$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$multicolumn$\{3\}\{|$c$|\}\{$Area cm $\backslash (\{\}^\{2\}\backslash )\}$ & $\backslash$multicolumn$\{6\}\{|$c$|\}\{$Coordinates $($m$)\}$ & Rad & Grade $\backslash \backslash$

$\backslash$hline A$1$ & A$2$ & A$3$ & x$1$ & X$2$ & X$3$ & Y$1$ & Y$2$ & Y$3$ & $0$ & $\backslash \backslash$

$\backslash$hline $4\mathrm{.}927$ & $4\mathrm{.}508$ & $1\mathrm{.}028$ & $0\mathrm{.}000$ & $2\mathrm{.}898$ & $9\mathrm{.}008$ & $0\mathrm{.}000$ & $3\mathrm{.}903$ & $\backslash (-0\mathrm{.}464\backslash )$ & $0\mathrm{.}352$ & S$235\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Q$2$ The section in Fig. Q$2\mathrm{.}1$ corresponds to a transversal beam of a tie bridge. During stage $1$ of the construction the single section must support its own weight in addition to the concrete slab. To mitigate stresses and deformations, a provisional masonry wall will be built at the centre of the span to act as a prop until the concrete cast.

rig. WL$.$ I

The bending moment diagram for construction stage $1$ is as shown in Fig. Q$2\mathrm{.}1.$ According to this, the sagging and hogging design moments equal $31\mathrm{.}22$ kNm and $55\mathrm{.}52$ kNm $,$ respectively. Consider these values to$,$

$($a$)$ Design a steel beam Grade S$420$ for construction stage $1$ assuming that the compression flange can reach its yield strength $($Class $1$ or Class $2$ section$).$

$[10]$

$($b$)$ Determine whether the masonry wall of $140$ mm thickness and $1$ m width $($out

$[10]$

of plane direction$)$ and $5$ m height can withstand the design unload of $139$ kN imposed by the bridge's deck $\backslash (\{\}^\{1\}\backslash ).$ The wall has a normalised compressive strength of $\backslash (20\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash )$ and uses M$4$ general$-$purpose mortar. Ignore the selfweight of the wall and take the strength reduction $\backslash (\backslash$mathrm$\{$K$\}=0\mathrm{.}75\backslash )$ and safety factor $\backslash (\backslash$mathrm$\{$ym$\}^\{2\}\backslash )\backslash (=3\mathrm{.}0\backslash ).$

$\backslash (\{\}^\{1\}\backslash )$ A bearing device placed at the top of the wall will ensure that the unload distributes uniformly on the cross section of the wall, hence no eccentricity takes place.

$($c$)$ The designer now considers that a timber strut would probably be best to

$[15]$

provide the vertical support to the steel beam while the concrete slab casts.