Modeling of Externally Prestressed Beams until Fracture in Non Linear Elasticity

Abstract

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.

Prediction of the Non-Linear Rupture of a Section Under Compound Deviated Bending

“…in nonlinear elasticity; taking into account the real behavior of the different materials, some details are given by ( Bouafia et al, 2000;Adjrad et al, 2015). The internal forces developed in the concrete by the deformations, based on the works of (Espion, 1986) and (Bouafia et al, 2000), are given by the following expressions Equation 3.…”

“…Several studies have been carried out around the world in the field of study of reinforced concrete structures in nonlinear elasticity. One can cite the studies carried out by (Islam and Shahria, 2013;Bouafia et al, 2000;Bouafia et al, 1998;Sargin, 1968;Virlogeux and M'rad, 1986;Virlogeux, 1986;Grelat and Nait rabah, 1988;Bratina, 2005), also, the calculation of reinforced concrete sections is a problem well known by several authors (Bouafia et al, 2002;Daunys and Rimovkis, 2006;Florent, 1999;Bonet et al, 2006;Choa and Kwonb, 2008;Liang and Fragomeni, 2009;Ronagh and Baji, 2014;Adjrad et al, 2016;Kachi et al, 2015;Adjrad et al, 2015). If all these studies carried out were focused on the simulation of the structural elements behavior in nonlinear elasticity, it was in an attempt to answer all the questions that have been chosen to be focused on in our research work, i.e.…”

Prediction of the Rupture of Circular Sections of Reinforced Concrete and Fiber Reinforced Concrete

“…The value of the function u (e) was considered zero beyond the compression and tension strength material, respectively for deformations e cu and e rt . The calculation was then carried out in the nonlinear elasticity; taking into account the actual behavior of the various materials, some details are given in (Bouafia et al 2000, Adjrad et al 2015. The internal efforts (N int , M int ) developed by the deformations (du, dw) are related by the following formulas (Eq.…”