$($a$)$ A thin$-$walled two cell wing section with dimensions as shown in Fig. Q$2($a$)$ is clamped at one end and loaded by a torque of $2000$Nm at its free end. The structure is made of Aluminium having shear modulus $\backslash (\backslash$mathbf$\{$G$\}=\backslash$mathbf$\{28$ G P a$\}\backslash )$ and shear strength of $200$MPa. The skin thicknesses are $1$ mm for sides $2-1,1-6,6-5$; $2$ mm for sides $5-4,4-3,2-3$ and $3$ mm for wall $5-2.$

Fig. Q$2($a$)$

$($i$)$ Determine the shear flow in each of the walls of the section.

$(12$ marks$)$

$($ii$)$ Determine the shear stress in each of the walls of the section, and also determine if the strength condition is satisfied when a safety factor of $1\mathrm{.}5$ is considered. What is the maximum torque the structure can safely withstand?

$($iii$)$ Determine the twist angle at the free end of the structure for the torque of $2000$Nm$.$