Consider a A$242$ steel $($corrosion resistant$)$ plate used in the construction of an oil rig. The plate is loaded in$-$plane with a stress defined by $11=150,22=50,12=50.$ If the yield stress in shear is $=100$ and the material can be described by the von Mises theory, determine: $($a$)(5$p$)$ Does the part yield? $($b$)(5$p$)$ Does it yield after it is placed in service, submerged in the ocean at $1$ Km depth? $($c$)(5$p$)$ Where $($on the surface of the plate$)$ do you expect the first signs of corrosion to be observed?