Keywords: cyclic behaviour, pinching effect, average stress-strain, cracking, nonlinear analysis, reinforced concrete.

Since reinforced concrete (RC) shear walls are frequently used to provide lateral stiffness for resisting horizontal forces such as earthquake excitations, they should be furnished with adequate deformation and energy dissipation capacity for ductile response. For seismic design when the primary objective is to insure adequate deformation capacity at a given shear stress level, it is necessary to determine design parameters affecting strength and deformation capacities of RC shear walls. Hence, many experimental and analytical studies for predicting the nonlinear behavior according to load reversals and for computing the ultimate resistance with hysteretic response of isolated RC shear walls have been performed [1,2,3].

In contrast, numerical models for FE analyses of RC shear walls, which can provide accurate simulations of cracking behavior under severe loading conditions such as seismic loadings and reversed cyclic loadings, are somewhat less commonly used due to the complexities in the modeling of reinforced concrete composite material after cracking of concrete and yielding of steel.

In advance, RC structures representing shear dominant structural behavior show pinched hysteresis responses, which mean poor energy absorption capacities and stiffness degradation as the number of cycles increases. The design procedures for RC shear walls, however, do not take into account these key features of hysteretic response [3]. There is no design code that mentions any criterion requested to reserve the ultimate resisting capacity and the corresponding ductility for a RC shear wall subject to cyclic loadings. Based on these aspects, nonlinear FE analysis considering shear deformation effect is definitely required. Moreover, it may be necessary for an enhanced evaluation of hysteretic behavior to model each constituent material and interaction between reinforcing steel and concrete appropriately with complex hysteretic stress-strain relationships.

This paper presents an analytical model for RC shear walls subject to general in-plane loading. The rotating crack assumption is adopted, and simple hysteretic stress-strain curves of concrete and reinforcing steel are introduced. In addition, to consider the shear stiffness degradation visualized as a pinching phenomenon in a hysteretic relation of low-rise shear wall, a direct modification of a hysteretic stress-strain relation of steel is suggested by referring to the existing moment-curvature model which takes into account the pinching effect according to the shear span length [4,5]. The developed numerical model is validated through comparison of the obtained numerical results with experimental data for two idealized orthogonally reinforced concrete shear panels subject to cyclic loadings [6]. In addition, to assess the applicability of the material model under different stress conditions, hysteretic load-deformation relationships obtained are compared with cyclic shear wall test results [2,7].

1

Penelis GG, Kappos AJ. Earthquake-resistant concrete structures. London: E & FN SPON, 1997.

2

Oesterle RG, Fiorato AE, Johal LS, Carpenter JE, Russell HG, Corley WG. Earthquake resistance structural walls-tests of isolated walls. Skokie, Illinois: Construction Technology Laboratories, Portland Cement Association, 315 p. 1976.

3

Sittipunt C, Wood SL. Influence of web reinforcement on the cyclic response of structural walls. ACI Struct. J. 1995;92:745-756.

4

CEB. RC elements under cyclic loading: state of the art report. London: Thomas Telford Services Ltd., 1996.

5

Roufaiel MSL, Meyer C. Analytical modeling of hysteretic behavior of R/C frames. J. Struct. Eng. ASCE 1987;113:429-444. doi:10.1061/(ASCE)0733-9445(1987)113:3(429)

6

Stevens NJ, Uzumeri SM, Collins MP. Reinforced concrete subjected to reversed cyclic shear-experiments and constitutive model. ACI Struct. J. 1991;88:135-146.

7

Cervenka V, Gerstle KH. Inelastic analysis of reinforced concrete panels, part II: experimental verification and application. In: IABSE, Proceedings of International Association for Bridge and Structural Engineering, 1972. Vol. 32-II, p. 25-39.

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