$[20$ points$]$ The square bar below is $3"33"$ and is made of mild steel. The steel has a

yield normal stress of ${}_{\text{y}\text{i}\text{e}\text{l}\text{d}}=36$ksi, yield shear stress of $t_{\text{y}\text{i}\text{e}\text{l}\text{d}}=22$ksi,$E=29{10}^3$ksi,

and $v=0\mathrm{.}30.$ For this element, determine the following for $P=150$kips :

a$)[6$ pts$]$ Determine the factor of safety against yielding in normal stress.

b$)[6$ pts$]$ Determine the factor of safety against yielding in shear stress.

c$)[8$ pts$]$ Using the axes given below, plot the relationship between the applied force

and the vertical deflection at point $b.$ Provide numerical values for all important

points on the diagram.