$3.(25$pts$)$ A force $\backslash (\backslash$mathrm$\{$P$\}=10\backslash$mathrm$\{$kN$\}\backslash )$ is applied as shown. The cylindrical supports $\backslash (\backslash$mathrm$\{$AD$\},\backslash$mathrm$\{$BE$\}\backslash ),$ and CF are $304$ stainless steel alloy with a diameter of $30$ mm $.$ Assume that the beam $\backslash ($ A B C $\backslash )$ is a "magic physics beam" that does not bend or distort, has no mass, etc. Assume that the supports remain vertical while under load and ignore any lateral$/$transverse distortion effects $($saves on math effort for little return...$).$

a$.$ What is the force in each support in kN$?$

b$.$ What is the average normal stress in each support in MPa? Does this exceed the yield strength of $304$ alloy stainless steel?

c$.$ What is the elongation of each support in mm$?$