Question $2$

$20$ pts

A solid stepped shaft with shear modulus $G=40$GPa and diameters $d_{AB}=40mm$ and $d_{BD}=60$ mm is fixed at both ends and subjected to a torque $T_{}$ at C as shown in the figure.

a$)$ If $T_0=100N-m,$ determine the reaction torques at ends A and D and the maximum shear stress in the shaft.

b$)$ Determine the applied torque $T_0$ if the angle of twist at O with respect to A is $-0\mathrm{.}01$ radians. The distance between points D and O is: $DO=1\mathrm{.}25m.$

Please include FBDs and neatly show all your work.

Figure $2$: Solid stepped shaft