Question $4$

The wall$-$mounted beam shown below $($length $L=955\mathrm{.}0mm)$ has a hollow

circular cross$-$section with the following properties:

$d_0=42\mathrm{.}5mm,d_i=41mm$

$A=98\mathrm{.}4m{m}^2,I_z={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{y}^{2}dA=21440m{m}^4,I_y={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{z}^{2}dA=21440m{m}^4$

and $J={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(y^2+z^2)dA=42881m{m}^4$

An external force is applied at the center of the end of the beam. The force

components are $F_x=34000N,F_y=15500N,$ and $F_z=-8000N,$ as

shown.

What is the maximum shear stress $({}_{\text{m}\text{a}\text{x}})$ in the material near the wall $($in units of

MPa $),$ expressed as a positive number?