Problem #$2$: $(25$ points$)$ A hollow tube of length L$=800$mm is fixed at one end and is subjected

to a torque T$=1000$N$-$m at its free end, as shown in Figure $2.$ The curved part of the tube's cross

section is a semicircle of radius r$=50$mm$,$ wall thickness t$\_(1)=2$mm$,$ and shear modus G$\_(1)=10$GPa;

the straight edge of the cross section has a length $2$r$=100$mm$,$ a wall thickness t$\_(2)=4$mm$,$ and a

shear modulus G$\_(2)=20$GPa.

aq everywhere on the cross section.

b$\backslash$tau $\_(1)$ on the curved semicircular part of the cross section, and find the shear

stress $\backslash$tau $\_(2)$ on the straight edge of the cross section.

c$\backslash$theta $,$ the angle of twist $\backslash$phi of the free end of the tube, the

torsional rigidity T$.$R$.$ of the cross section.

Figure $2$

Please draw all relevant free body diagrams