Bending of symmetrically sandwich beams and I-beams – Analytical study

Abstract

The paper is devoted to simply supported sandwich beams and I-beams of symmetrical structure. Two types of loads are taken into account: three-point bending and uniformly distributed load. Moreover, two models of deformation of planar cross sections of these beams are also considered: zig-zag theory – classical “broken line” hypothesis and nonlinear theory – “polynomial” hypothesis. Based on the principle of stationary total potential energy the differential equations of equilibrium are obtained. The system of the equations is analytically solved for two types of loads and the deflections of the beams are calculated for exemplary beams with consideration of the shear effect. The results of the two models of deformation of planar cross sections are compared and specified in Tables.