pp-Version nonlinear analysis of RC beams and slabs strengthened with externally bonded plates

The p-version nonlinear RC finite element model has been used to analyze the nonlinear behavior of RC beams and slabs as well as RC beams and slabs strengthened by externally bonded steel or FRP plates. The numerical approach is based on the p-version shell element, including the theory of anisotropic laminated composites considering geometric and material nonlinearities. In the nonlinear formulation of this model, the total Lagrangian formulation is adopted with large deflections and moderate rotations being accounted for in the sense of von Karman hypothesis. The material model is based on the Kupfer's yield criterion, hardening rule, crushing condition and plate-end debonding strength model. Integrals of Legendre polynomials are used for shape functions with p-level varying from 1 to 10. The Gauss–Lobatto numerical quadrature is applied to calculate the stresses at the nodal points instead of Gauss points. The validity of the proposed p-version of the finite element model for RC beams and slabs as well as externally strengthened RC beams and slabs is demonstrated in terms of ultimate load, effect of reinforcement, failure mode, stress in reinforcing steel, convergence characteristics, debonding failure at plate end, and compared with available experimental and numerical results.