The figure below shows a crank loaded by a force $F=190lbf$ which causes twisting and bending of the $0\mathrm{.}75-$in$-$diameter shaft. The crank has a yield strength $S_y=32k.$

$(1).$ Draw the free body diagram and calculate all the reaction loads at the cross section at the wall.

$(2)$ Calculate all three$-$dimensional stress elements of point A$.$ A is the top point of the cross section.

$(3)$ Compute factors of safety, based upon the maximum$-$shear$-$stress theory for point

A$.$

$(4)$ Jompute factors of safety, based upon the distortion$-$energy theory for point A$.$