A box lintel has been specified for a particular building project. The cross$-$section of the lintel

is shown in Figure $7b.$

$($a$)$

$($b$)$

Figure $7$ a$)$ Example of a lintel used in construction $($source:

Note: perform all calculation in $mm$ and provide numerical result to three significant

figures. Show all of your workings.

a$.$ Show that the centre of area $($CoA$)$ of the cross$-$section is approximately $92\mathrm{.}3mm($to

three sig. fig.$)$ above the bottom edge of the lintel cross$-$section.

b$.$ The second moment of area can be calculated by considering the cross$-$section as a

combination of a hollow box section and a horizontal flange. By separating the cross$-$

section in this way and by using the principle of the parallel axes, answer the questions

below to determine the second moment of area about the horizontal axis through the

centre of area.

i$.$ Show that the second moment of area about the centre of area for the box and

horizontal flange sections are $9\mathrm{.}28{10}^{6}m{m}^4$ and $2\mathrm{.}07{10}^{6}m{m}^4$ respectively $($to

three sig. fig.$).$

ii$.$ Therefore, show that the second moment of area of the complete section, as

shown in Figure $7$b$,$ about its centre of area is approximately $11\mathrm{.}4{10}^{6}m{m}^4($to

three sig. fig.$).$

c$.$ Use a spreadsheet, as demonstrated in Activity $12\mathrm{.}2b$ to check your calculations of the

second moment of area. Copy a screenshot of your spreadsheet as the answer to this

part.