A Note on the Pure Bending of Nonhomogeneous Prismatic Bars

Abstract

The paper examines the pure bending of a linearly elastic, isotropic, nonhomogeneous bar. The bending stress, elastic strain energy and the end cross-section rotations are determined for in-plane variation of the Young's modulus with small strains and displacements. It is shown that the governing formulae for elastic pure bending of nonhomogeneous bars have same forms as formulae for symmetrical bending (bending in the principal planes) of homogeneous bars. Two examples illustrate the application of the developed formulae. In the first, a composite beam is considered; the second deals with the determination of the maximum tensile and compressive stresses in a bent functionally graded elastic bar.