A bronze $[E=15000$ksi bar is rigidly attached to a stainless steel $[E=27000$ksi bar to form a composite beam. The dimensions of

the cross section are $b=5\mathrm{.}0in.,d_B=2\mathrm{.}15in.,$ and $d_S=1\mathrm{.}05in.$ The composite beam is subjected to a bending moment of $M=6300lb*ft$

about the $z$ axis. Determine:

$($a$)$ the maximum bending stresses in the bronze and stainless steel bars.

$($b$)$ the normal stress in each bar at the surface where they contact each other.