Question $2(25$ marks$)$

$($a$)$ Stating your assumptions clearly and defining the symbols, derive the

torsion formula for circular shafts:

$\frac{T}{J}=\frac{{}_{\text{m}\text{a}\text{x}}}{c}=\frac{G}{L}$

$($b$)$ The steel pipe shown in Figure Q$2$ has an outer diameter of $40$ mm and

an inner diameter of $38$ mm $.$ It is tightly secured to the wall at A and three

torques are applied to it as shown. Determine:

i$.$ The internal torques developed in segments $AB,BC$ and $CD$; also

draw the torque diagram

ii$.$ The absolute maximum shear stress developed in the pipe $(7$ marks$)$