Nonlinear multilevel analysis of reinforced concrete frames

Full range analysis of reinforced concrete (RC) members covering the post-crack and post-peak regimes is important for obtaining the deformation response and failure mode of structural members. When a RC member is subject to an increasing external load, the critical sections would exhibit cracking and/or softening. Due to stress relief effect in the proximity of crack opening and plastic hinging, unloading may occur at the adjacent regions. The variable stress states of discrete sections would lead to sectional variation of stiffness, which could not be accounted for by conventional structural analysis methods. In this paper, a nonlinear multilevel analysis method for RC frames whereby the frame members are divided into sub-elements and sectional analysis is utilised to evaluate stiffness degradation and strength deterioration is developed. At sectional level, the secant stiffness is determined from moment-curvature relation, where the curvature is evaluated based on both transverse displacements and section rotations of the frame member. Unloading and reloading behaviour of concrete and reinforcing steel is simulated. In implementing the multilevel analysis, secant iteration is performed in each step of displacement increment to obtain the convergent solution satisfying equilibrium. Numerical example of RC frame is presented to demonstrate the applicability and accuracy of the proposed nonlinear multilevel analysis method.