P$4\mathrm{.}6$ The rigid structure ABD in Figure P $4\mathrm{.}6$ is supported at $B$ by a $35-$mm$-$diameter tie rod $(1)$ and at $A$

by a $30-mm-$diameter pin used in a single shear connection. The tie rod is connected at $B$ and $C$ by $24-$

mm $-$diameter pins used in double shear connections. Tie rod $(1)$ has a yield strength of $250$ MPa $,$ and

each of the pins has an ultimate shear strength of $330$ MPa $.$ A concentrated load of $P=50kN$ acts as

shown at $D.$ Determine:

$($a$)$ the normal stress in rod $(1).$

$($b$)$ the shearing stress in the pins at A and $B.$

$($c$)$ the factor of safety with respect to the yield

strength for tie rod $(1).$

$($d$)$ the factor of safety with respect to the

ultimate strength for the pins at A and $B.$

FIGURE P$4\mathrm{.}6$