Analysis of large deflections in a nonsymmetrical three-point bending of beams

In a bending test of engineering materials such as spring steels and plastics, a fairly large deflection is observed without exceeding the elastic limit of the materials. It is of great technological interest to know the large-deflection behavior for various loading styles. This report deals with the problem of nonlinear large deflections of a thin elastic, three-point simply supported beam with a nonsymmetrical vertical load and gives analytical solutions for typical flexible quantities such as the deflection, arc length, curvature and bending stress. Moreover, a large flexural bending test is carried out in order to confirm the applicability and reliability of the proposed theory. The experimental results are in good agreement with the ones obtained by the analytical theory. Therefore the nonlinear large-deflection theory presented in this paper can be put to practical use.