A beam is attached to a vertical wall with a hinge. The mass of the beam is 1000 kg and it is 3 m long. A steel support wire is tied from the end of the beam to the wall, making an angle of 30o with the beam (see the figure below). Recall the important values for steel: Young's modulus is 200 x 109 N/m2, the shear modulus is 78 x 109 N/m2, the bulk modulus is 140 x 109 N/m2, the yield stress (elastic limit) is 290 x 106 N/m2, and the ultimate breaking strength is 400 x 106 N/m2.
(a) 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.
(b) What is the minimum cross-sectional area of the steel wire so that it is not permanently stretched?
