Mathematical Modeling of the Optimal Cost for the Design of Strap Combined Footings

Arnulfo Luévanos-Rojas (), Griselda Santiago-Hurtado, Victor Manuel Moreno-Landeros, Francisco Javier Olguin-Coca, Luis Daimir López-León and Eyran Roberto Diaz-Gurrola
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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
Francisco Javier Olguin-Coca: Área Académica de Ingeniería y Arquitectura, Universidad Autónoma del Estado de Hidalgo, Pachuca CP 42082, Hidalgo, Mexico
Luis Daimir López-León: Área Académica de Ingeniería y Arquitectura, Universidad Autónoma del Estado de Hidalgo, Pachuca CP 42082, Hidalgo, Mexico
Eyran Roberto Diaz-Gurrola: Instituto de Investigaciones Multidisciplinaria, Universidad Autónoma de Coahuila, Blvd. Revolución No, 151 Ote, Torreón CP 27000, Coahuila, Mexico

Mathematics, 2024, vol. 12, issue 2, 1-20

Abstract: This paper presents a novel mathematical model to determine the minimum cost for the design of reinforced-concrete strap combined footings under biaxial bending, with each column using a genetic algorithm. The pressure is assumed to be linearly distributed along the contact area. This study comprises two steps: firstly, identifying the smallest ground contact area, and secondly, minimizing the cost. The methodology integrates moment, bending shear, and punching shear calculations according to the ACI standard. Some authors present a smaller area (but limited to one or two property lines) and the design considers that the thickness of the footings and beam are equal, and do not show the lower cost of a strap combined footing; generally, the beam has a greater thickness than the footings and therefore the footings would have an unnecessary thickness that would generate a higher cost. A numerical example is shown to find the lowest cost for the design of strap combined footings considering four different conditions such as square footings and other limitation at the ends of the footings. The minimum area does not guarantee that it is the lowest cost. The proposed model is versatile, applicable to T-shaped and rectangular combined footings, and is not restricted to specific property lines. The contributions include eliminating trial and error practices, accommodating various design conditions, and emphasizing equilibrium in the derived equations. The model is adaptable to different building codes, offering a comprehensive approach to achieving optimal design and cost considerations for strap combined footings.

Keywords: minimum surface; minimum cost; strap combined footings; moments; bending shears; punching shear (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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