\[\hat{\sigma} = \begin{bmatrix} \frac{p_1(L - x)y}{I} + \frac{p_2}{A} & -\frac{3p_1}{2A}\left( 1 - \frac{y^2}{c^2}\right) & 0 \\ -\frac{3p_1}{2A}\left( 1 - \frac{y^2}{c^2}\right) & 0 & 0 \\ 0 & 0 & 0 \\ \end{bmatrix}\]