A circular shaft has a diameter $D=40mm$ and a length $L=1\mathrm{.}5m$ and is made of structural steel with elastic perfectly plastic behavior $(G=95\mathrm{.}98$ GPa and $y=160$MPa $).$ The shaft fixed at one end and cuhincted to a torque $T$ at the other end. The angle of $t.$ ist is measured between the ends as $=0\mathrm{.}2$rad.

a$)$ Calculat $r$ the yield shear strain $y.$

b$)$ Calculate the maximum shear strain ymax.

c$)$ Determine the radius $y$ to the elastic$-$ plastic boundary.

d$)$ Determine the torque T $.$ If the member has yielded and then unloaded.

e$)$ Determine the residual shear stress at $=5$ mm$.$

f$)$ Determine the radius $$ where the residual shear stress is zero.