44 THE LAWS OF EQUILIBRIUM. Art. 39. 



given in the force polygon. Forces are scaled from the fores 

 polygon and distances from the space diagram, or string polygon. 



An infinite number of string polygons may be drawn in a 

 given case, because the point A (Fig. 28) may be taken anywhere 

 in the line of action of P lf and the pole may also be chosen at 

 any convenient point, but the point G will always fall upon the 

 line of action of E if there is complete equilibrium. The string 

 polygon is simply a device for locating the point G. If the 

 directions of the components are carefully noted, it will be found 

 that they all balance each other; for example, 1 acts toward ^ 

 as a component of P and away from as a component of E. 

 This means that if the string polygon were a frame there would 

 be stresses in it equal to the components 1, 2, 3, 4 and 5 (7). 

 (Compression in AG-, tension in AB). Such an imaginary frame 

 is useful in finding reactions as will be explained later (47). 



If the five forces of Fig. 28 are in equilibrium, any one may 

 be considered the equilibrant of all the others (35), and any 

 string may be considered the closing line of the equilibrium poly- 

 gon. It is evident that the equilibrant of P 15 P 2 and P 3 would 

 pass through the intersection of the lines of action of 1 and 4, 

 and of P! and P 2 , through the intersection of the lines of 1 and 3. 



Further properties of the string polygon are explained in 

 Chapters IV and V. 



Fig. 27 shows a string polygon which results when the pole 

 is chosen at one of the apexes of the force polygon ; it is called a 

 resultant polygon. The pole is at a Fig. 26 (c). 



39. The Laws of Equilibrium. To insure equilibrium 

 among the forces acting upon a structure or upon any part of it, 

 as explained in Art. 29, it is only necessary to write the equations 

 of equilibrium and solve for the unknowns. These equations are 

 the very foundation of the whole subject, and are given in Art. 

 34 ; for practical application, however, they are stated as follows : 



1. S HORIZONTAL COMPONENTS = O. ( 5 ) 



2. S VERTICAL COMPONENTS =O. (6) 



3. S MOMENTS =0. (7) 

 or 



1. 2 Components acting toward the right = 

 S " left. 



2. 2 " " up = 

 2 " " down. 



3. 2 Clock wise rioments = 2 Anti-clockwise Homents. 7a 



