We start our foray into statically indeterminate $($SI$)$ torsion with a pretty easy one: two dissimilar

sections fixed at both ends where a single torque of $12k-$in is applied. Find the reactions at both

ends and the rotation at B$.$ The view from the side is shown below. $2\mathrm{.}96k($left support$),9\mathrm{.}04k$

$($right support, both reactions double arrow left$),{}_B=0\mathrm{.}00188$ rad double arrow right.

Cylinder $1(AB)$:$G_1=16,000$ksi,$d=2$ inches, $L_1=16$ inches.

Cylinder $2($BC$)$: $G_2=20,000$ ksi, $d_0=3$ inches, $d_i=2\mathrm{.}8$ inches, $L_2=8$ inches.