BENDING MOMENT 



Example 2. A beam 30 ft. long, supported at the ends, carries 

 a load which increases uniformly from at one end to 1 ton at 

 the other end. Find the expression for the bending moment at 

 any section and draw the bending moment diagram. What is 

 the greatest bending moment and where does it occur ? 



The total load on the beam is given by the area of the 

 load diagram ABC and it acts at the centroid of that diagram. 

 Hence the total load is 15 tons acting at a distance of 10 ft. 

 from B. 



The reactions of the supports are evidently 



Rj = 5 tons at A 

 and R 2 = 10 tons at B 



Considering a section D of the beam situated at a distance 

 x ft. from A. 



The forces acting on that part of the beam to the left of 

 D are : 



(a) R x = 5 tons acting vertically upwards at a distance x ft. 



(b) That part of the load, the magnitude of which is given by 



the area of the load diagram ADE ; this acts vertically 



downwards through the centroid of the area ADE. Hence 



gl 

 the magnitude of this force is tons and the distance 



60 



from D is - ft. 

 o 



Bending moment = 5x = r ft. tons. 



ISO 



