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

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...

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Main Authors: Eyran Roberto Diaz-Gurrola, Arnulfo Luévanos-Rojas, Griselda Santiago-Hurtado, Victor Manuel Moreno-Landeros, Aldo Emelio Landa-Gómez
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/11/1777
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author Eyran Roberto Diaz-Gurrola
Arnulfo Luévanos-Rojas
Griselda Santiago-Hurtado
Victor Manuel Moreno-Landeros
Aldo Emelio Landa-Gómez
author_facet Eyran Roberto Diaz-Gurrola
Arnulfo Luévanos-Rojas
Griselda Santiago-Hurtado
Victor Manuel Moreno-Landeros
Aldo Emelio Landa-Gómez
author_sort Eyran Roberto Diaz-Gurrola
collection DOAJ
description 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.
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spelling doaj-art-a57f32b5fe66496f889af32200fc22bc2025-08-20T03:11:19ZengMDPI AGMathematics2227-73902025-05-011311177710.3390/math13111777Mathematical Calculations for the Design of Elliptical Isolated Foundations with Optimal CostEyran Roberto Diaz-Gurrola0Arnulfo Luévanos-Rojas1Griselda Santiago-Hurtado2Victor Manuel Moreno-Landeros3Aldo Emelio Landa-Gómez4Instituto de Investigaciones Multidisciplinaria, Universidad Autónoma de Coahuila, Blvd. Revolución No, 151 Ote, Torreón CP 27000, Coahuila, MexicoInstituto de Investigaciones Multidisciplinaria, Universidad Autónoma de Coahuila, Blvd. Revolución No, 151 Ote, Torreón CP 27000, Coahuila, MexicoFacultad de Ingeniería Civil, Universidad Autónoma de Coahuila, Torreón CP 27276, Coahuila, MexicoInstituto de Investigaciones Multidisciplinaria, Universidad Autónoma de Coahuila, Blvd. Revolución No, 151 Ote, Torreón CP 27000, Coahuila, MexicoFacultad de Ingeniería Civil—Xalapa, Universidad Veracruzana, Lomas del Estadio S/N, Zona Universitaria, Xalapa CP 91000, Veracruz, MexicoThis 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.https://www.mdpi.com/2227-7390/13/11/1777optimal cost designelliptical isolated footingsmomentsbending shearpunching shear
spellingShingle Eyran Roberto Diaz-Gurrola
Arnulfo Luévanos-Rojas
Griselda Santiago-Hurtado
Victor Manuel Moreno-Landeros
Aldo Emelio Landa-Gómez
Mathematical Calculations for the Design of Elliptical Isolated Foundations with Optimal Cost
Mathematics
optimal cost design
elliptical isolated footings
moments
bending shear
punching shear
title Mathematical Calculations for the Design of Elliptical Isolated Foundations with Optimal Cost
title_full Mathematical Calculations for the Design of Elliptical Isolated Foundations with Optimal Cost
title_fullStr Mathematical Calculations for the Design of Elliptical Isolated Foundations with Optimal Cost
title_full_unstemmed Mathematical Calculations for the Design of Elliptical Isolated Foundations with Optimal Cost
title_short Mathematical Calculations for the Design of Elliptical Isolated Foundations with Optimal Cost
title_sort mathematical calculations for the design of elliptical isolated foundations with optimal cost
topic optimal cost design
elliptical isolated footings
moments
bending shear
punching shear
url https://www.mdpi.com/2227-7390/13/11/1777
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