Finite elements analysis of stresses in beam structures

Abstract

This Final project deals with determining of stresses in beam structures. First, warping function based on finite element formulations for determining shear stresses at beam cross-sections under biaxial bending and twisting are developed and discretized. Second, finite element programs for analysis of beams and three-dimensional frames are developed. These programs, which have been implemented in MATLAB® environment, are then combined to a program system, which determines efficiently the combined state of stresses at any cross-section of a beam or 3D frame. In order to compare the results of the presented approximate technique to practically exact ones, a program, based on the finite prism method, for solving stresses in a simply supported prismatic beam has further been developed. The results of the presented technique and finite prism method are compared using example problems. In general, closed thin-walled and solid cross-sections give really accurate results, whereas open thinwalled cross-sections do not. Some discrepancies in the shear stresses values can be found usually in the points of the beam where any load starts or finishes. Composite crosssections can be analysed applying this methodology. Finally, applications of the developed program are demonstrated with some more practical examples.