Question $3(18$ marks$)$

A rod is made from two solid segments. $AB$ is $A-36$ steel and has a diameter of $15$ mm and BD is C$83400$ red brass and has a diameter of $25$ mm as shown in Figure $3.$ The rod is fixed at both ends and is subjected to a torque $T=500Nm.G_{mf}=75$GPa and $G{m}_m=37$ GPa. Ignoring stress concentrations, determine:

a$.$ The minimum and maximum shear stress in the steel segment $(8$ marks$)$

b$.$ The minimum and maximum shear stress in the brass segment. $(10$ marks$)$