NON-LINEAR FEM ANALYSIS FOR CES SHEAR WALLS

Transcription

1 1NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 214 Anchorage, Alaska NON-LINEAR FEM ANALYSIS FOR CES SHEAR WALLS S. SUZUKI 1, H. KURAMOTO H 2 and T. MATSUI 3 ABSTRACT Steel Reinforced Concrete structures (SRC) are typical composite structural system consisting of steel and reinforced concrete (RC), which have an excellent earthquake resistance and deformability. However, the design process and construction work are more complicated than those for steel structures and RC structures. In order to solve these problems, Concrete Encased Steel (CES) structural system consisting of fiber reinforced concrete (FRC) and encased steels, have been proposed by the authors as a new composite structural system, and continuous and comprehensive studies have being conducted to make it practical. Cyclic loading tests were carried out on CES shear walls with different anchorage methods for the CES frame and FRC wall panel, and the basic structural performance, such as strength and failure mode, of the CES shear walls were investigated. As a result, it was confirmed that the effect of anchorage condition of wall longitudinal reinforcement on shear strength and flexural strength of CES shear walls is not significant. In addition, the deformability of CES shear walls improves by omitting anchorage of wall longitudinal reinforcement. However, it is difficult to fully understand the behavior of CES shear walls which consist of many members, such as boundary columns, wall panel, boundary beams, steels and wall reinforcing bars. In this study, a two-dimensional FEM analysis was carried out to clarify the shear transferring mechanism of the CES shear walls. Analytical results for the shear force versus drift angle relationships and deformation components of the shear walls showed good agreements with the experimental results. Thus, it was found that the behavior of the CES shear walls can be approximately simulated by the analytical model. It was also indicated through the analysis that the difference of anchoring method of longitudinal wall reinforcing bars to boundary beams affects little on the internal stress conditions and overall behavior of the shear walls. 1 Dept. of Architectural Engineering, Osaka University, Japan 2 Professor, Dept. of Architectural Engineering, Osaka University, Japan 3 Associate Professor, Dept. of Architecture and Civil Eng., Toyohashi University of Technology, Japan, Suzuki S, Kuramoto H, Matsui T. Non-linear FEM analysis for CES shear walls. Proceedings of the 1 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 214.

2 1NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 214 Anchorage, Alaska Non-Linear FEM Analysis for CES Shear Walls S. SUZUKI 1, H. KURAMOTO 2 and T. MATSUI 3 ABSTRACT The objective of this study is aimed to develop the shear walls in composite CES structures composed of steel and fiber reinforced concrete. In this study, a two-dimensional FEM analysis was conducted to verify the validity of analytical modeling assumed and constitutive modeling for material used. And internal stress conditions in the shear walls were also investigated through the FEM analysis. Analytical results for the shear force versus drift angle relationships of the shear walls showed good agreements with the experimental results. In was also indicated through the analysis that the difference of anchoring method of longitudinal wall reinforcing bars to boundary beams affects little on the internal stress conditions and overall behavior of the shear walls. Introduction Steel Reinforced Concrete (SRC) structures are typical composite structural system consisting of steel and reinforced concrete, which have an excellent earthquake resistance. However, the design process and construction work are more complicated than those for steel structures and RC structures. In order to solve these problems, Concrete Encased Steel (CES) structural system consisting of fiber reinforced concrete (FRC) and encased steels, has been proposed by the authors as a new composite structural system, and continuous and comprehensive studies have being conducted to make it practical. On the other hand, shear walls used as the major seismic member in RC structures are also effective to increase the strength and stiffness of the CES structural system. However, it would be difficult to arrange wall reinforcing bars in the CES shear walls. It is an important issue to improve the workability of the connection between CES frame and FRC wall panel in the CES structures. Therefore, cyclic loading tests were carried out on CES shear walls with different anchorage methods for the frame and wall panel [1]. As a result, it was confirmed that the effect of anchorage condition of longitudinal reinforcing bars in the wall panel on the maximum strength was not significant. In addition, the deformability of the CES shear walls can be improved by omitting anchorage of longitudinal wall reinforcing bars. However, it is difficult to fully understand the behavior of CES shear walls which consist of several components, such as 1 Dept. of Architectural Engineering, Osaka University, Japan 2 Professor, Dept. of Architectural Engineering, Osaka University, Japan 3 Associate Professor, Dept. of Architecture and Civil Eng., Toyohashi University of Technology, Japan, Suzuki S, Kuramoto H, Matsui T. Non-linear FEM analysis for CES shear walls. Proceedings of the 1 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 214.

3 1 25 and and transverse bar 25 1, , ,6 Column Steel H Beam Steel H Wall Reinforcement D6@75 Zigzag Anchorage Non-Anchorage Beam steel Longitudinal bar Figure 1. Test specimen Figure 2. Bar arrangement Table 1. Details of specimens columns, wall panel, beams, steels and Specimens wall reinforcement. In this study, a BxD 25x25 (mm) Column two-dimensional FEM analysis was Steel H-17x12x6x9 ( s p=4.9%) carried out to clarify the shear transfer BxD 2x25 (mm) Beam mechanism of the CES shear walls. Steel H-148x1x6x9 ( gp=5.2%) Thickness 1 (mm) Wall Longitudinal bar Analyzed Specimens D6@75 zigzag ( w p=.42%) Transverse bar Shear span ratio Description of Specimens Anchorage condition of 18 hook nonexistent longitudinal wall reinforcement in beam The specimens were designed to simulate the lower two stories of a multi-story shear wall in a medium rise building, and were 1/3 scale of the prototype walls. Four specimens were prepared for this test. The configurations and bar arrangements of the specimens are shown in Figs. 1 and 2. Details of the sections are shown in Table 1. The column had a 25mm square cross-section, and the beam section was 2x25mm. The column span length was 1,8mm, and the wall thickness was 1mm. The experimental variables were the shear-span ratio and anchorage condition of the longitudinal wall reinforcing bars. The shear-span ratio was 1.1 in Specimens and, and it was 1.65 in Specimens and. Specimens and were expected to be shear failure mode, although Specimens and were expected to be flexural failure mode. The longitudinal wall reinforcing bars for Specimens and were bent in wall panel. On the other hand, the longitudinal wall reinforcing bars for Specimens and were anchored to a beam or stubs, as shown in Fig. 2. The transverse wall reinforcing bars in all specimens were securely fixed by welding them to the steel web in the CES boundary columns. In addition, the H-section steels of the boundary columns were anchored to the upper and lower stabs in all specimens. The mechanical properties of the FRC and steel used are shown in Tables 2 and 3, respectively. Poly vinyl alcohol (PVA) fibers with a diameter of.66mm and a length of 3mm were used for the FRC. The volumetric ratio of the fibers was 1.%.

4 Table 2. Mechanical properties of FRC Specimen σ B (MPa) E C (GPa) ε c (μ) 1 story 2 story ,814 2,55 1 story 2 story ,587 2,558 1 story 2 story ,457 2,423 1 story ,765 2 story ,16 Table 3. Mechanical properties of steel σ y (MPa) E s (GPa) σ u (MPa) PL-6 (SS4) PL-9 (SS4) D6 (SD295A) Loading Program Hydraulic Jack 2kN W Measuring position for the δ Specimen 265 E Hydraulic Jack 2kN Figure 3. Loading apparatus LOAD + - West East Hydraulic Jack 2kN The loading apparatus used is shown in Fig. 3. The wall specimens were loaded with horizontal cyclic shear forces using a hydraulic jack with a 2,kN capacity, while applying a constant axial force of 1,26kN (N/N=.2, where N=axial load, N=axial load capacity including steel of boundary columns) using two vertical manual jacks, each of which had a 2,kN capacity. During the testing, additional moment was also applied to the top of the specimen using the two vertical jacks to maintain the prescribed shear-span ratio of 1.1 or The loading was conducted by controlling the relative drift angle, R, given by the ratio of the height corresponding to the measuring point for the horizontal displacement at the top of the specimen, h (2,5 mm), to the horizontal deformation, δ, i.e., R=δ/h. Experimental Results Shear force versus drift angle relationships of all specimens are shown in Fig. 4. The maximum shear forces of two specimens which have shear failure were almost the same. However, the deformability of Specimen and were different after reaching the maximum shear force. While the shear force of Specimen decreased slowly, that of Specimen decreased drastically at R of x1-2 rad. Horizontal slip between wall panel and beam versus drift angle relationships of shear failure specimens are shown in Fig. 5. In Specimens with longitudinal wall reinforcement anchorage, the horizontal slip between wall panel and beam hardly occurred. However, in Specimen without longitudinal wall reinforcement anchorage, the horizontal slip between wall panel and beam increased at R of 1.x1-2 rad. The reason why, the deformability are different between Specimens and, is that the damage of wall panel in Specimen is less than that in Specimen due to the development of slip between wall panel and beam in Specimen without longitudinal wall reinforcing bars anchorage.

5 Qmax=-1328kN Rmax=-.75x1-2 rad. Qmax=971kN Rmax=x1-2 rad Drift angle (x1-2 rad.) Qmax flange yield Qmax flange yield The maximum shear forces of two specimens and are almost the same. These specimens showed significant strength deterioration in the cycle of 3.x1-2 rad. However, the deformability of Specimen was slightly poorer than that of Specimen. Thus, it is found that the anchorage condition for the longitudinal reinforcement had little effect on the maximum shear force. In addition, the deformability can be improved by omitting the anchorage of the longitudinal wall reinforcement Figure 4. Shear force versus drift angle relationships Qmax=1336kN Rmax=.98x1-2 rad. Qmax=118kN Rmax=1.9x1-2 rad Drift angle (x1-2 rad.) Horizontal slip between wall panel and beam (mm) Qmax flange yield Qmax flange yield 3 4 Shear failure mode Drift angle ( 1-2 rad.) LOAD + - Measured position Analytical Model FEM Analysis Figure 5. Horizontal slip between wall panel and beam In this section, a two-dimensional FEM analysis was conducted for the CES shear walls using the commercial software FINAL [2]. The finite elements mesh layout for the CES shear walls is shown in Fig. 6. Each node at the bottom end of the under stub is fixed to restrain vertical and lateral displacement. The elements between the loading points prescribe shear span ratio of 1.1 or 1.65, and the top end of upper stub were defined as an elastic body, which is a virtual stub. A node at the top of the virtual stub was subjected to lateral displacement reversals with applying a constant initial axial force of 1,26kN. Material Model Concrete elements were modeled by the four node quadrilateral plane stress elements.

6 Reinforcing bars in the wall panel substituted equivalent layers with stiffness in the bar direction and superposed on the quadrilateral elements. As a stress-strain relationship of FRC, a modified Ahmad model [3] was adopted for the compressive stress-strain curve in the stressrising region, and in the stress-softening regions was modeled by a multi-linear model using substantial data from material tests shown in Fig. 7(a).The model by Kupher and Gerstle was adopted as the fracture criterion of concrete under biaxial stress state [4]. Tension stress was taken to be small after the crack occurred, and the concrete tension model by Izumo [5] with coefficient, c of.4 in the wall panel and c of 1. in the CES frame, was used in the descending branch (Fig. 7(b)). Stiffness reduction due to cyclic stress [6] was considered, as shown in Fig. 7(c). As a shear transfer model after crack occurred of FRC, a modified Al-Mahaidi model was adopted. where, in Al-Mahaidi model, β of 1. was changed.8 to decrease shear transfer stiffness, as shown in Fig. 7(d). As a result of conducting an analysis using the above constitutive laws, strength in the analysis deteriorated earlier than that of in the experimental results. Therefore, tension strength was reduced as listed in Table 4. Steel elements in the column flange and beam web were modeled by the four node quadrilateral plane stress elements, and steel elements in the column web and beam flange were modeled by the two node truss elements. The material model of steel was a plasticity model, which was the Von-Mises model failure surface with associated plastic rule. The stressstrain curve of the steel was idealized by the Modified Menegotto-Pinto model by Ciampi [6], as shown in Fig. 8. The film element and line elements were used as the bond model between concrete node and steel node. Bond stress versus slip relationships were modeled by a multi-linear + LOAD - Virtual stub Discrete crack element Holding the degree of freedom Figure 6 Finite element mesh σ (σ c, ε c ) (.4σ c,4 c ) ε (.2σ c, 8ε c ) (a) Compressive Crack point Compressive Stress Tensil Strain σ t.4 G cr / G (σ cr,ε cr ) ε cr Quad element (Concrete) Quad. elemtent (Flange) Truss element (Web) σ t =σ cr (ε cr /ε t ) c ε t (b) Tensil ε t c=.2 c=1. G cr /G =.4/(ε t /ε cr ) β β=.8:this model β=1.:al-mahaidi (c) Hysteresis (d) Shear transfer Figure 7 Constitutive laws for concrete Stress Strain Figure 8 Constitutive laws for steel Stress Crack point τ (τ max,s max ) τ=τ max (S max /S).1 τ max =3. (MPa) S max =.5 (mm) Figure 9 Bond stress and slip relationships Yield point S Displacement Figure 1 discrete crack model

7 model, as shown in Fig. 9. As for the anchorage condition of the longitudinal wall reinforcing bars, discrete crack elements between wall panel and beam or stub were adopted. In the Specimens and, tension stress after cracking was zero. In the Specimens and, the pullout of reinforcing bars after cracking were modeled, as shown in Fig. 1. Table 4. Mechanical properties of FRC used in the analysis Specimen σ B E C ε c σ cr (MPa) (GPa) (μ) (MPa) 1 story ,814 2 story ,55 1 story , story ,558 (Frame) 1 story , story ,423 (Wall ) 1 story ,765 2 story ,16 Analytical Results Hysteresis Characteristics and Slip between Wall Panel and Beam Figure 11 shows comparisons between experimental and analysis results on shear force versus drift angle relationships. For all specimens, although the initial stiffness in the analytical results tended to be larger than those in the experimental results, while the yield point of steel at the bottom in boundary column and the maximum shear force agreed well with the experimental results. The strength deterioration in the experimental results after the maximum strength of Specimen was slowly. That of Specimen in the experimental results occurred at R of x1-2 rad. The analytical results of these specimens showed the same tendency as experimental results. Strength deterioration of Specimens and with flexural Q max =1,275kN R=.76x1-2 rad. Q max =1,3kN R=1.86x1-2 rad. Analysis Yielding Q max Test Yielding Q max -5 Analysis Test -1 Yielding Yielding Q max Q max Drift angle (x1-2 rad.) Figure 11 Shear force versus drift angle relationships 5 Q max =1,312kN R=.77x1-2 rad. Q max =1,13kN R=6x1-2 rad. Analysis Yielding Q max Test Yielding Q max -5 Analysis Test -1 Yielding Yielding Q max Q max Drift angle (x1-2 rad.)

8 Horizontal slip (mm) Drift angle (x1-2 rad.) failure mode did not occur, the analytical results of these specimens showed the same tendency as experimental results. The unloading stiffness in analytical results for all specimens showed almost the same as experimental results. However, analytical result for Specimen is directed the origin as compared to the experimental result. Figure 12 shows horizontal slip between first-story wall panel and beam. The experimental result of Specimen was increased at R of 1.x1-2 rad. The analytical result was increased at R of.75x1-2 rad. The experimental and analytical results of the other specimens were not increase. Deformation Components Horizontal slip (mm) Figure 12 Slip between wall panel and beam Shear Flexural Test Analysis Flange Yeild Deformation (mm) Figure 13 Deformation components Shear Flexural Figure 13 shows shear force versus shear deformation and flexural deformation relationships. Flexural deformations of experiment and analysis were calculated using axial displacement of boundary columns. In Specimens and with shear failure, the shear deformations were larger than the flexural deformations. In Specimens and with shear flexural failure, the flexural deformations were larger than the shear deformations. The backbone curves by the analysis showed good agreement with the experimental results. Shear deformation had slipshaped hysteresis, and flexural deformation had spindle-shaped hysteresis. Analytical results were reappeared the hysteresis shape of the experimental results. 1. Drift angle (x1-2 rad.) Test Analysis Deformation (mm) Shear Flexural Deformation (mm) LOAD + - Measured position Shear Flexural Deformation (mm)

9 (a) (b) (c) (d) Figure 14 Distribution of minimum principle stress (R= rad.) With the increased of the loading cycle, the unloading stiffness of the shear deformation for Specimens and became lower than that in the experimental result. This is the same tendency as the shear force versus drift angle relationships shown in Fig. 11. However, the unloading stiffness of the shear deformation and flexural deformation for Specimens and agreed well with the experimental results. Distribution of Minimum Principle Stress Internal Stress Situation Figure 14 shows distribution of minimum principle stress of concrete at R of.75x1-2 rad. It can be seen that high stresses of concrete occurred at the corner of wall panel and the bottom of boundary column subjected to compression. And, the width of the compressive struts for Specimens and were smaller than that for Specimens and. However, regardless of failure modes, the effect of anchorage condition of longitudinal wall reinforcement was small, because the slip between wall panel and beam was small until R of.75x1-2 rad., as shown in Fig. 12. Contribution of Shear Force Figure 15 shows contribution of shear force in the horizontal cross-section at the bottom and the top if the first story wall panel. The positions of referring concrete and steel elements to the shear forces contributed are shown in Fig. 16. In the top of cross-section, the contribution of shear force in wall panel for Specimen was decreased gradually from R of.75x1-2 rad. That for Specimen was decreased drastically at R of x1-2 rad. This is the same tendency as strength deterioration shown in Fig. 11. The shear force for Specimen was decreased gradually, because the damage of concrete in the wall panel at the top was reduced. The contributions of shear force in the wall panel for Specimens and were not decreased. In the bottom of cross-section, the contribution of shear force in the compressive column

10 Contribution of shear (kn) Contribution of shear (kn) Top Bottom Wall Panel Compressive Column Tensil Column Compressive Steel Tensil Steel Top Bottom Top Bottom Top Bottom Drift angle (x1-2 rad.).625 Figure 15 Contribution of shear force Drift angle (x1-2 rad.) Drift angle (x1-2 rad.) Drift angle (x1-2 rad.) for Specimen was slightly larger than that for Specimen. On the other hand, that for Specimen was decreased at R of x1-2 rad. That for Specimen was decreased at R of.75x1-2 rad. In addition, the contributions of shear force in the compressive steel for these specimens increased with decreased of shear force in the compressive column. It was confirmed that the contribution of shear force in the column moved from concrete to steel. The ratios of contribution of shear force for each members were different, but the total shear forces for these specimens were almost the same. It was thought that the failure modes of these specimens were the same. Distribution of Shear Stress Figure 17 shows distribution of average shear stress at R of.5 and.75x1-2 rad. The average shear stress were used concrete elements as shown in Fig. 16, those are the average values of shear stress of 2 or 3 elements. As for the bottom, high shear stresses occurred at the boundary column and wall panel in the compression side. As for the top, shear stresses at the boundary column decreased as compared with the bottom. However, regardless of the anchorage condition of wall longitudinal reinforcement, the distribution of shear stress for the specimens with or without anchorage were almost the same at the maximum strength, so that the effects of the anchorage condition on the maximum strength for CES shear wall is small. Conclusion Top bottom Figure 16 Position of referring element to shear stress

11 Shear stress (MPa) (Top) (Top) (Top) (Top) Shear stress (MPa) (Bottom).5x1-2 rad..75x1-2 rad. (Bottom) (Bottom) (Bottom) Figure 17 Width (mm) Distribution of shear stress Width (mm) Width (mm) Width (mm) 2 A two-dimensional FEM analysis was carried out to clarify the shear transfer mechanism of the CES shear walls. The following conclusions can be drawn. 1) The CES shear walls was simulated by FEM analysis to produce the restoring characteristics and deformation components, and good agreement between experimental and analytical results was shown. 2) High stresses of concrete compressive struts are observed at the corner of wall panel in Specimen without longitudinal wall reinforcing bars anchorage. It was found that the analytical results corresponded to the damage situation of experimental results. 3) It was confirmed that the deterioration of shear force at the top of the wall panel in Specimen with longitudinal wall reinforcing bars occurred earlier than that in Specimen. This is why the deformability in Specimen was lower than that in Specimen. 4) The contribution of shear force in the column subjected to axial compression in Specimens and moved from concrete to steel 5) The difference of anchorage condition of wall longitudinal reinforcement affects little in the compressive struts and distributions of shear stress at the maximum strength. The effects of the anchorage condition on the maximum strength for CES shear wall is small. Reference 1. Suzuki S, Matsui T, Kuramoto H. Effect of anchorage condition of wall reinforcement on structural performance of CES shear walls. Proceedings of the Japan Concrete Institute 211; 32 (2): FINAL/99. ITOUCHU Techno-Solutions Corporation 3. Naganuma K. Stress-strain relationships for concrete under triaxial compression. Journal of structural and construction engineering 1995; 474: Kupfer H, Gerstle K. Behavior of concrete under biaxial stresses. Journal of the engineering mechanics division 1973: Izumo J, Shi H, Maekawa K. Analytical model for a reinforced concrete panel element subjected to reversed cycle in-plane stresses. Journal of structural mechanics and earthquake engineering 1989, 48: Naganuma K, Okubo M, An analytical model for reinforced concrete panels under cycle stresses. Journal of structural and construction engineering 2; 536: