and equatinp them to S„ ve have 



^(-^"7 + R (h^ -^ ) X / - R(hg -f)+R (h^ +h^) I = S, 



which, when solved for £ gives 



i-^ ^) (130) 



R (h^ . 2h^) 



358. Similarly the sum of all moments below C- must equal the moment H, 

 at Ge Using the same areas 



R( '^6 " ^ ) X I fh, - i) -r D(-J ~i^) (hg - |) - R(2hg + h^ -i) 



X I X (hg ^ ^) = M^ 

 which may be reduced to 



2h,^ » / (6h/ + 3h„hJ . ^ 2 ^^^ _^ 2hg) = -^ 



Substituting the solution for v from equation (188) the final expression for 

 ? ^ ? 



^6 ^" 



R 



^6 ^^6 " \^ - 2^ ^^V/2h6 " \^ ' ^oh^^^h " ^^o) - ^% = ^' ^^^^^ 



Substituting the oreviously determ.ined values for R, h , Mp, and S,, in this 

 eauation we have approximately 



145.8 h^^ + 1080hg^ - 2,730h.2 - 50, 970h^ = liO,U80 



which when solved for h^ gives 



hg = 7.Ji feet 



The length of piling to G is 15.36 feet, and the total length of pile of 

 minimum moment is about 22,8 feet. 



17il 



