The drawing shows a uniform horizontal beam attached to a vertical wall by a fri
ID: 2187049 • Letter: T
Question
The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle ? = 36o by a brace that is attached to a pin. The beam has a weight of 332 N. Three additional forces keep the beam in equilibrium. The brace applies a force to the right end of the beam that is directed upward at the angle ? with respect to the horizontal. The hinge applies a force to the left end of the beam that has a horizontal component and a vertical component . Find the magnitudes of these three forces. Five stars for explanation.
The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle ? = 36o by a brace that is attached to a pin. The beam has a weight of 332 N. Three additional forces keep the beam in equilibrium. The brace applies a force to the right end of the beam that is directed upward at the angle ? with respect to the horizontal. The hinge applies a force to the left end of the beam that has a horizontal component and a vertical component . Find the magnitudes of these three forces. Five stars for explanation.Explanation / Answer
How long is the beam? If the length of the beam is not important, then you can assume any length you wish and it should workout to the same answer Assume 2 m CM at 1 m from wall Moment from CG: 332N * 1 m = 332 N*m ===> Vertical component at end of beam is: 332N*m = Fv * 2 m Fv = 332/2 = 166 N tan 36 = Fv/Fh 0.726= 166/Fh Fh = 166/0.726 Fh = 228.65 N Force in brace sin 36 = Fv/Fb 0.588= 166/Fb Fb = 166/0.588 Fb = 282.31 N Forces in hinge (Down - UP + Right + Left -) Sum Forces Vertical: -332 + 166 = -1686N ===> We need 166 N up in hinge Sum Forces Horizontal 228.65 N RIGHT ===> We need 228.65 N Left in Hinge
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