1 08 



STATICS. 



[181. 



181. According to its definition the bending moment of a 

 beam at any cross-section is found by adding the moments, with 

 respect to the cross-section, of all the external forces on one 

 side of the section. 



Graphically, the bending moment is readily derived from the 

 funicular polygon. Thus in Fig. 54, for the cross-section a/3, 

 the resultant of the forces on the left is R' = A IV 1 W 2 = o 3 in 



Fig. 54. 



the force polygon. Its position is found by bringing to inter- 

 section the two sides A'B 1 and II III of the funicular polygon 

 met by the section a/3. For the funicular polygon resolves A 

 along A*B' and A'l, W l along I A' and I II, IV 2 along II I and 

 II III. The components falling into the same line being equal 

 and opposite (as appears from the force polygon), the forces A, 

 W lt JV 2 are together equivalent to the components along A'B* 

 and II III ; their resultant R' must therefore pass through the 

 intersection 5 of these lines. 



