The beam shown in Figure P8. will be constructed from a standard steel W-shape, with an allowable bending stress of $165 \mathrm{MPa}$. (a) Develop a list of four acceptable shapes that could be used for this beam. Include the most economical W310, W360, W410, and W460 shapes on the list of possibilities.

$\bold{Given:}$

• Allowable bending stress that will be used in constructing a standard steel W-shape beam, $\sigma_{\text{allow}}$ = $165~\text{MPa}$

$\bold{Required:}$

• Develop a list of four acceptable shapes that could be used for this beam. On this list, include the most economical $\text{W310, W360, W410,}$ and $\text{W460}$ shapes.
• Select the most economical W shape for this beam.