An Analysis of Large Deflection in a Symmetrical Three-point Bending of Beam

Abstract

The large deflection problem of a thin elastic simply supported beam is analysed for a symmetrical three-point bending .The derived nonlinear differential equation governing beam deflections is solved by applying the numerical method (R-K-G method) and the analytical method based on Legendre-Jacobi form's elliptic integrals of the first and the second kinds. Moreover, a reduction technique is proposed to estimate representative flexural quantities such as a maximum deflection, an end slope, and a maximum bending stress in large deflection states from the conventional linear bending theory in place of the exact large deflection theory. An experiment is also performed to confirm the applicability of the proposed large deflection theory. The experimental results agree well with those obtained from the exact large deflection theory.