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 $t_0$ 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?

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{1+sinax}=-\frac{1}{a}tan(\frac{}{4}-\frac{ax}{2})+C$