130 



DEFLECTION OF A BEAM. 



Art. 83. 



would not be bent. The above equation would give the slope of 

 this part when the value of x at the load is substituted. When 

 the deflection at the load is known, the deflection at the end can 

 be readily determined. Integrating again 



When x = 0, y and therefore C l = 0. 



The maximum deflection evidently occurs at the end when 



The slope at- =<'- W = 



83. Deflection of a Beam Supported at its Ends and 

 Uniformly Loaded. Fig. 101 shows a beam with a uniform load 

 W. The bending moment at a distance x form the left support 



is M x = y 2 Wxy 2 wx 2 . 



w / a* 2 \ 



Since w=- -j- this becomes . M x = l /^W( x -j- 1 



From equation (39) 



Since -JL-=Q evidently, when x 



- 4 X 



and C = 



= 0) 



The deflection is evidently a maximum when # = ^ 

 W 



If the load on a 10"x25.0 Ib. I beam having a span of 20 ft. 

 is 13000 Ibs., uniformly distributed, the deflection at the middle 



will be 



_ 5X13000X240X240X240 _ rr 



384X29000000X122.1 



With the same total load on a span of 10 ft., the deflection 

 of this beam would be only one-eighth as much, since the deflec- 

 tion varies as the cube of the length. 



