Problem $1.$ The beam section shown in the figure is subjected to a bending moment in a vertical plane of $20$ kNm $($bending moment vector is in the horizontal direction$).$ The thickness of the walls of the section is $2$ mm throughout.

Calculate the maximum direct $($normal$)$ stress in the cross$-$section of the beam and indicate its exact location. Determine the torsional rigidity of the section $($use a shear modulus G$=30$GPa $).$ If a clockwise torque of $10$ kNm is applied about the shear center and the length of the beam is $1000$ mm $,$ calculate the rate of twist and the angle of twist of the free end of the beam. What is the maximum shear stress due to torsion?

THE ANSWER FOR PART $(1)$ IS $173$ MPa and value of Ixx$=1\mathrm{.}45*10^7$ mm$^4.$ So$,$ solve accordingly all the parts!!!