Nonlinear Finite Elements Method Of Unbonded Prestressed Simply Supported Concrete Beams

The technology of inner un-bonded prestressed concrete has been extensively used in the field of civil engineering in both domestic and foreign countries. But studies of nonlinear analysis of inner unbonded prestressed concrete are few. So the non-linear finite element of inner un-bonded prestressed simply supported beam has been studied in this paper.In the phase of finite element analysis, the stress-strain relationship of concrete, the stress-strain relationship of prestressed reinforcement and regular reinforcement has been analyzed and summarized. The finite element model of reinforcement concrete, the damage criterion of concrete, the amendment of rigidity after the concrete cracking, and the solution of nonlinear equations has been discussed. FORTRAN language is used to establish the planar nonlinear finite element model of inner unbonded pretressed concrete simply supported beam while the material nonlinearity, geometric nonlinearity and the amendment of rigidity after the concrete cracking is considered. Using integral model, the structure is dispersed to planar quadrilateral isoparametric elements. Nonlinear elasticity constitutive relationship of concrete, elasticity constitutive relationship of prestressed reinforcement, the Kupfer strength theory and the amendment of rigidity after the concrete cracking is all used. Euler method and secant stiffness method is used to solve the nonlinear equations. The effect of inner unbonded prestressed reinforcement is considered as equivalent node load of beam element and the magnitude of equivalent node load applied to the beam element is adjusted by the compatibility between the whole deformation of inner unbonded prestressed reinforcement and the whole deformation of the concrete at the corresponding site under vertical load. The node incremental displacement is used as the convergence criterion. VC language is used to compile an interface which can be used to input parameter visually. Then it can be linked to the FORTRAN program to calculate. Choosing appropriate model and parameter, the program is used to simulate prestressed simply supported concrete beams with prestressed curve tendon and straight tendon. It indicates that the result calculated by the program has high degree of accuracy. And it supplies the method for further research of nonlinear finite element analysis of inner unbonded prestressed concrete beams.