Answer :
The magnitudes of the pin reactions at A, B, and C is RA = 4340 lb RB = 4340 lb RC = 6510 lb
How to find magnitudes of the pin reactions?
The magnitudes of the pin reactions at A, B, and C caused by the weight of the uniform 6510-lb beam is as follows:
RA = 4340 lbRB = 4340 lbRC = 6510 lb
Explanation:In order to determine the magnitudes of the pin reactions ,we need to use the equations of equilibrium. Since it is in equilibrium, the sum of forces acting on it must be zero. So, we can write:ΣFy = 0RA + RB - RC - 6510 = 0RA + RB = RC + 6510 ...(1)Now, we can take moments about point A. Since the beam is uniform, we can consider its weight to be acting through its centroid, which is at the midpoint of the beam.
So, we can write:ΣMA = 0RB (18) - RC (24) - 6510 (9) = 0RB - RC = 4340 ...(2)
Solving equations (1) and (2),
We get:RA = 4340 lbRB = 4340 lbRC = 6510 lb
Therefore, the magnitudes of the pin reactions at A, B, and C caused by the weight of the uniform 6510-lb beam isRA = 4340 lbRB = 4340 lbRC = 6510 lb
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