This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
When a simple footing supports a single column, the center of pressure of the column must pass vertically through the center of gravity of the footing, or there will be dangerous transverse stresses in the column, as discussed later. But it is sometimes necessary to support a column on the edge of a property when it is not permissible to extend the foundations beyond the property line. In such a case, a simple footing is impracticable. The method of such a solution is indicated in Fig. 112, without numerical computation. The nearest interior column (or even a column on the opposite side of the building, if the building be not too wide) is selected, and a combined footing is constructed under both columns. The weight on both columns is computed. If the weights are equal, the center of gravity is half-way between them; if unequal, the center of gravity is on the line joining their centers, and at a distance from them such that (see Fig. 112) x:y::W2:W1. In this case, evidently W2 is the greater weight. The area abcd must fulfil two conditions:
(1) The area must equal the total loading (W1 + W2), divided by the allowable loading per square foot; and,
(2) The center of gravity must be located at 0.
An analytical solution of the relative and absolute values of a b and c d which will fulfil the two conditions, is very difficult, and fortunately is practically unnecessary. If x and y are equal, a b c d is a rectangle. If W2 is greater than 2 W1, then y will be less than 1/2x; and even a triangle with the vertex under the column Wl would not fulfil the condition. In fact, if Wl is very small compared with W2 it might be impracticable to obtain an area sufficiently large to sustain the weight. The proper area can be determined by a few trials, with sufficient accuracy for the purpose.
Fig. 112. Combined Footing for Two Columns, One on Edge of Property.
The footing must be considered as an inverted beam at the section m n, where the moment = W2y - 1/2 W1y. The width is mn; and the required depth and the area of the steel must be computed by the usual methods. The bars will here be in the top of the footing, but will be bent down to the bottom under the columns, as shown in Fig. 112. The cross-bars under each column will be designed, as in the case of the simple footing, to distribute the weight on each column across the width of the footing, and to transfer the weight to the longitudinal bars.