$(20$ pts$.)$ A $8ft$ long $3^{\text{'}\text{'}}($wide$){12}^{\text{'}\text{'}}($tall$)$ beam is subjected to a uniform $($edge$-$to$-$edge$)$

distributed load of $1500\frac{\text{\#}}{f}t.$ The material has a Young's Modulus $E=2,000,000.$ If the

allowed $($FOS included$)$ bending stress is $2500$ psi, the allowed deflection is L$/360$ and the

allowed $($FOS included$)$ shear stress is $200$ psi:

a$)$ Is the beam safe in bending?

b$)$ Is the beam safe in deflection for $?$

c$)$ Is the beam safe in shear?