56 SIMPLE BEAMS 



Moment and Shear in Beams : Concentrated Loads. The bend- 

 ing moment in the beam shown in Fig. 37 may be found by constructing 

 the force polygon (a) and equilibrium polygon (b) as shown. 



R 2 I *- 



h f 



e (a) 

 ( _B Force Polygon 



(0 

 5hear Diagram 



FIG. 37. 



The bending moment at any point is then equal to the ordinate 

 to the equilibrium polygon at that point multiplied by the pole distance, 

 H. The ordinate is to be measured to the same scale as the beam, and 

 the pole distance, H, is to be measured to the same scale as the loads in 

 the force polygon. The ordinate is a distance and the pole distance 

 is a force. 



Or, if the scale to which the beam is laid off be multiplied by the 

 pole distance measured to the scale of the loads, and this scale be used 

 in measuring the ordinates, the ordinates will be equal to the bending 

 moments at the corresponding points. This is the same as making the 

 pole distance equal to unity. Diagram (b) is called a moment diagram. 



Between the left support and the first load the shear is equal to 



