Bending of beams with bisymmetrical cross sections under non-uniformly distributed load: analytical and numerical-FEM studies

The paper is devoted to simply supported beams subjected to non-uniformly distributed loads. Shapes of bisymmetrical cross sections of the beams are expressed by special functions. The analytical model of the beams is formulated with consideration of the shear effect. A nonlinear hypothesis of deformation of a planar cross section of beams is assumed. The bending moment and the shear transverse force are formulated. Moreover, numerical-FEM models of the beams are developed. Deflections are calculated with the use of two methods for an exemplary beam family. The results of the studies are presented in tables.