## Tuesday, January 29, 2013

### Balanced foundations (rectangular, cantilever, trapezoidal and holed) Design.

Design decisions
The decision to use a combination of column loads to produce a combined balanced foundation would depend upon a number of factors, for example:

(1) The spacing of the point loads.
(2) The combination of loads being considered.
(3) The restrictions of projections due to site boundaries.
(4) The overall eccentricities produced from the resultant of the loads.
(5) The bearing area available.
(6) The need to produce a uniform pressure.
(7) The economics compared to other possible alternatives, if any. For example, in some situations a combination of column loads can be used to balance out eccentric loads which would otherwise extend isolated foundations beyond the boundaries of the site. Balancing out these column loads means that the boundaries can be maintained within a base giving uniform pressure and this may prove more economic than say a piled solution.

In other situations an attempt to balance out the loads may produce cantilevers which would extend beyond the site boundaries therefore making it necessary to look at alternative column combinations or alternative means of support such as piling.

In most cases where these foundations are adopted they relate to: boundaries which are restrictive; foundations which would otherwise overlap; or situations where, by introducing a load from other columns onto the same  foundation, bending moments are reduced and pressures become more uniform.

Sizing up the design

(1) Rectangular balanced foundations
The foundation base is designed by calculating the position of the resultant applied load and making the centre of gravity of the base coincide with that of the downward load.

This is done by ﬁrst calculating the area of the base required to resist the resultant load and then ﬁnding the most  economic rectangular pad to achieve this. The pad is then located so that its centre of gravity is in the same position as the resultant load (see Fig. 12.6). Fig. 12.6 Rectangular balanced pad base.

The base is then designed to resist the bending moments and shear forces produced by the solution, and the depth and reinforcement are determined and detailed accordingly.

(2) Cantilever balanced foundations
The design of the cantilever balanced foundation is carried out by assuming locations for the pad supports based upon the physical considerations and calculating the reactions from the cantilever beam. The reactions are then accommodated by calculating the required size of rectangular pads for each reaction based upon a uniform bearing pressure.

The beam is then designed to support the loads from the superstructure taking account of the induced bending and shear forces, etc. (see Fig. 12.7 for a typical example). Fig. 12.7 Bending and shear diagram for typicalcantilever base.

(3) Trapezoidal balanced foundations
The design is carried out by ﬁrst of all calculating the area of the base required for a uniform pressure to resist the total applied load. The resultant load and its point of application is then calculated. By ﬁxing the dimensions for the length of the base, the dimensions A and B (see Fig. 12.8 (a)) can be calculated to give a centre of gravity which coincides with the location of the resultant load. Fig. 12.8 Trapezoidal and holed balanced foundation.

The applied bending moments and shear forces are then calculated and the reinforced foundation designed to suit.

(4) Holed balanced foundations
The design is carried out by ﬁrst calculating the resultant load and its location. The area required for the base is then determined by dividing the resultant load by the allowable bearing pressure. By ﬁxing the length of the base an average width can hence be determined, and by inspection  of the eccentricity of the resultant load, an allowance can  be made for an approximate size of hole and a trial width determined (see Fig. 12.8 (b)).

From this trial width a size and location for the hole can  be calculated to give a centre of gravity for the base which will coincide with that of the applied loads and result in a uniform pressure.

Having determined the base dimensions the bending moments and shear forces can be calculated and the foundation design completed.

(5) General sizing considerations
The size of the sections involved is based upon bending moments, shear forces and bond stresses in a similar manner to any other reinforced concrete section. With foundations, however, due to the slightly reduced shuttering cost for concrete below ground compared to elevated sections,  it is often more economic to go for slightly larger concrete sections to avoid the use of excessive shear reinforcement or large-diameter bars.
Each condition will demand dif- ferent sizes and therefore the engineer will need to deter- mine the initial size from a feel of engineering, which will develop with experience. The design may then be ﬁnalized by trial and error.