An Analysis of Large Deflections in a Four-point Bending : In the Case of the Presence of Friction at Loading Supports

Abstract

Concerning a symmetrical four-point bending, the nonlinear large deflection problem of a thin elastic beam in the presence of friction between beam and the loading supports is investigated analytically by applying Legendre-Jacobi form's elliptic integrals of the first and the second kinds. A reduction technique is proposed to estimate easily the maximum deflection, the end slope, and the maximum bending stress in large flexural states from the conventional linear bending theory. An experiment is also performed to confirm the applicability of the presented large deflection theory. The experimental results agree well with the solutions based on the large deflection theory.