A beam is attached to a vertical wall with a hinge. The mass of the beam is 2000

Question

A beam is attached to a vertical wall with a hinge. The mass of the beam is 2000 kg and it is 4 m long. A steel support wire is tied from the end of the beam to the wall, making an angle of 30degree with the beam (see the figure below). The yield strength (elastic limit) for steel is 290 times 10^6 N/m^2, and the ultimate breaking strength is 400 times10^6 N/m^2. 1) By summing the torque about the axis passing through the hinge, calculate the tension in the support wire. Assume the beam is uniform so that the weight acts at its exact center. (Express your answer to two significant figures.) 2) What is the minimum cross-sectional area of the steel wire so that it is not permanently stretched? (Express your answer to two significant figures.)

Explanation / Answer

Tension in the wire = T
from torque balance, Tsin(30)*l = mg*l/2
1. T = mg/2*sin(30) = 2000*9.8/sin(30)*2 = 19600 N = 19.6 kN
2. T/A = 400*10^10
A = 0.49*10^-8 m^2 = 0.49*10^-4 cm^2

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