Question 26.4: A generally orthotropic ply is subjected to direct stresses ......

Since the ply angle is 45°, the trigonometric terms in Eqs (26.24) are

\left\{\begin{matrix} \sigma _{l} \\ \sigma _{t} \\ \tau _{lt} \end{matrix} \right\} =\left[\begin{matrix} m^{2} & n^{2} & 2mn \\ n^{2} & m^{2} & -2mn \\ -mn & mn & m^{2}-n^{2} \end{matrix} \right] \left\{\begin{matrix} \sigma _{x} \\ \sigma _{y} \\ \tau _{xy} \end{matrix} \right\}            (26.24)

Then, substituting in Eqs (26.24),

so that