Optimal Area for a Rectangular Isolated Footing with an Eccentric Column and Partial Ground Compression

This manuscript aims to present a novel model to find the optimal area of a rectangular isolated footing with an eccentric column, taking into account that the footing is partially supported; that is, one part of the contact surface is compressed and the other part has zero pressure. The methodology is developed by integration and can also be verified using the geometric properties of a triangular-based pyramid to determine the axial load, the moments in the X and Y axes in terms of the available allowable soil pressure, the footing sides, the greatest distance on one of its sides in the X-direction where it crosses the neutral axis, the greatest distance on one of its sides in the Y-direction where it crosses the neutral axis, and the coordinates at the base of the footing. Four types of numerical problems are shown to find the optimal area of a rectangular footing with an eccentric column subjected to biaxial bending: (1) the column in the center of the footing; (2) the column on the edge of the footing in the X-direction; (3) the column on the edge of the footing in the Y-direction; and (4) the column in the corner of the footing. A comparison is presented of the new model against a model proposed by another author. The new model presents a reduction of up to 42.37% for the column in the center of the footing and up to 40.32% for the column in the corner of the footing compared to the model by the other authors. Therefore, the new model will be of great help to professionals in foundation design.