Pile Design and Construction Practice, Fifth edition

352 Piles to resist uplift and lateral loading
(a) M (b) M
P P
y
H
H
e
L
For soils having a constant modulus:
Depth to point of fixity z f � 1.4R
For soils having a linearly increasing modulus:
z f � 1.8T
x
(6.50)
(6.51)
The relationships 6.50 and 6.51 are only approximate, but Davisson and Robinson state that
they are valid for structural design purposes provided that l max, which is equal to L/R, is
greater than 4 for soils having a constant modulus and provided that z max, which is equal to
L/T, is greater than 4 for soils having a linearly-increasing modulus. From the above equations
the equivalent length L e of the fixed-base pile (or column) is equal to e�z f and the critical
load for buckling is
Pcr �
and
� 2EI for free-headed conditions
2 4(e � zf) Pcr � � 2EI for fixed- (and translating-) headed conditions
2 (e � zf) 6.4 Lateral loads on raking piles
e
z f
L e
Fixed base
Figure 6.37 Bending of pile carrying vertical and horizontal loads at head (a) Partly embedded
pile (b) Equivalent fixed base pile or column.
(6.52)
(6.53)
The most effective way of arranging piles to resist lateral loads is to have pairs of piles
raking in opposite directions as shown in Figure 6.5. The simple graphical method of