26 GRAPHIC STATICS 



graphically by twice the area of the triangle having one of the forces 

 as a base and the arm of the couple as an altitude. The moment of a 

 force about any point may be represented graphically by twice the 

 area of a triangle as shown in (c) Fig. n. 



It will be seen from the preceding discussion that in order that a 

 system of non-concurrent forces be in equilibrium it is necessary that the 

 resultant of all the forces save one shall coincide with the one and be 

 opposite in direction. Three non-concurrent forces can not be in equi- 

 librium unless they are parallel. The resultant of a system of non- 

 concurrent forces may be a single force or a couple. 



Equilibrium Polygon. First Method. In Fig. 12 the resultant, 

 a, of P and P 2 act s through their intersection and is equal and parallel 

 to a in the force polygon (a) ; the resultant, b, of a and P 3 acts through 





FIG. 12. 



their intersection and is equal and parallel to b in the force polygon; 

 the resultant, c, of b and P 4 acts through their intersection and is equal 

 and parallel to c in the force polygon ; and finally the resultant, R, of c 

 and P 5 acts through their intersection and is equal and parallel to R 

 in the force polygon. R is therefore the resultant of the entire system 

 of forces. If R is replaced by an equal and opposite force, , the sys- 

 tem of forces will be in equilibrium. Polygon (a) in Fig. 12 is called 



