EQUILIBRIUM OF FORCES 



the force polygon. The resultant of a system of concurrent forces 

 is always a single force acting through their point of intersection. 



Equilibrium of Non-concurrent Forces. If the forces are 

 non-concurrent (do not all meet in a common point), the condition that 

 the force polygon close is a necessary, but not a sufficient condition for 

 equilibrium. For example, take the three equal forces P lt P 2 and P 3 , 

 making an angle of 120 with each other as in (a) Fig. n. 



Resultant Moment 

 = -Rh 



(a) 



Positive Moment 

 Moment=+Ph 



FIG. ii. 



Negative Moment 



Moment = -Ph 



(C) 



The force polygon (b) closes, but the system is not in equilibrium. 

 The resultant, R f of P 2 and P 3 acts through their intersection and is 

 parallel to P lt but is opposite in direction. The system of forces is in 

 equilibrium for translation, but is not in equilibrium for rotation. 



The resultant of this system is a couple with a moment = P h, 

 moments clockwise being considered negative and counter clockwise 

 positive, (c) Fig. II. The equilibrant of the system in (a) Fig. II is 

 a couple with a moment = + P x h. 



A couple. A couple consists of two parallel forces equal in 

 amount, but opposite in direction. The arm of the couple is the per- 

 pendicular distance between the forces. The moment of a couple is 

 equal to one of the forces multiplied by the arm. The moment of a 

 couple is constant about any point in the plane and may be represented 



