Optimal Elasto-Plastic Analysis of Prestressed Concrete Beams by Applying Residual Plastic Deformation Limitations

This work introduces elasto-plastic analysis of prestressed reinforced concrete beams under different prestressing conditions by limiting the residual plastic behaviour inside the steel bars using complementary strain energy. A non-linear optimal method was used to limit residual plastic deformations in steel bars, including prestressed tendons, used to reinforce beams from two previous research investigations. This was considered by using an optimization approach with an objective function to find the maximum loading while applying constraints on the complementary strain energy of residual internal forces in steel elements to control residual plastic deformations. Thus, an elasto-plastic optimization programme was linked to models simulated by ABAQUS, as concrete was calibrated by the concrete damage plasticity (CDP) model. Some variables were considered regarding the force applied inside prestressed tendons and the number of tendons used inside the models. Thus, limits on complementary strain energy affected load values and model damage where an increase in the permissible strain energy value leads to an increase in the corresponding loading values produced; thus, this produces a higher stress intensity in steel and tension-damaged areas in concrete. Based on these data, many comparisons have been made to determine when beams behaved elastically and how they turned into plastic.