CIVIL ENGINEERING FORMULAS

112 CHAPTER FOUR

For square or rectangular footings subject to overturning about two principal
axes and for unsymmetrical footings, the loading eccentricities e 1 ande 2 are
determined about the two principal axes. For the case where the full bearing
area of the footings is engaged, qmis given in terms of the distances from the
principal axes, c 1 andc 2 , the radius of gyration of the footing area about the
principal axes, r 1 andr 2 , and the area of the footing Aas

(4.18)

For the case where only a portion of the footing is bearing, the maximum pres-
sure may be approximated by trial and error.
For all cases of sustained eccentric loading, the maximum (edge) pressures
should not exceed the shear strength of the soil and also the factor of safety
should be at least 1.5 (preferably 2.0) against overturning.

AXIAL-LOAD CAPACITY OF SINGLE PILES

Pile capacity Qumay be taken as the sum of the shaft and toe resistances, Qsu
andQbu, respectively.
The allowable load Qamay then be determined from either Eq. (4.12) or (4.13):

(4.19)

(4.20)

whereF,F 1 , and F 2 are safety factors. Typically, Ffor permanent structures
is between 2 and 3, but may be larger, depending on the perceived reliability
of the analysis and construction as well as the consequences of failure.
Equation (4.13) recognizes that the deformations required to fully mobilize
QsuandQbuare not compatible. For example, Qsumay be developed at dis-
placements less than 0.25 in (6.35 mm), whereas Qbumay be realized at
a toe displacement equivalent to 5 to 10 percent of the pile diameter. Conse-
quently,F 1 may be taken as 1.5 and F 2 as 3.0, if the equivalent single safety
factor equals For larger. (If Fless than 2.0 is usually considered
as a major safety factor for permanent structures.)

SHAFT SETTLEMENT

Drilled-shaft settlements can be estimated by empirical correlations or by
load-deformation compatibility analyses. Other methods used to estimate settle-
ment of drilled shafts, singly or in groups, are identical to those used for piles.

Qsu/Qbu1.0,

Qa

Qsu

F 1



Qbu

F 2

Qa

QsuQbu

F

qm

P

A

1 

e 1 c 1

r 12



e 2 c 2

r 22