Nonlinear multilevel analysis of reinforced concrete beams

Abstract

A nonlinear multilevel analysis method for reinforced concrete beams whereby the members are divided into sub-elements and sectional analysis is utilised to evaluate stiffness degradation and strength deterioration is developed. When a reinforced concrete member is subjected to an increasing load, the critical section starts to crack and softens, whereas unloading may occur at the adjacent sections. In order to calculate the actual displacements of beams, it is necessary to obtain the stiffness of various discrete sections by sectional analysis. At sectional level, the secant stiffness is determined from moment-curvature relation, in which the curvature is evaluated based on both transverse displacements and section rotations of the member. Unloading and reloading behaviour of concrete and steel reinforcement is simulated. In carrying out multilevel analysis, in each increment step of displacement, secant iteration is performed to obtain the convergent solution satisfying equilibrium. Examples are included to demonstrate the applicability of the multilevel analysis in predicting the nonlinear load-deflection response of concrete beam with varying reinforcement ratios. © 2007 Civil-Comp Press.