$3.$ A vertical force in $\backslash ($ y $\backslash )-$ax is of $150$ N and a horizontal force in x $-$ax is of $100$ N are applied to a pipe wrench, with its handle aligned parallel to the $\backslash ($ z $\backslash )-$axis, as depicted in Figure P$3.$ The pipe has an outer radius of $12$ mm and a thickness of $2$ mm $.[30$ pts$\backslash (]\backslash )$

$($a$)$ Determine the stress components at the surface $($points A and B $)$ of the cross$-$section where the pipe thread begins $[10$ pts$]$

$($b$)$ Construct Mohr's circle based on the stress components determined in $($a$).[10$ pts$]$

$($c$)$ Determine the principal stresses at the surface $($points A and B$)$ of the cross$-$section where the pipe thread begins. $[5$ pts$]$

$($d$)$ Determine the maximum in$-$plane shear stress at the surface $($points A and B$)$ of the crosssection where the pipe thread begins. $[5$ pts$]$

Cross section of A$-$B Points

Figure P$3$