Two ${15}^{\text{'}}$ simple beams are used to equally support thirty $300-$lbs$.$ crude oil barrels as shown in the figure. The beams are standard HSS steel sections made from ASTM A$-36$ structural steel, and the load is static. Assume the weight of the barrels is uniform along the length of the beam and neglect the weight of the beams.

a$.$ Determine the maximum shear force and maximum bending moment in the beams.

b$.$ Size the lightest HSS beams using the AISC specs based on bending stress.

c$.$ Calculate the maximum shear stress in the beams. Is it acceptable?

d$.$ It is proposed to replace the two standard HSS beams with two built$-$up I$-$beams by continuous welding $3$ steel plates each is $\frac{1}{2^2}-$ thick as shown in the figure.

i$.$ Calculate the section modulus. Is it satisfactory for bending stress?

ii$.$ Calculate the shear stress in the welds.

iii. It is decided to replace the continuous weld by spot welds, and each spot weld can resist $1500$ lbs $.$ in shear. Calculate the maximum spacing between the spot welds $($center$-$to$-$center$).$

$30300-$bs$.$ barrels$2$ HSS Beams$15$ ft$2$ HSS Beams