208 



CONTINUOUS GIRDER. 



[CHAP. xra. 



MOMENTS AT SUPPORTS TOTAL UNIFORM LOAD ALL SPANS EQUAL. 



Coefficients of u I* given in triangle. 





The Roman numerals along the sides of the triangle indicate 

 ,he number of spans, and the horizontal line to which they be- 

 long give the moments. Thus, for our example of seven spans 

 just worked out, we have the extreme moments M^ and M 8 = 0, 



15 11 



M a and M 7 = u 1?, M 3 and M 6 = u P, etc. 



Now, a simple inspection of this table will show us that for 

 any even number of spans, as VIII., for example, the numbers in 

 the horizontal line are obtained by multiplying the fraction 

 above in any diagonal column, both numerator and denomina- 

 tor, by 2, and adding the numerator and denominator of the 

 fraction preceding that. 



Thus,- 



15 x 2 + 11 41 11 x 2 + 8 



142 x 2 + 104 ~ 388 ' 142 x 2 + 104 



_30 _ 15 x2 

 388" 142x2 



. .. ,. 



in the other diagonal column; 



12 x2 + 9 



+ 



33 



or 



= :rjg r-rrj in the other diagonal column ; and so on. 



For any odd number of spans, as IX., we have simply to add 

 numerator to numerator and denominator to denominator, the 

 two preceding fractions in the aame diagonal column. 



