New model for complete design of rectangular isolated footings taking into account that the contact surface works partially in compression

  • Arnulfo Luévanos Rojas Instituto de Investigaciones Multidisciplinarias, Universidad Autónoma de Coahuila, Torreón, Coahuila, México. http://orcid.org/0000-0002-0198-3614
Keywords: rectangular isolated footings, new model for complete design, moments, flexural shearing, punching shearing

Abstract

This paper shows a new model for complete design of rectangular isolated footings under uniaxial and biaxial bending, considering that the footing area in contact with the soil partially works to compression. The methodology is presented by integration to obtain moments, flexural shearing and punching shearing. Numerical examples are presented for design of rectangular isolated footings under uniaxial and biaxial flexion and are compared with the current model (total area works in compression) in terms of concrete and steel volumes. The current model shows greater volumes of concrete and steel. Therefore, the new model is the most appropriate, since it presents better quality control in the resources used.

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Author Biography

Arnulfo Luévanos Rojas, Instituto de Investigaciones Multidisciplinarias, Universidad Autónoma de Coahuila, Torreón, Coahuila, México.

Instituto de Investigaciones Multidisciplinarias, Universidad Autónoma de Coahuila

References

ACI 318S-19 (2019), “Building Code Requirements for Structural Concrete and Commentary, Committee 318â€, New York, USA.

Aguilera-Mancilla, G., Luévanos-Rojas, A., López-Chavarría, S. and Medina-Elizondo, M. (2019), Modeling for the strap combined footings Part I: Optimal dimensioning. Steel and Composite Structures. 30(2):97-108. https://doi.org/10.12989/scs.2019.30.2.097

Al-Gahtani, H.J. and Adekunle, S.K. (2019), A boundary-type approach for the computation of vertical stresses in soil due to arbitrarily shaped foundations. World Journal of Engineering. 16(3): 419-426. https://doi.org/10.1108/WJE-02-2018-0051 DOI: https://doi.org/10.1108/WJE-02-2018-0051

Algin, H.M. (2000), Stresses from linearly distributed pressures over rectangular areas. International Journal for Numerical and Analytical Methods in Geomechanics. 24(8):681-692. https://doi.org/10.1002/1096-9853(200007)24:8<681::AID-NAG89>3.0.CO;2-X DOI: https://doi.org/10.1002/1096-9853(200007)24:8<681::AID-NAG89>3.0.CO;2-X

Algin, H.M. (2007), Practical formula for dimensioning a rectangular footing. Engineering Structures. 29(6):1128-1134. https://doi.org/10.1016/j.engstruct.2006.08.009 DOI: https://doi.org/10.1016/j.engstruct.2006.08.009

Aydogdu, I. (2016), New Iterative method to Calculate Base Stress of Footings under Biaxial Bending. Journal of Engineering and Applied Sciences. 8(4):40-48. https://doi.org/10.24107/ijeas.281460 DOI: https://doi.org/10.24107/ijeas.281460

Bezmalinovic Colleoni, A.S. (2016), Fórmulas analíticas para la presión de contacto lineal en fundaciones rectangulares altamente excéntricas. IX Chilean Congress on Geotechnical Engineering, Chilean Geotechnical Society, Universidad Austral de Chile.

Dagdeviren, U. (2016), Shear stresses below the rectangular foundations subjected to biaxial bending, Geomechanics Engineering. 10(2):189-205. https://doi.org/10.12989/gae.2016.10.2.189 DOI: https://doi.org/10.12989/gae.2016.10.2.189

Filho, W.L., Carvalho, R.CH., Christoforo, A.L. and Lahr, F.A.R. (2017), Dimensioning of Isolated Footing Submitted to the under Biaxial Bending Considering the Low Concrete Consumption. International Journal of Materials Engineering. 7(1):1-11. http://article.sapub.org/10.5923.j.ijme.20170701.01.html DOI: https://doi.org/10.5923/j.ijme.20170701.01

Galvis, F.A. and Smith-Pardo, J.P. (2020), Axial load biaxial moment interaction (PMM) diagrams for shallow foundations: Design aids, experimental verification, and examples. Engineering Structures. 213:110582. https://doi.org/10.1016/j.engstruct.2020.110582 DOI: https://doi.org/10.1016/j.engstruct.2020.110582

Girgin, K. (2017), Simplified formulations for the determination of rotational spring constants in rigid spread footings resting on tensionless soil. Journal Civil Engineering and Management. 23(4):464-474. https://doi.org/10.3846/13923730.2016.1210218 DOI: https://doi.org/10.3846/13923730.2016.1210218

Gör, M. (2022), Analyzing the bearing capacity of shallow foundations on two-layered soil using two novel cosmology-based optimization techniques. Smart Structures and Systems. 29(3):513-522. https://doi.org/10.12989/sss.2022.29.3.513

Irles-Más, R. and Irles-Más, F. (1992), Alternativa analítica a la determinación de tensiones bajo zapatas rectangulares con flexión biaxial y despegue parcial. Informes de la Construcción. 44(419):77-89. https://dialnet.unirioja.es/servlet/articulo?codigo=2768804 DOI: https://doi.org/10.3989/ic.1992.v44.i419.1338

Jahanandish, M., Veiskarami, M. and Ghahramani, A. (2012), Effect of Foundation Size and Roughness on the Bearing Capacity Factor, Nγ, by Stress Level-Based ZEL Method. Arabian Journal for Science and Engineering. 37(7):1817-1831. https://doi.org/10.1007/s13369-012-0293-3 DOI: https://doi.org/10.1007/s13369-012-0293-3

Kaur, A. and Kumar, A. (2016), Behavior of eccentrically inclined loaded footing resting on fiber reinforced soil. Geomechanics Engineering. 10(2):155-174. https://doi.org/10.12989/gae.2016.10.2.155 DOI: https://doi.org/10.12989/gae.2016.10.2.155

Khajehzadeh, M., Taha M.R. and Eslami, M. (2014), Multi-objective Optimization of foundation using global-local gravitational search algorithm. Structural Engineering and Mechanics. 50(3): 257-273. https://doi.org/10.12989/sem.2014.50.3.257 DOI: https://doi.org/10.12989/sem.2014.50.3.257

Kim-Sánchez, D.S., Luévanos-Rojas, A., Barquero-Cabrero, J.D., López-Chavarría, S., Medina-Elizondo, M. and Luévanos-Soto, I. (2022). A New Model for the Complete Design of Circular Isolated Footings Considering that the Contact Surface Works Partially under Compression. International Journal of Innovative Computing, Information and Control. 18(6):1769-1784. http://www.ijicic.org/ijicic-180607.pdf

Lee, J., Jeong, S. and Lee, J.K. (2015), 3D analytical method for mat foundations considering coupled soil springs. Geomechanics Engineering. 8(6):845-850. https://doi.org/10.12989/gae.2015.8.6.845 DOI: https://doi.org/10.12989/gae.2015.8.6.845

Lezgy-Nazargah, M., Mamazizi, A. and Khosravi, H. (2022), Analysis of shallow footings rested on tensionless foundations using a mixed finite element model. Structural Engineering and Mechanics. 81(3):379-394. https://doi.org/10.12989/sem.2022.81.3.379

López-Chavarría, S., Luévanos-Rojas, A. and Medina-Elizondo, M. (2017a), A mathematical model for dimensioning of square isolated footings using optimization techniques: general case. International Journal of Innovative Computing, Information and Control. 13(1):67-74. http://www.ijicic.org/ijicic-130105.pdf

López-Chavarría, S., Luévanos-Rojas, A. and Medina-Elizondo, M. (2017b), Optimal dimensioning for the corner combined footings. Advances in Computational Design. 2(2):169-183. https://doi.org/10.12989/acd.2017.2.2.169 DOI: https://doi.org/10.12989/acd.2017.2.2.169

López-Chavarría, S., Luévanos-Rojas, A. and Medina-Elizondo, M. (2017c), A new mathematical model for design of square isolated footings for general case. International Journal of Innovative Computing, Information and Control. 13(4):1149-1168. http://www.ijicic.org/ijicic-130406.pdf

López-Chavarría, S., Luévanos-Rojas, A., Medina-Elizondo, M., Sandoval-Rivas, R. and Velázquez-Santillán, F. (2019), Optimal design for the reinforced concrete circular isolated footings. Advances in Computational Design. 4(3):273-294. https://doi.org/10.12989/acd.2019.4.3.273

Luévanos-Rojas, A. (2012a), A Mathematical Model for Dimensioning of Footings Square. International Review of Civil Engineering. 3(4):346-350.

Luévanos-Rojas, A. (2012b), A Mathematical Model for the Dimensioning of Circular Footings. Far East Journal of Mathematical Sciences. 71(2): 357-367.

Luévanos-Rojas, A. (2013), A Mathematical Model for Dimensioning of Footings Rectangular. ICIC Express Letters Part B: Applications. 4(2):269-274.

Luévanos-Rojas, A., Faudoa-Herrera, J.G., Andrade-Vallejo, R.A. and Cano-Alvarez, M.A. (2013), Design of Isolated Footings of Rectangular Form Using a New Model. International Journal of Innovative Computing, Information and Control. 9(10):4001-4022. http://www.ijicic.org/ijicic-12-10031.pdf

Luévanos-Rojas, A. (2014a), A Comparative Study for Dimensioning of Footings with Respect to the Contact Surface on Soil. International Journal of Innovative Computing, Information and Control. 10(4):1313-1326. http://www.ijicic.org/ijicic-13-08003.pdf

Luévanos-Rojas, A. (2014b), Design of isolated footings of circular form using a new model. Structural Engineering and Mechanics. 52(4):767-786. http://dx.doi.org/10.12989/sem.2014.52.4.767 DOI: https://doi.org/10.12989/sem.2014.52.4.767

Luévanos-Rojas, A. (2014c), Design of boundary combined footings of rectangular shape using a new model. DYNA Colombia. 81(188):199-208. https://doi.org/10.15446/dyna.v81n188.41800 DOI: https://doi.org/10.15446/dyna.v81n188.41800

Luévanos-Rojas, A. (2015a), A New Approach for Dimensioning of Rectangular Footings Using Optimization Techniques. ICIC Express Letters Part B: Applications. 6(11):3141-3146.

Luévanos-Rojas, A. (2015b), A New Mathematical Model for Dimensioning of the Boundary Trapezoidal Combined Footings. International Journal of Innovative Computing, Information and Control. 11(4):1269-1279. http://www.ijicic.org/ijicic-110411.pdf

Luévanos-Rojas, A. (2015c), A new model for the design of rectangular combined boundary footings with two restricted opposite sides. Revista ALCONPAT. 6(2):172-187. http://dx.doi.org/10.21041/ra.v6i2.137

Luévanos-Rojas, A. (2015d), Design of boundary combined footings of trapezoidal form using a new model. Structural Engineering and Mechanics. 56(5):745-765. https://doi.org/10.12989/sem.2015.56.5.745 DOI: https://doi.org/10.12989/sem.2015.56.5.745

Luévanos-Rojas, A. (2016a), A Mathematical Model for the Dimensioning of Combined Footings of Rectangular Shape. Revista Técnica de la Facultad de Ingeniería Universidad del Zulia. 39(1):3-9. https://produccioncientificaluz.org/index.php/tecnica/article/view/21090/20946

Luévanos-Rojas, A. (2016b), Un nuevo modelo para diseño de zapatas combinadas rectangulares de lindero con dos lados opuestos restringidos. Revista ACONPAT. 6(2):173-189. http://dx.doi.org/10.21041/ra.v6i2.137 DOI: https://doi.org/10.21041/ra.v6i2.137

Luévanos-Rojas, A., López-Chavarría, S. and Medina-Elizondo, M. (2017), Optimal design for rectangular isolated footings using the real soil pressure. Ingeniería e Investigación. 37(2):25-33. http://dx.doi.org/10.15446/ing.investig.v37n2.61447 DOI: https://doi.org/10.15446/ing.investig.v37n2.61447

Luévanos-Rojas, A., López-Chavarría, S. and Medina-Elizondo, M. (2018a), A new model for T-shaped combined footings Part I: Optimal dimensioning. Geomechanics Engineering. 14(1):51-60. https://doi.org/10.12989/gae.2018.14.1.051

Luévanos-Rojas, A., López-Chavarría, S. and Medina-Elizondo, M. (2018b), A new model for T-shaped combined footings Part II: Mathematical model for design. Geomechanics Engineering. 14(1):61-69. https://doi.org/10.12989/gae.2018.14.1.061

Luévanos Rojas, A., López Chavarría, S., Medina Elizondo, M., Sandoval Rivas, R., Farías Montemayor, O. M. (2020), Un modelo analítico para el diseño de zapatas combinadas de esquina. Revista ALCONPAT. 10(3):317-335. https://doi.org/10.21041/ra.v10i3.432 DOI: https://doi.org/10.21041/ra.v10i3.432

Özmen, G. (2011), Determination of Base Stresses in Rectangular Footings under Biaxial Bending. Teknik Dergi Digest. 22(4):1519-1535. http://www.imo.org.tr/resimler/dosya_ekler/7b559795bd3f63b_ek.pdf?dergi=472

Rawat, S., Mittal, R.K. and Muthukumar, G. (2020), Isolated Rectangular Footings under Biaxial Bending: A Critical Appraisal and Simplified Analysis Methodology. Practice Periodical on Structural Design and Construction. 25(3):04020011. https://doi.org/10.1061/(ASCE)SC.1943-5576.0000471 DOI: https://doi.org/10.1061/(ASCE)SC.1943-5576.0000471

Rodriguez-Gutierrez, J.A. and Aristizabal-Ochoa, J.D. (2013a), Rigid Spread Footings Resting on Soil Subjected to Axial Load and Biaxial Bending. I: Simplified Analytical Method. International Journal of Geomechanics. 13(2):109-119. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000218 DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000218

Rodriguez-Gutierrez, J.A. and Aristizabal-Ochoa, J.D. (2013b), Rigid Spread Footings Resting on Soil Subjected to Axial Load and Biaxial Bending. II: Design Aids. International Journal of Geomechanics. 13(2):120-131. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000210 DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000210

Soto-Garcia, S., Luévanos-Rojas, A., Barquero-Cabrero, J.D., López-Chavarría, S., Medina-Elizondo, M., Farias-Montemayor, O.M. and Martinez-Aguilar, C. (2022). A New Model for the Contact Surface With Soil of Circular Isolated Footings Considering that the Contact Surface Works Partially Under Compression. International Journal of Innovative Computing, Information and Control. 18(4):1103-1116. http://www.ijicic.org/ijicic-180406.pdf

Vela-Moreno, V.B., Luévanos-Rojas, A., López-Chavarría, S., Medina-Elizondo, M., Sandoval-Rivas, R. and Martinez-Aguilar, C. (2022), Optimal area for rectangular isolated footings considering that contact surface works partially to compression. Structural Engineering and Mechanics. 84(4):561-573. https://doi.org/10.12989/sem.2022.84.4.561

Velázquez-Santillán, F., Luévanos-Rojas, A., López-Chavarría, S., Medina-Elizondo, M. and Sandoval-Rivas, R. (2018), Numerical experimentation for the optimal design for reinforced concrete rectangular combined footings. Advances in Computational Design. 3(1):49-69. https://doi.org/10.12989/acd.2018.3.1.049

Yáñez-Palafox, J.A., Luévanos-Rojas, A., López-Chavarría, S. and Medina-Elizondo, M. (2019), Modeling for the strap combined footings Part II: Mathematical model for design. Steel and Composite Structures. 30(2):109-121. https://doi.org/10.12989/scs.2019.30.2.109

Published
2023-05-01
How to Cite
Luévanos RojasA. (2023). New model for complete design of rectangular isolated footings taking into account that the contact surface works partially in compression . Revista ALCONPAT, 13(2), 192 - 219. https://doi.org/10.21041/ra.v13i2.671