Analysis of arbitrary steel and concrete beam sections subject to combined loading Development of a FE-program

Abstract

The structural analysis methods to determine sectional forces are widely known. However, the methods available to check sectional capacities are not well developed. This work attempts to improve the situation by the development of a FE program for sectional analysis of arbitrary beam cross sections. The program is based on an enhanced beam theory with 3D state of stress. This was achieved by introducing free warping displacements to account for longitudinal shear stresses. Steel and concrete material models were implemented. For reinforced concrete, the reinforcement and concrete were modelled by separate material models, which were combined together with a bond-slip. The material behaviour of concrete was described by a multi surface plasticity model. Two iterative methods were use, the Newton-Raphson and Arc-length methods, in order to solve the highly nonlinear system of equations coming from the analysis. The finite elements used to model the section correspond to a 2D quadrilateral element, considering displacements in all three directions. The reinforcing bars (stirrups and rebars) were modeled as truss elements that take into account the effect of bond-slip with spring elements. Finally, the results from the program were compared with analytical and experimental results to establish the validity of the proposed models for steel and reinforced concrete. These studies showed that the model for steel beams gives good agreement. For the reinforced concrete beams in the axial, bending, shear and torsion tests, agreement is also good. However, in the prestressed concrete bridge box girder some differences were found but the results are still rather good.