The effect of Poisson's ratio on the stiffness properties of composite beams

We investigate whether the stiffness of a non-uniform beam of a coaxial structure made of isotropic materials can be calculated using engineering (Bernoulli-Euler) theory. We derive a condition necessary and sufficient for the coincidence of the stiffnesses predicted by the asymptotic and the engineering theories. It turns out that this condition involves the Poisson's ratio, only. If the derived condition is not satisfied, the stiffnesses of the inhomogeneous beam always exceed those predicted by engineering theory. In other words, the engineering stiffnesses are exact low boundaries for the actual stiffnesses of a beam. Our numerical calculations verify our theoretical conclusions, and demonstrate that the difference in the mentioned stiffnesses can be very large. •For inhomogeneous rods/beams of coaxial structure, the formulas of the technical beam theory may be used if and only if the condition Δ(ν(y2,y3)yAν)=0 is satisfied (ν(y2,y3).•If the condition above is not satisfied, the stiffnesses given by the asymptotic theory are always higher than those given by the technical theory.•The differences between the stiffnesses given by the asymptotic and the technical theories can be large for rods/beams made of materials with Poisson's ratio close to −1 and 0.5.