Consequently, theeffect of cracking and overall stiffness degradation inreinforced concrete is not modeled by conventionalfinite element methods.

Since linear elastic analysis methods have no mech-anism for modeling the steel in a reinforced concretestructure, the gross section properties (or proportionof 1,) are modeled by plate or beam elements. Thispractice is used for both the static and dynamicanalysis.

It is well established that shear walls possess fargreater capacity than the design codes provide [5, 61.Specifically, experimental testing has demonstratedthat shear walls have high displacement ductility? (p)prior to complete failure. Current design method-ology does not account for this important aspect.

A primary reason for not including the effect of pinto design equations is that it would initiate anonlinear analysis of shear wall components. Nonlin-ear analysis of shear walls (and all reinforced concretestructures) is still an evolving area of research, andthere are no universally accepted formulas for assess-ing the complete failure envelope of a shear wall.

One of the major challenges of modeling thenonlinear static and dynamic response of a shear wallis to consider the composite effect of the steel andconcrete. Since both materials experience differentinelastic behavior, the finite element (FE) approachentails using two different ADINA elements withsteel and concrete material models. Although bondslip is one consideration in modeling reinforced con-crete, this is not considered in the scope of thisresearch.

The objective of this paper is to present a viablepractical approach for considering the effects of steelreinforcing in shear walls. There has been an abun-dance of research aiming to capture the nonlinearbehavior of reinforced concrete. Two experimentaltest cases are analyzed with the ADINA nonlinearmodel to confirm the method, and comparison withAC1 USD method is provided.

TDisplacement ductility [6] is defined as p = 6,,/S,, where6, = ultimate displacement at failure, and 6, = yield dis-placement. Therefore, structures with high p have greaterenergy absorption prior to failure. Energy absorption is avital criteria in earthquake resistance.

ADINA has formulated a nonlinear concrete ma-terial model that may be used for two dimensionalapplication. Several sources [7, 81 provide a detaileddescription of the intricacies of the ADINA concretemodel. As a brief summary, the formulation consistsof a hypoelastic model utilizing up to 27 constants forcalibration. Plane-stress elements are implementedfor two dimensional problems with in-plane forces.Shear walls are primarily intended to resist in-planeshear and flexural stresses.

Figure 1 outlines the concrete material stress-straincurve with constitutive equation and constants. TheADINA concrete model is more complex than otherestablished plasticity models. Chen [IO] discusses sev-eral plasticity models in great depth that includeMohr-Coulomb, Von-Mises, Drucker-Prager,Bresler-Pister Criterion, etc. The application of thesemodels to practical problems poses several challengeswhich ADINA has solved. Several advantages of theADINA concrete model may be summarized asfollows:l Material calibration capability. ADINA provides

the option to calibrate the material model forvarious concrete strength and ductility parameters.Failure envelopes may be adjusted to match theconcrete behavior accordingly. For example, theuser has the option to model both high-strength lowductility concrete and lightweight low-strengthhigh-ductility concrete with the same program byadjusting the constants in the ADINA concretemodel to calibrate with the material. Therefore, thescope of application is wide and varied.

l Multiaxial stress states. ADINA allows the capa-bility to include the effects of multi-axial loadconditions. Since multi-axial stress state changes thefailure envelope, ADINA accounts for two or threedimensional stress conditions, as specified by theuser. For example, a shear wall experiences a twodimensional stress condition with in-planeshear-flexure and vertical axial loads. The verticalaxial load alters the concretes uniaxial stress-straincurve. High vertical loads will compress the con-crete and increase its resistance to shear in horizon-tal direction. ADINA accounts for this complexbehavior.

l Full range of analytical options. ADINA concretemodel offers the full range of linear and nonlinearstatic, dynamic, buckling, and frequency analysiscapabilities in one program. Few software programshave all of these analytical tools linked together.

l Cracking patterns and configurations. ADINAshows crack patterns with user selection of thecrack width criteria. Cracking is a major indicationof failure in reinforced concrete, and is not offeredby any other finite element software program. Plot-ting of crack patterns enables an engineer to locatecritical areas of failure. It also serves as a valuabletool to confirm with experimental observations, andstrengthen these weak areas.


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Analysis of reinforced concrete shear wall components 487

at Gtz =

6Compr es s i on( t 5 ne ga t i ve )

p)$=+*(g)+B(;J:C %)31

St r a i n a t t e n s i o nc ut - of f : t / E.

at tC = 0: t o= 0a nd dt ' i - F- Y- ode

Fig. 1. Uniaxial stress-strain relation used in the concrete model

From an overall perspective, ADINA has devel-oped an outstanding finite element program that isthe first significant step towards providing a compre-hensive nonlinear FE program for use in practicalconcrete structural design. The scope of this paperfocuses on the nonlinear response of individual shearwalls subjected to monotonic loading. Plane stresselements are used to model the concrete, and nonlin-ear truss elements are used for the steel reinforcing.

Figure 2 shows the stress-strain curve for steel. AVon-Mises yielding model with elasto-plastic behav-

ior was assumed for the steel. The moduli of elasticityare taken as Es = 29 Ksi for the elastic response andEt = 10 Ksi for the inelastic area. Several iterationswere performed by using E, = 0 (i.e. elasto-plasticwithout strain hardening), but the convergence prob-lems were compounded and it was not possible to finda solution.

Figure 3(b) shows a typical shear wall model withfour-node plane-stress concrete elements representingthe wall. Nonlinear truss elements are attached alongthe boundaries of the plane stress elements to


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388 D Khatri and J C. Anderson

ELASTIC ; Ii E =STRAlNE 0YP

PLASTIC i--_,i

NO SlRAlN IiAFiDENING

Fig. 2. Steel stress vs strain curve.

(a) (b)NORMALSTFlENGTH

NORMAL SlRENGTHCONCREI-E FOR

i-f--2BOUNDARY STEEL 7 /WEB STEEL u4 Q 18 0.c eecil WBV. A0C0

1

:

E2 F

Gt-iIJ

K\\

ti.#

10Lo_. /

1 \3 .d 5 6 7

P-NODE NONUNEATRUSS ELEMENTSFOR HORIZONTAL

Fig. 3. (a) Reinforced concrete shear wall. (b) ADINA fimte element model.


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Analysis of reinforced concrete shear wall components 489represent the behavior of the steel. Together, these twoelements and material curves provide a compositemodel of reinforced concrete. The steel truss elementsaccept tension forces while the plane stress concreteelements accept compression forces.

U.C. BERKELEY TEST D ATA AND ADINA FINITEELEM EN T M O D ELS

Shear wall testing and analysis has received exten-sive attention for several years [2, 5,6, 10, 11, 121.After performing a thorough literature search, it wasdetermined that locating experimental results on hys-teresis and cyclic loading was not difficult. However,it was very difficult to find data on monotonicallyloaded specimens, specifically with force vs deflectioncurves. The Portland Cement Association [1,2, 31(PCA) has performed many shear wall tests to quan-tify their empirical wall design equations. Much of thedata was expressed in the form of moment (M) vscurvature (4), which is difficult to compare againstanalytical models. Instead, a graph of force (P) vsdeflection (6) can be readily compared.

A few common objectives of many experimental testmodels [1, 11, 121 was to assess the failure envelope ofshear walls with varying reinforcement ratios, wall

thickness, and the effect of confined concrete in theboundary elements. Consequently, hysterisis loadingwas appropriate to simulate dynamic and fatigueconditions. Monotonic loading was also tested, andthe results were shown with M vs 4 curves (i.e. failureenvelopes) of various walls. By comparing failureenvelopes of M vs 4 the researcher could provideconclusions as to the relative strength-weakness ofdifferent shear wall designs.

All of this experimental data is certainly useful forthe purpose of analyzing the relative performance ofshear wall test specimens, but has limited applicationin nonlinear finite element model (NFEM)comparisons. The reasons are summarized as follows:l omparing hysterisis M vs 4 curve with FEM

results is difficult because the nonlinear FEM mustfirst demonstrate its accuracy on quasi-staticmonotonic loading, before it may be comparedagainst cyclic loads.

l Monotonically loaded test specimens were found,but the results plotted M vs 4. Since a shear wallis very sensitive to curvature and each researcherhas a different definition of curvature, it is difficultto replicate the M vs 4 curve. Force vs deflectioncan be readily compared for accuracy.

(a)

0.279m1.854m 1-__1_ _

2.412m TT *9#5GpaNo7HooPsAT34mtll R AT 102mm

(b) 0.644Vi f0.644V (c) 0.522vi To. 522v434 kN 1 1 434 kN 299 kN1 1 299 kN

n57ggv&: 104v/fflo97vAU CB3 Specimen UCB5 Specimen

Fig. 4. (a) Cross section of UCB3 framed shear wall specimen. (b) Cross section of UCB5 shear wallspecimen. (c) UCB Experimental loading diagram.


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490 D. Khatri and 3. C. AndersonAOINA-PLOT VERSION 6.1, 7 NOVEMBER 1994LlCB3-i STATIC ANALYSIS OF A SHEAAWALL TEST SPECIMEN

AOINA OmAIGINAL XVMIN 0.000 2 XVMIN 0.000 2002 XVMAX 94.00AA YVMTN 0.000 _Y (b): Steel Elements ~$~ ~q,$$ L

YVMAX 120.0 \UCB3-1 Finite Element Model

(~1: P vs. 6 Curve (d): P vs. u Curve

A AC1 NOM. SHEAR CAP. = 203 K

4.FREE-END DISPLACEMENT (INCHES1 MAXIMUM TENSION STEEL STRESS (KS11

Fig. 5. Case UCB3-1 test

l Since the objective of various testing pro- and crack patterns. This can be analytically mod-grams [l, 2,3, 11, 121 was to compare the relative eled with FEM results. As a first iteration, a wallperformance of shear wall specimens, the walls were model with simpk loading (i.e. pure shear as inloaded in combination with vertical and lateral Fig. 3) would be more appropriate for comparingloads. Certain specimens had complicated behavior with analytical results. Complex loading situations


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Analysis of reinforced concrete shear wall components

CONFINED CONCRETE

F-0 WALL wmN0iA.M WALL

Fig. 6. Confined and unconfined concrete compression curves.

may be modeled from this platform. Analyticalresearch usually begins with successful comparisonof simple test problems, and then pursuing morecomplicated behavior.For these reasons, the U.C. Berkeley (UCB) shear

wall test data [131 were selected for comparison. UCBperformed a similar evaluation on their test data bycomparing nonlinear FEM analytical results of amodified wall model. The UCB comparisons areprovided in Ref. [13].

Two experimental shear wall specimens tested byUniversity of California, Berkeley [131 were selectedfor comparison. The data plotted F vs 6 curves formonotonic loading. The two test specimens are re-ferred to as UCB3 and UCBS. Several FEM meshconfigurations were utilized for UCB3 and UCBS. Amajor objective of performing various FEMs was tostudy the sensitivity of the meshing and convergenceparameters on solution time and accuracy. Details ofthe sensitivity analysis and conclusions are presentedin this section.

From the load configuration [Fig. 4(c)], the purposeof the UCB testing procedure was to simulate over-turning forces in a real earthquake. The area testedsimulated the lower three stories of the structural wall.Since the highest stress region of any shear wall isalways near the vicinity of the base, it is prudent tofocus attention on the stress variations in this area.UCB performed two tests on this wall: monotonicloading and hysterisis loading. The scope of thisresearch work addresses the monotonic loading case.CAS 6/2-,--T

The UCB3 shear wall specimen was a framed shearwall with confined concrete boundary elements. Across-section with loading diagram is shown in Fig.4 (axe), respectively. Framed shear wall componentsare particularly suited to resisting overturning mo-ments and flexurc-shear stresses. Boundary elementsperform as chord members that accept high com-pression and/or tension stresses. The web (i.e. wall)performs in shear with predominately diagonaltension stresses. Framed shear walls are used inbearing wall buildings to resist vertical dead and liveloads in addition to lateral loads (i.e. seismic and windforces). Therefore, typical framed shear walls willhave high vertical loads with in-plane moments gen-erated by lateral forces. Out-of-plane forces are notconsidered because these are transferred to perpen-dicular shear wall elements by horizontal diaphragmaction.

The FEM of the UCB3 specimen is shown inFig. S(a). The steel reinforcing mesh is shown inFig. 5(b), with output results in Fig. 5(c) and (d).Mesh discretization is a choice based on engineeringjudgment and also the objectives of the analysis. Inthe case of UCB3, higher mesh discretization ofelements is shown near the fixed-base boundary toaccurately calculate the local stress variation. Threemesh configurations were evaluated on UCB3 andUCB4. Figure 5(a) shows a high concentration ofelements near the base to calculate stress variationsacross the length of the wall. Steel stresses in thevertical reinforcing were also analyzed with thisapproach.


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492 D. Khatri and J. C. Anderson

AOINA-PLOT VERSION 6.1, 6 NOVEMBER 1994LICED-IOA ANALYSIS OF A SHEARWALL TEST SPECIMEN W/ UCB LOAD SCHEME

(a): UCB3-1OA (b): Steel ElementsFinite Element Model !

l cc :-cc *; :*;: c-4 . . . . .

, 0 ,

(c): P VS. 6 Curve (d): P vs. u Curve

0 AOINAA UC BERKELY EXPERIMENTAL DATA

2. 4.FREE-END DISPLACEMENT (INCHES) MAXIMUM TENSION STEEL STRESS (KS11

Since the boundary elements consisted of confined plane stress isoparametric elements. These plane-concrete, 12 elements [Fig. 5(a)] used a confined stress elements used the ADINA nonlinear concreteconcrete material curve [Fig. 61. Web elements are material model [lo] for the confined and normalunconfined-normal-strength concrete, and use the strength concrete. Figure 5(a) shows the full finitematerial curve of Fig. 6 (unconfined concrete). All of element mesh with confined and normal strengththe concrete was modeled with two-dimensional concrete elements.

Fig. 7. Case UCB3-IOA test


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Analysis of reinforced concrete shear wall components 493ADINA-PLOT VERSION 6.1, 6 NOVEMBER 1994UCE-1 STATIC ANALYSIS OF A SHEARWALL TEST SPECIMEN

(a): UCBS-1 Finite ElementModel

(b): Steel Elements

. . . . . l .

0 0 0 0. . :. : :. : :: -. .

(c): P vs. 6 Curve (d): I VS. ~curve

"0. I I I I20. 40. 60. 80.FREE-EN0 OISPLACEMENT (INCHES) MAX. TENSION STEEL STRESS (KS11

Fig. 8. Case UCBS-1 test.Steel reinforcing was modeled with ADINA non- spacing (in) was used to approximate the actual

linear truss elements using a Von-Mises elasto-plastic distribution. Horizontal and vertical steel was mod-failure criteria based on the stress-strain curve of eled using truss elements, respectively.Fig. 2. Figure 5(b) shows the nonlinear truss element For example, the web steel has vertical reinforcinglayout for UCB3. Since it was not feasible to model of # 2@,76 mm (3 o.c.). The total vertical web steelall the reinforcing steel, a typical rebar (in*) per unit was calculated to be (As)web = 2.5in2. For FEM


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494 D. Khatri and J. C. Andersonapplication, it was assumed four vertical nonlineartruss elements spaced equally would effectively simu-late the web steel. This calculates to 2.5 in*/fourelements = 0.625 in2/vertical-element. Similar calcu-lations for the vertical boundary steel and horizontalreinforcing were performed to determine the equival-ent element areas. Steel material properties were useddirectly from the UCB test data.

Two load configurations (with the same FEM)were performed:

(1) UCB3-1. Nonlinear static shear test: per-formed nonlinear static monotonic loading force-deflection analysis per the load configuration ofFig. 3.

(2) UCB3-10. UCB shear load test: performednonlinear static monotonic loading force-deflectionanalysis per the load configuration diagram of theUCB test specimen of Fig. 4(b).UCB3-1 was a static shear test analysis whichconsisted of a monotonically increasing load (P)applied at the top of the shear wall. Figure 5(b) showsthe results of force (P) vs deflection (6). Althoughthere were no experimental data for verification ofUCB3-1, the purpose of performing this analysis wasto compare the results with AC1 ultimate strengthdesign. UCB3-10 was a monotonic load test with theUCB load configuration [Fig. 7(c)]. This analyticaltest was compared with the experimental data.

The UCBS test specimen was a rectangular shearwall with confined concrete along the boundaryelements. Figure 4(b) shows the cross-section with thereinforcing schedule. Confinement of the boundaryelements was achieved by providing nine # 5 bars asshown. This enhances the performance of the con-crete by allowing maximum displacement ductilityprior to failure.

Similar to the UCB3 model, two constitutivematerial curves were prepared: normal strengthconcrete (unconfined) for the web elements andconfined concrete for the boundary elements. Hori-zontal and vertical reinforcing steel was modeledwith nonlinear truss elements using a Von-Misesfailure criterion with an elasto-plastic stress-straincurve. Figure 8 shows the FEM for the UCBS testspecimen.

Two FEMs were generated to study the effect ofmesh discretization. A fine mesh model (UCBS-1)consisting of 80 concrete-plane-stress elements and120 nonlinear three-node truss elements is shown inFig. 8(b). The loose-coarse mesh model (UCBS-5)consisted of 20 concrete elements and 18 nonlinearthree-node truss elements [Fig. 91. Results arepresented from both models.

UCBS was divided into the following output files:(1) UCBS-1. Fine mesh model with a nonlinear

static shear test file. Performed nonlinear staticmonotonic loading force-deflection analysis with oneforce (P) applied at the top of the wall.

(2) UCB5-5. Coarse mesh model with a nonlinearstatic shear test file. Performed nonlinear static

monotonic loading forcedeflection analysis with oneforce applied at the top of the wall.

(3) UCBS-10. Fine mesh model. Performed non-linear static monotonic loading force-deflectionanalysis per the load configuration diagram [Fig. 4(c)]of UCBS test specimen of Fig. 4(b).From the UCBS mesh configurations and a sensi-tivity analysis, it was determined that the run time(i.e. cost per run) of a coarse mesh model with 20elements far exceeded the fine mesh model with 100elements. The amount of effort (and total cost)required to run a coarse mesh exceeds that of a finemesh model, because the stress distribution must berepresented accurately for good convergence behav-ior and a sufficiently fine mesh is therefore needed.Table I summarizes the run parameters.

A coarse mesh model has limitations in producingstress variation graphs and does not account for theconfinement of concrete at the boundary elements.This may also be the reason why the coarse meshmodel produced a premature failure graph.

ANALYTICAL RES ULTS VS UCB TEST DATAThe figures given show the finite element models

used and results obtained for various UCB tests. Inaddition to comparing the analytical results with thetest data, several plots examine the performance ofthe shear wall prior to failure. For comparison withthe UCB data, two graphs [Fig. 7(a) and (c)] showreasonable correlation.

The framed shear wall of UCB3-10 [Fig. 7(c)]performed similar to the test data. Convergencecriteria is the principal factor that determines the easeor difficulty of solution time and accuracy. In work-ing with these shear wall models, there are certainguidelines that will enable reasonably good conver-gence.

Shear wall response to monotonic loading can beseparated into two distinct phases: preyield andpostyield. The preyield phase refers to the portion ofthe F vs 6 curve prior to the tension steel yielding, andthe postyield area begins after the tension steel hasyielded. Reinforced concrete shear wall behaviorcannot be separated into distinct linear and nonlinearregions because concrete has inherently plastic behav-ior. Although steel has a defined yield point, concreteis nonlinear from initial loading. Therefore, re-inforced concrete has a composite behavior of steel intension regions of the wall and concrete in com-pression areas.

Response characteristics of the pre and postyieldregions are very different. Most shear walls willdeflect close to a linear response in the preyieldregion. The postyield region consists of large deflec-tions for small incremental loads until failure. Conse-quently, the convergence parameters changedrastically between the preyield and postyield re-gions. For future applications it is recommended that


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Analysis of reinforced concrete shear wall components 495AOINA-PLOT VERSION 6.1, 8 NOVEMBER 1994UCB5-5 STATIC ANALYSIS OF A SHEARWALL TEST SPECIMEN

(a): UCBS-5 Finite ElementModel

(b): Steel Elements

. .0

(c): P vs. 6 Curve

* 0

(d): P vs. u Curve

0 AOINA

A AC1 NOM. SHEAR CAP.= 101 K

K50. 1 0 0 .

FREE-EN0 DISPLACEMENT (INCHES1 MAX. TENSION STEEL STRESS (KS11

Fig. 9. Case UCB5-5 test.the shear wall response should be performed in two with the maximum number of time steps of 40.consecutive files using the restart option (i.e. X-A.IN Iteration method was BFGS with line searching. Anand X-B.IN). This was done on several files with the energy convergence criterion was used withfollowing convergence criteria: ETOL = 0.5 and ITEMAX = 100. Large load incre-(1) UCB3-lA, UCB3-IOA, UCB5-5A, UCBS-1OA. ments (approximately 20 K per step) were used uptoThe automatic time stepping solution (ATS) method the steel yield point.


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496 D. Khatri and J. C. AndersonADINA-PLOT VERSION 6.1, 7 NOVEMBER 1994UC65 STATIC ANALYSIS OF A SHEARWALL TEST SPECIMEN W/ UC6 LOAD SCHEME

(a): UCBS-10 (b): Steel ElementsFinite Element Model

9 * l . . . .. :: : . - -. - :. :. d

0 0 0 0 0 0 0. :: :: -. : ;. : :. :. .: l


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Analysis of reinforced concrete shear wall components

AOINA-PLOT VERSION 6.1, 7 NOVEMBER 1994UCE3-1 STATIC ANALYSIS OF A SHEARWALL TEST SPECIMEN40INA ORIGINAL OEFORMEO X 2 AOINA ORIGINAL OEFORMEO X Z.OAO_STEPrIME 204.0 k29 - !L , LOAOSTEP L _ d -16.29 TIME 204.0 16.29 18.29 fLY

CRACK-STRESS CRACK-STRESSTIME 102.0 TIME 204.0FACE 3 FACE 3:; 1.656 i j 5.039CRACKS CRACKS

(a): Crack Pattern at P= 102 K (b): Crack Pattern at P= 204 K

(c): G vs. 0 Curve

0 AOINA

SHEAR STRAIN (RAO)

Fig. 11. Case UCB3-I test.

497

In the preyield phase, convergence with reasonable deflections for small load steps. This results in anaccuracy is not difficult because wall deflections are unstable solution with difficult convergence prob-stable between load steps. The AUTOMATIC-ATS lems. In order to obtain a solution, E, was taken asmethod provided good results within reasonable 10 Ksi. The ATS method performed well in thesolution times. preyield region because the solution has a stable

During postyield, the shear wall experiences large stiffness matrix. After yielding of the steel, the


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498 D. Khatri and J. C. AndersonADINA-PLOT VERSION 6.1, 8 NOVEMBER 1994UC.831OA ANALYSIS OF A SHEARWALL TEST SPECIMEN W/ UC8 LOAD SCHEME

rOINA ORIGINAL OEFORMEO X Z AOINA,OAO_STEP I. _ J - ORIGINAL DEFORMED ; ZLOAO_STEP L - > IIME 240.0 16.52 16.52 ; 16.52 18.52Y L y IME 240.0 Q--YCRACKSTRESS CRACKSTRESSTIME 100.0 TIME 240.0FACE 3 FACE 3:; 2.633CRACKS

ii 8.641CRACKS


(c): G vs. 8 Curve

8 0 AOINA

dSHEAR STAAIN (RAOI

Fig. 12. Case UCB3-1OA test

stiffness matrix degrades rapidly, and the LDC web elements. Boundary elements perform as chordmethod performs well in these regions of high dis- members in tension or compression to increase theplacement per load step and close to failure. moment-flexure capacity of the wall, while the web

It is important to model the confined concrete elements handle the in-plane shear stresses. If theelements. Shear walls have confined concrete bound- boundary elements are not distinguished in the modelary elements with extra reinforcing compared to the (as in UCBS-S), this will result in premature yielding


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Analysis of reinforced concrete shear wall componentsAOINA-PLOT VERSION 6.1. 7 NOVEMBER 1994UCBZ-I STATIC ANALYSIS OF A SHEARWALL TEST SPECIMEN

iOINA,OAO_STEP ORIGINAL DEFORMED ; 2IME 220.0 ;Siei - 8.87

CRACK-STRESS CRACK-STRESS

:; 3.325CRACKS


\OINA ORIGINAL DEFORMED X 2.OAOSTEPrIME 220.0 k.8; - fL ,8.87TIME 220.0FACE 3

CRACKS

(c): G VS. 8 Curve

0 AOINA

SHEAR STRAIN (RAO)

Fig. 13. Case UCBS-1 test.

499

of the steel and failure of the specimen. To accurately in the pre- and postyield regions. These results weremodel the specimen, boundary elements with obtained without altering any specific calibrationconfined concrete material properties must be in- parameters. ADINA [7] allows the user to select theeluded into the mesh generation. failure-plasticity curves (i.e. failure envelope) in the

The models of UCB3-10 and LJCBS-10 [Figs 7 and concrete material model. Since there was no availablelo] both showed reasonable correlation with the data compression test data on the shear wall specimens


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500 D. Khatri and J. C. AndersonAOINA-PLOT VERSION 6.1, 7 NOVEMBER 1994UC85 STATIC ANALYSIS OF A SHEARWALL TEST SPECIMEN W/ UCB LOAD SCHEME

WINA ORIGINAL DEFORMEO ; Z ADINA ORIGINAL DEFORMED X Z_OAO_STEP L _ J - LOAOSTEP c _ J ITIME 200.0 18.39 18.39 g--Y TIME 200.0 18.39 19.39

CRACKSTRESS CRACKSTRESSTIME 100.0 I TIME 200.0FACE 3 FACE 3+-I ICRP

3.215LKS

(a): Crack Pattern at P= 102 K

I ICRAC

5.956:KS

(b): Crack Pattern at P= 204 KI

(c): G vs. 8 Curve

I01 1 I t 1 I 1 I I I I0. 2. 4. 6. 8. 10 12. 14. 16. le. 20*1o-3SHEAR STRAIN (RAD)

Fig. 14. Case UCBS-IO test.(except forf: and E,), the default option of using the Failure patterns for shear walls vary between twoKupfer failure envelope was selected. For future extremes: Aexure vs shear failure. Flexure failureapplications, the user could calibrate the concrete occurs in tall walls (h-l > 2) that behave in bendingmodel to specific test data and then apply the model more than shear. This results in high tension andto a practical problem. Despite the fact that there were compression stresses along the boundary elementsno compression tests available for calibration, a which eventually cause shear cracking in the web.reasonable correlation was obtained. Shear failure occurs in short walls (h-l < 1) that have


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Analysis of reinforced concrete shear wall components 501ADINA-PLOT VERSION 6.1. 0 NOVEMBER 1994UCE3-IOA ANALYSIS OF A SHEAAWALL TEST SPECIMEN W/ UCE LOAO SCHEME

TIME 60.00(a): Base Reaction Plot at P- 60 K01 1

Z -2Z _zsL5r _.uo$r:

0'0. I I I I I20. 40. 60. 80. 100.

LINE COORDINATE. FIXEOBASE

o_51(b): Base Reaction Plot at P= 140 K TIME 140.0

20. 40. 60. 80. 100.LINE COORDINATE, FIXEOBASE

(c): Base Reaction Plot at P= 240 Kr oz

LINE COORDINATE, FIXEOBASE

Fig. 15. Case UCB3-1OA test.pure shear stresses with minimal bending behavior. All of the walls examined in this study failed inThe term shear walls is commonly used for both combined flexure-shear conditions, but still providedtall and short walls, despite their difference in failure displacement ductility factors (p) of 3 or 4. Bypatterns. For walls between these two extremes examining Fig. S(c) of UCBS-1 shows P, = 163 K(1 < hl-


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502 D. Khatri and .I. C. Anderson--

-

AOINA-PLOT VERSION 6.1. 7 NOVEMBER 1994UC65 STATIC ANALYSIS OF A SHEARWALL TEST SPECIMEN W/ UC6 LOAD SCHEMETIME 40.00

z 7 (a): Base Reaction Plot at P= 40 Kw2 s-2X

40. I I I , I20. 40. 60. 80. 100.

LINE COORDINATE. FIXEDBASE

(b): Base Reaction Plot at P= 100 KTIME 100.0

=:. .._.D. 20. 40. 60. n!? ?!lcJ.LINE COOROINATE, FIXEOBASE

(c): Base Reaction Plot at P= 200 K TIME 200.0

5 -LOa ,o-&! p:

8: I f I I I0. 20. 40. 60. 80. 100.

LINE COOROINATE. FIXEOBASE

Fig. 16. Case UCBS-10 test.5. Similarly, from UCB3-1 Fig. 5(c), p is calculated advent of reliable analytical models, practical appli-to be at least 4. this is a significant step for practical cation of nonlinear analysis to shear wall problems isanalysis because research in reinforced concrete struc- possible.tures has traditionally relied on experimental testing If the wall has oversized boundary elements (i.e.as the primary system for assessing nonlinear re- stronger than the web section), then the wall will failsponse curves and maximum ductility. With the in web shear. This results in a premature failure of the


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Analysis of reinforced concrete shear wall components 503web because the boundary elements still have furthercapacity. Consequently, the wall has a nonductilefailure [14]. The opposite is true if the wall hasoversized web reinforcing, the shear capacity is highbut the flexural strength is weak. The wall will fail inliexure. Baiancing the decision of boundary reinforc-ing (flexure strength) vs web reinforcing (shearstrength) is a critical design decision that has receivedattention in the practical arena. Engineers can actu-ally defeat the strength of the building by adding toomuch boundary reinforcing because this initiates anonductile failure.

By using ADINA, the balance of reinforcementcan be addressed very specifically through F vs 6comparisons with varying reinforcement ratios. Thiscan offer insight into the optimum solution withmaximum shear wall displacement ductility.

Figures 5, 7-10(d) show the lateral load (P) vstension steel stress (f,) curve. This curve delineatesclearly the preyield and postyield regions: UCBS-1has Py = 165 K, and UCB3-I with P, = 202 K. Asexpected, the yield points change with respect to loadconfigurations: UCBS-10 has VY= 160 K, and UCB3-10 a V, = 220 K.

Another interesting plot is the shear modulus (G)vs shear strain (0) curve:

G = f = shear modulus (Ksi)g

0 = 4 = shear strain (rad)

whereP = laterai shear force

A, = gross cross sectional area6 = horizontal deflectionh = wall height.

There are several reasons for plotting the G vs 0curve. It is a good measure of the overall in-planeshear wall stiffness degradation that occurs due toirlFX.IOPTI narlinn 1 r ml l r a a nt ; nn l l l ; nc =l r I r n l l . , P i E r :111W1VUUIUUU,&. 111 XI.IIL.ILU .11*Vu1UUJY., is assumed constant. Figures 11-14(c) show clearlythat G varies drastically from 350 Ksi (UCBS-1) anddegrades to less than 25 Ksi at failure.

Contrary to conventional assumptions, G vs 0is a highly nonlinear relationship. Additionally,the G vs 8 curve changes slightly depending onload configuration. Models UCB3-1OA [Fig. 12(c)]and UCBS-10 [Fig. 14(c)] have different G vs 0curves from UCB3-1 [Fig. 1 l(c)] and UCBS-1 [Fig.13(c)], respectively. The importance of this obser-vation is that other researchers [151 have relied onsimple linear relationships between G and 8. It ispossible to assume an average G, but this should becalculated from the full G vs 6 stiffness graph.Quantifying the G vs 6 relationship is important,because applying nonlinear finite element methods to

perform a full building analysis rests on this basicassumption.

ADINA provides the capability to plot crack pat-terns. This enables the analyst to determine the modeof failure (i.e. flexure, shear, or both). Figuresii-i4jaj an d jbj sh ow tha t th ese waiis aii faiied incombined flexure-shear stress. Shear cracking is indi-cated in the web elements by diagonal tension cracks,and compression crushing is shown along the bound-ary elements. Along the tension side, crack patternsshow the concrete has failed and the steel reinforcingcaptures the tension stresses. Throughout the web,diagonal (45) lines show diagonal tension cracks.Crushing failures are indicated along the compressionface of the wall. Practical applications of crackpatterns allow engineers to assess critical failure zonesof structures and adequately detail them for increasedcapacity. There is no finite element program availablethat currently offers plotting of concrete crackpatterns.

From preyield to postyield the neutral axis of theshear wall shifts towards the compression fibers of thewall because the tension concrete fails, and steel rebarcaptures the tension forces. This is depicted inFig. 15(a)-(c) [UCB3-IOA] for various load levels(P). At failure, the tension rebar has forces of about200 K, and compression forces peak to about 400 K.Similarly, for UCBS-10, Fig. 16(a)-(c) depicts thesame shift in the neutral axis.

Base reaction plots of the preyield and postyieldregions can be used to assess a shear walls failurecapacity and maximum displacement ductility bydeveloping a simplified version of this behavior. If allshear walls exhibit this neutral axis shift, it may bepossible to formulate an empirical equation thatapproximates the faiiure shear and moment ioad ofa wall, without having to perform an extensive non-linear analysis. This may be the next step of researchto extend the current design methodology for encom-passing shear wall failure capacity beyond the yieldpoint.

CONCLUSIONS AND RECO MMENDATIONSTwo shear wall specimens tested by the University

of California, Berkeley were analyzed by the ADINAconcrete material model using plane stress isopara-metric elements. Steel reinforcing was modeled usingnonlinear truss elements. The correlation of theanalysis was reasonably accurate with respect to theexperimental data.

The most difficult aspect of solving the shear wallresponse problem was selecting the convergence cri-teria. It was concluded that using two separate runswith different convergence criteria was the mostpractical solution. Shear walls have two distinctphases, preyield and postyield, that govern the dis-placement ductility of the wall.

It was also concluded that the shear module is notconstant during the loading process, but rather


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504 D. Khatri and .I. C. Andersondegrades significantly. The shear module is goodparameter to judge the wall stiffness degradationfrom initial loading. Crack patterns enable the engin-eer to evaluate the weak areas of the wall, andstrengthen them accordingIy.

Severai areas reauire investigation for further de-

E. Hognestad, Design provisions for shear walls. PCAResearch and Development Bulletin, RD 028.01D(1973).4. Building code requirement for reinforced concrete andcommentary. AC1 318889 (Revised 1992).5. J. W. Wallace and J. P. Moehle, Ductility and detailingrequirements of bearing waii buiidings. j. Struct. Engngvelopment of the shear wall design process: 118(6), 1625-1643 (1992).l Additional testing with comparison of the ADINA 6. J. P. Moehle and M. Eeri, Displacement-based design ofRC structures subjected to earthquakes, Earthquakeconcrete model results to confirm accuracy. Spectra 8(3), 403-427 (1992).l Development of standard guidelines for conver- 7. ADINA R&D Report 92-8, ADINA theory and model-

gence to enable the user to quickly process a ing guide. ADINA Research & Development (1992).problem. 8. K. J. Bathe, J. Walczak, A. Welch and N. Mistry,

l Develop a simplified equation to predict failure Nonlinear analysis of concrete structures. Cornput.Struct. 32(3,4), 563-590 (1989).moment and shear loads from the base reaction 9. M. Ala Saadeghvaziri, A user-supplied concrete ma-plots. Confirm these equations with analytical and terial model for ADINA. Comput. Struct. 47(4,5),test results. 591-600 (1993).10. W. F. Chen, Plasticity in Reinforced Concrete. McGraw-Hill, New York (1982).Through additional research, a practical design 11. M. Ueda and T. Kawai, Discrete limit analysis of R/C

methodology may be developed to quickly assess the shear walls. Int. ConJ Finite Element Analysis of Re-full capacity of the shear walls. iFforced Concrete Slructures, pp. 277-879.12. N. Inoue, N. Koshika, and N. Suzuki, Analysis of shear

REFERENCESI. A. E. Cardenas, Magura, Strength of high-rise shearwalls-rectangular cross section. PCA Research & De-velopment Bulletin, RD 029.01D (1975).2. A. T. Derecho, M. Iqbal, M. Fintel and W. G. Corley,Loading history for use in quasi-static simulated earth-quake loading tests, pp. l-29. Portland Cement

Association, R&D (1978).3. A. E. Cardenas, J. M. Hanson, W. G. Corley and

wall based on Collins panel test. Int. Conf. FiniteElement Analysis of Reinforced Concrete Structures,pp. 288-299.13. Bertero and Vulcano, Analytical models for predictingthe lateral response of RC shear walls: evaluation oftheir reliability, UCB/EERC-87/19 (1987).14. D. Strand, Brandow and Johnston, 1994 UBC proposedconcrete shearwall boundary member design. StructuralEngineers Association of California (1994).15. Mengi, McNiven and Tanrikulu, Models for nonlinearearthquake analysis of brick masonry buildings.UCBIEERC-92/03 (1992).

Analysis of Reinforced Concrete Shear Wall

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