Modeling of Externally Prestressed Beams until Fracture in Non Linear 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.