Nonlinear Analysis on Large Deformations in a Slender Beam with Hinged Support subjected to Eccentric Compressive force: Considerations concerning to Young's modulus Measurement of Compressive Large Deformation Beams

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 hinged at both ends. Using the elliptic integral, relationships between arc length s, horizontal distance x, deflection y, curvature 1/R, bending moment M and bending stress δ 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's prediction and the large deformation experiment result were in good agreement and it became clear that if the offset amount was less than 10% of the beam length, it would have almost no effect on Young's modulus measurement. On the other hand, some typical deformation states are represented graphically so that the large deformation can be easily understood visually. In these considerations of issue, the offset beam is defined as the state in which their compression fulcrums are not on the same straight line.