166 



CONCENTRATED MOVING LOADS. 



Art. 101. 





= ~- (L- 



x = y 2 L+y 2 b, that is, P 4 is y 2 6 to the right and E is %6 to 

 the left of the center line. 



The maximum moment does not necessarily occur under the 

 load which is nearest the resultant, but might occur under P 3 , 

 for example, in which case R would have to be placed on the 

 right of the center line. The moments for both cases should be 

 calculated, and compared. 



As the load is not usually turned end for end, the maximum 

 shear may occur at either A or B ; there must evidently be a load 

 at A or B, and it is uncertain which load at either end will give 

 the maximum shear. P 2 at A, for example, might produce the 

 maximum shear, in which case P x would not be on the beam at 

 all. The shear for each case should be calculated, and the results 

 compared. The maximum shear will be equal to R or R 2 , of 

 course. 



For a complete discussion of this problem as applied to 

 train wheel loads, see Chapter XIII. 



102. A Continuous Uni- 

 form Moving Load. A uniform 

 live load is usually assumed to 

 be of indefinite length so that it 

 may come onto a beam from 

 either end and cover the whole 

 beam. 



Fig. 119 shows a beam of 

 span L which is to carry a live 

 load of w Ibs. per ft. What is 

 the value of a for a maximum 

 moment at C ? A load anywhere 



on the beam will produce a posi- 



Fig7Ti9. the moment at C, (Fig. 96), 



therefore there should be as much load as possible on the beam, 



that is, the beam should be fully loaded. For maximum moment 



at any point of a beam supported at its ends, it should have a 



full load. The maximum moment in the beam occurs, of course, 



. at its middle. See Fig. 101. It may, of course, be proven 



[analytically, that for maximum moment at C, a should equal x. 



