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Mathematical Modeling for the Optimal Cost Design of Circular Isolated Footings with Eccentric Column

Author

Listed:
  • Arnulfo Luévanos-Rojas

    (Instituto de Investigaciones Multidisciplinaria, Universidad Autónoma de Coahuila, Blvd. Revolución No, 151 Ote, Torreón CP 27000, Coahuila, Mexico)

  • Victor Manuel Moreno-Landeros

    (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)

  • Francisco Javier Olguin-Coca

    (Área Académica de Ingeniería y Arquitectura, Universidad Autónoma del Estado de Hidalgo, Carretera Pachuca-Tulancingo Km 4.5, Pachuca de Soto CP 42082, Hidalgo, Mexico)

  • Luis Daimir López-León

    (Área Académica de Ingeniería y Arquitectura, Universidad Autónoma del Estado de Hidalgo, Carretera Pachuca-Tulancingo Km 4.5, Pachuca de Soto CP 42082, Hidalgo, Mexico)

  • Miguel Ángel Baltazar-Zamora

    (Facultad de Ingeniería Civil—Xalapa, Universidad Veracruzana, Lomas del Estadio S/N, Zona Universitaria, Xalapa CP 91000, Veracruz, Mexico)

  • Eyran Roberto Diaz-Gurrola

    (Instituto de Investigaciones Multidisciplinaria, Universidad Autónoma de Coahuila, Blvd. Revolución No, 151 Ote, Torreón CP 27000, Coahuila, Mexico)

Abstract

This article shows a model for the design of circular isolated footings and the column placed anywhere in the footing under minimum cost criteria. Some designs for obtaining the diameter, effective depth, and steel areas of the footing under biaxial bending assume the maximum and uniform pressure at the bottom of the footing supported on elastic soils. All these works consider the column placed at the center of the footing. Three numerical problems are given (each problem presents four variants) to determine the lowest cost to design the circular footings under biaxial bending. Problem 1: Column without eccentricity. Problem 2: Column with eccentricity in the direction of the X axis of one quarter of the diameter of the footing. Problem 3: Column placed at the end furthest from the center of the footing on the X axis. The results are verified by the balance of moments, one-way shear or shear and two-way shear or punching. The new model shows a saving of 17.92% in the contact area with soil and of 31.15% in cost compared to the model proposed by other authors. In this way, the proposed minimum cost design model for circular footings will be of great help for the design when the column is placed on the center or edge of the footing.

Suggested Citation

  • Arnulfo Luévanos-Rojas & Victor Manuel Moreno-Landeros & Griselda Santiago-Hurtado & Francisco Javier Olguin-Coca & Luis Daimir López-León & Miguel Ángel Baltazar-Zamora & Eyran Roberto Diaz-Gurrola, 2024. "Mathematical Modeling for the Optimal Cost Design of Circular Isolated Footings with Eccentric Column," Mathematics, MDPI, vol. 12(5), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:733-:d:1348988
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