[UM LIVE LOAD MOMENT. 



171 



For the end spans there 

 are, therefore, two cases 

 as in a two span bridge. 

 A load in the middle 

 span will evidently pro- 

 duce a negative moment 

 in both end spans. Figs. 

 129 to 132 show the 

 four cases for any sec- 

 tion in the first span. 

 The minimum value of 

 :r is gotten by substi- 

 tuting the value of R\, 

 as given with Fig. 112 

 in the equation for the 

 general value of XQ and 



making k = 0. XQ Cmin.) = 



The value of k is given with Fig. 112. 



FIG. 131. 



H 



L 



