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Examining the results of these examples together with what has been said regarding two parallel forces on p. 40, we may state that the resultant of two parallel forces has the following properties (1) The resultant is : equal to the sum or diflerenee of the given forces according as they are of like or unlike sense. (2) The resultant larger ; it falls the larger force is parallel to the given forces between the given forces if if and acts nearer to the these are of like sense and outside of unlike sense.
FIG. 39. Forces in a derrick crane. Find the push in the jib and the pull in the tie for different values and different dimensions of the apparatus by observing the Check the results by means of the polygon of spring balances. of W forces. The methods are similar It may be assumed to those adopted for the roof truss that the pulley at C merely changes the direction of the cord without altering the force in it. Hence (p. 30). MATERIALS AND STRUCTURES 34 p=W in (Fig. 39 (a) ). which The polygon of forces w _ ^A is shown in Fig.
30). and T T acting P and S, by applications of the R The resultant is parallelogram of forces. found by a third application of the parallelo- A better solution is gram, as shown. obtained by repeated application of the triangle of forces. In Fig. 31(0), four forces P, Q, S and are given. To ascertain T the net effect of the system, first find the equilibrant Ej of P and E l reversed in sense of forces the by triangle (Fig. 31 (^)). will give P is so shown in Fig. 31(0), the resultant of and and Q, I} ABC Q R and is AC represented by in Fig.