Question $5$: A beam, with the cross section shown in Figure Q$5$ is subjected to torque $T.$

Determine the maximum torque which may be applied and the maximum shear stress if the beam

must not twist by more than $5\%m.$ G $=70G\frac{N}{m^2}.$

Question $6$: The cross$-$section of a thin tube having variable wall thickness $t$ is shown in Figure Q$6.$

The median line of the cross$-$section is a circle of radius $r,$ and the thickness is given by the

equation:

$t=t_o(1+sin\frac{}{2})$

where $t_{\text{@}}$ is the thickness at the section where $=0.$ If the tube is subjected to a torque $T,$ what is

the maximum shear stress, minimum shear stress, and angle of twist?

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{1+sin}=-\frac{1}{a}tan(\frac{}{1}-\frac{ax}{r})+C$