Example

One half of the solid shaft has a radius $c$ and the other half has a radius $2c.$ The shaft is fixed at A and attached to a rigid rod at $C.$ The rigid rod CD of length $L$ is subjected to a force $P.$ The entire shaft is made of a material with shear modulus $G.$

a$)$ Find Max shear stress due to torsion in portion BC of the shaft.

Example

b$)$ Find the concentrated torsion $T($applied at B$)$ such that the maximum shear stress due to torsion remains the same throughout the entire shaft $($i$.$e$.,$ the maximum shear stress in portion $AB$ equals that in por

c$)$ What is the angle of twist ${}_C$ at the end $C?$

d$)$ What is the vertical displacement of point $D$ due to torsion only?