Do for group $19$ please

Q$1$a$)$ Fig. Q$1$a shows a thin$-$walled single$-$cell section with variable thickness made of aluminium. The section is

that of a L$($m$)$ long cantilever subject to a torque of T$($MNm$)$ about the shear centre $($Sc$)$ at its the free end.

The section is symmetric with respect to the y$-$axis. As a result of the applied torque, the tube twists for theta$^($@$)$

degrees. Determine,

i$)$ the applied torque.

ii$)$ the maximum shear stress and its location.

iii$)$ the strain energy stored.

Q$1$b$)$ A web made of titanium with the thickness of t$\_(4)($mm$)$ is placed along DE$,$ as shown in Fig. Q$1$b$.$ The section

is subject to a torque of T$($MNm $)$ about its shear centre. As a result of the applied torque, the tube twists

for theta$^($@$)$ degrees. Determine,

i$)$ the applied torque.

ii$)$ the maximum shear stress and its location.

iii$)$ the strain energy stored.

$[$N$.$B$.$ For the dimensions, material properties and angle of twist refer to Table Q$1.]$