Art. 33. 



FOUR FORCES IN EQUILIBRIUM. 



33 



force Tnangfc 



three non-concurrent forces P lt P 2 , 

 and P 3 forming a closed triangle, but 

 these cannot be in equilibrium be- 

 cause even if P 3 should happen to be 

 equal and opposite to R, as shown, 

 they form a couple. If P 3 intersects 

 R, the triangle will not close. p. _ 



Three parallel forces may, however, be in equilibrium, as 

 is clear in the case shown in Fig. 17; they may be considered 

 concurrent, intersecting at infinity. 



It is important to note that when three forces are in equi- 

 librium, their lines of action inter- 

 sect in a point. In Fig. 23, P is the 

 resultant of the wind load on one 

 side of a roof; it is desired to de- 

 termine the reactions R : and R 2 ap- 

 plied at A and B so that R 2 will be 

 vertical. R : passes through C be- 

 cause the three forces are to be io 

 equilibrium. Now the force tri- 

 angle may be drawn, because one 

 side P, and the directions of all are 

 known. This determines the mag- 

 nitudes of R and # 2 as shown. 



33. Four Forces in Equilibrium. If four forces are in 

 equilibrium, the resultant of any two must be the equilibrant of 

 the other two. This is evident for concurrent forces. For non- 

 concurrent forces see Fig. 24. The directions of the four forces 



Fig. "^3. 



f 



Fig. 24. 



P!, P 2 , R 2 , and R lt and the magnitude of one of them, say P t , are 

 known. The resultant of P t and R 2 passes through D and must 



