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

92.3mm

(to\ three sig. fig.) above the bottom edge of the lintel cross-section.\ (3 marks)\ 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

9.28\\\\times 10^(6)mm^(4)

and

2.07\\\\times 10^(6)mm^(4)

respectively (to\ three sig. fig.).\ (10 marks)\ ii. Therefore, show that the second moment of area of the complete section, as\ shown in Figure

7b

, about its centre of area is approximately

11.4\\\\times 10^(6)mm^(4)

(to\ three sig. fig.).

Lintels such as that shown in Figure 7a span openings such as doors and windows, and support the load positioned above the aperture. They come in various forms depending on the application. A box lintel has been specified for a particular building project. The cross-section of the lintel is shown in Figure 7b. (a) Figure 7 a) Example of a lintel used in construction (source: https-//catnic.com/products/lintels/overview/steel-lintels-for-solid-walls) and b) lintel dimensions (dimensions in mm ) 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 92.3mm (to three sig. fig.) above the bottom edge of the lintel cross-section. (3 marks) 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 crosssection 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 9.28106mm4 and 2.07106mm4 respectively (to three sig. fig.). (10 marks) ii. Therefore, show that the second moment of area of the complete section, as shown in Figure 7b, about its centre of area is approximately 11.4106mm4 (to three sig. fig.)