ARCHES AND ARCHED RIBS 



193 



In this case, however, the distance EE 1 is not constant from A to F, 

 but varies as the ordinates to a triangle, being equal to M l at A and 

 to J/ 2 at F. Hence, for a point at a distance x from A, 



'), = Jfi- -(Jf,--sg, 



where 2 c is the length of the span. Also BE = r - DE, and CE' = z. 

 Therefore 



ir=r-DE-z- M.+ (M. - M 2 ). 

 2 c 



Let this value of M be inserted in equations (103). Then, if the 

 expressions under the integral signs are evaluated for a number of 



vertical sections taken at equal distances along the center line of the 

 rib, and their sums taken, the integrations in equations (103) can be 

 replaced by summations giving the three conditions 



ZDE ^ z 1 



-LJ- 



^^ D E x ^"^ zx ^^ x 



^ DE'z ^ z 2 _ 



_ 



~ ' 



- Mo 



