Question $2$

A simply$-$supported highway bridge has a span length of $50$ ft $.$ A vehicle with the following axle loads is positioned on the bridge:

Front axle load: $8$ kip $($located $22$ ft from the right support$)$

Two middle axle loads: $32$ kip each $($spaced $14$ ft apart, with the closest axle $36$ ft from the left support$)$

Assume that the impact factor is $1\mathrm{.}33,$ and the live load distribution per axle is uniformly distributed. Also, take into account a

distributed lane load of $w_{Ln}=0\mathrm{.}65ki\frac{p}{f}twLn=0\mathrm{.}65ki\frac{p}{f}t.$

Task:

Determine the unfactored bending moment at midspan due to the vehicular live load.

Determine the unfactored shear force at the supports due to the vehicular live load.

Given:

Span Length: $50$ ft

Live Load Axle Distribution: As described above

Distributed Lane Load: $w_{Ln}=0\mathrm{.}65ki\frac{p}{f}twLn=0\mathrm{.}65ki\frac{p}{f}t$

Impact Factor: $1\mathrm{.}33$

Axle Loads:

Front Axle $=8$kip

Middle Axles $=32$ kip each

Axle Spacing:

$14$ ft between middle axles

Front axle is $22$ ft from the right support