Steel construction beams, with an industry designation of \"W12 ? 22,\" have a w

Question

Steel construction beams, with an industry designation of "W12 ? 22," have a weight of 18 pounds per foot. A new business in town has hired you to place its sign on a 4.0 m long steel beam of this type. The design calls for the beam to extend outward horizontally from the front brick wall (see figure). It is to be held in place by a 5.0 m-long steel cable. The cable is attached to one end of the beam and to the wall above the point at which the beam is in contact with the wall. During the initial stage of construction, the beam is not to be bolted to the wall, but to be held in place solely by friction.

Explanation / Answer

given, lnear mass density = 18 pounds/foot

= 18*4.44822 N/(0.3048 m)

= 262.7 N/m

weight of the beam, W = 4*262.7

= 1050.8 N

angle made by the string with beam, theta = cos^-1(4/5)

= 36.87 degrees

Let T is the tension in the string.

As the beam is in equilibrium, net focre and net torque acting on the beam must be zero.

Apply, net torque on beam about left end = 0

T*4*sin(36.87) - W*2*sin(90) = 0

T = 2*W/(4*sin(36.87))

= 2*1050.8/(4*sin(36.87))

= 875.6 N or 196.8 lb

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