CHAP. Xin.] 



ANALYTICAL FOEMULJE. 



210 



REACTIONS AT UNLOADED SPANS. 

 Supports counted from left. Supports counted from right. 



Tables give the numerators of the coefficients of w I. Denominators from 

 triangle on page opposite. 



These tables may be carried out to any desired extent by the 

 law of the Clapeyronian numbers in the vertical columns. 



As an example of their use, take seven spans load in fifth 

 from left, that is, in third from right. (Make sketch.) From 

 the triangle we take the common denominator 11644. Then 

 from first table in the horizontal column of III/ we have for 

 left end 



11 



66 264 990 



/J ^~ 11644 ' 11644 J ***~ 11644* 

 For supports right of loaded span, we must take the second 

 table, and look in horizontal column for V. We thus obtain 



153 918 



*= 11644 wl >*i=-UGi wL 



We can now, therefore, either by our tables or formulas, or 

 both, find the moments, reactions, and shearing force at any 

 support for both cases of loading given in Fig. 87. The reader 

 will do well to take the example of Art. 127, and find the mo- 

 ment and shear at D for both cases, and thus check our results 

 as given in Art. 127. Thus, from the data there given, we find 

 for the 1st case + 788.2 ft. tons, and for the 2d case 382.5 ft. 

 tons for the moments and 14.55 tons for shear. 



