^'tiatever this force is, the least length of nile I J over which it is applied 

 would be that length corresponding to the highest possible point of application 

 of the pressure P-ir. But the magnitude of p-,^ at this highest point can be 

 no greater than the pressure which may be generated by the earth. Therefore 

 for miniraum pile length, p-_. must be as large as this maximum permissible 

 earth pressure. 



3li9^ The raaxiraurri rate of pressure change between po and p^ has already 

 been determined as 



R = w, 



tan 





(118) 



= 21)i pounds per square foot of depth (equation 97) 

 and the distance between F and G with this rate was found to be h^- = 2,3.6. 

 Oiq!uation 98) The majcimura positive moment in terms of the moment at F, the 

 dredged bottom, has been shown to be 



M7 = M^, + 

 ^1 ' 



x(Pp + 2o ) 

 1 



(equation 109). It may be seen from Figure 111 that in going from F to G, the 

 moments increase negatively. K is related to M„ by K„ = E.^ - JA I where A 



is the area of the shear diagram between F and G. 



Therefore M„ = M^ + A 

 ^^ b s 



. 2p ) 



(119) 



The magnitude of the shear at any point x above G up to F at xfhich point x = h^^, 

 is given by ^ 



R 

 S = S^ - -4— ' (120) 



therefore since Rh, 



Ag 



^G^-5 



the area A is 

 ^8^ 



The maximum positive moment in terms of M and S^ 



G G 



M, 



= ¥c - S^h^ 



Pgh^ 



(Pq + 2p„ ) 



Z^ ^'^G ■ "G"5 ^T 2 ^^8 ■ '■^Z^ 



(121) 



(122) 



and the maximum negative moment (e^^uation 11?) is 



= M, 



G 



s^v^/r 



170 



