Geometric and Material Nonlinear Analysis of a RC Foot-Bridge

To deal with the safety problems with regard to the failure of reinforced concrete (RC) foot-bridge, it is necessary to know the ultimate deformations, that the failure calculation based on the principles of limit analysis does not allow taking into account. In this study, we develop a method of nonlinear analysis of plane RC frames based on the displacement method. Nonlinearity is considered under its two aspects, material and geometric. The foot-bridge is discretized into one-dimensional finite elements connecting two nodes and the loading is applied, step by step, until the structural failure. For the equilibrium state of the structure, an iterative procedure is used at each step of increase in loading where the nonlinear system is solved by using the method of successive substitutions based on the stiffness matrix connecting the increases of applied forces to the increases of nodal displacement. The influence of the tensile concrete between the cracks is taken into account in order to correctly assess the displacements under external loads and the redistribution of stresses. An automatic calculation program is thus developed. The developed method is applied to a practical example of a foot-bridge realized in Bordj Bouararidj (Algeria), whose dimensioning is realistic. The comparison of the numerical results obtained with the mathematical model and those obtained with Abaqus^© software is satisfactory and shows a very good agreement.