Large deflection of a cantilever beam under transverse loading. A modification of linear theory.

The paper provides a modification method for a classical linear theory of strength of materials in case of a cantilever under transverse loading. The modification uses a condition of saving arc-length of a cantilever. A sagging deflection of the modified linear theory has accuracy comparable with exact solutions in elliptic integrals and functions. The modification expand loading interval of applicability of the linear theory significantly. A comparison with an exact solution was made. We also considered a cantilever under combined loading: concentrated transverse load and uniformly distributed load (an own weight of a cantilever). A comparison with experimental data confirms accuracy of the proposed modification method.