BEAM 163 



The maximum value of A is equal to 3; when x equals L, and 



PL 3 



To find the maximum deflection we may take the moment of the 

 entire bending-moment parabola about the point I, and 



PL 2 2 

 = - X A and 

 2 3 



PL 3 



This method of finding the maximum deflection of a cantilever 

 beam is the one to use in calculations, and will be used in the solu- 

 tion of the problem of the transverse bent. 



Simple Beam Graphic Method. In Fig. 5 a simple beam is 

 loaded with a load P, as shown. With force polygon (b), draw 

 equilibrium polygon (c). Now load the beam with equilibrium polygon 

 as in (c), and divide the area of the equilibrium polygon into segments, 

 which are treated as loads acting through their centers of gravity. Con- 

 struct force polygon (d) and draw equilibrium polygon (e). 



Now, the deflection at any point having an ordinate y in (e) will 

 be, if proper scales are used, 



_yXHXH* 



El 



In Fig. 5, if P equals 3000 Ibs., and the area of the equilibrium 

 polygon and pole distance H 1 are measured in square-foot pounds, 

 pole distance H in pounds, and y in feet, we will have 



A; V H V H 1 V 1728 

 y /\ ** /\ ** /\ * / -^o 



El 



= 1.88 inches at center, while maximum value of deflection is 

 A 1 1.92 inches. 



Tangents to Elastic Curve. If strings I and 3 in (e) be pro- 



