Axial load biaxial moment interaction (PMM) diagrams for shallow foundations: Design aids, experimental verification, and examples

Galvis, Francisco A.; Smith-Pardo, J. Paul

doi:10.1016/j.engstruct.2020.110582

Cited by 5 publications

(3 citation statements)

References 16 publications

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“…Several models have been developed for the comprehensive design of reinforced concrete for circular, square and rectangular isolated footings subjected to biaxial bending [15][16][17][18][19][20]. Likewise, models for combined footings have been investigated for the complete design of reinforced concrete under biaxial bending in each column of trapezoidal-shaped [21], rectangular [22], L or corner [23], strap [24] and T [25] footing.…”

Section: Introductionmentioning

confidence: 99%

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

Luévanos-Rojas,

Santiago-Hurtado,

Moreno-Landeros

et al. 2024

Mathematics

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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.

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Section: Introductionmentioning

confidence: 99%

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

Luévanos-Rojas,

Santiago-Hurtado,

Moreno-Landeros

et al. 2024

Mathematics

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“…The bearing capacity has been investigated for shallow footings subjected to biaxial bending, which takes into account a linear ground pressure distribution and this contact area works partly in compression (Irles-Más and Irles-Más, 1992;Özmen, 2011;Rodriguez-Gutierrez and Aristizabal-Ochoa, 2013a, b;Lee et al, 2015;Kaur and Kumar, 2016;Bezmalinovic Colleoni, 2016;Dagdeviren, 2016;Aydogdu, 2016;Girgin, 2017;Turedi et al, 2019;Al-Gahtani and Adekunle, 2019;Galvis and Smith-Pardo, 2020;Rawat et al, 2020;Lezgy-Nazargah et al, 2022;Gör, 2022).…”

Section: Introductionmentioning

confidence: 99%

Nuevo modelo para el diseño completo de zapatas aisladas rectangulares tomando en cuenta que la superficie de contacto funciona parcialmente en compresión

Rojas

2023

Revista de la Asociación Latinoamericana de Control de Calidad,

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Este documento muestra un nuevo modelo para diseño completo de zapatas aisladas rectangulares bajo flexión uniaxial y biaxial, tomando en cuenta que el área de la zapata en contacto con el suelo funciona parcialmente a compresión. La metodología se presenta por integración para obtener momentos, cortantes por flexión y penetración. Los ejemplos numéricos se presentan para el diseño de zapatas aisladas rectangulares bajo flexión uniaxial y biaxial, y se comparan con el modelo actual (área total funciona en compresión) en términos de volúmenes de concreto y acero. El modelo actual muestra mayores volúmenes de concreto y acero. Por lo tanto, el nuevo modelo es el más adecuado, ya que presenta mejor control de calidad en los recursos utilizados.

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“…Luévanos-Rojas et al [17] developed an optimal model for the design of rectangular isolated footings using computation to solve various integrals according to the American Concrete Institute ACI 318-13. Galvis and Smith-Pardo [18] presented design aids and simplified closed form equations to obtain the coupled axial load and biaxial moment capacity of hollow and solid circular and rectangular shallow foundations. Rawat and Mittal, Rawat et al [19,20] developed a simplified approach for the design of reinforced concrete rectangular isolated footings with eccentric load according to the American Concrete Institute ACI 318-14.…”

Section: Introductionmentioning

confidence: 99%

Minimum Cost Design for Rectangular Isolated Footings Taking into Account That the Column Is Located in Any Part of the Footing

Luévanos-Rojas

2023

Preprint

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This work presents a new model to obtain the minimum cost design for a rectangular isolated footing, taking into account that the column is located in any part of the footing. The methodology is developed by integration to obtain the moments, bending shear and punching shear according to the American Concrete Institute ACI 318-14. This document presents the simplified and precise equations of the four moments, four bending shears and one punching shear acting on the footing. Some designs have been developed by the trial and error method to determine the footing dimensions, and later the thickness and steel area of the footing are obtained. Some authors present the minimum cost design for a rectangular isolated footing taking into account that the column is located in the center of gravity of the footing, and other authors present very complex algorithm. Numerical examples are presented to obtain the minimum cost design of rectangular isolated footings under biaxial bending, and some results are compared with those of other authors considering the same conditions. The new model presents a smaller contact area with the soil and a lower design cost than those presented by other authors.

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Axial load biaxial moment interaction (PMM) diagrams for shallow foundations: Design aids, experimental verification, and examples

Cited by 5 publications

References 16 publications

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

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

Nuevo modelo para el diseño completo de zapatas aisladas rectangulares tomando en cuenta que la superficie de contacto funciona parcialmente en compresión

Minimum Cost Design for Rectangular Isolated Footings Taking into Account That the Column Is Located in Any Part of the Footing

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