BENDING MOMENTS IN A BEAM 



33 



Bending Moments in a Beam. It is required to find the mo- 

 ment at the point M in the simple beam loaded as in (b) Fig. 19. The 



FIG. 19. 



moment at M will be the algebraic sum of the moments of the forces 

 to the left of M. The moment of P = H x B C, the moment of P 2 = 

 H x C D and the moment of RI = H x B A. The moment at M will 

 therefore be 



M^HxB C + HxCD HxB A=HxAD = Hy 

 The moment of the forces to the right of M may in like manner be 

 shown to be 



M 1 = + Hy 



In like manner the bending moment at any point in the beam may be 

 shown to be the ordinate of the equilibrium polygon multiplied by the 

 pole distance. The ordinate is a distance and is measured by the same 

 scale as the beam, while the pole distance is a force and is measured 

 by the same scale as the loads. 



To Draw an Equilibrium Polygon Through Three Points. 

 Given a beam loaded as shown in Fig. 20, it is required to draw 

 an equilibrium polygon through the three points a, b, c. Construct a 

 force polygon (b) with pole o, and draw equilibrium polygon a b' c' in 

 (a). Point b' is determined by drawing through b a line b b' parallel 

 to b^ b" which is the line of action of the resultants of the forces to the 



