Art. 31. 



TWO FORCES IN EQUILIBRIUM. 



37 





spect the same except that it acts in the opposite direction. // 

 the resultant is a couple, it is only necessary that the equilibrant 

 be a couple of equal moment tending to turn in the opposite 

 direction ; the forces of the two couples may make any angle with 

 each other and be of different magnitudes. In Fig. 18, if P=1000 

 Ibs. and bd 5 ft., the moment of the couple is 5000 foot-pounds, 

 and it can be held in equilibrium by another couple acting on 

 the same body in the opposite direction, located anywhere in the 

 same plane, so long as the moment of the latter is 5000 foot- 

 pounds. ; for example, by forces of 5 Ibs., 1000 ft. apart or 100 

 Ibs., 50 ft. apart. 



No single force can hold a couple in equilibrium, and no 

 single force can be an equivalent of a 

 couple. A simple case is that shown in 

 Fig. 19, where the wind load P produces 

 the reactions H whose sum equals P thus 

 forming a couple; another couple must act 

 at the supports, and its moment is Vb = Pa. 

 Fig. 20 shows an exactly similar case. If 

 there be more than one parallel load, the 

 resultant of the loads with the direct re- 

 action will form a couple, thus reducing to 

 Fig. 19. the same case. 



In Fig. 20, if the wind force P were just sufficient to over- 

 turn the car, the right-hand reaction V would be zero, and the 

 resisting couple would be the weight of the car acting at its 

 center of gravity, and the upward pressure of the left-hand rail 

 V. In this case V would equal W, the weight of the car, and 

 the arm of the couple would be \ b. 



The components of a force are any 

 forces of which the given force is the 

 resultant. It is often convenient to re- 

 solve a force into two components, es- 

 pecially two components at right angles to 

 each other. It is also sometimes conven- 

 ient to work with the resultant of two or 

 more forces in place of the forces* them- 



selves. 

 Fig. 20. 

 31. Two Forces in Equilibrium. In order that two forces 



may be in equilibrium, it is not only necessary that they be equal 

 and act in opposite directions, but they must have the same line 



