Large Deflections of Beam Subject to Three-points Bending

TL;DR

This paper presents an analytical solution for large deflections of an elastic beam under three-point bending using Jacobi elliptical functions, including approximation formulas and comparisons with existing results.

Contribution

It introduces a novel analytical approach for large deflections in three-point bending using Jacobi elliptical functions, expanding the understanding of beam equilibrium configurations.

Findings

Analytical solutions derived using Jacobi elliptical functions.

Approximation formulas for beam load as a polynomial of deflection.

Numerical results validated against existing studies.

Abstract

In the paper a solution for equilibrium configurations of an elastic beam subject to three points bending is given in terms of Jacobi elliptical functions. General equations are derived and the domain of solution is established. Several examples that illustrate a use of the solution are discussed. The obtained numerical results are compared with results of other authors. Approximation formula by which the beam load is given as polynomial function of beam deflection is also derived. The range of applicability of the approximation is illustrated by numerical example.