Note: Assume a positive internal torque.

The angle of twist of segment $\left(1\right)$ can be computed from the torque-twist relationship:

$$\begin{gathered} {\mathrm{\varphi }}_1=\frac{{\mathrm{T}}_1{\mathrm{L}}_1}{{\mathrm{J}}_1{\mathrm{G}}_1} \\ =\frac{(50 \mathrm{N}-\mathrm{m})(1,800 \mathrm{mm})(1,000 \mathrm{mm/m})}{(102,944 {\mathrm{mm}}^4)(37,000 {\mathrm{N/mm}}^2)} \end{gathered}$$