Question $4(20$ marks$)$

The $\backslash (50-\backslash$mathrm$\{$mm$\}\backslash )$ diameter rod is subjected to the loads shown in Figure Q$4.$

$($a$)$ Determine the state of stress at point $\backslash (\backslash$mathbf$\{$A$\}\backslash ),$ and show the results on a differential element located at this point.

$(15$ marks$)$

$($b$)$ If the yield stress of steel pole is $\backslash (\backslash$sigma$\_\{$y$\}=250\backslash$mathrm$\{$MPa$\}\backslash ),$ check whether point $\backslash (\backslash$mathbf$\{$A$\}\backslash )$ yields according to the maximum shear stress theory.

Figure Q$4$