Problem # $3(20$ points$)$

$(3-$a$)$ The assembly consists of two sections of galvanized steel pipe connected using a reducing coupling at B $.$ The smaller pipe has an outer diameter of $18\mathrm{.}75$ mm and an inner diameter of $17$ mm $.$ In contrast, the larger pipe has an outer diameter of $25$ mm and an inner diameter of $21\mathrm{.}5$ mm $.$ If the pipe is tightly secured to well at C $,$ determine the maximum shear stress in the assembly and the twist angles at point $A.$

Take: $J_{AB}=3\mathrm{.}934{10}^{3}m{m}^4,J_{BC}=17\mathrm{.}372{10}^{3}m{m}^4,G=75{10}^3$MPa, $L_{AB}=1\mathrm{.}0m$ and $L_{BC}=1\mathrm{.}5m.$