Large deflections of a beam subject to three-point bending

• A new analytical solution of the problem is given in terms of Jacobi elliptical functions and the Jacobi zeta function.
• The domain of the solution is established.
• Approximation expressions for load factor as a polynomial function of deflection is derived.

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