Please show as much work as possible:

A major six$-$story steel framed office building is laid out in a ${35}^{\text{'}}$ by ${35}^{\text{'}}$ grid and has secondary beams spaced at $7^{\text{'}}-0^{\text{'}\text{'}}$ feet o$.$c$.$ Design$/$select the secondary beam, which spans ${35}^{\text{'}}-0^{\text{'}\text{'}}$ feet between girders. Select the lightest $18"$ deep steel beam from Ambrose Table A$\mathrm{.}3$ that will work for moment, shear and deflection. Use A$992$ steel. Assume the secondary beams have full lateral support from the metal deck. Include beam self$-$weight as shown below. Assume the beam is a compact shape. Refer to the attached partial framing plan. Check deflection two ways including L$/360$ for live load only and L$/240$ for live plus dead load. $($Note that the final beam size must work for both deflection criteria$).$

Values for distributed loads $"w"$ are given. Provide the tabulations to confirm these values in the table on the following page. Only items marked with an asterisk will contribute this assignment's point total; the final beam selection is worth four points.

Floor live load $=100$ psf

Floor dead load $=80psf$

Estimated beam self weight $=50$ plf

Live Load Factor: $1\mathrm{.}2$

Dead Load Factor $1\mathrm{.}6$

A$992$ steel

Fy $=50,000$ psi

$Fv=30,000$ psi

E $=29,000,000$ psi

WLRFD in Lbs$/$ft $($Live $+$ Dead$)$: $1,852$ plf

Wurtactered in Lbs$/$ft $($live load only$)700$ plf

Wurtactered in Lbs$/$ft $($live load $+$ dead load$)1,310$ plf