For Girder (G - 1) | Solution to Problem 542

For Girder (G - 1)
$S_{live-load} = \dfrac{M}{f_b} = \dfrac{40(1000^2)}{120}$
$S_{live-load} = 333.33 \times 10^3 \, \text{mm}^3$
 

From Appendix B, Table B-2 Properties of Wide-Flange Sections (W Shapes): SI Units, of text book:

 
Consider W310 × 28 with S = 351 × 10³ mm³
 
Checking:
$S_{supplied} \ge S_{required} + S_{own-weight}$
 
$S_{supplied} = 1790 \times 10^3 \, \text{mm}^3$
$S_{required} = 333.33 \times 10^3 \, \text{mm}^3$
$S_{own-weight} = \dfrac{M_{own-weight}}{f_b} = \dfrac{[ \, \frac{1}{8}(274.68)(6^2)](1000)}{120}$
$S_{own-weight} = 10\,300.5 \, \text{mm}^3$
 
$(1790 \times 10^3) \ge (333.33 \times 10^3) + 10\,300.5$
$(1790 \times 10^3) \ge (343.63 \times 10^3) \,\,$ (ok!)
 
Use W310 × 28 for G-1. answer
 
Solution for Beams (B - 1)
Solution for Girder (G - 1)
Solution for Beams (B - 2)
Solution for Beams (B - 3)
Solution for Girders (G - 2)