helpA bridge is to be constructed using three I$-$beams as the girder. Figures $1$ to $3$ shows some detail

of the construction and Table $1$ shows some information regarding the bridge.

Determine a suitable dimension for the bridge girder. The bridge girder should meet the

following wide$-$ranging requirements: the moment of inertia for your I$-$beam must be higher

than the required value, $I_x$ and lower than the maximum allowable value $I_{x-\text{m}\text{a}\text{x}}$ and the width of

each I$-$beam should be less than $\frac{1}{5}$ of the value of $B$ given in Table $1.$

Apply the fundamentals of engineering statics and use the self$-$weight information given in

Table $1$ to calculate the support reaction at each abutment. Use abstract reasoning to explain

how the support reactions at the abutments can be reduced.

Table $1$: Bridge information

$B=$ width of the bridge ;$L=$ length of the bridge; ${}_d=$ self$-$weight of bridge deck; ${}_g=$ self$-$

weight of bridge girder; $I_x=$ required moment of inertia for I$-$beam about the centroid, $I_{x-\text{m}\text{a}\text{x}}=$

maximum allowable moment of inertia for I$-$beam about the centroid.