296 



PRACTICAL MATHEMATICS 



156. (3) A beam of length / ft. supported at both ends and 

 carrying a concentrated load W tons at the middle. 



w 



The reaction at each support is -W tons. 



Let the centre of the beam be the origin, and let a be the length 

 of the half span. 



Let A be a section situated at a distance x ft. from O. 



W 



Bending moment at A = (a x) ft. tons 



Hence 

 and 



2 



dy 



2 V"" 2 

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



/7'Y) 



Uvmt 



W/ 



El = 



dx 2 \ 



(^-^ 2 ) 



Then 



Ely =oa -* + Const 



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



W 



y- 



3 



* 



and 



w 



" 12EI 



This gives the value of y for any point distant x ft. from the 

 centre, and y is greatest when x = a. 



Wa 3 



/ 



W/ 3 



48ET smcea =2 



