Modeling of Internally or externally prestressed concrete beams until fracture in nonlinear elasticity

In this paper, we present an analytical model to analyze reinforced and prestressed concrete beams loaded in combined bending, axial load and shear, in the frame of non linear elasticity. In this model, the equilibrium of the beam is expressed by solving a system of equations, governing beams equilibrium, based on the stiffness matrix of the beam, which connects the load vector to the node displacements vector of the beam. It is built from the stiffness matrix of the section which takes into account a variation of the shearing modulus (depending on the shear variation) instead of assuming a constant shearing modulus as in linear elasticity. For the internal tendons, the stiffness matrix is completed by the terms due to the prestress effect in flexural equilibrium and by the balancing of one part of the shear by the transverse component of the force in the inclined cables. A computing method is then developed and applied to the calculus of some internally or externally prestressed concrete beams. The comparison of the results predicted by the model with several experimental results show that, on the one hand, the model predictions give a good agreement with the experimental behavior in any field of the behavior (after cracking, post cracking, post steel yielding and fracture of the beam); and, on the second hand, that the model leads to the prediction of tendons slipping at deviators and to the tension increase in the tendons.