Consider the proposed three$-$span continuous road bridge shown in Figure $1$ and answer

Questions $1$ to $4$ below. The bridge superstructure is to be a concrete box girder that carries a

$6\mathrm{.}3m$ wide carriageway with noise barriers provided along both sides of the deck. The

entire deck is assumed to have the same deck section with dimensions as shown in Figure

The bridge has normal wind exposure. Deck surfacing of $100mm$ thick is provided and

the deck is to carry utility cables across the spans.

The density of concrete and deck surfacing could be taken as $25k\frac{N}{m^3}$ and $20k\frac{N}{m^3}$

respectively. The weight of utility cable is assumed to be $1\mathrm{.}0k\frac{N}{m}.$ Influence lines for

$BM$ at the middle of each span and the internal supports are to be generated from

SAP$2000.$ If the area under the influence line is necessary, you need to numerically

integrate using trapezoidal rule.

Question $1$

$($a$)$ Determine the characteristic values of permanent actions by the self$-$weight of the box

girder only $($no need to take into account the concrete footing of the noise barrier$).$ Express

the actions as uniformly distributed loads $($UDLs$)$ along the span $($i$.$e$.$ in $k\frac{N}{m}).$

$($b$)$ Determine the characteristic values of permanent actions by the superimposed dead load

$($SDL$)$ due to $($i$)$ deck surfacing and $($ii$)$ utility cables. Express the actions as UDLs along

the span $($i$.$e$.$ in $k\frac{N}{m}).$ Note that there should be an upper and lower value of the actions.

$($c$)$ With the aid of influence lines, determine the maximum and minimum moment $(M_x)$ at

Location A due to characteristic values of permanent actions by $($i$)$ self$-$weight of the box

girder; $($ii$)$ SDL due to deck surfacing; and $($iii$)$ SDL due to utility cables, which are

calculated in $($a$)$ and $($b$).$ Location $A=$ to be confirmed.Figure $1-$ Structural arran ement of the bridge