The laminate described in problem 9 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., \(\kappa_{x} eq 0\) ), but the transverse curvature is constrained (i.e., \(\kappa_{y}=0\) ). Determine the ply stresses \(\left(\sigma_{x}\right)_{k}\) as in problem 9 (give equations and numerical results) and compare with the results of problem 9.

Data From Problem 9:

A \([0 / 90]_{\mathrm{S}}\) 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, \(\left(\sigma_{x}\right)_{k}\), in terms of the moment, \(M_{x^{\prime}}\) the bending stiffnesses, \(D_{i j}\) the ply stiffnesses, \(Q_{i j}\) and the distance from the middle surface, \(z\). Determine the ply stresses \(\left(\sigma_{x}\right)_{k}\) in terms of \(M_{x^{\prime}} z\), and a numerical coefficient if the properties are \(E_{1}=129 \mathrm{GPa}, E_{2}=12.8\) \(\mathrm{GPa}, G_{12}=4.6 \mathrm{GPa}, v_{12}=0.313\), and \(t=1 \mathrm{~mm}\).