Problem $3$

A three$-$span concrete bridge structure is designed as shown below. The bridge deck is idealized

as a continuous beam with one end pinned to the ground and the other end fixed to the ground.

Two bridge piers are assumed to be fixed to the riverbed and support the deck.

The following parameters are obtained from the design:

Dimension:

$|AB|=20ft$;$|BC|=60ft$;$|CD|=40ft$;

$|BE|=|CF|=15ft$

Section bending stiffness: $E{I}_{\text{d}\text{e}\text{c}\text{k}}=EI0$; and $E{I}_{\text{p}\text{i}\text{e}\text{r}}=5EI0.$

In the meantime, the deck $($from A to D$)$ is subject to an equivalent traffic load of

$2\mathrm{.}5ki\frac{p}{f}t.$

Use the moment distribution method to determine the resulting moment diagram

due to the traffic load.