Problem $1$:

As shown in the figure, a stepped shaft ABCD consisting of solid circular segments is

subjected to three torques. The torques have magnitudes $T_D=4$kips$-ft,Tc=-9$kips$-ft,$

and $T_B=14$kips$-$ft$.$ The length of each segment is $2$ ft $,$ and the diameters of the segments

are $4$ in$.,3$ in$.,$ and $2$ in for segments AB$,$ BC$,$ and CD$,$ respectively. The material is steel

with a shear modulus of rigidity $G=11,200$ksi. Calculate the angle of twist ${}_D$ at end $D.$

$L=2ft.$