Two solid bars are joined and loaded with torques as shown in the figure.

The lengths of the bar$-1$ is$,L_1=30in,$ and bar$-2$ is$,L_2=20in.$ The diameter of the bars are $d_1=3\mathrm{.}0in,$ and $d_2=2\mathrm{.}0in.$ The shear modulus of the bars are, $G_1=15{10}^3$ksi, and $G_2=10{10}^3$ksi.

Point$-$D is in the middle of bar$-1.$

Determine the following:

a$.$ The magnitude and location of maxmupshear stress in the bar$-1$ and bar$-2.(15$ points$)$

b$.$ Angle of twist of the structure at point C and indicate the direction of rotation. $(10$ points$)(-6)$

c$.$ Sketch the shear stress distribution that acts on the cross$-$section of bar$-2.(5$ points$)$