Stiffness Assessment of Cracked Reinforced Concrete Beams Based on a Fictitious Crack Model

A fictitious crack model is introduced into cracked reinforced concrete beams to assess the changing beam stiffness under loads. Firstly, nonlinear concrete stress distributions near cracks are built based on the model. Then the stress of the steel bar at the cracked section is considered as cohesive stress. The concrete and steel stresses are substituted into the equilibrium equations of forces to solve the concrete stress. Based on the solution, the section inertias are estimated by iterating the calculation of the cracking open displacement, and finally the beam stiffness is assessed. Experimental data from seven concrete beams after cracking are adopted to validate the effectiveness of the proposed method, and the results show that the fictitious cracks ahead of actual cracks increase their depth with the load, which will raise the neutral axis and change the inertias of cracked sections and their neighboring sections. These changes are taken into account in the stiffness assessment, so the results predicted by the proposed method are shown to coincide well with the nonlinear deflections measured in the experiments.