Two torsion members AHB and CD have the same radius $({0\mathrm{.}8}^{\text{'}\text{'}})$ and the same shear modulus

$)$ as shown. The ends A and D are fixed $($against rotation and displacement$).$ A torque

of $6000$ in $.$# is applied at point H $.$

a$).$ Calculate the reaction torques at fixed ends A and $D.$

b$).$ Calculate the contact force between gear $B$ and gear $C.$

c$).$ Calculate the angle of rotation for gear B and gear C$.$

d$).$ Calculate maximum shear stress.

e$).$ The reaction torques at A and D do not add up to $6000$ in$.$#$.$ Explain why.

$G_1=G_2=4000$ksi

$r_1=r_2=0\mathrm{.}8in$