33 



THREE FORCES IN EQUILIBRIUM. 



Art. 82 



Fig. 21. 

 21 (6) and (c). 



of action ; if their lines of action be parallel, they form a couple 

 which will produce rotation. 



32. Three Forces in Equilibrium. The resultant of two 

 forces is shown in magnitude and direc- 

 tion by th diagonal of a parallelogram 

 whose adjacent sides represent the given 

 forces in magnitude and direction as 

 shown in Fig. 21. The equilibrant is 

 the same as the resultant except that it 

 has an opposite direction. It is, how- 

 ever, necessary that the line of action of 

 R or E pass through the point F, the 

 common point in the lines of the com- 

 ponents P l and P 2 . 



The resultant or equilibrant may 

 also be found by simply constructing 

 one of the triangles ABC or ACD, Fig. 

 It is necessary that the directions of the given 

 forces follow each other. Fig. 21 (d) shows a wrong construction 

 because the directions of P and P 2 are opposite in going around 

 the triangle. 



A triangle which represents three forces in magnitude and 

 direction is called a FORCE TRIANGLE. It is evident that the force 

 triangle does not represent the location of the forces with respect 

 to each other. 



// the forces in a force triangle all have the same direction 

 they represent a concurrent system in equilibrium, and any one 

 force is the equilibrant of the other two. If the direction of any 

 one is opposite to that of the other two, it is their resultant. It 

 follows that a component may be greater than a resultant. 



Although the force triangle represents concurrent forces, it 

 is, nevertheless, the foundation of graphic statics, as will be seen 

 by what follows; by its means the resultant of any number of 

 forces may be found, first finding the resultant of two of them, 

 then the resultant of this resultant and a third force, and so on. 



Three non-concurrent forces can not be in equilibrium, be- 

 cause the resultant of two of them would have to be equal to the 

 third and in the same line of action; this makes them con- 

 current because the resultant passes through the point of inter- 

 section of the lines of action of the first two. Fig. 22 shows 



