Determining Transversal Shear Stress in Layered Composites

An engineering approach to calculate transversal shear stresses in a layered composite stack is proposed. It is based on the Zhuravsky formula expressing shear stress in an isotropic beam exposed to transverse bending. In general, applying this formula to a composite beam is incorrect because of inhomogeneous beam structure. According to the method proposed, the first stage of the algorithm involves transition to an equivalent model of a homogeneous beam to which Zhuravsky formula is applicable. The transition is carried out by changing the shape of the cross section of the beam provided that it retains the flexural rigidity and generalized elastic modulus. The shear stresses calculated in the equivalent beam are then converted into stress values in the initial composite beam on the basis of the condition that the equilibrium equations remain valid. The basic relationships of the method are given and the analytical formula to determine shear stresses is provided for a composite beam. The technique is verified by comparing the analytical results with the data obtained numerically using the finite element method (FEM). It is shown that stacking of monolayers provides a significant effect on both the character of distributing shear stresses and on the stress value. The limits of applicability of the method obtained are explored. These limits are associated with conditions of meeting requirements set forth in a straight normal hypothesis. It is noted that under this hypothesis the shear stresses do not depend on the layer shear modulus, which explains the absence of this parameter in obtained formula. The classical theory of layered composites is based on similar assumptions, which gives grounds to apply this formula to estimate shear stresses in a layered composite stack.