$2.$

$1.$ Given a cross section of a wing box with $2$ closed section and a open section with shear modulus $\backslash (\backslash$mathrm$\{$G$\}=25000\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash )$ and $\backslash (10^\{8\}\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash )$ respectively. The section is subjected to a torque of $100$ kNm and the entire section is $2$ mm in thickness. Please calculate

a$.$ Rate of twist of the section

b$.$ Maximum shear stress

$2.$ Now the closed section has been removed and the remaining cross section becomes symmetric. The section is now subjected to an anticlockwise torque of $100$ kNm $.$ Calculate the distribution of warping around the cross$-$section. Illustrate your answer clearly by means of a sketch and insert the principle values of the warping displacements.