A bronze $[E=15200$ksi bar is rigidly attached to a stainless steel $[E=27500$ksi bar to form a composite beam. The dimensions of the cross section are $b=4\mathrm{.}3in.,d_B=2\mathrm{.}00in.,$ and $d_S=0\mathrm{.}90in.$ The composite beam is subjected to a bending moment of $M=6700lb*ft$ about the $z$ axis. Determine:

$($a$)$ the maximum bending stresses in the bronze and stainless steel bars. Tensile stress is positive, while compressive stress is negative.

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

Answer:

$($a$){}_{\text{b}\text{r}\text{o}\text{n}\text{z}\text{e}\text{,}\text{m}\text{a}\text{x}}=$ psi

${}_{\text{s}\text{t}\text{e}\text{e}\text{l}\text{,}\text{m}\text{a}\text{x}}=$ i $$ psi

$($b$){}_{\text{b}\text{r}\text{o}\text{n}\text{z}\text{e}\text{,}\text{i}\text{n}\text{t}\text{e}\text{r}\text{f}\text{a}\text{c}\text{e}}=$ i $$ psi

${}_{\text{s}\text{t}\text{e}\text{e}\text{l}\text{,}\text{i}\text{n}\text{t}\text{e}\text{r}\text{f}\text{a}\text{c}\text{e}}=$ psi