Structural behavior of reinforced concrete frame-wall components

Transcription

1 Materials and Structures/Matériaux et Constructions, Vol. 31, November 1998, pp Structural behavior of reinforced concrete frame-wall components Y. L. Mo 1 and C. J. Kuo 2 (1) Professor (2) Graduate Student, Department of Civil Engineering, National Cheng Kung University, Tainan, 701, Taiwan SCIENTIFIC REPORTS Paper received: September 29, 1997; Paper accepted: January 27, 1998 A B S T R A C T Reinforced concrete buildings with shearwalls are very efficient to resist earthquake disturbances. In general, reinforced concrete frames are governed by flexure and shearwalls are governed by shear. If a structure includes both frames and shearwalls, the complicated interaction of these two components will exist. This paper describes experiments on frames and frame-wall structures, and the experimental results are used to check the analytical models. The tests include four frames and two frame-wall structures. The effects of concrete compressive strength, section size and wall on the frames are investigated. For frames, the horizontal force-displacement relationship predicted by the trilinear theory is in good agreement with the test data. However, for framewall structures, both the softening truss model and the IDARC program give deviations from the test values in the horizontal force-displacement relationship. R É S U M É Des constructions en béton armé utilisant des murs de refend s avèrent très efficaces pour résister aux perturbations d un tremblement de terre. En règle générale, des cadres en béton armé sont influencés par la flexion tandis que les murs de refend sont influencés par le cisaillement. Si une construction comprend des cadres ainsi que des murs de refend, l interaction complexe entre ces deux composantes aura lieu. Cet article décrit des expériences effectuées sur des cadres et des constructions cadres - murs ; les résultats de ces expériences sont utilisés pour vérifier les modèles analytiques. Les essais concernent quatre cadres et deux constructions cadres - murs. Les effets de la résistance en compression du béton, de la section et du mur sur les cadres sont soumis à l étude. En ce qui concerne les cadres, le rapport force horizontale - déplacement prédit par la théorie trilinéaire est confirmé par les tests. Cependant, au sujet des constructions cadres - murs, le modèle d armature allégeante ainsi que le programme «IDARC» fournissent des écarts vis-à-vis des valeurs données par les tests dans le rapport force horizontale - déplacement. 1. INTRODUCTION During the earthquakes of the last three decades, buildings containing shear walls have exhibited very satisfactory earthquake performance [1]. In most cases, the shear walls were reinforced in the traditional manner for gravity and overturning, without consideration given to special details for ductility, as required in recent United States building codes [2, 3]. In order to design a shear wall to behave in a ductile manner, which requires that its strength be governed by flexure rather than by shear, its shear capacity must be known and must be larger than the shear corresponding to its moment capacity. In other words, we need to know not only the ultimate shear capacity but also what happens between the onset of shear cracking and shear failure. Whether and to what extent the grinding within shear cracks, caused by reversible cycles of lateral movement, can serve as an energy dissipation mechanism needs to be determined and has not yet been sufficiently investigated. Therefore, there is a growing need for techniques that allow an engineering understanding of complex frame-wall behavior and a qualitative interpretation of the overall inelastic response of frame-wall structures to cyclic reversible loads. With regard to reinforced concrete frames with side sway, their actual behavior is complicated not only by the influence of second-order deformation, but also by the fact that considerable redistribution of moments may occur due to the cracking of structural members and the plastic behavior of materials. A trilinear theory proposed by Mo [4] was devised to predict theoretically the actual behavior of reinforced concrete frames. This method utilizes the trilinear moment-curvature curve, as well as the principle of virtual work to express the compatibility condition and to find deflections. The design concern of a framed shearwall is to promote failure in the wall panels while suppressing failure in the columns. The failure in the wall panel need not be brittle if properly designed. This design concept considers the wall panels as sacrificial elements to absorb energy during an earthquake to insure the safety of the frame system. The wall panels can also be rapidly repaired afterward. For framed shearwalls, the equilibrium equations can be derived from the truss model theory [5]. Also, when the /98 RILEM 609

2 Materials and Structures/Matériaux et Constructions, Vol. 31, November 1998 compatibility conditions of a wall element are considered, compatibility equations can be derived that relate the shear distortion to the strains in the reinforcement and concrete. To accurately predict the shearwall behavior, the stress-strain curve proposed for the softened diagonal concrete struts [6] needs to be incorporated. More recently, using modern concepts in concrete modeling, a computational tool (IDARC) [7] for the seismic evaluation of reinforced concrete frame-wall systems was presented. The IDARC program performs a static collapse mode analysis to estimate the base shear coefficient, and an inelastic dynamic response analysis under horizontal and vertical base excitations. In this model, a frame-wall system includes four elements, namely, inelastic axial springs for edge columns, shear and flexure spring for shearwall, a rigid beam element for foundation and an equivalent shear-flexure spring for beam. In this paper, the trilinear theory for frames, the softening truss model for framed shearwalls, and the IDARC program for both frames and frame-wall structures will be examined by the tests on frames and frame-wall structures. 2. TEST PROGRAM Results from four frames and two frame-wall structures tested under reversed cyclic loads are presented. The parameters of the tests (Table 1) are concrete strength, column size and whether or not the wall exists. 2.1 Concrete Fig.1a Dimensions and reinforcement of all specimens. monitor concrete strength with age. The compressive strength of the concrete used in each specimen is shown in Table 1. The nominal maximum size of the coarse aggregate was 10 mm diameter. The concrete compressive strength for the ready-mix concrete varies from 25 MPa to 62 MPa. The slump was 250 mm to produce high performance concrete for all the specimens. Twenty-four standard cylinders ( mm) were cast with each pour and tested frequently to Table 1 Material properties Specimen f c (Mpa) fy (Mpa) 4.1 mm Ø 9.7 mm Ø 12.7 mm Ø NF NF MF MF NW MW Notes: f c = Concrete compressive strength; Fy = Yield stress of steel. 2.2 Rebars Deformed 9.5 mm Ø, 12.7 mm Ø and 4.1 mm Ø bars were used. In the beams, longitudinal steel consisted of four 9.5 mm Ø bars (two top, two bottom) and six 9.5 mm Ø bars (three top, three bottom) in specimens NF1, MF1, NW1, MW1 and specimens NF3, MF3, respectively, providing the corresponding steel ratios of 1.26 percent and 0.48 percent of the gross cross-sectional areas of the beams. Similarly, in the columns, longitudinal steel consisted of four 12.7 mm Ø bars and four 9.5 mm Ø bars as well as four 12.7 mm Ø bars in specimens NF1, MF1, NW1, MW1 and specimens NF3, MF3, respectively, providing the corresponding steel ratios of 2.3 percent and 0.88 percent. Ties were made of deformed 6.4 mm Ø and 9.5 mm Ø bars for Specimens NF1, MF1, NW1, MW1 and Specimens NF3, MF3, respectively. Seventeen deformed 4.1 mm p rebars were used in both the vertical and horizontal directions in the wall of 610

3 Mo, Kuo each of Specimens NW1 and MW1, providing a steel ratio of 0.26 percent. The mechanical properties of the rebars are also shown in Table 1. These values are based on the average of three samples. 2.3 Specimens The dimensions and reinforcement for each of the specimens are presented in Fig. 1. Since all six specimens were reversed cyclic loaded, the tie spacing was determined according to the seismic shear design requirements specified in Chapter 21 of the ACI code [2]. The first letter N or M in the specimen designation stands for normal- or middle high-strength concrete, respectively. The second letter F or W refers to frame or frame-wall structure, respectively. The last number 1 or 3 represents mm or mm of cross section in the beam and column, respectively. 2.4 Instrumentation Fig. 2 shows the test set-up and the locations of strain gages on the longitudinal steel in the beam. A total of eight gages was used in each specimen. Four gages (two in front, two in back) are in each of the two critical sections of the beam. The horizontal displacement of the specimen was measured using six linear variable differential transducers (LVDTs), as shown in Fig. 2. The LVDT signal of the servo-controlled testing was used to control the tests. The horizontal force was measured by a 500 kn load cell. 2.5 Testing All six specimens were tested under reversed cyclic loads with the displacement history shown in Fig. 3. The number of the scheduled cycles for each specimen is 28. At the base of each specimen, a reinforced concrete foundation was attached, which prevented the supports from rotating. This mechanism made the specimen fixed at the base. Actual testing started with the application of horizontal load following the displacement history shown in Fig. 3. All test data were collected by a data acquisition system at a sampling rate of 50 Hz. Fig.1b Dimensions and reinforcement of all specimens (cont d). for all six specimens are examined first. The hysteretic loops under reversed cyclic loads are discussed next. The failure mode of each of the six specimens is then described. Finally, the theoretical predictions are compared with the experimental results. 3.1 Primary curves The primary curves of all six specimens are the envelope curves of the hysteretic loops. Using the primary 3. TEST RESULTS Results are presented here primarily in the form of horizontal force-displacement relationships. The test results are summarized in Table 2. The primary curves Fig. 2 Test set-up. 611

4 Materials and Structures/Matériaux et Constructions, Vol. 31, November 1998 Fig. 3 Displacement history. curves, the effects of concrete strength, section size and wall on the structures are discussed in this section. It can be seen from Fig. 4 that the maximum horizontal force increases with increasing concrete strength. Before yielding of the rebars, the specimens with higher concrete strength have greater stiffness. Also for the specimens with higher concrete strength, the displacements at the maximum horizontal forces are greater. It can be seen from Fig. 5 that when the greater section is used, the maximum horizontal force is greater, the displacement corresponding to the maximum horizontal force is smaller, and the stiffness after the maximum horizontal force decreases faster. It can be seen from Fig. 6 that the specimens with wall have much greater maximum horizontal forces and much smaller displacements. In other words, the walls result in greater stiffness and smaller ductility of the specimens. Since the ductility factor has multiple connotations [8], it is defined as the displacement at the maximum horizontal force divided by the yield displacement. The ductility factor of each of the six specimens is also shown in Table 2. It can be seen from Table 2 that the ductility factor increases with increasing concrete strength and decreases when a wall is added to the frame. Also, the ductility factor increases with an increasing section size. 3.2 Hysteretic loops The hysteretic loops for all six specimens under reversed cyclic load tests are shown in Fig. 7. It can be seen from Fig. 7 that the pinching effect increases with increasing section size (Specimens NF3 vs. NF1 and MF1 vs. MF3) and the pinching effect is even more obvious when a wall is added to the frame (Specimens NW1 vs. NF3 and MW1 vs. MF3). The dissipated energy is determined by calculating all the areas enclosed by the hysteretic loops. It can be seen from Table 2 Fig. 4 Effect of concrete strength. Table 2 Experimental results Specimen V c δ c (mm) V y (kn) δ y (mm) V u (kn) δ u (mm) D.F. Dissipated energy (kn) (mm) (kn) (mm) (kn) (mm) (kn-mm) NF NF MF MF NW MW Notes: V c = Cracking force; δ c = Cracking displacement; V y = Yielding force; δ y = Yielding displacement; V u = Maximum force; δ u = Displacement at maximum force; D.F. = Ductility factor. 612

5 Mo, Kuo Fig. 5 Effect of section size. and Fig. 7 that the dissipated energy increases with increasing concrete strength and decreases when a wall is added to the frame. Also, the dissipated energy increases with an increasing section size. 3.3 Failure Modes The failure modes of all six specimens are shown in Table 2. Basically, the failure modes for the six specimens can be classified into two types, namely flexural failure (due to the occurrence of four plastic hinges in the critical sections) and shear failure (due to the concrete crushing in the wall). Fig. 8a indicates the crack pattern and failure mode of specimen NF3. The remaining specimens without wall have the same crack pattern and failure mode as specimen NF3. It can be seen from Fig. 8a that the failure of specimen NF3 results from four plastic hinges (two in the beam-column connections and two at the bottom of the columns). Fig. 8b indicates the crack pattern and failure mode of Specimen NW1. specimen MW1 has the same crack pattern and failure mode as specimen NW1. It can be seen from Fig. 8b that the failure of specimen NW1 results from the concrete crushing of the wall. Fig. 6 Effect of wall. 3.4 Comparison of analytical models with experimental results The trilinear theory for frame analysis, the softening truss model for frame-wall analysis and the IDARC program for analyses of both frames and frame-wall structures are compared with experimental results in this section. The comparison of analytical models with experimental results is shown in Tables 3 and 4 for frames and framewall structures, respectively. Fig. 9a also indicates the horizontal force-displacement relationships of specimen NF1. In Fig. 9a, the experimental results are represented by a solid curve, and the results from both the trilinear theory and the IDARC program are represented by a dashed curve and a dotted curve, respectively. It can be seen from Fig. 9a and Table 3 that the trilinear theory is in very good agreement with the experimental results throughout the loading history; however, the stiffness prediction of the IDARC program is much less than the experimental results, although the maximum horizontal force predicted by IDARC is also very close to the experimental resuts. Fig. 9b indicates the horizontal force-displacement relationships of specimen MW1. Similar to specimen NF1, in Fig. 9b the experimental results, the results predicted by both the softening truss model and the IDARC program are represented by a solid curve, a dashed curve and a dotted curve, respectively. It can be seen from Fig. 9b and 613

6 Materials and Structures/Matériaux et Constructions, Vol. 31, November CONCLUSIONS Fig. 7 Hysteretic loops of all specimens. Table 4 that the maximum horizontal force predicted by the softening truss model is close to the test data. However, the stiffness predictions by both the softening truss model and the IDARC program overestimate the test value. In other words, the displacement prediction for frame-wall structures needs to be studied further. 1. When a wall is added to the frame, the maximum horizontal force will greatly increase and the drift will greatly decrease. However, the ductility factor and dissipated energy for framewall structures are less than those for frames. 2. When the section size increases in the frame structures, the maximum horizontal force, the ductility factor and the dissipated energy will increase, and the displacement will decrease. 3. When the concrete strength increases in the frames and frame-wall structures, the maximum horizontal force, the ductility factor and the dissipated energy will increase, and the displacement will decrease. 4. For frames, the pinching effect increases with increasing section size and becomes even more obvious when a wall is added to the frame. 5. For frames, the horizontal force-displacement relationship predicted by the trilinear theory is in good agreement with the test data. However, the IDARC program can only give good agreement of the maximum horizontal force with the test value; it provides greater deviation in the displacement prediction. 6. For frame-wall structures, the maximum horizontal force predicted by the softening truss model is in good agreement with the test value, and the prediction of stiffness overestimates the test result. The horizontal force-displacement relationship predicted by the IDARC program gives greater deviation from the test data. 7. Based on the research reported in this paper, the displacement prediction for frame-wall structures needs to be studied further. 614

7 Mo, Kuo Fig. 8 Crack patterns and failure modes. Fig. 9 Comparison of theories with experimental results. Table 3 Ratios of experimental results to theoretical predictions for frames Specimen Test / Trilinear theory Test / IDARC V y δ y V u δ u D.F. V y δ y V u δ u D.F. NF NF MF MF Average Covariance See notes from Table 2 for abbreviations. Table 4 Ratios of experimental results to theoretical predictions for frame-wall components Specimen Test / Softening truss model Test / IDARC V y δ y V u δ u D.F. V y δ y V u δ u D.F. NW MW Average Covariance See notes from Table 2 for abbreviations. ACKNOWLEDGMENT The research reported in this paper was financially supported by a grant from the National Science Council, NSC P , Taiwan. REFERENCES [1] Fintel, M., Performance of buildings with shear walls in earthquakes of the last thirty years, PCI Journal 40 (3) (1995) [2] ACI , Building Code Requirements for Structural Concrete and Commentary (Detroit, American Concrete Institute, 1995). [3] UBC 1991, Uniform Building Code (International Conference of Building Officials, Whittier, California, USA, 1991). [4] Mo, Y. L., Investigation of reinforced concrete frame behavior-theory and tests, Magazine of Concrete Research 44 (160) (1992) [5] Mo, Y. L. and Rothert, H., Effect of softening models on behavior of reinforced concrete framed shearwalls, ACI Structural Journal 94 (6) (1997) [6] Vecchio, F. J. and Collins, M. P., Compression response of cracked reinforced concrete, Journal of Structural Engineering, ASCE 119 (12) (1993) [7] Valles, R. E., Reinhorn, A. M., Kunnath, S. K., Li, C. and Madan, A., IDARC2D Version 4.0: A Computer Program for the Inelastic Damage Analysis of Buildings, Technical Report NCEER (National Center for Earthquake Engineering Research, USA, 1996). 615