Analysis on Large Deformation in a Slender Beam subjected to Eccentric Compressive Load (In Case of a Slender Beam with Non-Rotation Fixed Supports)

Abstract

The large deformation behavior of flexible thin wires when subjected to axial compressive load has already been analyzed and applied to Young’s modulus measuring method for thin wires. However, from the viewpoint of material testing, it is necessary to analyze the effect of offset compression on Young’s modulus measurement. Therefore, this paper deals with a nonlinear analysis on large deformation when axial compression is applied to an offset beam fixed at both ends. Using the elliptic integral, analytical solutions of relations among arc length s, horizontal distance ξ, deflection η, curvature 1/R, bending moment M and bending stress σ, etc. were derived. Furthermore, the large deformation state was theoretically calculated using the analytical theory, and the effect of the offset amount on the buckling load was clarified. In addition, in order to confirm the effectiveness of the analytical theory, a large deformation experiment using a PVC (polyvinyl chloride) thin plate beam was carried out. As a result, the analytical theory' prediction and the large deformation experiment result were in good agreement. On the other hand, some typical deformation states are represented graphically so that the large deformation can be easily understood visually. In this paper, the offset beam is defined as the condition where both fulcrums are not on the same straight line.