## Thursday, January 31, 2013

### Design Example: Rectangular Balanced Foundation.

A ﬁve-storey concrete-framed ofﬁce building has columns located on a regular 6 m × 6 m grid. The soil is a sandy clay with a net allowable bearing pressure, na = 150 kN/m2.

The column loads are as follows:
Internal column: 2000 kN
Perimeter column: 1000 kN
Corner column: 500 kN

The imposed load may be taken to be 55% of the total load for all columns. Thus, from Fig. 10.20, the combined partial load factor γP = 1.51. Fig. 10.20 Combined partial safety factors for dead +imposed loads.
Normal internal column foundations have been chosen to be isolated pad foundations, with an area given by

which for a square base gives plan dimensions of 3.65 m × 3.65 m. This size will be used for internal columns,  with proportionally smaller sizes for perimeter and corner columns.

The building is however built tight to the site boundary along two sides, as shown in Fig. 12.9. To keep foundations within the site boundary, the four columns adjacent  to the corner will share a combined base.
The base  will be designed as a rectangular balanced foundation  in order to minimize bearing pressures and differential  settlements. Fig. 12.9 Rectangular balanced foundation design example.

Size of combined base
Superstructure total load, ∑ P = 2000 + 1000 + 1000 + 500 = 4500 kN

Taking moments about grid line 2 to calculate the distance of the centroid of the column loads from this grid line,

Similarly, by symmetry, Y = 2.0 m.

To achieve a balanced foundation, it is necessary to provide a base whose centre of gravity coincides with the centroid of the applied loads. The distance, in either direction, from the centroid of loads to the site boundary edge of the base  is 6.5  − X = 4.5 m: therefore if the opposite edge is like- wise located 4.5 m from the centroid of loads, the two will coincide. Thus a 9 m × 9 m base will provide a balanced foundation in this situation.

The base will only remain exactly balanced if all four columns have the same level of imposed loading. From a foundation point of view this is unlikely to be critical unless extreme variations in the distribution of imposed loads occur. Where such variations are expected, these should be designed for as a separate load case.

Bearing pressure
The actual bearing pressure will be equal to

The value of p (= 56 kN/m2) indicates that, although the  balanced foundation would limit differential settlement between the four columns sharing the base, it would not, for this particular building example, reduce differential  settlements between columns on this base and those on adjacent bases. Adjacent bases would be sized to give bearing pressures close to the allowable value of na = 150 kN/m2.

The superstructure would therefore be required to accom- modate the differential settlement between the combined corner base and the adjacent isolated bases. If it is unable  to accommodate these differential settlements, the bearing pressure on the balanced foundation could be increased, within limits, by turning the foundation into a holed balanced foundation. In this particular example this would involve cutting a hole out of the centre of the base, thus reducing the area of the base. Provided the centre of gravity of the base remains in line with the centroid of applied loads, the bearing pressure would remain uniform, but its magnitude would increase.

Ultimate design pressure
The ultimate design pressure for reinforcement design  is given by pu =γPp, where  γP is the combined dead and imposed partial load factor.