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Required information

The solid cylinders $AB$ and $BC$ are bonded together at $B$ and ore ottached to fixed supports ot A and $C.$ The modulus of rigidity is $3\mathrm{.}5{10}^6$ psi for oluminum and $5\mathrm{.}4{10}^6$ for brass. If $T=13\mathrm{.}5$kip. $in,a=1\mathrm{.}3$ in$.$ and $b=2\mathrm{.}3in,$ determine

$($b$)$ The resction torque et $A$

$($b$)$ Maximum shear stress in $BC$

FBD and equilib. equations

Assuming the reaction torque ot $A$ is $T_A($kip in$)(1),T_A<mn>1</mn><mn>3</mn><mn>.</mn><mn>5</mn><mtext></mtext><mi>(</mi>$kip in$)$ and using the FBDs shown

$M_x=0T_{AB}=T_A($kipin$)$

$M_x=0T_{BC}=(13\mathrm{.}5-T_A)($kipin$)$

Assuming the reaction torque ot $A$ is $T_A($kipin$)(3),T_A<mn>1</mn><mn>3</mn><mn>.</mn><mn>5</mn><mi>(</mi>$kipin$)$

$($i$)$ Express the magnitude of the ongle of twist of $B$ relative to $A$ as