Calculation of the Overall Stiffness and Irreversible Deflection of Cracked Reinforced Concrete Beams

The method proposed in this paper aims to assess both the irreversible deflection of cracked reinforced concrete beams when unloaded and their overall stiffness under loading cycles which is relevant for in-situ analysis of existing structures. Only service stage is modeled and time-dependent effects such as creep and shrinkage are not taken into account. The modeling approach combines an existing model based on an empirical moment-curvature analytic relationship with a new Macro-Finite-Element (MFE) both implemented in a linear finite element analysis. MFEs are Beam Finite Elements, characterized by their average moment of inertia. The average moment of inertia is calculated by homogenization of the steel strain, concrete strain and neutral axis modeled between two consecutive bending cracks. The results of the MFE model have been successfully compared to experiments. The irreversible deflection represents a significant proportion of the total deflection in service and the overall stiffness of the cracked beams during the loading cycles is strongly under-estimated by existing models based on empirical moment-curvature relationships.