Problem $1)$ A simply supported floor beam must be designed to support a reinforced concrete slab which is $4$

inches thick. The beam has a span of $24$ feet. The floor beams are spaced $8$ feet on center. The beam will be

made from A$36$ steel. A safety factor of $1\mathrm{.}6$ must be used for stresses due to bending and $1\mathrm{.}45$ for stresses due to

shear. The floor supported by this beam is used for heavy manufacturing. Do the following:

Determine the dead and live loads for the beam.

Determine the allowable bending stress for the beam.

Determine the allowable shear stress for the beam.

Determine the supporting reactions at the end of the beam.

Determine the maximum shear load in the beam.

Determine the maximum moment load in the beam.

Determine the required Section Modulus for the beam $($ignore beam weight$)$

Select the lightest wide flange beam to use for this beam.

Show that the bending stress in the wide flange beam selected is ok $($include beam weight$).$

Show that the average shear stress is also ok $($include beam weight$).$

Make sure all $10$ items above are clearly shown with a clear presentation of the calculations for each.