Derive the linked interpolation of Eq.(2.68) for the 2-noded Timoshenko beam element.
Eq.(2.68) : w=\frac{1}{2}\left ( 1-\xi \right )w_{1}+\frac{1}{2}\left ( 1+\xi \right )w_{2}+\left ( 1-\xi ^{2} \right )\frac{l^{(e)}}{8}\left ( \theta _{1}-\theta _{2} \right )