$6\mathrm{.}2-15$ A composite beam is constructed from

a wood beam $(3$ in$.6$ in$.)$ and a steel plate $(3$ in$.$

wide$).$ The wood and the steel are securely fastened

to act as a single beam. The beam is subjected to a

positive bending moment $M_z=75$kip$-$in$.$ Calculate

the required thickness of the steel plate based on the

following limit states:

$($a$)$ Allowable compressive stress in the

wood $=2$ksi

$($b$)$ Allowable tensile stress in the wood $=2$ksi

$($c$)$ Allowable tensile stress in the steel plate $=16$ksi

Assume that $E_w=1,500$ksi and $E_s=30,000$ksi.

The answer is about $0\mathrm{.}8937$in$.$