Nonlinear finite element analysis of reinforced concrete beams

Abstract

A nonlinear finite element program to simulate the behavior of reinforced concrete (RC) members under the action of monotonic increasing loading has been developed. The nonlinear response of the RC members is mainly due to the nonlinear material characteristics including nonlinear biaxial stress-strain relations and cracking of concrete and yielding of steel reinforcement.

A constitutive model of concrete under biaxial stress state is adopted in this thesis. In this model, concrete fails and critical cracks occur when the tensile strain of concrete exceeds the limiting tensile strain. The complete stress-strain relationship of concrete under compression and tension are employed in the study to investigate the post-peak behavior of reinforced concrete members. An elaborate cracking model has been implemented which allows concrete to crack in one or two directions. The tension stiffening effect of cracked concrete is also incorporated into this model by including a descending branch in the stress-strain curve of concrete under tension. Other nonlinear effects such as crushing of concrete in compression and yielding or strain hardening of steel reinforcement are also taken into account.

A nonlinear finite element program was developed, in which the abovementioned nonlinear effects have all been included in modeling the reinforced concrete structures. The nonlinear equations of equilibrium are solved using an incremental-iterative technique performed under displacement control. The validity of the model including the confinement effect of secondary reinforcements has been examined by analyzing three reinforced concrete beams. The performance of the numerical model was assessed by comparing results with those from available experimental data.