24 GRAPHIC STATICS 



Force Polygon. If more than three concurrent forces (forces 

 which meet in a point) are in equilibrium as in (a) Fig. 10, R^ in (b) 

 will be the resultant of P and P 2 , R 2 will be the resultant of R^ and P 3 , 



Ps ^ 



.(a) 



FIG. 10. 



and will also be the equilibrant of P 4 and P 5 . The force polygon in (b) 

 is therefore only a combination of force triangles. The force polygon 

 for any system of forces may be constructed as follows: Beginning 

 at any point draw in succession lines representing in magnitude and 

 direction the given forces, each line beginning where the preceding one 

 ends. If the polygon closes the system of forces is in equilibrium, if 

 not the line joining the first and last points represents the resultant 

 in magnitude and direction. As in the case of the force triangle, it 

 is immaterial in what order the forces are applied as long as they 

 all act in the same direction around the polygon. A force polygon is 

 analogous to a traverse of a field in which the bearings and the distances 

 are measured progressively around the field in either direction. The 

 conditions for closure in the two cases are also identical. 



It will be seen that any side in the force polygon is the equilibrant 

 of all the other sides and that any side reversed in direction is the re- 

 sultant of all the other sides. 



Equilibrium of Concurrent Forces. The necessary condition 

 for equilbrium of concurrent coplanar forces therefore is that the force 

 polygon close. This is equivalent to the algebraic condition that 2 

 horizontal components of forces = o, and 2 vertical components of 

 forces = o. If the system of concurrent forces is not in equilibrium 

 the resultant can be found in magnitude and direction by completing 



