288 



PRACTICAL MATHEMATICS 



(3) Considering a section between C and D situated at a dis- 

 tance x ft. from the end. The forces acting to the right 

 of this section are : 

 5 



(a) R 2 = 10 tons acting vertically upwards at a distance x ft. 



128 



(6) 5 tons acting vertically downwards at a distance (x 5) ft. 



(c) 10 tons acting vertically downwards at a distance (x 15) ft. 



q 



(d) '-(x 20) tons acting vertically downwards at a distance 



Bending moment = x - 5(x - 5) - 10(a> - 15) - (x - 20) 2 ft. 

 \a o 



tons, and this expression can only be used when x has values 

 between 20 ft. and 30 ft. 



Taking these three expressions for the bending moment arid 

 giving x values suitable to each, values of the bending moment 

 can be calculated for different sections of the beam. 



The bending moment is evidently greatest at a section situated 

 in the middle span and for that span 



dM 125 



-j = 5 (x 10) 



dx 12 



<M 



For a maximum value -= = 

 dx 



That is, when 

 and 



M TO(W; = 93-83 ft. tons 



