Lateral Force Resisting Mechanism of a Multi-story Shear Wall and Peripheral Members

Transcription

1 Fédération Internationale du Béton Proceedings of the 2 nd International Congress June 5-8, 26 Naples, Italy ID 9-17 Session 9 Lateral Force Resisting Mechanism of a Multi-story Shear Wall and Peripheral Members Sakashita, M., Kono, S., Watanabe, F. Department of Architecture, Kyoto University, Nishikyo, Kyoto, Japan Tanaka, H. Division of Earthquake Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji, Kyoto, Japan INTRODUCTION In current design procedures [1,2], cantilever structural walls are normally assumed to stand on a solid foundation, and foundation beams, slabs and piles are designed separately without considering their interactions. This is because their interactions have not been thoroughly studied for their complexity. Also neglected in the practical design is the fact that shear transfer mechanisms along the wall base vary depending on the crack patters and inelastic deformation levels at the shear wall base. This study aims to experimentally clarify the variation of the lateral load resisting mechanisms considering the interaction between a shear wall, foundation beams, slabs and piles, and to establish more rational design procedures for each structural component. In our earlier studies [3,4], experiments using two 2% scale specimens and two 15% scale specimens were performed. From these experiments, it was clear that the shear transfer mechanism along the wall base varied according to the deformation of the shear wall. This mechanism could be simulated by a simple section analysis of the foundation beam. In this study, more realistic experimental conditions were set up than in earlier experiments, such as the scale of the specimen, the steel ratio of the longitudinal reinforcement in the foundation beam and the loading methods. As our earlier studies, this study focuses on clarifying the transition of the shear transfer mechanism from experiment and analysis. The specimen configuration in this experiment was determined from typical fourteen story residential buildings in Japan. They normally have multiple spans of a RC moment resisting frame in the longitudinal direction and a single span of shear wall system in the transverse direction. In this study, the assemblage consisting of the lowest three floors of shear wall with a foundation beam, the first floor slab, and two piles in the transverse direction was scaled to 25%. This scale enable to use deformed reinforcing bars in the shear wall and observe more realistic crack distributions in the shear wall. Keywords: shear wall, foundation beam, pile, interaction EXPERIMENTAL SETUP Specimens Figure 1 shows specimen configuration and Fig. 2 shows reinforcement arrangement. The first floor slab extended 75 mm on either side of the shear wall and the total width was 15mm. The shear wall and the slabs had the same thickness of 7mm. Pile caps were omitted and the piles were extended to the midheight of the foundation beam to simplify the construction. The distance between the contraflexural points of the piles (the center points of supporting pin and roller) and the midheight of the foundation beam was set 125mm and the shear span ratio of the piles was fixed as 1.84 although the shear span ratio is supposed to vary depending on the soil, axial force, and lateral force under earthquakes. The center-to-center distance of the piles was 3mm.

2 June 5-8, 26 Naples, Italy Material properties are shown in Tab. 1. Table 2 shows types of reinforcement. In this study, the shear wall was designed to fail in flexure and the piles were designed to be elastic in order to focus on the shear transfer mechanism along the shear wall base. Loading Beam Shear wall (Width 7mm) 1F Floor Slab (Thickness 7mm) Beam Beam Lateral Column Transverse Foundation Beam Foundat ion Beam Slab Width 15mm The cent er dist ance bet ween piles 3mm The distance between the cont raflexural point of the piles and the midheight of the foundation beam 125mm Fig. 1. Specimen configuration (a) Elevation (b) Plan view Fig. 2. Reinforcement arrangement (unit: mm) 36 Tab. 1. Material properties of concrete and reinforcement (a) Concrete (b) Reinforcement Yield strength Tensile strength (MPa) (MPa) D D1(SD295A) D1(KSS785) D D D D Compressive strength (MPa) Tensile strength (MPa) Young's modulus (GPa) Foundation beam, Pile Wall, Column, Beam Young's modulus 2

3 June 5-8, 26 Naples, Italy Member Column (26 26mm) Beam (14 2mm) Shear Wall (7mm) Pile (44 44mm) Foundation Beam (15 88mm) Slab (7mm) Transverse Foundation Beam (26 88mm) Loading Beam (35 4mm) Tab. 2. Types of reinforcement Type of bars Steel ratio(%) Longitudinal 8-D Transeverse (KSS785).549 Longitudinal 4-D1 (SD295A) 1.18 Transeverse Vertical Horizontal Longitudinal 8-D Transeverse Longitudinal 4-D Transeverse (SD295A).634 Longitudinal Longitudinal 8-D Transeverse (SD295A).366 Longitudinal 8-D Transeverse (SD295A).272 In Japanese design guideline [5], the required amount of the longitudinal reinforcement in the foundation beam under shear walls are determined separately based on the following two external forces as shown in Fig. 3. Moment from piles (Mp) Axial force /2 (tensile force) [ is the total lateral force applied to the shear wall.] As shown in Fig. 3 (b), large rotation of the shear wall makes the shear force transfer through the limited area under compression. In gerenal, the lateral force applied to piles that are subjected to tensile axial force is smaller than the lateral force applied to piles that are subjected to compressive axial force. Axial force /2 is given as the possible maximum axial force in the foundation beams at the ultimate state. As for Mp in Fig. 3 (a), foundation beam is modeled as a line element and Mp is calculated by the lateral load applied to the piles and the distance between the contraflexural point of the piles and the midheight of the foundation beam. Ai Dist ribution Ai Dist ribution Mp= 1 h1 h1 Mp= 2 h2 h2 1 2 (a) Moment from piles (Mp) (b) Axial force /2 Fig. 3. Design of foundation beams 3 / 2 Tension / 2 / 2 In experiment, monolithic action between foundation beam and peripheral members, such as a shear wall, slabs and piles, is expected and it restricts the damage of the foundation beam at least until the shear wall yields and the shear wall base begins to be separeted from the foundation beam. In this study, the amount of longitudinal reinforcement in the foundation beam was set smaller than the requirement of the Japanese design guideline [5]. Figure 4 shows moment distributions and reaction forces at =36kN. At this time shear

4 June 5-8, 26 Naples, Italy wall yields in flexure and moment applied to the foundation beam from piles was 296kN m. Flexural yield strength of the foundation beam ignoring contributions of peripheral members was 23 kn m. The safety factor of the foundation beam was 23/296=.78. According to this design guideline, the yielding of the foundation beam precedes the yielding of the shear wall. Japanese design guideline [5] allows that the required strength of foundation structure can be decreased using ductile pile system. The steel ratio of the longitudinal reinforcement in this study became closer to those designed by the Japanese guideline. Njack Njack =36kN Moment capacity of shear wall=2455kn m Moment capacity of foundat ion beam=23kn m h=125mm.3 =18kN Mp=.7 h =296kN m.7 =252kN Fig. 4. Moment distributions and reaction forces at =36kN Test Setup As shown in Fig. 5, lateral load was applied statically through a 1kN horizontal jack (A) to the loading beam. Two 2kN vertical jacks were adjusted to create appropriate column axial forces at the shear wall base, N1 and N2, which are a linear function of lateral load to simulate loading conditions of the prototype fourteen-story shear wall system under earthquakes. N1 and N2 = ± (unit:kn) (1) 2kN jack Loading beam mm 1kN Jack (A) 595mm 169mm 1145mm Pin Roller kN Jack (B) 175mm 3mm 35mm Fig. 5. Loading system 4

5 June 5-8, 26 Naples, Italy At the roller support,.7 was applied horizontally to the pile when was positive and.3 was applied to the pile when was negative by a 1kN jack (B) in the opposite direction to the 1kN horizontal jack (A). As shown in Fig. 6 (a), the load was applied two cycles at each prescribed load stage until the first story drift angle reached.6%. Then the displacement control was used with two cycles at each prescribed displacement in Fig. 6 (b). The first story drift angle is hereinafter called α. In this experiment, it was difficult to measure the drift angles of the shear wall because of the rotation and the deformation of the foundation. So they were calculated from the flexural deformation and the shear deformation of the shear wall and the relative sliding of the shear wall base. They were measured with the multiple displacement gauges placed at the shear wall F Drift Angle (%) Cycle (times) (a) Load control Cycle (times) (b)displacement control Fig. 6. Loading Cycle TEST RESULTS Observed Damage Observed damage is as follows. Figure 7 (a) shows crack distribution. Flexure-shear cracks of the shear wall penetrated the slabs transversely and developed to the foundation beam. Bold lines showed flexure-shear cracks whose widths were especially wide in positive loading. In this experiment, the shear wall deformed along these cracks involving the parts of the foundation beam, the pile, the transverse foundation beam and the slabs. Concrete crushing was hardly observed at the base of the columns in this experiment. Figure 7 (b) shows damage of the shear wall base. On the west side longitudinal bars of the column buckled. From the midspan of the shear wall to the east column, vertical bars of the shear wall fractured. The first result stated above was different from those of common experiments of shear wall with basement. Lateral Load- First Story Drift Angle (α ) Relation Figure 8 shows the lateral load first story drift angle (α ) relation and yielding points of the shear wall and the foundation beam. As shown in Fig. 8, contrary to the design based on the Japanese design guideline [5], the yielding of the shear wall preceded the yielding of the foundation beam. It is thought that the foundation beam acted monolithically with peripheral members containing the shear wall and the damage of the foundation beam became small. After α =2%, specimen was pushed monotonically to 3% in positive direction. As noted in observed damage, concrete crushing was hardly observed at the shear wall base. The lever arm of the shear wall was made constant and the reduction of the lateral load didn t occur. 5

6 June 5-8, 26 Naples, Italy East - + West (a) Crack distribution East West Ten vertical bars of the shear wall fractured. (b) Damage of the shear wall base Five longitudinal bars of the column buckled. Fig. 7. Damage after the loading test was finished 4 Foundation Beam [Upper] (.35%, 34.3kN) Foundation Beam [Lower] (.35%, 34.3kN) Lateral Load (kn) Shear Wall (.94%, 313.4kN) Shear Wall (-.128%, kN) Foundation Beam [Lower] (-.188%, kN) Foundation Beam [Upper] (-.374%, kN) F Drift Angle α (%) Fig. 8. Lateral load first story drift angle (α ) relation Strain Distributions of Longitudinal Reinforcement in the Foundation Beam and in the Slabs Figure 9 (a), (b) shows the strain distribution of longitudinal reinforcement in the foundation beam at seven representative loading stages. Location in the foundation beam in Fig. 9 (a), (b) is illustrated with Fig. 9 (d). Until α became.11% (at this time the shear wall yielded in flexure.), the strains were restricted to small values. This is due to the monolithic action with peripheral members. After α became.11%, strains began to increase rapidly. This is because the shear transfer mechanism varied and the foundation beam begins to behave independently as the deformation of the shear wall increases. Transition of strain distributions of the upper longitudinal reinforcement was larger than that of the lower longitudinal reinforcement. 6

7 June 5-8, 26 Naples, Italy Figure 9 (c) shows the average strain distribution of longitudinal reinforcement in slabs. Compared with Fig. 9 (a), each point and each distribution at seven representative loading stages agreed with that of Fig. 9 (a) except strains at midspan of the foundation beam. As shown in Fig. 9 (d), the height of the longitudinal reinforcement in slabs was almost same as that of the upper longitudinal bars in the foundation beam. The foundation beam could be considered as T beam =+15kN(. 94%, 147. kn) =+25kN(. 334%, 252.7kN) α =+. 6%(. 653%, 285.9kN) α =+. 12%(. 132%, 32.6kN) α =+. 27%(. 269%, 336.8kN) α =+. 4%(. 394%, 342.8kN) α =+. 68%(. 637%, 354.8kN) データ 2 22: 4: 37 26/ 1/ (a) Upper longitudinal bar (Foundation beam) =+15kN(. 94%, 147.kN) =+25kN(. 334%, 252.7kN) α =+. 6%(. 653%, 285.9kN) α =+. 12%(. 132%, 32.6kN) α =+. 27%(. 269%, 336.8kN) α =+. 4%(. 394%, 342.8kN) α =+. 68%(. 637%, 354.8kN) データ 2 22: 7: 4 26/ 1/ (b) Lower longitudinal bar (Foundation beam) =+15kN(. 94%, 147. kn) =+25kN(. 334%, 252.7kN) α =+. 6%(. 653%, 285.9kN) α =+. 12%(. 132%, 32.6kN) α =+. 27%(. 269%, 336.8kN) α =+. 4%(. 394%, 342.8kN) α =+. 68%(. 637%, 354.8kN) データ 2 22: 26: 12 25/ 1/ 7 East South Longitudinal bars in the slabs( D6) North Upper longitudinal bars in the foundation beam( D22) Lower longitudinal bars in the foundation beam( D22) Location of the longitudinal bars in the foundation beam and in the slabs (c) Longitudinal bars (Slabs) (d) Location in the foundation beam Fig. 9. Strain distributions of longitudinal reinforcement West X SIMULATION OF STRAIN DISTRIBUTIONS OF THE FOUNDATION BEAM Analytical Methods In the ultimate strength design based on Japanses design guideline [5], as shown in Fig. 3, moment from piles (Mp) and axial force (N) were checked in the design of the foundation beams. This design procedure does not consider the variation of the shear transfer mechanism. In this study, two additional moment were considered. One is moment due to lateral force acting on the top surface of the foundation beam (Mq). The other is moment due to vertical longitudinal bars in the shear wall (Mw). The 7

8 June 5-8, 26 Naples, Italy distributions of N, Mq and Mw vary as the shear wall rotates and the contact area between the shear wall and the foundation beam decreases. As for Mp, the distribution does not vary as shown in Fig. 11. Figure 1 shows a schematic figure of contact and detachment of the shear wall base. Numbers beside each figure indicate the degree of detachment (D). It is assumed that the shear wall rotates and applied is transferred uniformly through the contact region (shaded region in Fig. 1). Figure 12 shows the models of the distributions of N, Mq and Mw corresponding to the degree of detachment in Fig. 1. The foundation beam was replaced with a line element. Calculating moment and axial force at each section, the strain distributions of the longitudinal reinforcement in the foundation beam were computed by a simple section analysis at each loading stage. The foundation beam was considered as T beam with slabs from experimental results. Degree of detachment Column(Tension side) Shaded region is the area of contact. Shear stress is assumed to distribute uniformly. Shear wall White region has no contact. No stress transfer is assumed. Column(Compression side) Shear Force Fig. 1. Degree of detachment (D) h'' h.3.7 Mp=.7 h' (.3 h') h'':dist ance between t he t op surface and the centroid of the foundation beam h :Distance between the contraflexural point of the pile and the centroid of the foundation beam Fig. 11. Distribution of Moment from piles (Mp) Tension Tension Tension Tension Tension N=.3 Compression Compression Compression Compression N N N N N (a) D= (b) D=.25 (c) D=.5 (d) D=.75 (e) D=1. (1) Axial force due to lateral force (N) Fig. 12. Distributions of the moment and axial force corresponding to the degree of detachment (D) (continue) 8

9 June 5-8, 26 Naples, Italy h'' h'' h'' h'' h'' Mq= h'' Mq Mq Mq Mq (a) D= (b) D=.25 (c) D=.5 (d) D=.75 (e) D=1. (2) Moment due to lateral force acting on the top surface of the foundation beam (Mq) T=MIN(Esw( (15mm- X)/ 3mm),Fsw) Asw 75mm 15mm 225mm 3mm T=Fsw Asw T=Fsw Asw T=Fsw Asw T=Fsw Asw Mw Mw Mw Mw Mw Esw:The modulus of elast icity of the shear reinforcement bar of the wall :The yield strain of the longitudinal bar of the column Asw:The area of the shear reinforcement bar of the wall Fsw:The yield strength of the shear reinforcement bar of the wall (a) D= (b) D=.25 (c) D=.5 (d) D=.75 (e) D=1. (3) Moment due to vertical longitudinal bars in the shear wall (Mw) Fig. 12. Distributions of the moment and axial force corresponding to the degree of detachment (D) Comparison between Computed and Experimental Results The comparison between the computed and experimental strain distributions are shown in Fig. 13, Fig. 14, Fig. 15 and Fig. 16 at 4 different loading stages. Figure 13 shows the distributions until the shear wall yielded and Fig. 14 shows immediately after the shear wall yielded. Figure 15 and Fig. 16 show after the shear wall yielded. As shown in Fig. 13, especially the strains of the upper longitudinal bars were restricted to smaller values than the computed strains. This is due to the monolithic action with peripheral members. When the shear wall yielded, the strain distribution began to agree with the computed strain distributions as shown in Fig. 14. The strains of the lower longitudinal bars near the pile with.3 lateral force indicated by a break line circle were larger than the computed strains. This behavior is explained later. Exper i ment +. 6%(. 653%, kN) Anal ysi s ( Degr ee of det achment =) Exper i ment +. 1%(. 653%, kN) Anal ysi s ( Degr ee of det achment =) (a) D = (b) Upper longitudinal bar (c) Lower longitudinal bar Fig. 13. Strain distributions of the foundation beam α =.6% 9

10 June 5-8, 26 Naples, Italy Exper i ment +. 12%(. 132%, 32. 6kN) Anal ysi s ( Degr ee of det achment =) Exper i ment +. 12%(. 132%, 32. 6kN) Anal ysi s ( Degr ee of det achment =) (a) D = (b) Upper longitudinal bar (c) Lower longitudinal bar Fig. 14. Strain distributions of the foundation beam α =.12% As the deformation of the shear wall increased, the strain distributions varied. In analysis, as shown in Fig. 15 and Fig. 16, the transition of strain distributions could be simulated well near the pile with.7 lateral force that was indicated by solid line circles. In this experiment, the flexural yield strength of the foundation beam was set smaller than the requirement of the Japanese design guideline [5]. Though Mq and Mw should be considered in addition to Mp and N, due to the compressive axial force as shown in Fig. 12 (1) and the contribution of the slabs, the foundation beam didn t yield near the pile with.7 lateral force until α =.35%. In this study, degree of detachment was adjusted to agree with the experimental results. In order to utilize this analytical method in design, it is necessary to establish the procedure to determine appropriate degree of detachment corresponding to design conditions. As for the strain distributions near the pile with.3 lateral force, the computed results could not agree with the experimental results. This seems to be related to the stress transfer mechanism from tensile pile to the foundation beam as shown in Fig. 17. Near the pile with.3 lateral force, compression force is transferred to the foundation beam forming diagonal concrete strut. This mechanism makes lever arm of the foundation beam small and the tensile force acting on the lower longitudinal reinforcement in the foundation beam increase. This problem could not be clarified by a section analysis. The analysis considering the whole structure should be conducted Exper i ment +. 27%(. 269%, 336.8kN) Anal ysi s ( Degr ee of det achment =) Anal ysi s ( Degr ee of det achment =. 25) (a) D = and.25 (b) Upper longitudinal bar (c) Lower longitudinal bar Fig. 15. Strain distributions of the foundation beam α =.27% Exper i ment +. 27%(. 269%, 336.8kN) Anal ysi s ( Degr ee of det achment =) Anal ysi s ( Degr ee of det achment =. 25) 1

11 June 5-8, 26 Naples, Italy Exper i ment +. 68%(. 637%, 354.8kN) Anal ysi s ( Degr ee of det achment =. 25) Anal ysi s ( Degr ee of det achment =. 5) (a) D =.25 and.5 (b) Upper longitudinal bar (c) Lower longitudinal bar Fig. 16. Strain distributions of the foundation beam α =.68 % Exper i ment +. 68%(. 637%, 354.8kN) Anal ysi s ( Degr ee of det achment =. 25) Anal ysi s ( Degr ee of det achment =. 5) h Mp=.7 h (.3 h') Compression Lever Arm Tension Compression Tension.3.7 Fig. 17. Stress distributions near the piles CONCLUSIONS One 1/4-scale cantilever structural wall system was tested to clarify the variation of the lateral load resisting mechanisms considering the interaction between a shear wall, a foundation beam, slabs and piles. The main conclusions can be summarized as follows. Contrary to the design, the yielding of the shear wall preceded the yielding of the foundation beam. This is due to the monolithic action between a foundation beam and peripheral members. From strain distributions of longitudinal reinforcement in the foundation beam in experiment, the transition of the shear transfer mechanism was confirmed. In the analysis of the foundation beam, it is assumed that the foundation beam is subjected to moment from the piles (Mp), moment (Mq) and axial force (N) due to lateral force, acting on the upper edge of the foundation beam, and moment due to vertical longitudinal bars in the shear wall (Mw). The analytical method using degree of detachment of the interface between the shear wall base and the foundation beam made shear transfer mechanism clear. Other minor conclusions can be summarized as follows. Flexure-shear cracks of the shear wall penetrated the slabs transversely and developed to the foundation beam and the shear wall deformed along these cracks involving the parts of the foundation beam, the pile, the transverse foundation beam and the slabs. 11

12 June 5-8, 26 Naples, Italy Near the pile with.3 lateral force, the tensile force acting on the lower longitudinal reinforcement in the foundation beam in experiment was larger than that calculated in analysis. This is because compression force is transferred forming the diagonal concrete strut from the pile to the foundation beam. REFERENCES 1. Architecture Institute of Japan. AIJ Standard for Structural Calculation of Reinforced Concrete Structures Based on Allowable Stress Concept, 1999: Paulay, T. Priestley, M.J.N. Seismic Design of Reinforced Concrete and Masonry Buildings. John Wiley & Sons, 1992: Sakashita M, Bechtoula H, Kono S, Tanaka H, Watanabe F. A Study on The Seismic Force Resisting Mechanism of A Multi-story Shear Wall System Considering The Interaction Between Wall, Slab, Foundation Beam, and Pile Elements. 13th World Conference on Earthquake Engineering Conference Proceedings, 24:pdf.No Sakashita M, Urabe A, Murakami K, Kono S, Tanaka H, Watanabe F. Lateral Load Resisting Mechanism of a Monolithic Shear Wall or a PCa Shear Wall and Peripheral Members Part1-2. Summaries of Technical papers of Annual Meeting Architectural Institute of Japan C-2 Structures 4, 25: (in Japanese). 5. The building center of Japan. Design and Construction Guidelines for Multiple Story Frame Structures with Shear Wall, 1999:9-54, (In Japanese) 6. Architecture Institute of Japan. Design Guidelines for Earthquake Resistant Reinforced Concrete Buildings Based on Inelastic Displacement Concept, 21:91-24, , (In Japanese) 12