Give the following problem a try. If you get stuck, here is one way to work it: Essential Solution Video.

The beam shown will be constructed from a standard steel $W-$shape using an allowable bending stress of $155$MPa. Assume $L=3\mathrm{.}3m,$

$w_A=49k\frac{N}{m}$ and $P=14kN.$

$($a$)$ Develop a list of four acceptable shapes that could be used for this beam. Include the most economical W$310,$ W$360,$ W$410,$ and

W$460$ shapes on the list of possibilities.

$($b$)$ Select the most economical W shape for this beam.

Answers:

$($a$)$

The most economical W$310$ shape is

W$310$x

The most economical W$360$ shape is

W$360$x

The most economical W$410$ shape is

W$410$x

The most economical W$460$ shape is

W$460$x

$$

with $5$

$$

with $5$

$({10}^3)m{m}^3$

$({10}^3)m{m}^3$

$({10}^3)m{m}^3$

$({10}^3)m{m}^3$

$($b$)$ The most economical W shape has a mass of