Keywords: shear, confinement, retrofitting, biaxial loading, columns, reinforced concrete, non-linear analysis, seismic, fibre-reinforced polymer.

Reinforced concrete columns can be subjected to combined biaxial bending, shear and axial forces, particularly under seismic actions. The actual response of such elements is complex, due to the coupling between the normal and shear forces and to the three-dimensional phenomena taking place. Moreover, in some built structures, poor detailing of the transverse reinforcement may exist, and thus a brittle shear failure can be expected. In this context, plane sectional analysis based on fibre discretization with one-dimensional behaviour may not produce plausible results. Thus, analytical models capable of capturing the above phenomena are needed for a safe and rational design and assessment.

In this paper, the response of reinforced concrete columns under different loading conditions including biaxial loading, biaxial shear and the effects of confinement of the transverse reinforcement is investigated by means of a non-linear coupled analytical model. The model uses a particular functional equation to achieve internal three-dimensional equilibrium among cross-section fibres and considers section's distortion and warping in order to obtain full three-dimensional tensors of strain and stress [1]. Materials constitutive models considered are, in general, three-dimensional. Most three-dimensional aspects involved in the above mentioned phenomena can be captured by means of a cross-sectional model. The concrete constitutive model described in [2] is considered in this study.

The case studies investigated analyses the effect of confinement and shear forces under biaxial loading where the influence of stirrups distribution is captured by the model. An experimental study [3] in which columns with poor transversal reinforcement fail in shear or are retrofitted with external fibre-reinforced polymer (FRP) jacketing is reproduced by the model. The model is proved to be capable of correctly predicting the performance of the original specimen which had brittle failure with yielding of the transversal reinforcement due to shear force. The performance of the retrofitted specimens was also captured correctly including the stress and strain distribution of FRP and the assistance of the original transversal reinforcement. Capturing these phenomena by a cross-section model is a novel application of frame element modelling, which enables failure modes with the relevant three-dimensional influence to be determined.

1

J.M. Bairán, A.R. Marí, "Coupled model for the nonlinear analysis of anisotropic sections subjected to general 3D loading. Part 1: Theoretical formulation", Computers & Structures, 84(31-32), 2254-2263, 2006. doi:10.1016/j.compstruc.2006.08.036

2

J.M. Bairán, A.R. Marí, "Multiaxial-couped analysis of RC cross-sections subjected to combined forces", Eng. Structures, 29, 1722-1738, 2007. doi:10.1016/j.engstruct.2006.09.007

3

Y. Xiao, H. Wu, G.R. Martin, "Prefabricated composite jacketing of RC columns for enhanced shear strength", ASCE J. of Structural Eng., 125(3), 1999. doi:10.1061/(ASCE)0733-9445(1999)125:3(255)

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