Experimental Mechanics / A Course of Lectures Delivered at the Royal College of Science for Ireland

by Robert S. Ball

It represents the principle of the framework in the common lifting crane, and has numerous applications in practical mechanics. A rod of wood b c 3' 6" long and 1" × 1" section is capable of turning round its support at the bottom b by means of a joint or hinge: this rod is called the “jib”; it is held at its upper end by a tie a c 3' long, which is attached to the support above the joint. a b is one foot long. From the point c a wire descends, having a hook at the end on which a weight can be hung. The tie is attached to the spring balance, the index of which shows the strain. The spring balance is secured by a wire-strainer, by turning the nut of which the length of the wire can be shortened or lengthened as occasion requires. This is necessary, because when different weights are suspended from the hook the spring is stretched more or less, and the screw is then employed to keep the entire length of the tie at 3'. The remainder of the tie consists of copper wire.

39. Suppose a weight of 20 lbs. be suspended from the hook w, it endeavours to pull the top of the jib downwards; but the tie holds it back, consequently the tie is put into a state of tension, as indeed its name signifies, and the magnitude of that tension is shown to be 60 lbs. by the spring balance. Here we find again what we have already so often referred to; namely, one force developing another force that is greater than itself, for the strain along the tie is three times as great as the strain in the vertical wire by which it was produced.

Fig. 17.

40. What is the condition of the jib? It is evidently being pushed downwards on its joint at b; it is therefore in a state of compression; it is a strut. This will be evident if we think for a moment how absurd it would be to endeavour to replace the jib by a string or chain: the whole arrangement would collapse. The weight of 20 lbs. is therefore decomposed by this contrivance into two other forces, one of which is resisted by a tie and the other by a strut.

Fig. 18.

41. We have no means of showing the magnitude of the strain along the strut, but we shall prove that it can be computed by means of the parallelogram of force; this will also explain how it is that the tie is strained by a force three times that of the weight which is used. Through c ([Fig. 18]) draw c p parallel to the tie a b, and p q parallel to the strut c b then b p is the diagonal of the parallelogram whose sides are each equal to b c and b q. If therefore we consider the force of 20 lbs. to be represented by b p, the two forces into which it is decomposed will be shown by b q and b c; but a b is equal to b q, since each of them is equal to c p; also b p is equal to a c. Hence the weight of 20 lbs. being represented by a c, the strain along the tie will be represented by the length a b, and that along the strut by the length b c. Remembering that a b is 3' long, c b 3' 6", and a c 1', it follows that the strain along the tie is 60 lbs., and along the strut 70 lbs., when the weight of 20 lbs. is suspended from the hook.

42. In every other case the strains along the tie and strut can be determined, when the suspended weight is known, by their proportionality to the sides of the triangle formed by the tie, the jib, and the upright post, respectively.

43. In this contrivance you will recognize, no doubt, the framework of the common lifting crane, but that very essential portion of the crane which provides for the raising and lowering is not shown here. To this we shall return again in a subsequent lecture ([Art. 332]). You will of course understand that the tie rod we have been considering is entirely different from the chain for raising the load.