A rectangular beam made using concrete with f$$c $=6000$ psi and steel with fy $=60000$ psi

has a width b $=16$ inches and an effective depth d $=21\mathrm{.}5$ inches and a total depth h $=24$

inches. The concrete modulus of rupture fr $=530$ psi. The elastic moduli of concrete and

steel are, respectively, Ec $=4030000$ psi and Es $=29000000$ psi. The tensile steel consists

of four No$.10$ bars. $(20$ points$)$

a$)$ Find the maximum service load moment that can be resisted without stressing the

concrete above $0\mathrm{.}45$f$$c or stressing the steel above $0\mathrm{.}4$fy$.$

b$)$ Determine if the beam will crack before reaching the service load moment determined in

part a