CONCENTRATED MOVING LOADS 63 



There will be a maximum moment when either of the loads satis- 

 fies the above criterion, the bending moments being equal. 



By equating the maximum moment above to the moment due to 

 a single load at the center of the beam, it will be found that the above 

 criterion holds only when 



a < 0.586 L 



Where two unequal moving loads are at a fixed distance apart the 

 greater maximum bending moment will always come under the heavier 

 3ad. 



The maximum end shear at the left support for a system of con- 

 centrated loads on a simple beam, as in Fig. 40, will occur when the 

 left reaction, R lt is a maximum. This will occur when one of the wheels 

 is infinitely near the left abutment (usually said to be over the left 

 abutment). The load which produces maximum end shear can be 

 easily found by trial. 



The maximum shear at any point in the beam will occur when 

 one of the loads is over the point. The criterion for determining: which 

 load will cause a maximum shear at any point, x, in a beam will now 

 be determined. 



In Fig. 40, let the total load on the beam, P + P 2 + P 3 + P 4 = 

 W , and let x be the distance from the left support to the point at which 

 we wish to determine the maximum shear. 



When load P 1 is at the point, the shear will be equal to the left 

 reaction, which is found by substituting x + a for x in (19) to be 



W+P.a- P,6- P 4 (6 + c) 



and when P 2 is at the point the shear will be 

 (L x) 



L 

 Subtracting S 2 from Si we have 



PiL-Wa 



