Experimental studies on low-rise structural walls

Transcription

1 Materials and Structures/Matériaux et Constructions, Vol. 31, August-September 1998, pp Experimental studies on low-rise structural walls Y. L. Mo 1 and J. Y. Kuo 2 1) Professor, Dept. of Civil Eng., National Cheng Kung University, Tainan, Taiwan. 2) Graduate Student, Dept. of Civil Eng., National Cheng Kung University, Tainan, Taiwan. SCIENTIFIC REPORTS Paper received: February 28, 1997; Paper accepted: May 13,1997 A B S T R A C T Based on equilibrium and compatibility conditions, as well as a softening stress-strain relationship for concrete, a truss model theory was presented to predict the behavior of low-rise structural walls under static loads. In this paper, shake table tests on low-rise structural walls are performed, so that the previously proposed truss model theory can be examined by the test results, and the effect of acceleration frequency on such walls is studied. It is found that both the experimental ductility and dissipated energy decrease with increasing acceleration frequency, and when such walls are subjected to dynamic forces, the static truss model theory can be used for the prediction of the shear strength, but not for the prediction of the displacement at the maximum shear force. R É S U M É Un modèle théorique de treillis, basé sur les conditions d équilibre et de compatibilité, ainsi que sur la relation contrainte-déformation de radoucissement du béton, a été présenté afin de prédire le comportement des murs porteurs à hauteur limitée sous charge statique. Dans cet article, des essais sur de tels murs ont été réalisés sur table à secousses, afin de comparer les résultats des essais avec le modèle théorique précédemment proposé, et d étudier l effet de la fréquence de l accélération sur de tels murs. On a constaté que la ductilité expérimentale et l énergie dissipée décroissent avec l accroissement de la fréquence d accélération. Lorsque de tels murs sont soumis à des forces dynamiques, le modèle théorique de treillis statique peut être utilisé pour prédire la résistance au cisaillement, mais ne peut pas prédire le déplacement de l effort tranchant maximal. 1. INTRODUCTION During the earthquakes of the last three decades, buildings incorporating shearwalls have exhibited very satisfactory earthquake performance [1-3]. Such walls are used in a variety of buildings and can be divided into two groups: (1) the high-rise shearwalls and (2) the lowrise shearwalls. A high-rise shearwall is governed by flexural behavior and its behavior is readily predictable. In contrast, the behavior of a low-rise shearwall is governed mainly by shear which is more difficult to predict. In [4] a static theory is presented to predict the shear behavior of low-rise shearwalls. The theory uses the truss model concept coupled with a softening stressstrain relationship of concrete. When compared to the test results of 24 low-rise walls available in the literature [5-8], the theory was shown to predict the shear strength, shear distortion, steel strains, and concrete strains with acceptable accuracy throughout the loading history. The theory applies to low-rise shearwalls with a height-to-width ratio less than unity. The shearwalls are assumed to have boundary columns that are strong enough to resist the applied bending moment and the shear force without premature failure, which means that bending failure and sliding-shear failure will not occur. Within these limitations, the mean value and the standard deviation of the test-to-calculated shear-strength ratio of the wall tests described in [4] are and 14.7 percent, respectively. In [4], the behavioral history of the low-rise shearwalls is traced by solving a set of simultaneous equations iteratively. Such a trial-and-error method is suitable for analysis but not for design purposes. In [9] it is shown that a direct solution without iteration can be developed to predict the behavioral history. In particular, shear strength can be explicitly represented in simple forms. Based on these representations, a set of design recommendations is proposed in [9]. The design recommendations given in [9] can be used for static loads but are not applicable to dynamic loads. The response analysis of low-rise structural walls subjected to dynamic shear forces requires a realistic conceptual model that accounts for the continually varying stiffness and energy absorbing characteristics of such walls. Therefore, the purpose of this paper is to describe the results of shake table tests on such walls as a basis for the development of a dynamic analytical model. Further, the effect of acceleration frequency on such walls is also studied /98 RILEM 465

2 Materials and Structures/Matériaux et Constructions, Vol. 31, August-September STATIC ANALYSIS The softened truss model theory for low-rise structural walls [4] consists of three parts and is summarized below. 2.1 Equilibrium conditions Low-rise structural walls can be represented by the truss model shown in Fig. 1. From the equilibrium equations, the average shear stress τ and the angle of inclination of concrete struts α may be obtained in terms of the average stress in the concrete struts σ d : τ= σ d sin cos (1) cos 2 α = Af l l (2) btσd where A l = area of longitudinal steel; f l = stress of longitudinal steel; b = effective width of the wall; t = thickness of the wall. 2.2 Compatibility conditions The compatibility conditions of the truss model provide two basic equations. From these equations, the shear distortion in the wall γ and the strain in the longitudinal steel ε l in the wall may be obtained in terms of the compressive strain in the diagonal concrete struts ε d, as follows: γ ε α 2 = d tan ε = tan 2 α 1 ε l ( ) 2.3 Stress-strain relationship d Vecchio and Collins [11] tested 89 cm 89 cm 7 cm reinforced-concrete panels subjected to pure shear. From these tests a stress-strain curve was proposed for the softening diagonal concrete struts. For the ascending portion of the curve, the equation is: (3) (4) εd σ λ ε d d = fc 2 (5) εo 2 εo where f c = maximum compressive stress of a standard concrete cylinder; ε o strain at maximum compressive stress, usually taken as 0.002; and λ = coefficient for the softening effect (1/λ is defined as the softening coefficient). For the descending portion of the curve, the equation is: f ε ε c d p σd = 2 1 (6) λ 2εo ε p where ε p = ε o / λ. The coefficient λ is found from: εl + εt + 2εd λ = 03. (7) εd In addition, it is acceptable to assume that for lowrise structural walls the transverse steel strain ε t is zero [4]. Neglecting the small effect of the constant 0.3 in equation (7), and substituting equation (4) into equation (7), λ may be expressed in a simple form [4]. λ = 1 cosα 2.4 Solutions The relationships within the set of the seven quantities (τ, α, l, λ, σ d, γ and d ) may be obtained by assuming the value of one quantity, ε d, and solving the six equations (1-4, 5 or 6, and 8), as shown in Fig TEST PROGRAM 12 Four shake table tests were performed on one eighth small-scale low-rise framed shearwalls. The parameter of the tests is the input acceleration frequency to study its effect on the behavior of such walls. All the test walls had the same dimensions and reinforcement, as shown in Fig. 3. The last number in the specimen designation refers to the acceleration frequency (Table 1). (8) Table 1 Principal test results compared to theory Specimen f c V y,test V y,calc V y,test V u,test V u,calc V u,test δ y,calc δ u,test δ u,calc µ test µ calc Dissipated Failure V Energy (MPa) (kn) (kn) y,calc V (kn) (kn) u,calc Mode (mm) (mm) (mm) (kn-mm) H-HZ B H-HZ A H-HZ A H-HZ A Average Failure Mode A: The wall concrete crushed. Failure Mode B: The wall concrete had crushed; afterwards, steel anchorage of boundary element failed. 466

3 Mo, Kuo Fig. 1 Equilibrium of shearwall subjected to shear force. 3.1 Concrete The target compressive strength for the ready-mix concrete was 17 MPa in all the specimens due to the capacity limit of the shake table. Fifteen standard cylinders were cast with each pour and tested frequently to monitor concrete strength with age. The nominal maximum size of the coarse aggregate was 9.5 mm. 3.2 Reinforcement Deformed 12.7, 9.5 and 4 mm diameter bars were used in the specimens with yielding stresses of 226, 235 and 259 MPa, respectively. The 12.7 mm diameter bars were used in the boundary elements of the walls, while the 9.5 mm diameter bars were used in both the top beam and the bottom foundation. In the walls, the longitudinal steel consisted of four 4 mm diameter bars in each specimen, providing a steel ratio of percent of the effective area of the walls. Similarly, the transverse steel consisted of three 4 mm diameter bars in each specimen, providing a percent steel ratio. In other words, the steel ratios in both the longitudinal and transverse directions of the wall are greater than the ACI minimum requirement of 0.25 percent [12]. Fig. 2 Flow chart of the solution procedure for shearwall. 467

4 Materials and Structures/Matériaux et Constructions, Vol. 31, August-September 1998 at various locations in the specimen. Actual testing started with the excitation of the shake table to give the acceleration histories shown in Fig. 5. The frequencies of testing on Specimens H-HZ4, H-HZ6, H-HZ8 and H-HZ10 are 4, 6, 8 and 10 Hz, respectively. All the data were collected by a data acquisition system, and a continuous plot of the input acceleration history was observed from the monitor of the control system. 4. TEST RESULTS 4.1 Primary curves Fig. 3 Test specimen. 3.3 Instrumentation Fig. 4 shows the test configuration and the location of the transducers. Four strain gages were used for each specimen and were located in the two internal longitudinal rebars (Fig. 3). They were glued on the smooth-grinding surface of the reinforcing bars, so that the yielding of the steel can be measured with these strain gages. The horizontal displacement of the wall was measured at both the top plate and the bottom foundation using LVDTs. The fixation of LVDTs was very stiff to avoid the error of the displacement measurement. The LVDT at the bottom foundation was used to ensure that no foundation slip occurred during excitations. One accelerometer was attached to the top plate and the other to the foundation. To control the input acceleration another accelerometer was used on the shake table. Totally 800 kg mass was fixed by the screws at the top and bottom of the top plate to produce the inertia force and to remain within the capacity limit of 900 kg of the shake table. 3.4 Testing Details of the test setup are shown in Fig. 4. All the specimens were tested under horizontal excitations. Preparations before each test included alignment of the specimen and of strains, displacements, and accelerations The envelopes of hysteretic loops for all the four specimens are shown in Figs The theoretical predictions under monotonic loading according to [4] are also plotted in the corresponding figures. Before yielding of the bars, the theoretical curves in Figs. 6-9 are close to the corresponding test curves. In the ultimate state, the calculated shear strengths are also in good agreement with the experimental values. The average V u,test / V c,calc is 1.02 with a standard deviation of However, the calculated displacements at the maximum shear forces, δ u,calc, are always less than the experimental values, δ u,test, as shown in Table 1. It can also be observed from Table 1 that the effect of the acceleration frequency on the shear strength is not apparent. However, the effect of acceleration frequency on the displacement at the maximum shear force is significant because the displacement at the maximum shear force decreases with increasing acceleration frequency. In other words, when the walls are subjected to dynamic forces, the static truss model theory [4] can be used for the prediction of the shear strength but not for the prediction of the displacement at the maximum shear force. 4.2 Ductility and energy dissipation The effect of acceleration frequency on the walls can be observed from the ductility and energy dissipation, as shown in Table. 1. The calculated ductility, µ calc, is defined as the calculated displacement at the maximum shear force, δ u,calc, divided by the calculated displacement at the occurrence of steel yielding, δ y,calc. Similarly, the experimental ductility, µ test, is defined as the experimental displacement at the maximum shear force, δ u,test, divided by the calculated displacement at the occurrence of steel yielding, δ y,calc. Since the average yielding value of the measured strains of reinforcing bars was difficult to determine, the calculated value for yielding was used. It is noted that the maximum measured strain is Also, the experimental dissipated energy is determined by inte- 468

5 Mo, Kuo (b) Fig. 4 Test setup. grating the areas bounded by all the experimental hysteretic loops. The hysteretic loops for all four specimens are shown in Figs A few high points of each figure were used to draw the envelope because they represent the static horizontal force-displacement relationship. From Table 1 the following observations can be made: 1. The theoretical ductilities remain almost the same for all cases. 2. The experimental ductilities decrease with increasing acceleration frequency and are greater than the theoretical values. 3. Similar to ductility, the experimental dissipated energies also decrease with increasing acceleration frequency. However, it is not unlikely that the decrease of ductility and dissipated energy with increasing frequency is not caused by the higher frequency, but rather by the increase of damage associated with the larger number of loading cycles. Unfortunately, the tests have not been designed in a way so that the effects of frequency and number of cycles may be seperated. 4.3 Failure modes The failure modes of all four specimens are given in Table 1 and can be classified into two types, namely, concrete crushing (denoted by A in Table 1), as shown in Fig. 14, and concrete crushing followed by anchorage failure of boundary element (denoted by B in Table 1). It can be seen from Table 1 that specimen H-Hz4 needs longer development lengths of boundary element steel to avoid anchorage failure due to the occurrence of greater displacement at the ultimate state. 469

6 Materials and Structures/Matériaux et Constructions, Vol. 31, August-September 1998 Fig. 5 Acceleration histories. Fig. 6 Primary curves of specimen H-HZ4. Fig. 7 Primary curves of specimen H-HZ6. 470

7 Fig. 8 Primary curves of specimen H-HZ8. Fig. 9 Primary curves of specimen H-HZ10. Fig. 10 Hysteretic loops of specimen H-HZ4. Fig. 11 Hysteretic loops of specimen H-HZ6. Fig. 12 Hysteretic loops of specimen H-HZ8. Fig. 13 Hysteretic loops of specimen H-HZ

8 Materials and Structures/Matériaux et Constructions, Vol. 31, August-September 1998 Sheu, Professor G. Yao and Professor D. S. Hsu, at National Cheng Kung University, are acknowledged for their generous support of this experimental study. REFERENCES Fig. 14 Ultimate state of specimen H-HZ8. 5. CONCLUSIONS 1. When low-rise framed shearwalls are subjected to dynamic forces, the static truss model theory can be used for the prediction of the shear strength, but not for the prediction of the displacement at the maximum shear force. 2. Both the experimental ductility and dissipated energy decrease with increasing acceleration frequency. 3. Longer development lengths of boundary elements to avoid anchorage failure are needed due to the occurrence of greater displacement at the ultimate state when the walls are subjected to dynamic forces. 4. The primary curve of the walls needs to be studied further considering dynamic effects. ACKNOWLEDGMENTS Support for this research by the National Science Council, Taiwan, ROC, under grant NSC P B, is gratefully acknowledged. Professor M.S. [1] Fintel, M., Performance of buildings with shear walls in earthquakes of the last thirty years, PCI Journal 40 (3) (May-June 1995) [2] Ghosh, S. K., Observations on the performance of structures in the Kobe earthquake of January 17, 1995, Ibid. (March-April 1995) [3] Iverson, J. K. and Hawkins, N. M., Performance of precast/prestressed building structures during Northridge earthquake, Ibid. 39 (2) (March-April 1994) [4] Hsu, T. T. C. and Mo, Y. L., Softening of concrete in low-rise shearwalls,, ACI Journal, Proceedings 82 (6) (Nov.-Dec. 1985) [5] Barda, F., Shear Strength of Low-rise Walls with Boundary Elements, PhD thesis, Lehigh University, Bethlehem, 1972, 265 pp. [6] Barda, F., Hanson, J. M. and Corley, W. G., Shear Strength of Low-Rise Walls with Boundary Elements, Reinforced Concrete Structures in Seismic Zones, SP-53, American Concrete Institute, Detroit, 1977, [7] Galletly, G. D., Behavior of Reinforced Concrete Shear Walls Under Static Load (Department of Civil and Sanitary Engineering, Massachusetts Institute of Technology, Cambridge, Aug. 1952) 123 pp. [8] Benjamin, J. R. and Williams, H. A., The behavior of one-story reinforced concrete shear walls, Proceedings, ASCE, ST3, (May 1957) [9] Mau, S. T. and Hsu, T. T. C., Shear design and analysis of lowrise structural walls, ACI Journal Proceedings 83 (2) (Mar.-Apr. 1986) [10] Mo, Y. L., Analysis and design of low-rise structural walls under dynamically applied shear forces, ACI Structural Journal 85 (2) (March-April 1988) [11] Vecchio, F. and Collins, M. P., Stress-strain characteristics of reinforced concrete in pure shear, Final Report, IABSE Colloquium on Advanced Mechanics of Reinforced Concrete, International Association for Bridge and Structural Engineering, Zürich, 1981, [12] ACI Committee 318, Building Code Requirements for Reinforced Concrete (ACI 318-9), American Concrete Institute, Detroit,