DEFLECTION OF BEAMS 



This also gives the maximum value of the deflection. 

 In order to obtain 8, the deflection at any point, 



- 



297 



Wa 3 W 

 flEl 



W 



157. (4) A beam of length I ft. supported at both ends and 

 carrying a uniformly distributed load of w tons per foot run. 



O x 



FIG. 102. 



The reaction at each support is wa tons, where a is the length 

 of the half span. 



Let the centre of the beam be the origin, and let A be a section 

 situated at a distance x ft. from O. 



Bending moment at A = wa(a x) - - (a x) 2 



t _ 



= 5 (a 2 - x 2 ) ft. tons 



Then 



and 



dx 

 dij 



Con* 



But at O, where x = 0, / = 0. Then Const = 



dx 



Then 



- T^tf 4 1 + Const 



