Many reinforced concrete structures, e.g. shear walls, beams, box bridges, nuclear containment vessels, concrete offshore structures can be visualized as assemblies of reinforced concrete membrane elements, or called plane stress elements. Using the nonlinear finite element method, the behavior of these structures subjected to monotonic, reversed cyclic and dynamic loading can be simulated if the accurate constitutive models of reinforced concrete are applied.
Large amount of the experimental studies to establish the constitutive relationships of reinforced concrete have been conducted at the University of Houston over the past two decades. The full-size reinforced concrete panels subjected to shear and normal stresses have been tested using the universal panel tester (Hsu et al., 1995). From the experimental behavior of reinforced concrete elements, a series of three monotonic models and one cyclic model have been developed. The three monotonic models are the rotating-angle softened truss model (RA-STM) (Hsu, 1993; Belarbi and Hsu, 1994, 1995; Pang and Hsu, 1995), the fixed-angle softened truss model (FA-STM) (Pang and Hsu, 1996; Hsu and Zhang, 1997), and the softened membrane model (SMM) (Hsu and Zhu, 2001; Hsu and Zhu, 2002). The cyclic model is the cyclic softened membrane model (CSMM) (Mansour and Hsu, 2003).
The RA-STM assumes cracks will develop in a direction parallel to the principal compressive stresses of concrete, in contrast, the FA-STM assumes cracks will develop along the direction of principal compressive stresses of the applied stresses. The advantage of FA-STM is that it is capable of taking into account the concrete contribution along the cracks. Both RA-STM and FA-STM can predict the prepeak ascending branches of the response curves, but not the postpeak descending branches. This is because that the stresses and strains due to the Poisson effect were neglected. To take into account the Poisson effect, Zhu and Hsu (2002) performed the RC panel tests under shear loading to determine the Hsu/Zhu ratios. By using the Hsu/Zhu ratios, the SMM was proposed to predict the entire monotonic shear stress - shear strain curves of reinforced concrete panels, including both the ascending and the descending branches (Hsu and Zhu, 2002). In addition, the constitutive relationship of concrete in shear was established using a simple and rational shear modulus (Zhu, Hsu and Lee, 2001). CSMM was developed to extend the SMM for prediction of the behavior of RC elements under reversed cyclic loading. Taking into account the interaction of normal and shear stresses, CSMM has been generalized recently.
By adopting the finite element framework OpenSEES (Fenves, 2001), the generalized CSMM is implemented and a nonlinear finite element program is developed to predict the behavior of RC structures under monotonic, reversed cyclic or dynamic loading. Nonlinear finite element analysis of ten test shear walls under cyclic loadings was conducted, and the comparison between the experimental data and predicted results shows very good agreement.