382 NOTE TO ART. 128. [APPENDIX. 



to its strain, and the actual girder erected is not of constant 

 -s-section, but more nearly one of uniform strength. Formu- 

 lae for the case of supports out of level, as well as determina- 

 tions of the best differences of level, are hence of but little prac- 

 tical importance, and have not been given. If, however, it be 

 required to find the effect due to the sinking of any one pier, 

 the following may be found of service. 



Let the 71 th support be depressed below the level of the others 

 by the distance h. Then the moments at all the supports are 

 changed. The moments at n and at each alternate support 

 from n are diminished, and at the others increased. 



Let H = 36EI . 



Then, when all the spans are equal, the following formulae 

 give the moment at any support : 



\st. All spans equal, n = number of lowered support, from 

 left, 



when m<n, M,,, = CmCg - n+8 H. 



^8 + 1 



M m ^ _ - ^L=Ei H , 



m > n, M m = 8 - m + 2 " H, 



where c^ = 0, c% = -f 1, Cg = 4, c 4 = + 15, c 6 = 56, 

 Ct = + 209, etc. 



From the moments at the supports the shears can be readily 

 determined from the formula of Art. 148, viz. : 



M m -M m+1 _ M m - M m _ t 



~~ 



7 

 where q = P (1 &) for concentrated load and r ; for uniform, 



2d. Spans all unequal. 



< n, C 



TVT - 



When m < n, C m \ ^-n+l ^a-n+a ^_ g-n+3 ~ ^g-n+a I p. ^ E T 



TVT -L ^ > ^ 



I* d^ + 2 ft + 



