Question 1
a.Imagine the case of a shorter bicycle (or of the rack being located slightly higher) where the lower wheel is just above the floor. In this worst case, draw a free body diagram for the rack.
b.For a bicycle of mass 10kg, estimate the force, to 3 sig. fig., acting to pull out the rack’s screw fastener using the dimensions in Table 2.
c.Why might the actual load be slightly lower than you have estimated?
Notes
Table 2
Dimension In mm
Vertical height between wall screws securing the bicycle rack 510
Horizontal distance to where the bicycle’s weight acts on the rack 580
Question 2
An architect has requested an asymmetric hollow section be used as a structural support in a building. The cross section of the beam is shown below.
Note: perform all calculations in mm and provide numerical results to 3 significant figures. Show all of your workings.
a.Show that the centre of area (CoA) of the cross section is approximately 31.0 mm (to 3 sig. fig.) above the bottom edge of the cross section.
b.Using the principle of parallel axes, answer the questions below to perform a manual calculation to show that the second moment of area about the horizontal axis through the centre of area for the asymmetric hollow section is 194 x 103 mm4 (to 3 sig. fig.). Show all your workings.
i. Show that the second moment of area of the box section about the centre of area of the asymmetric hollow section in Figure 4 is 136 x 103 mm4 (to 3 sig. fig.).
ii. Show that the second moment of area of the side flange about the centre of area of the asymmetric hollow section in Figure 4 is approximately 58.2 x 103 mm4 (to 3 sig. fig.).
iii. Show that the second moment of area of the complete asymmetric hollow section in Figure 4 about its centre of area is approximately 194 x 103 mm4 (to 3 sig. fig.).
c.Use the engineers’ theory of bending to calculate the maximum bending stress in the asymmetric hollow section shown in Figure 4 if it is subjected to a bending moment of 1750 N m about a horizontal axis through the centre of area.
