SEISMIC-FORCE-RESISTING MECHANISMS OF MULTI-STORY STRUCTURAL WALLS SUPPORTED ON PILES ABSTRACT

Transcription

1 Proceedings of the 8 th U.S. National Conference on Earthquake Engineering April 18-22, 26, San Francisco, California, USA Paper No. 634 SEISMIC-FORCE-RESISTING MECHANISMS OF MULTI-STORY STRUCTURAL WALLS SUPPORTED ON PILES Susumu KONO 1, Masanobu SAKASHITA 2 and Hitoshi TANAKA 3 ABSTRACT Tests were conducted on two fifteen percent scale sub-assemblage models of the lower three stories of a twenty-story prototype shear wall structure. The shear wall was of monolithic construction for one model and of precast shear wall construction for the other. The objective was to study the seismic force resisting mechanisms of the two shear wall systems considering their interaction with the foundation beam, ground floor slabs and piles that supported the walls. Static lateral loads were applied with proportionally varying vertical loads to simulate loading conditions for the twenty-story prototype building during an earthquake. The strain distributions in the longitudinal reinforcement of the foundation beams were used to determine the shear transfer mechanisms at the base of the shear wall. That shear transfer mechanism is shown to depend on the crack width between the shear wall and foundation beam. The observed strain distributions at different loading stages are predicted by considering the degree of crack opening at the base of the wall. Introduction Typical Japanese mid-rise and high-rise residential buildings have multiple bay RC moment resisting frames in the longitudinal direction and single bay shear wall systems in the transverse direction. Extensive studies have been made of the seismic behavior of each member in such frames, of the shear walls, and of the foundation beams and piles that support those frames and walls. Further, design procedures for these structural members are well established. However, the seismic behavior of a multi-story shear wall, considering its interaction with peripheral members such as foundation beams, ground floor slabs, and piles, has not been studied in detail. Designers choose appropriate design procedures based on their engineering judgment. As a result, the ultimate failure mechanism may not be correctly identified and the seismic force resisting mechanisms between the shear wall and the peripheral members incorrectly evaluated, leading to irrational designs of each member of the system. In current Japanese design (Architecture Institute of Japan), cantilever structural walls 1 Associate Professor, Dept. of Architectural Eng., Kyoto University, Japan. kono@archi.kyoto-u.ac.jp 2 PhD candidate, Dept. of Architectural Eng., Kyoto University, Japan. rc.sakashita@archi.kyoto-u.ac.jp 3 Professor, Disaster Prevention Research Institute, Kyoto University, Japan. tanaka@sds.dpri.kyoto-u.ac.jp

2 are normally assumed to stand on a solid foundation, and the foundation beams, slabs and piles that support those walls are designed separately without considering interaction effects. Also neglected in practical design is the fact that the shear transfer mechanism along the wall base varies with the crack patterns and the degree of inelastic deformation at the shear wall base. Two shear wall specimens with peripheral members were tested to clarify the variations in the seismic-force-resisting mechanisms of a shear wall considering its interaction with foundation beams, ground floor slabs and piles. Based on the experimental results, the forces acting on the foundation beams are determined and a rational design procedure for foundation beams is suggested. Experimental phase Setups Specimens In this study, two specimens (MNW and PCW) consisting of the bottom three story of a shear wall with a foundation beam, first floor slab, and piles beneath each of the boundary columns of the wall were built at 15% scale as shown in Figure 1. The two specimens were identical except that the wall of PCW had four vertical slits that extended the height of each story and were filled with joint mortar to simulate a precast wall system. The horizontal joints of the precast wall were not modeled to simplify specimen construction. MNW was cast monolithically. For both specimens the shear walls were designed to fail in flexure and the point of contraflexure for the piles was fixed at 75 mm from their top, even though the depth of the contraflexure point in practice varies with soil conditions, and the intensity of the axial and lateral forces acting on the piles. The first floor slab extended 45 mm on either side of the centerline of the wall. The shear wall and the slab had a thickness of 5mm. The square piles were designed to remain elastic throughout the test so that the lateral load could be increased until the shear wall failed. The piles extended to midheight of the foundation beam and were without caps for simplicity even though piles in practice are circular and have solid pile caps. Material properties are shown in Table 1 and the types of reinforcement are listed in Table 2. Loading system As shown in Figure 2, the lateral load,, was applied statically to the loading beam on the top of the wall using a 1MN hydraulic jack. When the jack extended its force was transferred to the north end of the loading beam. When it contracted, it pulled on PC bars that were anchored on the south side of the loading beam, so that the jack force was transferred to the south end of the loading beam. In this way, loading conditions were symmetric for both the positive and negative loading directions. Two vertical jacks in the plane of the wall created appropriate column axial forces, N1 and N2, which were liner functions of to simulate the loading conditions on the prototype twenty-story shear wall system during earthquakes. N and N = 133 ± 3.1 ( kn ) (1) 1 2 For the roller supported pile, a horizontal force was applied to the pile by a 5kN jack so that the pile on the tension side carried 3% of and the pile on the compression side carried the rest. Thus, the south pile carried 3% of for positive loading and 7% of for negative loading. Two cycles of load were applied at each preselected increasing value of lateral drift until crushing occurred in the core concrete of the columns.

3 Location (a) Concrete Compressive strength (MPa) Table 1: Material properties (b) Reinforcement Tensile strength (MPa) Young's modulus (GPa) Foundation beam, Pile Wall, Column, Beam Joint mortar Member (Section size) Column (16 16mm) Beam (1 12mm) Shear Wall (Thickness 5mm) Pile (35 35mm) Type Yield strength (MPa) Tensile strength (MPa) Young's modulus (GPa) φ D6(S) D6(K) D D D Table 2: Reinforcing bars in MNW and PCW Bar Type Steel ratio (%) Longitudinal 4-D Transverse Upper Long. 4-D6(S).65 Lower Long. 4-D6(S).65 Transverse 2 φ4@1.25 Vertical φ4@1.25 Horizontal φ4@1.25 Longitudinal 8-D Transverse 4-D1@1.82 Member (Section size) Foundation beam (1 54mm) Transverse Foundation beam (1 54) Slab (Thickness 5mm) Loading beam (4x6 mm) Bar Type Steel ratio (%) Upper Long. 8-D Lower Long. 8-D Shear rebar 2-D6(S)@1.63 Upper Long. 3-D1.25 Lower Long. 3-D1.25 Shear rebar 2-D6(S)@1.4 Both direction φ4@1.25 Upper Long. 8-D Lower Long. 8-D Shear rebar 2-D1@1.36 * D6(S) and D6(K) had different mechanical properties as shown in Table Loading beam 3 Shear w all (thickness 5m m ) Mortaljo int (w idth 5m m ) B eam B eam Column 1st floor slab (thickness 5m m ) Slab w idth 9m m 4 75m m P ile Foundation beam C enter-center distance = 18m m Transverse beam (a) Perspective of PCW (MNW has no slits.) (b) Dimensions and reinforcement Figure 1: Specimen configuration and reinforcement arrangement (Unit: mm)

4 South North Positive loading for 1MN hydraulic jack 2MN hydraulic Jack Roller support 5kN hydraulic jack Pin support Figure 2: Loading system Test Results Load-Drift relations Figure 3 shows lateral load-first story drift relations. Both specimens showed ductile behavior up to a drift angle, R, of 2%. After R=2%, the lateral load carrying capacity degraded because the concrete at the base of the compressive column started to crush. Loads and drift angles at cracking and yielding of the walls are listed in Table 3. Flexural cracking loads, cr, were close to the flexural yield loads, y, for both specimens. Drift angles at cr and y varied widely and this shows the difficulty of measuring the deformations of this stiff system. Major differences with regard to the load-drift relations were not observed since the damage to the two specimens was similar except for the crack patterns as explained in the following section. Observed Damage Figure 4 shows the damage observed in the specimens after test. As designed the cracks in the walls of both specimens were dominated by flexure. PCW had some diagonal cracks running down the vertical slit to the bottom of each story after those cracks reached the slits. Because of this crack pattern, the wall cracks in PCW were concentrated more along the slits and the beam interfaces as compared with the cracks in MNW. The foundation beams of both specimens showed similarly large amounts of shear cracking after the crack at the wall base opened due to the rotation of the shear wall. In addition, large gaps due to flexural actions were found at the interface between the foundation beam and the piles. The foundation beam was expected to act monolithically with the shear wall, piles, and slabs, because the vertical reinforcement of the shear wall was well anchored into the foundation beam and the longitudinal reinforcement of the foundation beam was well anchored into the pile as specified in the design guidelines (Architecture Institute of Japan, 1997). Hence, damage in the foundation beam was expected to be minimal. However, the observed damage indicated that the foundation beam did not act monolithically with the peripheral members to resist the external loads once the rotation of the shear wall became significant and the gap between the wall and the foundation beam opened. Strain distributions of longitudinal reinforcement in foundation beams Figure 5 shows the strain distributions in the longitudinal bars of the foundation beams. Lines in each figure show the strain distributions at different loading stages. Strains in the upper longitudinal reinforcement near midspan tended to be larger than strains at the beam ends up to

5 Stage 4. After Stage 5 where the cracks between the shear wall and the foundation beam became large, the strains on the tensile side increased to similar values to those at midspan. Strain distributions in the lower longitudinal reinforcement were nearly linear for any loading stage as shown in Figures 5(b) and (d) Shear Force (kn) Analysis MNW Experiment Drift Angle of 1F Shear Wall (%) Shear Force (kn) Analysis PCW Experiment Drift Angle of 1F Shear Wall (%) (a) MNW (b) PCW Figure 3: Lateral load - first story drift angle relations Table 3: Load and drift angle at cracking and yielding of shear wall Type of damage Analysis MNW PCW Positive Negative Positive Negative Flexural Load cr (kn) cracking Drift (%) Flexural Load y (kn) yielding Drift (%) (a) MNW (b) PCW Figure 4: Observed damage of the east face after testing

6 (-.31%,-76.kN) 2(-.928%,-94.1kN) 3(-.241%,-11.5kN) 4(-.495%,-14.4kN) 5(-.841%,-11.5kN) 6MAX(-1.194%,-18.8kN) 7(-2.718%, -91.1kN) データ 9 14:19:53 24/4/ Location in the foundation beam (mm) (a) Upper longitudinal bar in MNW (-.685%,-55.4kN) 2(-.821%,-88.7kN) 3(-.314%,-92.6kN) 4(-.583%,-99.kN) 5(-.828%,-12.4kN) 6(-1.565%,-98.1kN) 7MAX(-2.474%,-14.9kN) データ 9 13:1:39 24/4/ Location in the foundation beam (mm) (-.31%,-76.kN) 2(-.928%,-94.1kN) 3(-.241%,-11.5kN) 4(-.495,-14.4kN) 5(-.841%,-11.5kN) 6MAX(-1.194%,-18.8kN) 7(-2.718%, -91.1kN) データ 9 14:19:12 24/4/ Location in the foundation beam (mm) (b) Lower longitudinal bar in MNW (-.685%,-55.4kN) 2(-.821%,-88.7kN) 3(-.314%,-92.6kN) 4(-.583%,-99.kN) 5(-.828%,-12.4kN) 6(-1.565%,-98.1kN) 7MAX(-2.474%,-14.9kN) データ 9 13:2:9 24/4/ Location in the foundation beam (mm) (c) Upper longitudinal bar in PCW (d) Lower longitudinal bar in PCW Figure 5: Strain distributions in longitudinal reinforcement of foundation beams

7 Numerical modeling Modeling lateral load resisting mechanism of foundation beams Simulation of Lateral Load-drift relations The wall response was modeled by superposing results for two spring elements with trilinear load-displacement relationships. One spring represented the flexural behavior of the wall and the other represented the shear behavior. The two springs were set parallel to obtain the total response. The spring properties were derived using Hirata et al. s model (Hirata et al.) as shown in Figure 6. Figure 3 and Table 3 compare the analytical and experimental results. The computed flexural cracking strengths were about half as small as the experimental results but the computed flexural yield loads agreed well with the experimental results. Figure 3 shows that the resulting computed envelope curves were adequately accurate up to the peak load for the specimens. Simulation of strain distributions in the foundation beam Figure 7 shows the moment distributions in the foundation beam due to the three force types acting on it. Mp: Moment and shear forces from the piles, as transferred to the foundation beam, are shown in Figure 7(a). Mp is due to the moment from the piles. Mw: Vertical tensile forces activated at the wall base due to the action of the vertical reinforcement of the shear wall. The reinforcement tends to lift up the foundation beam as the wall rotates and the moment, Mw, distributes as shown in Figure 7(b). Mq: Tangential force at the wall base, a shear force that comes from dowel action of the vertical reinforcement and concrete shear at the interface. Concrete shear consists of aggregate interlock at the cracked interface and elastic/plastic shear at remaining ligaments. The moment, Mq, due to these shear forces is assumed as distributed along the interface as shown in Figure 7(c). Since the largest crack width between the wall base and the foundation beam was as large as several centimeters, the crack width must have affected the stress transfer mechanisms at that interface. Hence the region with a large crack opening was separated from the rest of the wall base and taken as a detached region as shown in Figure 8. Assuming that the lateral force acts from left to right, the length of the detached portion increases as the wall rotates. Although there is no quantitative definition of detachment at this moment, Figure 8 conceptually represents the behavior at an interface with a large crack opening. It was assumed that no shear force is transferred over the detached interface and the shear force is distributed evenly along the length of the remaining ligament. Figure 9 shows moment distributions due to the interface shear force at the wall base for the five different degrees of detachment. Using the model, the strain distributions in the longitudinal reinforcement of the foundation beam were computed using a simple sectional analysis. The computed results for three different loading stages are shown in Figure 1 and Figure 11. Varying degrees of detachment were assumed so that the computed strain distributions best matched the experimental results. Although there are some local discrepancies between computed and experimental results, the simple model assuming a given degree of detachment can be used to predict the forces acting on the foundation beam.

8 F F F c y F K e α K F3 F e F le xu ra ly ie ld α F2 K α K F e Flexuralc ra c k S 2 S 1 S K e S2 S e α K S3 S e S h e a r y ie ld S h e a r c ra c k Fδ c Fδ Sδ 1 Sδ 2 Sδ (a) Flexural element (b) Shear element Figure 6: Shear force drift relations for the flexural element and shear element Nt Nc L H Mp.3.7 Mv.3.7 Tension N.3.7 C om pression (a) Shear and moment from piles (b) Vertical tension from wall (c) Shear from wall Figure 7: Forces acting on the foundation beam and the resulting moment distributions Column(Tension side) Shaded region is the area of contact. Shear stress is assumed to distribute uniformly. Degree of detachment Shear wall Column(Compression side) White region has no contact. No stress transfer is assumed Figure 8: Degree of detachment at the wall base due to the rotation of wall

9 D/2 D e g re e o f D etachm ent Mq Mq Mq Mq M q= D / Figure 9: Moment distribution in the foundation beam due to shear stress at the shear wall base for different levels of detachment Experim ent (upper longitudinalbar) D egree of D etachm ent= Experim ent (upper longitudinalbar) Degree of Detachm ent=.25 Degree of Detachm ent= Experim ent (upper longitudinalbar) Degree of Detachm ent=.75 Degree of Detachm ent= (a) Before yielding of wall (b) After yielding of wall (c) Ultimate stage (Stage 1) (Stage 3) (Stage 6) Figure 1: Strain distribution in the upper longitudinal reinforcement of the foundation beam Experim ent (low er longitudinalbar) Degree of Detachm ent= Experim ent (low er longitudinalbar) Degree of Detachm ent=.25 Degree of Detachm ent= Experim ent (low er longitudinalbar) Degree of Detachm ent=.75 Degree of Detachm ent= (a) Before yielding of wall (b) After yielding of wall (c) Ultimate stage (Stage 1) (Stage 3) (Stage 6) Figure 11: Strain distribution in the lower longitudinal reinforcement of the foundation beam

10 Summary of numerical modeling Unless the degree of detachment and the additional moments, Mw and Mq, were considered, the strain distributions in the longitudinal reinforcement of the foundation beams were not correctly estimated. Although the degree of detachment does not need to be modeled for predicting the deformations of the shear wall, it does need to be considered for correctly predicting the behavior of the foundation beam. Conclusions Two 15% scale cantilever structural wall sub-assemblages were tested to failure to clarify the lateral load resisting mechanisms considering interaction between the shear wall, foundation beam, first floor slab and piles. Conclusions were as follows. Monolithic action between the foundation beam and peripheral members, such as the shear wall and piles, was much less than expected and unexpected shear cracking spread extensively over the length of the foundation beam at the ultimate stage when the width of the crack between the shear wall base and the foundation beam became large. Forces acting on the foundation beam can be summarized as the shear and moment from the piles, and the stresses transferred at the wall base interface. Stresses transferred at the wall base can be quantified by assuming the degree of detachment. Procedures for determining the degree of detachment are currently being studied. The lateral loads for cracking and yielding of the wall were well predicted by a model that used a simple superposition of flexural and shear elements. However, drifts at cracking and yielding varied widely in the experiments and predictions were not precise. References Architecture Institute of Japan, AIJ Standard for Structural Calculation of Reinforced Concrete Structures Based on Allowable Stress Concept, pp Architecture Institute of Japan, Design guidelines for earthquake resistant reinforced concrete buildings based on inelastic displacement concept. (In Japanese) Hirata, M., Naraoka, S., Kim, Y., Sanada, Y., Matsumoto, K., Kabeyazawa, T., Kuramoto, H., Hukuda, T., Kato, A., Ogawa, M., 21. Dynamic Test of Reinforcement Concrete Wall-Frame System with Soft First Story Part 1-Part 4 Summaries of technical papers of annual meeting of Architectural Institute of Japan, pp (in Japanese). Paulay, T. and Priestley, M.J.N., Seismic Design of Reinforced Concrete and Masonry Buildings, John Wiley & Sons, pp