$1\mathrm{.}3-17$ A stepped shaft ABC consisting of two solid,

circular segments is subjected to torques $T_1$ and $T_2$

acting in opposite directions, as shown in the fig$-$

ure. The larger segment of the shaft has a diameter

of $d_1=2\mathrm{.}25in.$ and a length $L_1=30in.$; the smaller

segment has a diameter $d_2=1\mathrm{.}75$ in$.$ and a length

$L_2=20in.$ The torques are $T_1=21,000lb-$in$.$ and

$T_2=10,000lb-$in$.$

$($a$)$ Find reaction torque $T_A$ at support $A.$

$($b$)$ Find the internal torque $T(x)$ at two locations:

$x=\frac{L_1}{2}$ and $x=L_1+\frac{L_2}{2}.$ Show these inter$-$

nal torques on properly drawn free$-$body dia$-$

grams $($FBDs$)\mathrm{.}1\mathrm{.}3-17$ A stepped shaft ABC consisting of two solid, circular segments is subjected to torques T$1$ and T$2$ acting in opposite directions, as shown in the fig$-$ ure. The larger segment of the shaft has a diameter of d$12\mathrm{.}25$ in$.$ and a length L$130$ in$.$; the smaller segment has a diameter d$21\mathrm{.}75$ in$.$ and a length L$220$ in$.$ The torques are T$121,000$ lb$-$in$.$ and

T$210,000$lb$-$in$.$

$($a$)$ Find reaction torque TA at support A$.$

$($b$)$ Find the internal torque T$($x$)$ at two locations: x L$1/2$ and x L$1$ L$2/2.$ Show these inter$-$ nal torques on properly drawn free$-$body dia$-$ grams $($FBDs$).$