Mathematical Calculations for the Design of Elliptical Isolated Foundations with Optimal Cost

Eyran Roberto Diaz-Gurrola, Arnulfo Luévanos-Rojas (), Griselda Santiago-Hurtado, Victor Manuel Moreno-Landeros and Aldo Emelio Landa-Gómez
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Eyran Roberto Diaz-Gurrola: Instituto de Investigaciones Multidisciplinaria, Universidad Autónoma de Coahuila, Blvd. Revolución No, 151 Ote, Torreón CP 27000, Coahuila, Mexico
Arnulfo Luévanos-Rojas: Instituto de Investigaciones Multidisciplinaria, Universidad Autónoma de Coahuila, Blvd. Revolución No, 151 Ote, Torreón CP 27000, Coahuila, Mexico
Griselda Santiago-Hurtado: Facultad de Ingeniería Civil, Universidad Autónoma de Coahuila, Torreón CP 27276, Coahuila, Mexico
Victor Manuel Moreno-Landeros: Instituto de Investigaciones Multidisciplinaria, Universidad Autónoma de Coahuila, Blvd. Revolución No, 151 Ote, Torreón CP 27000, Coahuila, Mexico
Aldo Emelio Landa-Gómez: Facultad de Ingeniería Civil—Xalapa, Universidad Veracruzana, Lomas del Estadio S/N, Zona Universitaria, Xalapa CP 91000, Veracruz, Mexico

Mathematics, 2025, vol. 13, issue 11, 1-20

Abstract: This paper presents an optimal model for the design of elliptical isolated footings subjected to biaxial bending under the minimum cost criterion, assuming that the footing rests on elastic soils and that the soil pressure distribution is linear. The methodology is developed in two parts. The first is used to obtain the minimum area, and the second is used to determine the minimum cost. Some authors show the equations for circular and elliptical footings for moments, bending shear, and punching shear. However, they do not present the minimum cost, and the numerical examples are presented only for circular footings and not for elliptical footings. Two numerical problems are given (each problem presents five variants), and the optimal cost design for elliptical isolated footings subjected to biaxial bending are shown. Problem 1: Modifying the moment on the Y axis. Problem 2: Modifying the axial load. In addition, a comparison is made between elliptical footings and circular footings. The results show that the minimum area is smaller for elliptical footings than for circular footings, and the minimum cost appears in elliptical footings when the footing dimensions are governed by the minimum pressure. Therefore, the new model for elliptical footings will be of great help to foundation engineering specialists.

Keywords: optimal cost design; elliptical isolated footings; moments; bending shear; punching shear (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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