Tests of structural walls to determine deformation contributions of interest for performance-based design

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1 Tests of structural walls to determine deformation contributions of interest for performance-based design Authors: Beth Brueggen, University of Minnesota, Minneapolis, MN, Jon Waugh, Iowa State University, Ames, IA, Sriram Aaleti, Iowa State University, Ames, IA, Benton Johnson, University of Minnesota, Minneapolis, MN, Catherine French, University of Minnesota, Minneapolis, MN, Sri Sritharan, Iowa State University, Ames, IA, Suzanne Dow Nakaki, Nakaki-Bashaw Group, Irvine, CA, ABSTRACT A collaborative research project is underway at the University of Minnesota Multi-Axial Subassemblage Testing (MAST) Laboratory regarding the behavior of structural wall systems. The investigation included tests and numerical simulations of three rectangular reinforced concrete wall systems to investigate the effect of continuous, spliced, and mechanically connected longitudinal reinforcement at the wall-foundation interface. It was anticipated that the different reinforcement details would have an effect on the plastic hinge length, local strain demands, and consequent flexural (deformation) response including the damage state of the wall systems. The walls were instrumented to investigate the overall behavior and to isolate the individual deformation components attributed to flexure and shear. Understanding the sources of deformation and correlation of the results with models that can be used to predict the behavior is important for development of performance-based seismic design procedures. The project was funded by the National Science Foundation (NSF) grants CMS32454 and CMS BACKGROUND Engineers often use structural walls as the primary lateral load resisting elements in buildings because of their large in-plane stiffness and strength which enables them to resist large lateral loads due to wind and earthquakes while minimizing lateral drifts and damage to nonstructural elements. A displacement-based design approach has been recommended for detailing reinforced concrete shear walls in design codes. This approach was first introduced into the model building codes with the 1994 edition of the UBC and was adopted into ACI 318 in 1999 [6]. Field experience [8] and testing [6] have shown that these provisions lead to walls with good seismic behavior and that they provide a more rational design basis than the previously used strength-based requirements, which were overly conservative for the design of slender walls [9]. Performance-based design of shear walls requires additional knowledge of wall behavior under the applied seismic loading. A relationship must be established between the applied lateral load, drift, and damage state. While extensive research has been done studying the behavior of rectangular shear walls with continuous longitudinal reinforcement [6], little research has been

2 done specifically studying the effects of using mechanical couplers or lap splices. These are commonly used in practice for constructability reasons. Local irregularities in the reinforcement caused by bar splices can significantly affect the response of the wall, especially when they occur in the plastic hinge region. It was suspected that the splices in the reinforcement would thus lead to differences in performance as compared to a wall with continuous reinforcement. In this study, three rectangular shear walls were tested to failure under reversed cyclic loading. These walls were identical except that one (RWN) used continuous longitudinal reinforcement from the footing to the top of the wall, one (RWC) used mechanical couplers to splice the reinforcement near the wall-foundation interface, and the third (RWS) used lap splices near the wall-foundation interface. TEST UNIT DESCRIPTION The test units for the rectangular wall tests were detailed to simulate large strain gradient effects. Associated with this project was an investigation of the behavior of nonrectangular T-shaped wall systems. For the T-wall systems, the neutral axis depth was very shallow in the case of flange-in-compression loading, which resulted in large strain gradients in the web tip. In the case of flange-in-tension loading, the neutral axis depth was much deeper in the wall to balance the large tension force generated by the reinforcement in the flange, as shown in Figure 1. The rectangular walls were used to investigate the performance of lap splices and couplers for use in the T-shaped wall system. In order to simplify the test units, the three individual rectangular wall test units had nonsymmetric reinforcement in the wall tips to mimic the neutral axis depths and strain gradients of the web of the T-shaped wall. Each rectangular wall test unit was 229 mm (9 in.) long, 15 mm (6 in.) thick, and 6.4 m (21 ft.) tall. At one end of the wall, intended to represent the web tip of a one-half scale T-shaped wall tested in the study, four No. 6 bars and two No.5 bars were used. At the other end, simulating the flange, eight No. 9 bars were used. FIGURE 1 STRAIN GRADIENTS The required boundary element detailing was determined based on the appropriate provisions of ACI One provision for boundary reinforcement was neglected. Section (a) limits the maximum spacing of confining reinforcement to one-quarter of the shallowest member dimension. This provision was neglected because of concerns that using a 38 mm (1 ½ in.) spacing would lead to excessive congestion and poor consolidation of concrete. The required shear reinforcement was determined based on the capacity design concept recommended in ACI for the design of beam-column joints to avoid joint shear failure preceding full development of plastic hinges in beam regions adjacent to the joint [2]. The provided moment strength of the wall was determined using BIAX [7]. This model included the effects of concrete

3 confinement and of strain hardening of the steel. The shear force required to develop the computed moment was then calculated and used to determine the required size and spacing of the wall shear reinforcement. Following the guidance provided for beam-column joints in Sections 9.3.4(c) and of ACI 318-2, a strength-reduction factor φ of 1. was used with the provided moment strength, and a φ of.85 was used to determine the required shear strength associated with this moment strength. It was then confirmed that this shear strength was greater than the code-required minimum shear strength for walls given in Section of ACI Figure 2 shows cross-sectional views of the rectangular wall test units just above the foundation block. RWN - continuous bars #6 #5 # " 31 2 " " 6" " #2 hoops & 2 1 2" Transverse bars hooked into confined core FIGURE 2 TEST UNIT CROSS SECTIONS 18" o.c. 9" 7 1 2" RWC - mechanical couplers Shading - maximum dimension of coupler RWS - lap splices Bar anchored in foundation " #2 2" Lap splice bar initiating in wall 4" o.c. ASTM A76 Grade 6 weldable deformed bars were used for all of the longitudinal and transverse reinforcement in the test units. Because No. 2 deformed bars were not readily available, ASTM A496 D-5 deformed wire was used for the confinement reinforcement. All reinforcement of a given size was obtained from a single heat to maintain consistency among the test units. The difference among the three test units was in the detailing of the longitudinal reinforcement near the base of the walls. Test unit RWN incorporated continuous reinforcement from the foundation block to the top of the structure, test unit RWC incorporated threaded couplers to mechanically splice the reinforcement at the wall-foundation interface, and test unit RWS incorporated conventional lap splices at the wall base. The 4 series mechanical couplers manufactured by Headed Reinforcement Corporation were attached to the bars in RWN by friction welding. These couplers have been certified by the manufacturer to meet the requirement of ACI (b) Type 2 mechanical connectors; they are able to develop 125% of the yield strength and 1% of the tensile strength of the bars they connect before failing. The lap splices in RWS met the length requirements for splices subjected to seismic loading of ACI , including the factor of 1.6 in for straight bars not within a confined core. Figure 3 shows elevation views of each test unit. Each test unit was cast in three lifts: the foundation block, the bottom 335 mm (11 ft.) of the wall, and the top 35 mm (1 ft.) of the wall. Each cold joint was roughened and a latex-based bonding agent was applied prior to the next cast. Table 1 summarizes material strengths in the walls and mechanical coupler dimensions of RWC. The concrete strength given is for the bottom portion of each wall " "

4 RWN - Continuous Bars RWC - Mechanical Couplers RWS - Lap Splices 7'-6" 1'-" FIGURE 3 TEST UNIT ELEVATIONS 21'-" 1'-9" 3'-9" 3'-2" 1'-9" Concrete RWN RWC RWS Steel #2 #4 #5 #6 #9 Coupler #4 #5 #6 #9 f c ' (MPa)* f y (MPa)** Length (mm) *average of 3 tests f u (MPa)** Diameter (mm) **average of 2 tests TABLE 1 MATERIAL PROPERTIES TESTING AND INSTRUMENTATION A schematic of the rectangular wall test setup is given in Figure 4. A ±979 kn (±22 kip) capacity hydraulic actuator was used to apply the cyclic lateral displacements to the wall. This actuator was mounted horizontally to a reaction wall 6.1 m (2 ft.) above the base of the wall. To distribute the applied forces over the entire horizontal length of the wall, this actuator was connected to a pair of steel channels that was bolted to the wall at five points distributed over the horizontal length. Out-of-plane restraint was provided by pairs of rollers to prevent twisting of the top of the wall during loading. The walls were not subjected to any external vertical load. 5'-8" Figure 5 shows the lateral displacement histories applied to the test units. Throughout this paper, positive loads and displacements indicate loading the No. 5 and No. 6 bars in tension. As can be seen in Figure 5, all three walls were subjected to the same displacement history until near the end of testing, when instabilities of the walls occurred. Primary interest was in the wall behavior when the No. 5 and No. 6 bars were in tension, which simulated reinforcement in the web tip of the T-shaped wall in the investigation. The test units were expected to reach much higher load levels with the No. 9 bars in tension, and there was some concern that applying many

5 cycles at this higher load level would lead to excessive shear degradation in the wall and that obtaining the desired information about the wall behavior in the direction of interest would not be possible. In order to avoid this situation, the applied displacements were asymmetric for drift levels beyond 1%. The applied drift level was increased to 1.5% and 2.% in the direction that induced tension in the No. 5 and No. 6 bars while the applied drift level was maintained constant at 1.% in the opposite loading direction. The drift level was then increased to 2.5% in the direction with the No. 5 and No. 6 bars in tension and 2.% in the direction with the No. 9 bars in tension. When the instabilities occurred, the walls were subsequently loaded primarily in one direction only with the load path controlled by the damaged condition of the wall to maximize the amount of information obtained from each test unit. Out-of-plane restraint Actuator 6.1 m (2 ft.) Lateral Drift 4% 3% 2% 1% % RWN 7-1% #5 & 6 bars in -2% compression RWS -3% #5 & 6 bars in tension all test units Load Step # FIGURE 4 FIGURE 5 TESTING SETUP APPLIED DISPLACEMENT HISTORIES Linear variable displacement transducers (LVDTs) and string potentiometers (string pots) were used to measure the in-plane and out-of-plane global displacements over the height of the test units and the relative deformations within each wall. The locations of the instruments are shown in Figure 6. LVDTs were attached vertically at the wall-foundation interface to measure the rotation of the base of the wall with respect to the foundation block. To refine the displacement measurements, a set of LVDTs was attached 152 mm (6 in.) and another set 35 mm (12 in.), respectively, above the wall-foundation interface. Each wall was divided into four large panels over the height of the wall to investigate the relative contributions of shear and flexural deformations; the bottom panel was subdivided into four smaller panels to refine those measurements. Flexural deformations of the wall were measured using LVDTs and string pots mounted vertically along the edges of the wall. Strain penetration into the foundation block was measured by welding a small stud to selected reinforcing bars 25 mm (1 in.) above the foundation block. Foam was used to block out a small region around these studs when the wall concrete was cast, and an LVDT was used to measure the slip of the bar relative to the foundation block during testing. Shear deformations were measured using the aforementioned panel devices that included string pots oriented in X configurations. LVDTs were also used to measure any unintentional uplift or horizontal slip of the foundation blocks, which were rigidly attached to the laboratory strong floor. RWC

6 channels '' Reference frame String pots measuring out-of-plane deformations 54'' '' 69'' 21'' East side (string pots) 6'' 21'' 16'' 16'' 16'' 21'' West side (LVDTs) LVDTs measuring vertical deformations: 6" above wall-foundation interface 12" above wall-foundation interface FIGURE 6 EXTERNAL INSTRUMENTATION RESULTS AND DISCUSSION GLOBAL BEHAVIOR At drift levels below 1%, all three test units exhibited similar responses including crack patterns. Fine horizontal cracks aligned with the transverse reinforcement were observed in all three test units prior to testing or after the first ramp was applied. The wall with lap splices was slightly stiffer than the other two walls, which was expected due to the additional steel in the lap region. In all of the walls, flexural cracks were observed before diagonal shear cracks. Figure 7 shows each of the test units at a drift of 2.%. In all three test units, the flexural cracks were more closely spaced but substantially narrower within the confined end regions of the walls where the longitudinal reinforcement was concentrated compared to the adjacent cover region and mid region across the horizontal length of the walls. The concentrated longitudinal steel more effectively restrained the crack opening. This behavior is shown in Figure 8 for RWN at a drift of 2.5%. Typically, crack widths increased by a factor of three when they crossed from the boundary element into the web. Table 2 provides information on the differences in major crack width measurements obtained in the boundary element regions and center regions of the wall within the bottom 122 mm (48 in.) of the wall that illustrates this behavior. 12''

7 a) RWN c) RWS b) RWC FIGURE 7 DAMAGE STATE OF TEST UNITS AT 2.% DRIFT 1 mm FIGURE 8 CHANGE OF CRACK DISTRIBUTION AND WIDTH ACROSS CONFINED END REGION, 2.5% DRIFT, TEST UNIT RWN Cracking at the interface between the wall and the foundation block was not visible until yielding occurred. At drift levels below 1%, this crack opening was no wider than other cracks in the wall. This behavior was maintained in RWN and RWC until the end of the test; whereas in RWS, a large amount of deformation was concentrated in the crack at the wall-foundation interface due to the abrupt discontinuity of the lap splices. This observation is quantified in Table 2, which provides typical crack widths measured near at the wall-foundation interface for each test unit at drift levels of.3 and 2%. As the test progressed, the distinct large crack at the base of RWS continued to increase with increased drift levels. Figures 9, 1, and 11 show the opening of the crack at the wall-foundation interface of each test unit as the applied displacement was increased. RWS also had large cracks at the discontinuities at the top of the lap splices. However, the height of the discontinuity varied according to the different splice lengths, as shown in Figure 3. Test units RWN and RWC failed similar to one another as a result of eventual global instability, as shown in Figure 12. The compression force required to equilibrate the tension force in the No. 9 bars caused sidesway buckling of the compression region of the wall near the base. This occurred at a drift of 2.5%. The wall straightened when the load was reversed, but in future cycles, large out-of-plane deformations occurred before this drift level could be reached.

8 Drift:.3% Drift: 2% Wall-foundation Wall-foundation Confined Unconfined interface Confined Unconfined interface RWN.18 mm.51 mm <.13 mm.64 mm 1.8 mm 6.4 mm RWC.23 mm.64 mm <.13 mm 1. mm 3. mm 5.1 mm RWS.13 mm.41 mm <.13 mm 1.5 mm 3.6 mm 13 mm TABLE 2 TYPICAL CRACK WIDTHS MEASURED IN DIFFERENT REGIONS OF TEST UNITS AT.3% AND 2% DRIFT LEVELS a).25% drift b).75% drift c) 1.5% drift FIGURE 9 OPENING OF CRACK AT BASE OF RWN a).25% drift b).75% drift c) 1.5% drift FIGURE 1 OPENING OF CRACK AT BASE OF RWC a).25% drift b).75% drift c) 1.5% drift FIGURE 11 OPENING OF CRACK AT BASE OF RWS

9 FIGURE 12 GLOBAL BUCKLING OF COMPRESSION REGION OF RWC, 4% DRIFT In test units RWN and RWC, the concrete in the lower portion of the walls had visible crushing at a drift of 2.5% with the No. 5 and No. 6 bars in tension. The damage was concentrated over a region approximately 9 mm (3 ft.) or.4d high just above the wall base, where d was the distance from the compression face of the wall to the centroid of the tension steel. In addition to spalling of cover concrete in the boundary elements, the confined concrete began to degrade and the unconfined concrete was broken into large chunks before the out-ofplane wall movement occurred. When RWN was deconstructed after testing, no fractures or necking of the steel were found. When RWC was deconstructed after testing, no fractures or necking of the steel were found in the boundary elements, but some of the No. 4 distributed longitudinal reinforcement was overstressed near the boundary element with the No. 5 and No. 6 bars. One of these No. 4 bars fractured and another exhibited necking approximately 2 mm (3/4 in.) from the coupler; a third bar had fractured at the weld joint between the coupler and the bar. This damage was not visible until the cover concrete was removed from the wall after testing was completed. In RWS, the crack at the interface between the wall and foundation block grew to 25 mm (1 in.) wide at drift levels of 1.5% and larger. Deformation of the wall was dominated by rotation at the base, and the shear and flexural cracks within the wall did not grow as larger displacements were applied to the wall. Relative slip between spliced bars was visible at drift levels of 1.5% and greater, as shown in Figure 13. A marker was used to label the location of the bottom of the top bar relative to the bottom bar prior to this ramp so that the bar slip could be measured. This bar slip did not reverse and the crack remained open when the load on the wall was reversed and the cracked region was placed in compression; a large portion of the compression force was transmitted through the steel. Because there was no concrete around these bars to provide restraint against buckling, the No. 5 and No. 6 reinforcement, as well as some of the No. 4 distributed web reinforcement, buckled and then fractured when the load was reversed and subsequently reloaded in tension, respectively. This failure occurred in RWS

10 during the first cycle at 2.5% drift with the No. 5 and No. 6 bars subjected to tension. Figure 14 shows this reinforcement after concrete and confinement steel were removed from around it at the end of the test. As the wall was cycled to 2.5% drift with the No. 9 bars in tension, the base of the compression boundary element offset to one side approximately 76 mm (3 in.) and rested on one of the 38 mm (1 ½ in.) thick steel plates used to anchor the foundation block to the floor. 19 mm (3/4 in.) FIGURE 13 BAR SLIPPAGE AND OPENING OF INTERFACE CRACK IN RWS AT 2% DRIFT FIGURE 14 BUCKLING AND FRACTURE OF BARS IN RWS WITH CONVENTIONAL LAP SPLICES RWS suddenly lost capacity when the No. 5 and No. 6 bars fractured as the wall was unloaded from a drift of 2.% with the No. 9 bars in tension. As mentioned previously, the damage to this test unit was concentrated at the interface between the wall and the foundation, and this test unit dissipated approximately 6% less energy than RWC prior to becoming unstable. Figures 15, 16, and 17 show the condition of three walls at the conclusion of tests, and Figures 18, 19, and 2 show lateral force vs. displacement histories for each of the three test units. There was much less energy dissipation in the loading direction with the No. 9 bars in tension than in the opposite loading direction; this was a result of the asymmetric loading protocol at large drift levels, where the demand on the wall in the loading direction with the No. 9 bars in tension was not enough to develop significant nonlinear deformations. In all cases, there was not a lot of pinching of the hysteresis loops observed until the last cycles of the tests, where the damage to the walls was extensive and they were observed to become unstable.

11 FIGURE 15 FIGURE 16 DEGRADATION OF RWN AT END OF TESTING, LOAD DEGRADATION OF RWC AT END OF TESTING, LOAD REMOVED REMOVED Force (k) 12 8 First Yield 4-3% -2% -1% -4% 1% 2% 3% 4% Global Buckling -24 First Yield FIGURE 17 FIGURE 18 DEGRADATION OF RWS AT END OF TESTING, LOAD REMOVED LATERAL FORCE RESISTANCE VS. DRIFT RWN Load (k) 12 8 First Yield 4-3% -2% -1% -4% 1% 2% 3% 4% Global Buckling -24 First Yield Drift Load (k) 12 8 First Yield Drift -3% -2% -1% -4% 1% 2% 3% 4% Bar Buckling First Yield Drift Bar Fracture FIGURE 19 FIGURE 2 LATERAL FORCE RESISTANCE VS. DRIFT RWC LATERAL FORCE RESISTANCE VS. DRIFT - RWS

12 channels channels The next two sections describe the shearing and flexural of deformation. The applied loading caused uniform shear forces and linearly increasing flexural loading from the point of application of the actuator load to the foundation. SHEAR DEFORMATIONS Shear deformations within each panel were calculated from the measurements of the diagonals of each panel using the relationship d1 o ( d1 d1 o ) d 2o ( d 2 d 2o ) U = (1) 2hl Where U is the average shear strain over a rectangular panel, d 1 and d 2 are the measured dimensions of each diagonal, d 1o and d 2o are the original dimensions of each diagonal, h is the vertical dimension of the panel, and l is the horizontal dimension of the panel. In each test unit, the magnitude of shear deformations was approximately constant over the height of the test unit prior to yielding of the wall. When the wall yielded in flexure, the shear behavior in the region of flexural yielding also became nonlinear. At drift levels of 2.5% and greater, the damage, shown in Figures 15 and 16, to the lower portion of the test units with continuous reinforcement and with mechanical couplers led to shear sliding across horizontal planes in the wall, which was restrained only by dowel action of the longitudinal reinforcement. At the end of testing, the shear strains measured in the bottom 86 mm (34 in.) of the walls with continuous reinforcement and mechanical splices were approximately 3.5 times greater than those measured in the upper 46 mm (16 in.) of the wall at the end of the testing. This is shown for RWN in Figure 21, where The portion of the wall considered in each plot is shaded in the inset. This effect was observed to a lesser degree in RWS because the damage to this wall was concentrated at the wall-foundation interface, which was below the attachment of the string pots measuring shear deformations, and the wall failed before this level of overall damage was reached. a) -86 mm (-34 in.) above base block b) mm ( in.) above base block force (k) Predicted cracked stiffness shear strain (in./in.) force (k) shear strain (in./in.) FIGURE 21 SHEAR STRAINS OVER HEIGHT OF RWN Figure 21 has a predicted cracked shear stiffness superimposed over the data, shown as a dashed line. Park and Paulay [5] derived the elastic shear stiffness of a cracked member assuming truss action and shear cracks forming at angles of 45, K v,45 :

13 K v,45 = ρv Esbwd 1+ 4nρ (2) v Where ρ v is the shear reinforcement ratio, n is the ratio of steel modulus to concrete modulus, E s is the modulus of the steel, b w is the thickness of the wall, and d is taken as 9% of the length of the wall. This assumed shear stiffness reasonably reflected the measured shear stiffness before the flexural reinforcement in the panel of interest yielded. FLEXURAL DEFORMATIONS AND PLASTIC HINGING The average curvature of each panel was calculated from the measurements of the vertical edges of the panel. Figures 22, 23, and 24 show plots of average moment vs. average curvature for several panels of RWN. These plots are representative of all three test units. Superimposed on each is a predicted moment-curvature plot calculated using BIAX [7]. In this model, a cubic spline was fit to the strain hardening portion of the steel model. The modified Kent and Park model was used for the concrete. When the #5 and #6 bars were in tension, the magnitudes of curvature were similar in the panels from 89 to 51 mm (3 ½ to 2 in.) above the foundation block and from 51 to 91 (2 to 36 in.) above the foundation block. The magnitudes of curvature decreased in the panels more than 91 mm (36 in.) above the foundation block. There was only a very small amount of plastic curvature in the panel from 175 to 312 mm (69 to 123 in.) above the foundation block, and none in the panels above 312 mm (123 in.) from the foundation block. When the #9 bars were in tension, only the panels from 89 to 51 mm (3 ½ to 2 in.) above the foundation block and from 51 to 91 mm (2 to 36 in.) above the foundation block experienced plastic curvature because smaller drift levels were applied to the test unit and the plastic hinge was not fully developed in that direction. COMPARISON TO ANALYSES The load vs. deflection response of each of the walls was compared to analyses that predicted the flexural response of the wall; the shearing response of the wall was then superimposed onto these results. None of the analyses included special consideration for the couplers or lap splices, nor did they consider global buckling stability. A pushover analysis was conducted using OpenSees [4] to calculate the load vs. deflection response of the walls. This analysis used one degree-offreedom (1DOF) bending elements. The model used a force-based beam-column element developed by Fillipou and Taucer [3] to capture the spread of plasticity along the element better than previous elements. The element idealized regions of concrete and reinforcement as uniaxial fibers with appropriate material models. A bilinear model with an ascending slope to represent strain hardening was used for the steel. In this model, the failure strain was taken as one third the actual value to ensure that the stresses in the steel did not become excessively large. In both loading directions, this model predicted that failure would occur when the reinforcement ruptured. As shown in Figure 25(a), this analysis predicted the flexural response of the walls with good accuracy; however, it did not consider the observed failure modes (i.e., global buckling instability observed in RWN and RWC, the walls with continuous reinforcement and mechanical couplers, respectively; and vertical sliding of the reinforcing bars in wall RWS, which had longitudinal reinforcing bars with lap splices), and it overestimated the drift capacities of the walls.

14 channels channels channels measured BIAX measured BIAX M (k-in) M (k-in) phi (1/in.) -4-5 phi (1/in.) FIGURE 22 FIGURE 23 AVERAGE MOMENT VS. CURVATURE IN RWN 51 TO AVERAGE MOMENT VS. CURVATURE IN RWN 135 TO 91 MM (2 TO 36 IN.) ABOVE FOUNDATION BLOCK 175 MM (53 TO 69 IN.) ABOVE FOUNDATION BLOCK M (k-in) measured BIAX phi (1/in.) FIGURE 24 AVERAGE MOMENT VS. CURVATURE IN RWN 175 TO 312 MM (69 TO 123 IN.) ABOVE FOUNDATION BLOCK The moment vs. curvature relationship calculated using BIAX [7] was used for a simple analysis representative of one that could be done quickly without specialized tools. A bilinear fig was used to approximate the moment vs. curvature relationship. The deformations corresponding to yielding and failure of the section were calculated from this approximation. The expected plastic hinge rotation associated with failure of the section was calculated assuming that the plastic curvature was constant over a plastic hinge length of d/2. Figure 25(b) shows a comparison of the measured load vs. deflection relationship with this prediction. This analysis overestimated the initial stiffness of the test units in both loading directions, but it estimated the load at yielding well. The model overestimated the flexural deflection associated with failure of the walls, but it also did not consider the premature failure modes observed in the walls. The predicted failure modes are rupture of the steel when the No. 5 and No. 6 bars are in tension and crushing of the concrete when the No. 9 bars are in tension. A third analysis was done by integrating the moment-curvature relationship predicted using the BIAX model over the height of the wall. The results of this analysis are similar to those of the pushover analysis done with OpenSees. The differences between them can be attributed to the material models used. With the No. 5 and No. 6 bars in tension, the analysis with OpenSees predicted steel rupture at a lower curvature than the BIAX model because the failure strain of the steel was much smaller in OpenSees. With the No. 9 bars in tension, the BIAX model predicted that the section would not

15 recover capacity after spalling of the cover concrete, while the OpenSees model predicted steel failure at a higher curvature. a) OpenSees pushover analysis b) Analyses based on BIAX results Load (k) % -4% 2% 4% 6% Flexural Component of Drift RWN OpenSees Load (k) % -4% 2% 4% 6% 8% -8 RW -12 FIGURE 25 FLEXURAL COMPONENT OF DEFLECTION IN RWN COMPARED TO ANALYSES Flexural Component of Drift best-fit bilinear integrating BIAX Figure 26 shows the pushover analyses with elastic shear deformations added compared to backbone curves obtained experimentally for each of the three test units. Equation (2) was used to predict the elastic shearing deformations of the walls. With the exception of the BIAX model with the No. 9 bars in tension, the models for flexural deformations overestimated the flexural drift at failure, but the elastic model for shearing deformations underestimated the shearing drift at failure. a) OpenSees pushover analysis b) Integration of BIAX results Load (k) % -2% -1% -4 % 1% 2% 3% 4% Drift RWN RWC RWS OpenSees+shear % -2% -1% -4 % 1% 2% 3% 4% FIGURE 26 LOAD VS. DEFLECTION BACKBONE CURVES INCLUDING ALL COMPONENTS OF DEFORMATION CONCLUSIONS AND RECOMMENDATIONS Load (k) Drift RWN RWC RWS BIAX+shear Lateral load behavior of the walls, including failure mode and displacement capacity, was influenced by the reinforcement detailing at the wall base. The wall with mechanical couplers (RWC) performed similarly to the wall with continuous reinforcing bars (RWN). The global lateral buckling observed in the test units with continuous reinforcing bars and mechanical couplers might have been mitigated by floor diaphragms, which were not included in these tests. Conventional lap splices did not perform as well as continuous reinforcement or mechanical couplers at drift levels of 1.5% and greater. The combination of an abrupt change in the reinforcement area and bar slip of the lap splices led to increased localized strain demands and large flexural cracks that did not close when the loading was reversed. This led to bar buckling and fracture of reinforcement at lower drift levels than in walls without lap splices.

16 A simple analysis combining an assumed elastic stiffness with plastic hinging determined by moment-curvature section analysis may not be adequate for detailed design. The plastic hinge length, as measured by observation of damage in the test units and measured flexural deformations, were shorter than expected. This contributed to overestimation of the drift capacity of the walls by this simple analysis. Single degree-of-freedom pushover analysis, however, does predict the flexural response of the wall well up to the point of failure. By including elastic shear deformations, it was possible to use the pushover analysis to predict the load vs. deflection response envelope well up to the onset of failure, although inelastic shear deformations were not included. This approach did not capture the effects of bar slippage in the wall with lap splices nor the global instability that led to premature failure. Throughout the testing protocol, flexural deformations made up 65-95% of the total deflection. Prior to cracking, flexural deformations represented 95% of the total deflection. This proportion decreased as shear cracks developed in the test units. At yielding, 75-8% of the total deflection was attributed to flexure when the No. 5 and No. 6 bars were in tension, and 6-65% was attributed to flexure when the No. 9 bars were in tension. When the applied drift was increased and a plastic hinge developed in the wall, the proportion of deflection attributed to flexure increased slightly in both loading directions. When the walls were near failure, approximately 8% of the total deflection was attributed to flexure when the No. 5 and No. 6 bars were in tension, and approximately 7% was attributed to flexure when the No. 9 bars were in tension. The portion of deformation attributed to flexure did not increase significantly after yielding because the degradation of the bottom portion of each test unit led to nonlinear shearing deformations in addition to the expected nonlinear flexural deformations. Shearing deformations were not consistent over the height of the test units as assumed with elastic analysis. ACKNOWLEDGEMENT Funding for this work was provided by NSF grants CMS32454 and CMS Opinions, findings, conclusions, and recommendations in this paper are those of the authors, and do not necessarily represent those of the sponsor. In-kind support was provided for the construction of the test walls by Headed Reinforcement Corporation, EFCO Corporation, Ivy Steel and Wire, and Cemstone, which is gratefully acknowledged. REFERENCES [1] ACI Committee 318, 22. Building Code Requirements for Structural Concrete (ACI 318-2), American Concrete Institute, Farmington Hills, MI. [2] Brueggen, B.L., C.W. French, N. Jung, and S.D. Nakaki, 26. Non-rectangular reinforced concrete shear walls: design issues and performance, Proceedings CD-ROM, 1 th Anniversary Earthquake Conference, San Francisco, CA. [3] Taucer, Fabio F., E. Spacone, and F.C. Filippou, A Fiber Beam-Column Element for Seismic Response Analysis of Reinforced Concrete Structures. Report No. UCB/EERC-91/17. Earthquake Engineering Research Center, College of Engineering, University of California, Berkeley. [4] Mazzoni, S., Frank McKenna, Michael H. Scott, Gregory L. Fenves, et al., 26. Open System for Earthquake Engineering Simulation User Command-Language Manual, Pacific Earthquake Engineering Center, University of California, Berkeley. [5] Park, R. and T. Paulay, Reinforced Concrete Structures, New York, Wiley. [6] Thomsen IV, J.H., and J.W. Wallace, 24. Displacement-based design of slender reinforced concrete structural walls experimental verification, Journal of Structural Engineering 13 (4), [7] Wallace, J.W., BIAX: Revision 1 Computer program for the analysis of reinforced concrete and reinforced masonry sections, Report CU/CEE-92/4, Structural Engineering, Mechanics, and Materials, Clarkson University, Potsdam, NY. [8] Wallace, J.W., Evaluation of UBC-94 Provisions for Seismic Design of RC Structural Walls, Earthquake Spectra 12 (2), [9] Wallace, J.W. and K. Orakcal, 22. ACI Provisions for Seismic Design of Structural Walls, ACI Structural Journal 99(4),