EXAMPLES XIX 815 



NOW e - & 



r * 



I 2r 2 T 



Nr 2 7r(rf r 



2/T 



5 JT radians 



rr 



= rrf radians 

 NI 



If a shaft is making n revolutions per minute, and H is the 

 horse-power transmitted, 



H= 



12x33000 



6 x 33000 

 where T is the twisting moment or torque in inch pounds. 



6 x 33000H . 



Also T = - inch Ib. 



Trn 



and these two relations can be combined with those already 

 obtained for solid and hollow cylindrical shafts. 



EXAMPLES XIX 



(1) A beam 30 ft. long is supported at the ends A and B. It 

 carries loads of 5 tons, 10 tons, and 8 tons at points situated at 

 distances of 5 ft., 16 ft., and 22 ft. respectively from A. Find 

 the reactions at the supports and the values of the bending 

 moment at points situated at distances of 10 ft., 18 ft., and 25 ft. 

 from A. 



(2) A beam 20 ft. long is supported at the ends and is divided 

 into two equal lengths. The first length carries at its centre a 

 load of 10 tons, while the second length carries a uniformly dis- 

 tributed load of 1 ton per foot run. Calculate the values of the 

 bending moment at points situated at distances 5 ft., 10 ft., and 

 15 ft. from one end. 



(3) A beam 20 ft. long is supported at the ends and is divided 

 into two lengths of 8 ft. and 12 ft. The first length carries a 

 uniformly distributed load of 1^ tons per foot run, and the second 

 length carries a uniformly distributed load of f ton per foot run. 

 Find expressions for the bending moment at any point for each 



