The effect of cyclic loading on the nonlinear response of structural concrete members with arbitrary cross-sectional shapes

This paper presents a numerical methodology for analysis of the behaviour of structural concrete sections subjected to cyclic loading. Classical beam theory was utilised to calculate sectional deformations (strain and curvature) under normal force and biaxial moment, while a nonlinear sectional analysis is performed via computer software written in Python by discretising the section of any shape, that is a combination of polygons and circles, into infinitesimal triangles or quadrilaterals. The stress-strain relationship of concrete and steel materials under monotonic loading was also implemented to evaluate the concrete’s secant modulus of elasticity at any strain level. A concrete cyclic model representing stress-strain relationships during unloading is thus proposed in which the secant modulus of elasticity of each mesh element is modified based on the stress level attained at the start of the unloading stage. Cyclic behaviour in tension and compression was investigated, including the transition from compression to tension and vice versa. The cyclic model was then implemented in sectional analysis to allow computation of the behaviour of the section at different loading stages. This study also proposes a new technique to calculate residual deformation during each analysis step and thus to plot the hysteresis behaviour of the section. Software was thus developed to estimate the failure load and produce a biaxial moment-curvature diagram, interaction diagram, and stress-strain diagram across the depth of the section for each load case.