The laminate described in Problem 7.12 is subjected to a single bending moment per unit length, M x , and the two edges on which M x acts are fixed so that bending along the x-direction occurs freely,...

The laminate described in Problem 7.12 is subjected to a single bending moment per unit length, M_x, and the two edges on which M_x
acts are fixed so that bending along the x-direction occurs freely, but bending along the y-direction is prevented. That is, the longitudinal curvature is unconstrained (i.e., κ_x
≠ 0), but the transverse curvature is constrained (i.e., κ_y
= 0). Determine the ply stresses (σ_x)k as in Problem 7.12 (give equations and numerical results) and compare with the results of Problem 7.12.

Problem 7.12

A [0/90]s laminate is subjected to a single bending moment per unit length, M_x. If the laminate is unconstrained, so that bending along both the x- and the y-directions occurs freely, determine the ply stresses, (σ_x)k, in terms of the moment, M_x, the bending stiffnesses, D_ij, the ply stiffnesses, Q_ij, and the distance from the middle surface, z. Determine the ply stresses (σ_x)k in terms of M_x, z, and a numerical coefficient if the properties are E₁
= 129 GPa, E₂
= 12.8 GPa, G₁₂
= 4.6 GPa, ν₁₂
= 0.313, and t = 1 mm.