You have been asked to help suspend a road-sign over a narrow Hobart street. The sign has a mass of 100 kg and will need to be suspended from the end of a 5-m long steel beam which will be attached at the other end to a building. If the beam has a square cross-section, how thick will it need to be to carry the weight without sagging by more than a centimetre? Young's modulus for steel is 2.0x1011 N m-2.
A)20 cm.
B)15 cm.
C)12.5 cm.
D)10 cm.
E)7.5 cm.

Question

Quizplus · Accepted Answer

The maximum deflection of the beam under the weight of the road sign should be 1 cm or less. To calculate the required thickness of the beam, we need to use the formula for the deflection of a beam under a point load:

δ = (4FL³) / (Ed⁴)

where:
δ = maximum deflection
F = weight of the road sign = 100 kg x 9.8 m/s² = 980 N
L = length of the beam = 5 m
E = Young's modulus for steel = 2.0x10¹¹ N/m²
d = thickness of the beam (assumed to be square)

Rearranging the formula to solve for d, we get:

d = (4FL³) / (Eδ)⁴

Substituting the given values, we get:

d = (4 x 980 x 5³) / (2.0x10¹¹ x 0.01)⁴
d ≈ 0.125 m = 12.5 cm

Therefore, the thickness of the beam should be 12.5 cm or more to carry the weight of the road sign without sagging by more than 1 cm. The best choice is C) 12.5 cm.

You Have Been Asked to Help Suspend a Road-Sign Over