156 METHODS OF LOADING. [dTAr. XT. 



_ PA_^ 8 . nce ?i + ^ _ Therefore M" - M' < *ii. 



C (/ 



Since, however, ^< I, we have also M" M'< P 1%. Hence, if 

 M' is < M", we have also R' positive. R' is therefore always 

 positive whatever may be the position of the load. In the same 

 way it may be shown that R" is always negative. 



If now the load is to the right of the point distant x from 

 the left support, then for this point the shearing force S' = R', 

 and is therefore positive. If the load is to the left of this 

 point, the shearing force S = R' P = R", and is therefore 

 negative. S for any point is therefore positive or negative, 

 according as the load lies right or left of this -point. Hence 

 for a uniform load we deduce directly 



The shearing force at any point is a positive or negative 

 maximum when the load extends from this point to the right 

 or left support respectively. 



The same principle holds good for the simple girder. 



2. Thus far we have considered the load in the span itself. 

 Suppose now the load is in some other span, and the span in 

 question is unloaded, then 



M' - M" M'' - M'" 



R =- -j- R =i 



As we pass away from the loaded span the moments at the 

 supports are alternately positive and negative, and each is 

 greater than the one following (Art. 94). Since the moments 

 M' and M" are alternately positive and negative, R' will have 

 the same sign as M', and R" as M", and generally Rm as M^. 



Adopting, then, the notation shown in PI. 18, Fig. 68, we 

 have for the span m -i 



where Rm has the same sign as M m . 

 In the same way 



_M m -M m+1 



"m+l 7 > 



I'm 



and therefore 



Mni 

 1 



' 



