212 CONTINUOUS GERDEB. [CHAP. XU1. 



For the left support, 



For the right support, 



M r+l =_!,? r*L*i*=Ei~i 



4: CB+I J 



These formulae, it will be seen, are very simple and easy of 



application. 



Thus, for seven spans, load over the fourth from left, we 



have s = 7, r = 4, and hence 



Both moments are equal, as should be the case for a middle 

 span. Inserting now the proper values for the Clapeyrouian 

 numbers from the preceding Art., we have 



|"l5x-56 + 15 2 "j 

 2911 



615 



So for any desired number of spans, the values of r and s 

 being known, the corresponding Clapeyronian numbers can be 

 easily found, and, inserted in our formulas, give us at once the 

 moments at the supports. 



Turning again to our example, Art. 127, and making w = 2 

 tons, and I = 80 ft., we have w& = 12800, and therefore M 4 = 

 676, and dividing by depth of truss = 10 ft., we find the strain 

 in A a (Fig. 88) 67.6 tons, nearly what we may find by the 

 summation of the strains due to the loads P 1-4 in our tabulation. 



13. Triangle of Moments Uniform Live Load over any 

 single Span. If from the above formulae we find the moments 

 at supports for a number of spans, and tabulate as before, we 

 shall have a triangle of moments similar to those already given, 

 which may be produced to include any desired number of 

 spans. We have only to observe that the numerator or de- 

 nominator of any fraction in the table follows the law of the 

 Clapeyronian numbers that is, is four times the preceding in 

 the same diagonal column minus the one preceding that. 



