there is a timber $($MGP$10,$ untreated pine$)$ roof truss spanning over a small residential building. The roof trusses are spaced at $900$ mm$.$ The roof pitch is $22\mathrm{.}5.$ According to AS $1720\mathrm{.}3$ standard, the roof permanent and imposed loadings are $0\mathrm{.}40$ kPa, and $0\mathrm{.}25$ kPa, respectively. The ceiling permanent load is $0\mathrm{.}12$ kPa. The imposed concentrated load is also $1\mathrm{.}1$ kN$.$ All cross$-$sections for the truss members are shown in the drawings. Further notes and assumptions are as follows:

Ignore the self$-$weight of timber members.

Ignore the truss cantilever.

All member$-$to$-$member connections are pinned.

The ceiling has no imposed load.

The imposed concentrated load only moves on the nodes of the top chord.

Considering a representative $2$D truss:

$4.$ The mechanical engineering team has informed you that for protecting the electrical and mechanical services the maximum deflection at the mid$-$span $($top node$)$ of the truss cannot be larger than $5$ mm$.$ Furthermore, close inspection of the truss has revealed that the middle member at the bottom chord is constructed $2$ mm shorter than what is shown in the geometry. Does the truss satisfy this criterion under the load combination of the permanent load $+$ imposed load $+$ fabrication error? Use analysis in detail $($truss and virtual loading$)$ ANSWER THIS QUESTION IN FULL DETAIL WITH WORKING OUT USING VIRTUAL LOAD. PLEASE AMSWER WITH FULL CALCULATIONS