Problem $3(40$ points$)$

A local land developer needs a single lane bridge across a small

stream. He figured that it could be built with two I$-$beams bridging

the stream and smaller $C4x7\mathrm{.}25$ channel sections every few feet

supporting the concrete deck. He asks you to check the channel

members for both shear and bending stress. He mentions that dump

trucks will have to use the bridge to bring fill dirt to the construction

site.

What is known:

The bridge span is $20$ feet long and $10$ feet wide.

The heaviest load is a $19$ ton dump truck. The front wheels

will support $20\%$ of the load and the dual back wheels $80\%.$

As a worst case, the two back wheels are assumed be a single

point load and will be loaded on a single channel.

The wheels are $8$ feet apart.

Assume the I$-$beam supports are pinned supports, $10$ feet

apart.

The maximum allowable shear stress is $18$ksi.

The maximum allowable bending stress is $36$ksi.

Assume the concrete decking carries none of the loading.

Question

What is the maximum shear and bending stress in the channel mt

Hints:

Construct a free body diagram to understand all loading on a

typical channel.

Determined the location of the maximum shear load and

bending moment.

Calculate Q for the channel.

Use the shear and bending stress equations to calculate the

stresses.

vievvs ui Lulir IIuun vil DluyeA local land developer needs a single lane bridge across a small

stream. He figured that it could be built with two I$-$beams bridging

the stream and smaller C$4$x$7\mathrm{.}25$ channel sections every few feet

supporting the concrete deck. He asks you to check the channel

members for both shear and bending stress. He mentions that dump

trucks will have to use the bridge to bring fill dirt to the construction

site