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

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 M 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.

a. Under maximum load, what is the x-component of the force exerted on the beam by the pivot at P?

b. Under maximum load, what is the y-component of the force exerted on the beam by the pivot at P?

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=18000sinu=18000x3/5=10800N.

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