A timber deck as shown below is used as a shop floor for the sale and display of merchandise in a shopping complex in Brisbane, Queensland. Timber floor sheeting is $28$ mm thick and has a density of $900\backslash (\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$

a$)$ Joist spacing Z $=0\mathrm{.}45$ m $($centres$),$ joist span Y $=2\mathrm{.}5$ m$,$ cross$-$section $=175$ mm x $50$ mm$.$

The density of the joists $=900$ kg$/$m$3.$

Calculate the line load G of the typical joist in the unit of kN$/$m$.$

b$)$You are now asked to use the relevant design standard to calculate the line load Q$,$ in the unit of kN$/$m$,$ for the typical joist chosen in a$)$

c$)$The joist spacing $($Z$)$ is now changed to $0\mathrm{.}5$ m$.$ With this new spacing, the line load G of the typical joist has become $0\mathrm{.}2009$ kN$/$m and you are now tasked to calculate the line load G$2$ of the bearer. Below is the following additional design information:

Joist span $($Y$)$ is now $2\mathrm{.}59$ m$.$

The bearer is supported by the post in the middle and two wall hangers at two ends.$$

Bearer span X $=3$ m; bearer cross$-$section $=300$ mm $75$ mm$.$

The density of bearers $=1150$ kg$/$m$3$which is higher than the density of joists and floor sheeting.

d$)$Continuing from c$),$ use the relevant design standard$/$s to calculate the line load Q$,$ in the unit of kN$/$m$,$ for one bearer.

e$)$ Assuming below are the final line load values of the bearer:

$*$Line load G $=0\mathrm{.}7848$kN$/$m

$*$ Line load Q$=5\mathrm{.}142$ kN$/$m

Find the critical strength limit state load combination for this bearer, in the unit of kN$/$m

Enter the magnitude of this critical load combination, rounded to the nearest $3$ significant figures.

In addition, draw a line load diagram for this combination $($for submission of working notes at the end$).$ The diagram should have all the details needed for further analysis.