Non-Linear Behaviour Modelling of RC Panels Subjected to In-Plane Loads

Reinforced concrete panels find widespread use in many engineering structures and accurate prediction of their structural behaviour is important in achieving a safe structural design. The shear strengths of these panels depend strongly on the softening of concrete struts in the principal compression direction due to the principal tension in the orthogonal direction. Intensive investigations of the nonlinear structural behaviour of RC panels and shear walls by finite elements method have been reported in the last decades. Despite commendable progress made in developing new computational methods, accurate and efficient prediction of both the overall load-deflection and the local stress-strain cyclic responses of RC panels is still challenging because of the complicated nonlinear behaviour of these structures, especially in the case of coupled in-plane membrane-shear nonlinear behaviours. The main issues are the development of proper finite element models and the enhancement of effective constitutive laws for concrete, for reinforcement and for their interactions.\nMany finite element models have been developed for the nonlinear analysis of RC elements and generally there are three types of models: the discrete model, the smeared-crack model, and the layered model. In the discrete approach [1]-[2], the concrete and steel reinforcement are modelled separately by two different types of finite elements. The creation of discrete models can be quite difficult especially for complex structures. Since a large number of degrees of freedom are generated in the discrete model, it is significantly less efficient, which is of particular concerns in the nonlinear analysis of these structures [2]. In the smeared-crack model [3]-[4], the cracking of concrete and the degradation of its material properties are considered by using averaged stress-strain relationships, that are established directly from full-scale biaxial tests. The resulting models turn out to have low computational efficiency or even to cause numerical instability. The layered approach has been widely used for FE analysis of RC structures, and it has been demonstrated to be effective, particularly in predicting the cracking and the ultimate behaviour of RC panels and slabs in bending and shear [5]-[6]. In this model, the element is formulated by assembling a finite number of concrete layers and equivalent smeared steel layers. Each layer may have different material properties corresponding to its particular material states, and the material properties of each layer are usually assumed to be constant throughout the thickness of the layer. In this case the material constitutive laws for general stress states can follow analytical approaches as the theory of fracture and the theory of continuum damage mechanic. For out-of-plane loaded slabs, cracking and crushing of concrete and yielding of reinforcement through the thickness of the cross-section can be monitored progressively using the layered model, thereby providing an accurate and realistic representation of the structural behaviour [6].\nThe aim of the work herein is the investigation of the nonlinear modelling of reinforced concrete panels by means of a concrete constitutive law based on damage mechanics applied to a layered quadrilateral element. The concrete constitutive law, that took its bases on the works of Faria et al. [7], Lee et al. [8], Berto et al. [9], is presented in its general formulation having the possibility to represent softening isotropic and orthotropic material behaviour. The tensile branch takes into account the concrete energy of fracture and the tension-stiffening effects. A particular effort has been made to improve the convergence speed through the definition of an adequate secant material stiffness matrix. For what concerns the reinforcing steel, in sake of simplicity, a simple elastic-plastic law has been used with both kinematic and isotropic hardening. The material models have been implemented in the finite open source code Opensees of the University of California, Berkeley [10]. The already implemented quadrilateral layered element has been enhanced with the possibility of taking into account more than one nonlinear material.\nThe validation of the proposed model has been made by comparison with entire experimental sets such as Bhide and Collins [11] and Mansour and Hsu [12]. These test campaigns have been chosen for representing a wide range of coupled membrane-shear nonlinear behaviours. In particular Bhide and Collins [11] carried out 32 tests on square panels applying combined tension, compression and shear stressed on their edge whereas Mansour and Hsu [12] presented 12 full-size reinforced concrete panel tests investigating the behaviour of reinforced concrete membrane elements under reversed cyclic shear stresses. These last set outlined the effects of the variation of angle of steel bar orientation with respect to the applied principal vertical stress and different percentages of reinforcing steel in the panels. The results of the numerical simulations are presented critically with the aim of showing the achievements and the model drawbacks in order to clearly delineate the future developments. The model showed its ability to interpret the experimental evidences especially in uniaxial stress states, biaxial compression and biaxial tension both locally and discretely, but it demonstrated the need of improvements on biaxial tension-compression due to its simplified definition of the damage limit surface in these stress regions.\n\nReferences \n[1]\tNonlinear analysis of reinforced concrete slabs by a discrete finite element approach, J. Jiang, F.A. Mirza, Comput. Struct. 65 (4), 585–592, 1997.\n[2]\tNonlinear finite element for reinforced concrete slabs, K. Phuvoravan, E.D. Sotelino, J. Struct. Eng., ASCE 13 (4), 643–649, 2005.\n[3]\tThe modified compression field theory for reinforced concrete elements subjected to shear, F.J. Vecchio, and M.P. Collins, ACI Journal, 83 (2), 219-231, 1986.\n[4]\tMultiscale modeling of reinforced/prestressed concrete thin-walled structures, A. Laskar, J. Zhong, Y.L. Mo, T.T.C. Hsu, Interaction and Multiscale Mechanics, 2 (1), 69-89, 2009.\n[5]\tCracking and punching shear failure analysis of RC flat plates, Y.C. Loo, H. Guan, J. Struct. Eng., ASCE 123 (10), 1321–1330, 1997.\n[6]\tA layered shear-flexural plate/shell element using Timoshenko beam functions for nonlinear analysis of reinforced concrete plates, Y.X. Zhang, M.A. Bradford, R.I. Gilbert, Finite Elements Analysis and Design, Elsevier, 43, 888-900, 2007.\n[7]\tA strain-based plastic viscous-damage model for massive concrete structures, R. Faria, J. Oliver, M. Cervera, International Journal of Solid and Structures, 35, 1533-1558, 1998.\n[8]\tPlastic-Damage Model for Cyclic Loading of Concrete Structures, J. Lee, L. Fenves, J. Eng. Mech., ASCE, 124 (8), 892-900, 1998.\n[9]\tAn orthotropic damage model for masonry structures, L. Berto, A. Saetta, R. Scotta, R. Vitaliani, International Journal for Numerical Methods in Engineering, 55 (2), 127-157, 2002.\n[10]\tAnnual workshop on Open System for Earthquake Engineering Simulation, L. Fenves, Pacific Earthquake Engineering Research Center, UC Berkeley, 2005.\n[11]\tReinforced concrete elements in shear and tension, S.B. Bhide, M.P. Collins, University of Toronto, Publication n. 87-02, 1987.\n[12]\tBehavior of Reinforced Concrete Elements under Cyclic Shear. I: Experiments, M. Mansour and T.T.C. Hsu, J. Structural Engineering, ASCE, 131 (1), 44-53, 2005.

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