Spatial Fine Beam Model Based on Vector Form Intrinsic Finite Element Analysis

Abstract

Different from the Euler beam and Timoshenko beam, the spatial fine beam model considers some effects such as shear displacement, the additional axial displacement produced by lateral bending and the additional transverse displacement induced by reduced stiffness due to transverse shear deformation. In this paper the internal force formula of the spatial fine beam model, applying to Vector Form Intrinsic Finite Element (VFIFE) analysis, are derived and corresponding programs are developed. A spatial cantilever beam and a space frame are analyzed and the load-displacement curves are compared using different beam element models. The results show that when the depth-span ratio is relatively small, the load-displacement curves nearly have no difference. When the depth-span ratio becomes larger, the yield load gotten by the fine beam model is significantly smaller than that obtained by the Euler beam and Timoshenko beam. Therefore, when the deep beam is analyzed, the shear displacement, the additional axial displacement and the additional transverse displacement caused by stiffness reduction can’t be ignored. The spatial fine beam model proposed in this paper has good accuracy in the analysis of deep beam.