Geotechnical Engineering

DHARM

SHALLOW FOUNDATIONS 623

Resultant force within the middle third of the base

A footing subjected to moment is shown in Fig. 15.15.

Kern or core

L e b R H e

Middle third

V h

—=—VA VbL

e

V

qmin

H

(a) Plan

(b) Elevation

(c) Direct stress

(d) Bending stress Mc/I

(e) Resultant soil pressure qmax

6M=

bL^2

6V e

bL^2

V

P

A

Fig. 15.15 Footing subjected to moment—Resultant force within the middle-third of base
The forces acting on the footing including self-weight are resolved into V and H. The
moment M may be expressed as M = H · h = V · e.

We have, e = M/V ...(Eq. 15.2)
This equation enables one to determine the eccentricity of the resultant of all forces
acting on the base regardless of how complicated the conditions of loading may be.

If the vertical load V acts alone, it produces uniform soil pressure due to the direct
stress as shown in Fig. 15.14 (c). If the horizontal load H acts alone, it produces a shear that
must be resisted by the soil at the base and also a moment which produces soil pressure distri-
bution shown in Fig. 15.14 (d), due to bending.

The resultant soil pressure will be the combined effect of V and M is shown in
Fig. 15.14 (e).

The maximum and minimum soil pressure are obtained as:

q =

V

bL

e

b

1

6

FHG ± IKJ ...(Eq. 15.3)