The standard design method (classical method) for reinforced concrete rectangular footings is: First, a dimension is proposed and should comply with the allowable stresses; subsequently, the effective depth is obtained from the maximum moment and is checked against the bending shear and the punching shear until, it complies with these conditions and, then, steel reinforcement is obtained, but it is not guarantee that the minimum cost will be obtained. This paper shows an optimal design for reinforced concrete rectangular footings using the new model. A numerical experimentation is presented to show the model capability to estimate the minimum cost design of the materials used for a rectangular footing that supports an axial load and moments in two directions in accordance to the building code requirements for structural concrete and commentary (ACI 318-13). Also, a comparison is made between the optimal design and current design for rectangular footings. The solutions show that the optimal design is more economical and more precise with respect to the current design, because standard design is done by trial and error. Then, the optimal design should be used to obtain the minimum cost design for reinforced concrete rectangular footings.

This paper presents a comparative study for design of reinforced concrete isolated footings of rectangular and circular form subjected to axial load and bending moments in two directions using new modelsto obtain the most economical footing. The new models consider the real soil pressure acting on contact surface of the footing and this pressure is different in all contact area, with a linear variation, this pressure is presented in terms of the axial load, the larger moment around the “X” axis and the smaller moment around the “Y” axis, where the centroidal axes are “X” and “Y” of the footing. The main part of this research is to show the differences of the two models. Results show that the circular footings are more economical with respect to the rectangular footings. Therefore, the new model for design of circular isolated footings should be used, and complies with the real conditions.

Este trabajo muestra un modelo analítico para el diseño de zapatas combinadas de esquina sometidas a una carga axial y dos momentos flexionantes ortogonales por cada columna. El modelo toma en cuenta la presión real del suelo debajo de la zapata, y la metodología se basa en el principio de que la integración de la fuerza de corte es el momento. El diseño actual considera la presión máxima en todos los puntos de contacto. Este modelo se verifica por equilibrio de fuerzas de corte y momentos. La aplicación del modelo se presenta por medio de un ejemplo numérico. Por lo tanto, el modelo propuesto es el más apropiado, ya que genera un mejor control de calidad en los recursos utilizados.

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.