$($c$)$ Using the forces determined in $($b$),$ determine the stresses exerted on each of the four pins. The

pins are circular in cross$-$section, $8$ mm in diameter, and are all subjected to double shear

transverse loads. $($Note: Recall the shear

stress formula for a pin subjected to double shear.$)$

$($d$)$ On the basis of the forces determined in $($b$)$ and the stresses determined in $($c$),$ determine the

safety factor $($for the static loading condition$),$ assuming that the pins are $8$ mm in diameter, are

subject to double shear, and are made of a material with a yield strength of $Sy=400$MPa.

$($Note: in principle, each pin should have a

different safety factor value.$)$

$($e$)$ On the basis of the forces determined in $($b$)$ and the stresses determined in $($c$),$ determine the

safety factor $($for the dynamic loading condition$),$ assuming that the pins are $8$ mm in diameter, are

subject to double shear, and are made of a material with a yield strength of $Sy=400$MPa and

an ultimate strength of Sut $=520$ MPa; assume an operating life of $50,000$ cycles.

$($Note: this is a case of fatigue by alternating and reversible cyclic loading where the

alternating component of the von Mises stress is given by $a=0\mathrm{.}5{}^{\text{'}}$; for calculation purposes

introduce the Marin factors that you consider relevant for estimating the endurance limit stress

Se$.)$