Relevant data from Appendix B, Table B-4 Properties of I-Beam Sections (S-Shapes): SI Units, of text book.
Designation |
S310 × 74 |
S |
833 × 103 mm3 |
From the shear diagram:
$M_{max} = \frac{1}{2}(3)(3w)$
$M_{max} = 4.5w \, \text{N}\cdot\text{m}$
$(\,f_b\,)_{max} = \dfrac{M}{S}$
$120 = \dfrac{4.5w (1000)}{833 \times 10^3}$
$w = 22,213.33 \, \text{N/m}$
$w = 2,264.36 \, \text{kg/m}$
$w = DL + LL$
$2\,264.36 = 74 + LL$
$LL = 2,190.36 \, \text{kg/m}$
$LL = 21.5 \, \text{ kN/m}$ answer