A uniform 600 kg beam, 6 m long, is freely pivoted at P. The beam is supported i

Question

A uniform 600 kg beam, 6 m long, is freely pivoted at P. The beam is supported in a horizontal position by a light strut, 5 m long, which is freely pivoted at Q and is loosely pinned to the beam at R. A load of mass is suspended from the end of the beam at S. A maximum compression of 18, 000 N in the strut is permitted, due to safety. In the figure, under maximum load, the x-component of the force exerted on the beam by the pivot at P is closest to: A) 14, 400 N B) 16, 200 N C) 10, 800 ND) 18, 000 N E) 12, 600 N

Explanation / Answer

The beam is in equilibrium under the following forces:

(1) its weight 600kg,

(2) the weight M hanging at its end,

(3) the reaction of the hinge at R on it (horizontal and vertical components X and Y respectively) and

(4)the reaction S of the strut on it at R (the mid-point of the beam).

We assume that M is adjusted so that the compression in the strut = S=18000 (maximum value), and that the joint at R is smooth so that the reaction of the strut on the beam is outwards (away from the compression) in the direction of the line of the strut.

Let u be the angle the strut makes with the wall. Resolving horizontally for the equilibrium of the beam,

we get X= 18000*sinu = 18000x3/5 =10800 N (option C)

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