foundation design - rectangular spread bases

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Examples ofFoundation Design

6.1 Simple Bases

6.1.1 Column on Square Base

The average ground pressure isW

a2

The thickness of the base must be so proportioned that the column does no

punch through to the soil below, the base does not fail in shear or in bending

Assume W = 200 kN. a = 1 m, c = 300 mm on a soil where the allowablebearing pressure has been assessed at 214 kN/m2. (2 T/sq.ft).

8

Chapter 6



88 Examples of Foundation Design

Punching shear

The load spreads down from the column into the shaded portion of area (c

3t)2 and generates a shear along the perimeter line length 4c + 12t. The pass

upload from the soil is given byW(a2 — (c + 3t)

2) on the area outside the sh

a2

perimeter so that the shear stress on this line is given byW (a2 — (c + 3t)

2)

(4c + 12t)t

W = 200 kN/m2 c = 300 mm.

Assume that the shear stress is fs. N/mm2.

a2

a2



Simple Bases 8

200,000 1 - (300 + 3t)

1000

2 —= fs. (1200 + 12t)t[

and this presents a quadratic equation from which the value of t is given in mm

This is the depth to the reinforcement so the overall thickness of the base

becomes t + ½d + 50 where d is the bar diameter and 50 mm is the cover

required against the earth.

Bending shear

As in the punching shear the column spreads the load out directly-to the soiover a distance l·5t from the column face leaving the passive upload from th

soil as

a - c - l·5t

2 2

× a × W

Again if fs is the shear force

fs. a. t. = (a - c - 1·5t) a × W

or t = ( a - c ) W

(fs + 1·5W)

Critical sectionfor shear

a2

2 2 a2

a2

2 a2

]

( )




Bending moment

The critical section for bending is at the face of the column and the passive

on the shaded area bends the base upwards from the right putting the re

forcement into tension.

The bending moment is (a-c) W × (a-c) 12 a 2 2

This is carried by the full width section 'a' of effective depth 't' and the amo

of reinforcement is then calculated. In bases more than in other reinformembers except pile caps it is important to ensure that the diameter of rforcement chosen is such that the bond length can be established. This m

mean bending the bar well up the face of the base.When reinforcing such bases, whether rectangular or square, it must

remembered that the same calculation must be made in each direction at r

angles; the innocent might be tempted to assume bending of only half the t

load in each direction.There is an obvious concentration of load underneath the column and it is gpractice to put 2 / 3 of the total reinforcement into the mid width of the base

6.1.2 The Eccentric Load on a Rectangular Base

Eccentric loads can derive from two situations. The load itself may be ou

centre of the base in two directions at right angles, or the central column ma

subjected to an added bending moment.The latter is the more general case and is now considered with load W

moment M. Assume the base is of sides a and b.If the magnitude of M is such that the ground pressure at A remains posi

then the problem is quite simple the average ground pressure being



Simple Bases

and the bending moment ground pressure being the moment divided by

modulus of the plan shape of the base,

i.e. M negative at A positive at B

a

2

b/6

However, the value of M may be such that the answer at A. W — M6 may

ab a2b

negative. This means that the corner of the base A is effectively not induci

any passive pressure from the soil and the pressure diagram has changed t

This would require a far more complicated calculation to arrive at the soil str

under the base. However, falling back on the Newtonian principle that retions are equal and opposite, the W/M situation can be represented by




where x = M and this in turn becomes

W

where x is described as the eccentricity about the base centre.

Now applying the equal and opposite theory, the soil pressure resultant musbeneath W and in turn must be the centre of gravity of the triangle of

pressure.Now the pressure p is twice the average pressure which is W and

31b

calculable as it is (a—x)2

i.e. provided the eccentricity can be determined, the centre of gravity of the

pressure is directly beneath it and this can often produce a very quick rwhen a number of base lengths are being investigated.

foundation design - rectangular spread bases

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