SIMPLE BEAM 161 



with a force polygon having a pole distance equal to E I f construct 

 an equilibrium polygon; this polygon will be the elastic curve of the 

 beam. It is not commonly convenient to use a pole distance equal to 

 E /, and a pole distance H is used, where N H equals E I ; the de- 

 flection at any point will then be equal to the measured ordinate di- 

 vided by N. 



Simple Beam. The simple beam will be considered when loaded 

 with concentrated and uniform loads, using both algebraic and graphic 

 methods. 



Algebraic Method Concentrated Load at Center of Beam. The 

 simple beam in (a) Fig. 2, is loaded with a load P at the center. The 

 bending moment diagram is shown in (b) and the beam is loaded with 

 the bending moment diagram in (c) Fig. 2. 



To find the equation of the elastic curve take moments of the 

 forces to the left of a point at a distance x from the left support, and 



P x* 



12 

 and 



3 L*.v) (8) 





FIG. 2. FIG. 3. 



The maximum deflection will occur when x=y 2 L in (8), or it 

 may be found by taking moments of forces to left of x = y* L to be 



PL 3 



Beam Uniformly Loaded. The simple beam in (a) Fig. 3, is 



