168 



MAXIMUM LIVE LOAD SHEARS. 



Art. 104. 



left-hand span, for instance) at a distance x from the support, 

 to find the loading- which will give the maximum shear at the 

 section. For any section in the other span the reasoning will be 

 the same, or the beam may be considered turned end for end. 



1 



In Fig. 121, the shear at 

 any section in the first span 

 is evidently ^ = = + ^(91). 

 If there were any load to the 

 left of the section, it would 

 ^increase R^ (and therefore Fig. 121. 



the shear) but it would decrease the shear more, because only 

 part of it goes to the left support (102). Any load to the right of 

 the section would increase R arid the shear the same amount. 

 The loading then, for maximum live load shear, so far as the 

 first span is concerned, is the same as for a single span. It re- 

 mains to consider the effect of loads in the second span. Any load 

 in the second span causes a negative reaction at the left end- 

 Figs. 109 and 111 reversed. This would decrease R and there- 

 fore the positive shear at the section ; the second span should be 

 free from live load. 





It follows that the second 

 span should be fully loaded 

 for maximum negative shear 



Fig. 122. at the section as shown in 



Fig. 122. In this case, the first span should be loaded to the 

 left of -the section, for while any load in this part will increase 

 the positive reaction (i2j), it will increase the negative shear 

 more. The load in the first span produces a 4-JRj, and that in the 

 second span a R lt but whichever is the greater, the loading 

 shown in Fig. 122 will give the maximum negative shear. 



If the live loads are concentrated loads, they should be 

 confined, as far as possible, within the spaces indicated by the 

 above uniform loads, at the same time bringing as much load as 

 possible near the section. See Chapter XIII. 



It may be possible for the live load to advance from both 

 ends, but it may not be possible for it to cover an intermediate 

 space as in Fig. 121; this must be determined in every particular 

 case from the character of the live load. 



