164 



LIVE LOADS ON BEAMS. 



Art. 9. 



however, usually calculated upon a simple assumption. 1 Railway 

 rails and long lines of shafting are continuous beams. 



When a continuous beam is arranged at certain points 

 (points of contra-flexure, for example) so that it can not take 

 any moment at these points (hinges), it becomes a cantilever 

 structure, and the stresses are statically determinate and not 

 affected by small changes in the "level" of the supports. 



99. Live Loads on Beams. Since live loads are moving 

 loads, it becomes a question of finding the position of the load 

 which will produce the maximum moment or maximum shear at 

 a section of a beam. Having determined the position of the 

 load, the procedure is the same as for stationary or dead load. 



It is evident that a single concentrated load moving over a 

 cantilever beam will produce the greatest moment when it is -at 

 the free end; moving over a beam supported at both ends, it 

 will produce the greatest moment when it is at the middle of the 

 span, and the greatest shear (at the end) when it is at the sup- 

 port or just to the right of the left support. See the general 

 equations accompanying Figs. 94 and 96. 



To determine the proper position of a moving load on a 

 cantilever beam for any maximum stress is usually a very simple 

 matter, and will not be discussed further. The common cases, 

 including both concentrated and uniform loads, will now be 

 considered. 



100. Two Concentrated Moving Loads a Fixed Distance 

 Apart. In Fig. 117, P^ is greater than P 2 and they are a given 



]/=> fixed distance a apart. The re- 



FM I* 

 I i 



T 



Shear Diagram 



Fig. 117. 



sultant R, of P 1 and P 2 , should 

 be at the center of the beam for 

 a maximum moment in the beam 

 if it were not for the fact that 

 it always comes under a load as 

 shown by Hie moment diagram 

 (94), and by the fact that tlio 

 shear passes through zero at n, 

 load. Evidently the maximum 

 moment occurs under the great- 

 er load, but this load cannot be 

 at the middle of the span with- 



'See the General Specifications of tin- Am. Ivy. Eng. Assoc. 



