CHAP. Xm.] ANALYTICAL FORMULAE. 217 



For all other reactions, 



Thus for load covering the first span of seven spans, we find 

 from the known moment, given in preceding Art., for the fourth 

 support, 



6 x 56 336 



For load over third span from left, 



6 x 616 ,1 , 6607 



For load on sixth span, 



45 270 



" = 



Hence, total reaction at fourth support for first case of loading 



7213 

 is w I. In the same way we can find the reactions at the 



first, second, and third supports, for the second case of loading, 

 as shown in Fig. 87, and then can easily find the shear at any 

 support, as D, by taking the algebraic sum of all the reactions 

 and loads between that support and the end. 



We can now, therefore, find the shear and moment at D, and 

 thus determine the strains in the span D E for both cases of 

 loading, as given in our tabulation, Art. 127. 



142. Triangle for Reactions Single Span loaded. If 

 we calculate from our formulae the reactions at supports of 

 loaded span, for a number of spans, we can tabulate the results, 

 as on next page, in a triangle, where each number is four 

 times the preceding minus the one preceding that, all in the 

 same diagonal column. 



