3 2 



GRAPHIC STATICS 



Graphic Moments. In Fig. 18 (b) is a force polygon and (a) 

 is an equilibrium polygon for the system of forces P lf P 2f P Z) P 4 . Draw 



FIG. 18. 



the line M N = Y parallel to the resultant R, and with ends on strings 

 o e and o a produced. Let r equal the altitude of the triangle L M N 

 and H equal the altitude of the similar triangle o e a. H is the pole 

 distance of the resultant R. 



Now in the similar triangles L M N and o e a 



R :Y : :H :r 

 and Rr = HY 



But R r = M = moment of resultant R about any point in the line 

 M N and therefore 



M = H Y 



The statement of the principle just demonstrated is as follows: 

 The moment of any system of coplanar forces about any point in 

 the plane is equal to the intercept on a line drawn through the center 

 of moments and parallel to the resultant of all the forces, cut off by the 

 strings which meet on the resultant, multiplied by the pole distance of 

 the resultant. It should be noted that in all cases the intercept is a 

 distance and the pole distance is a force. 



This property of the equilibrium polygon is frequently used in 

 finding the bending moment in beams and trusses which are loaded with 

 vertical loads. 



