Relevant data from Appendix B, Table B-8 Properties of I-Beam Sections (S-Shapes): US Customary Units, of
text book.
Designation |
S18 × 70 |
S |
103 in3 |
$(\,f_b\,)_{max} = \dfrac{M}{S}$
$20 = \dfrac{M}{2(103)}$
$M = 4120 \, \text{kip}\cdot\text{in}$
$M = \frac{1030}{3} \, \text{kip}\cdot\text{ft}$
From the moment diagram:
$M = 22.5w$
$\frac{1030}{3} = 22.5w$
$w = 15.26 \, \text{kip/ft}$
$w = \text{dead load, } DL + \text{live load, } w_o$
$15.26(1000) = 2(70) + w_o$
$w_o = 15\,120 \, \text{lb/ft}$
$w_o = 15.12 \, \text{ kip/ft}$ answer