Coupled systems mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Minimum area for circular isolated footings with eccentric column taking into account that the surface in contact with the ground works partially in compression

  • Received : 2024.02.24
  • Accepted : 2024.03.15
  • Published : 2024.06.25
⟨ Previous Next ⟩

Abstract

This study aims to develop a new model to obtain the minimum area in circular isolated footings with eccentric column taking into account that the surface in contact with the ground works partially in compression, i.e., a part of the contact area of the footing is subject to compression and the other there is no pressure (pressure zero). The new model is formulated from a mathematical approach based on a minimum area, and it is developed by integration to obtain the axial load "P", moment around the X axis "Mx" and moment around the Y axis "My" in function of σmax (available allowable soil pressure) R (radius of the circular footing), α (angle of inclination where the resultant moment appears), y0 (distance from the center of the footing to the neutral axis measured on the axis where the resultant moment appears). The normal practice in structural engineering is to use the trial and error procedure to obtain the radius and area of the circular footing, and other engineers determine the radius and area of circular footing under biaxial bending supported on elastic soils, but considering a concentric column and the contact area with the ground works completely in compression. Three numerical problems are given to determine the lowest area for circular footings under biaxial bending. Example 1: Column concentric. Example 2: Column eccentric in the direction of the X axis to 1.50 m. Example 3: Column eccentric in the direction of the X axis to 1.50 m and in the direction of the Y axis to 1.50 m. The new model shows a great saving compared to the current model of 44.27% in Example 1, 50.90% in Example 2, 65.04% in Example 3. In this way, the new minimum area model for circular footings will be of great help to engineers when the column is located on the center or edge of the footing.

Keywords

Acknowledgement

The research described in this paper was financially supported by the Universidad Autonoma de Coahuila and Universidad Juarez del Estado de Durango, Mexico.

References

  1. Agrawal, R. and Hora, M.S. (2012), "Nonlinear interaction behaviour of infilled frame-isolated footings-soil system subjected to seismic loading", Struct. Eng. Mech., 44(1), 85-107. https://doi.org/10.12989/sem.2012.44.1.085.
  2. Aguilera-Mancilla, G., Luevanos-Rojas, A., Lopez-Chavarria, S. and Medina-Elizondo, M. (2019), "Modeling for the strap combined footings Part I: Optimal dimensioning", Steel Compos. Struct., 30(2), 97-108. https://doi.org/10.12989/scs.2019.30.2.097.
  3. Al-Ansari, M.S. (2013), "Structural cost of optimized reinforced concrete isolated footing", Int. Scholar. Scientif. Res. Innov., 7(4), 193-200.
  4. Al-Ansari, M.S. (2014), "Cost of reinforced concrete paraboloid shell footing", J. Struct. Anal. Des., 1(3), 111-119.
  5. Alazwari, M.A., Daikh, A.A., Houari, M.S.A., Tounsi, A. and Eltaher, M.A. (2021), "On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations", Steel Compos. Struct., 40(3), 389-404. https://doi.org/10.12989/scs.2021.40.3.389.
  6. Alijani, M. and Bidgoli, M.R. (2018), "Agglomerated SiO2 nanoparticles reinforced-concrete foundations based on higher order shear deformation theory: Vibration analysis", Adv. Concrete Constr., 6(6), 585-610. https://doi.org/10.12989/acc.2018.6.6.585.
  7. Anil, O ., Akbas, S.O., BabagĪray, S., Gel, A.C. and Durucan, C. (2017), "Experimental and finite element analyses of footings of varying shapes on sand", Geomech. Eng., 12(2), 223-238. https://doi.org/10.12989/gae.2017.12.2.223.
  8. Basudhar, P.K., Dey, A. and Mondal, A.S. (2012), "Optimal Cost-Analysis and Design of Circular Footings", Int. J. Eng. Technol. Innov., 2(4), 243-264.
  9. Dagdeviren, U. (2016), "Shear stresses below the rectangular foundations subjected to biaxial bending", Geomech. Eng., 10(2), 189-205. https://doi.org/10.12989/gae.2016.10.2.189.
  10. Garay-Gallegos, J.R., Luevanos-Rojas, A., Lopez-Chavarria, S., Medina-Elizondo, M., Aguilera-Mancilla, G. and Garcia-Canales, E. (2022), "A comparative study between the new model and the current model for T-shaped combined footings", Geomech. Eng., 30(6), 525-538. https://doi.org/10.12989/gae.2022.30.6.525.
  11. Garcia-Galvan, M., Luevanos-Rojas, A., Lopez-Chavarria, S., Medina-Elizondo, M. and Rivera-Mendoza, J.B. (2022), "A general model for rectangular footings Part I: Optimal surface", DYNA: Revista de la Facultad de Minas. Universidad Nacional de Colombia. Sede Medellin, 89(221), 132-141. https://doi.org/10.15446/dyna.v89n221.100028.
  12. Garcia-Galvan, M., Luevanos-Rojas, A., Lopez-Chavarria, S., Medina-Elizondo, M. and Rivera-Mendoza, J.B. (2022), "A comparative study between trapezoidal combined footings and T-shaped combined footings", Couple. Syst. Mech., 11(3), 233-257. https://doi.org/10.12989/csm.2022.11.3.233.
  13. Garcia-Graciano, M.L., Luevanos-Rojas, A., Lopez-Chavarria, S. and Medina-Elizondo, M. (2022), "Mathematical modeling for corner strap combined footings resting on the ground: Part 1", Computacion y Sistemas, 26(4), 1429-1443. http://dx.doi.org/10.13053/cys-26-4-4080.
  14. Golewski, G.L. (2019), "New principles for implementation and operation of foundations for machines: A review of recent advances", Struct. Eng. Mech., 71(3), 317-327. https://doi.org/10.12989/sem.2019.71.3.317.
  15. Gor, M. (2022), "Analyzing the bearing capacity of shallow foundations on two-layered soil using two novel cosmology-based optimization techniques", Smart Struct. Syst., 29(3), 513-522. https://doi.org/10.12989/sss.2022.29.3.513.
  16. Hadzalic, E., Ibrahimbegovic, A. and Dolarevic, S. (2018), "Failure mechanisms in coupled soil-foundation systems", Couple. Syst. Mech., 7(1), 27-42. https://doi.org/10.12989/csm.2018.7.1.027.
  17. Hadzalic, E., Ibrahimbegovic, A. and Dolarevic, S. (2018), "Failure mechanisms in coupled poro-plastic medium", Couple. Syst. Mech., 7(1), 43-59. https://doi.org/10.12989/csm.2018.7.1.043.
  18. Hadzalic, E., Ibrahimbegovic, A. and Dolarevic, S. (2018), "Fluid-structure interaction system predicting both internal pore pressure and outside hydrodynamic pressure", Couple. Syst. Mech., 7(6), 649-668. https://doi.org/10.12989/csm.2018.7.6.649.
  19. Hadzalic, E., Ibrahimbegovic, A. and Dolarevic, S. (2020), "3D thermo-hydro-mechanical coupled discrete beam lattice model of saturated poro-plastic medium", Couple. Syst. Mech., 9(2), 125-145. https://doi.org/10.12989/csm.2020.9.2.125.
  20. Himeur, N., Mamen, B., Benguediab, S., Bouhadra, A., Menasria, A., Bouchouicha, B., Bourada, F., Benguediab, M. and Tounsi, A. (2022), "Coupled effect of variable Winkler-Pasternak foundations on bending behavior of FG plates exposed to several types of loading", Steel Compos. Struct., 44(3), 353-369. https://doi.org/10.12989/scs.2022.44.3.353.
  21. Ibrahimbegovic, A. and Mejia-Nava, R.A. (2021), "Heterogeneities and material-scales providing physically based damping to replace Rayleigh damping for any structure size", Couple. Syst. Mech., 10(3), 201-216. https://doi.org/10.12989/csm.2021.10.3.201.
  22. Jelusic, P. and Zlender, B. (2018), "Optimal design of pad footing based on MINLP optimization", Soil. Found., 58(2), 277-289. https://doi.org/10.1016/j.sandf.2018.02.002.
  23. Kaur, A. and Kumar, A. (2016), "Behavior of eccentrically inclined loaded footing resting on fiber reinforced soil", Geomech. Eng., 10(2), 155-174. https://doi.org/10.12989/gae.2016.10.2.155.
  24. Khajehzadeh, M., Taha M.R. and Eslami, M. (2014), "Multi-objective optimization of foundation using global-local gravitational search algorithm", Struct. Eng. Mech., 50(3), 257-273. http://doi.org/10.12989/sem.2014.50.3.257.
  25. Kim-Sanchez, D.S., Luevanos-Rojas, A., Barquero-Cabrero, J.D., Lopez-Chavarria, S., Medina-Elizondo, M. and Luevanos-Soto, I. (2022), "A new model for the complete design of circular isolated footings considering that the contact surface works partially under compression", Int. J. Innov. Comput. I., 18(6), 1769-1784.
  26. Lee, J., Jeong, S. and Lee, J.K. (2015), "3D analytical method for mat foundations considering coupled soil springs", Geomech. Eng., 8(6), 845-850. https://doi.org/10.12989/gae.2015.8.6.845.
  27. Lezgy-Nazargah, M., Mamazizi, A. and Khosravi, H. (2022), "Analysis of shallow footings rested on tensionless foundations using a mixed finite element model", Struct. Eng. Mech., 81(3), 379-394. https://doi.org/10.12989/sem.2022.81.3.379.
  28. Lopez-Chavarria, S., Luevanos-Rojas, A. and Medina-Elizondo, M. (2017a), "Optimal dimensioning for the corner combined footings", Adv. Comput. Des., 2(2), 169-183. https://doi.org/10.12989/acd.2017.2.2.169.
  29. Lopez-Chavarria, S., Luevanos-Rojas, A. and Medina-Elizondo, M. (2017b), "A mathematical model for dimensioning of square isolated footings using optimization techniques: General case", Int. J. Innov. Comput. I., 13(1), 67-74.
  30. Lopez-Chavarria, S., Luevanos-Rojas, A., Medina-Elizondo, M., Sandoval-Rivas, R. and Velazquez-Santillan, F. (2019), "Optimal design for the reinforced concrete circular isolated footings", Adv. Comput. Des., 4(3), 273-294. https://doi.org/10.12989/acd.2019.4.3.273.
  31. Luat, N.V., Lee, K. and Thai, D.K. (2020), "Application of artificial neural networks in settlement prediction of shallow foundations on sandy soils", Geomech. Eng., 20(5), 385-397. https://doi.org/10.12989/gae.2020.20.5.385.
  32. Luevanos-Rojas, A. (2014a), "A comparative study for dimensioning of footings with respect to the contact surface on soil", Int. J. Innov. Comput. I., 10(4), 1313-1326.
  33. Luevanos-Rojas, A. (2014b), "Design of isolated footings of circular form using a new model", Struct. Eng. Mech., 52(4), 767-786. https://doi.org/10.12989/sem.2014.52.4.767.
  34. Luevanos-Rojas, A. (2015a), "A new mathematical model for dimensioning of the boundary trapezoidal combined footings", Int. J. Innov. Comput. I., 11(4), 1269-1279.
  35. Luevanos-Rojas, A. (2015b), "Design of boundary combined footings of trapezoidal form using a new model", Struct. Eng. Mech., 56(5), 745-765. http://doi.org/10.12989/sem.2015.56.5.745.
  36. Luevanos-Rojas, A. (2016a), "A comparative study for the design of rectangular and circular isolated footings using new models", Dyna, 83(196), 149-158. https://doi.org/10.15446/dyna.v83n196.51056.
  37. Luevanos-Rojas, A. (2016b), "A mathematical model for the dimensioning of combined footings of rectangular shape", Revista Tecnica de la Facultad de Ingenieria Universidad del Zulia, 39(1), 3-9.
  38. Luevanos-Rojas, A. (2023a), "Minimum cost design for rectangular isolated footings taking into account that the column is located in any part of the footing", Build., 13(9), 1-16. https://doi.org/10.3390/buildings13092269.
  39. Luevanos-Rojas, A. (2023b), "Optimization for trapezoidal combined footings: Optimal design", Adv. Concrete Constr., 16(1), 21-34. https://doi.org/10.12989/acc.2023.16.1.021.
  40. Luevanos-Rojas, A. (2023c), "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.
  41. Luevanos-Rojas, A., Barquero-Cabrero, J.D., Lopez-Chavarria, S. and Medina-Elizondo, M. (2017b), "A comparative study for design of boundary combined footings of trapezoidal and rectangular forms using new models", Couple. Syst. Mech., 6(4), 417-437. https://doi.org/10.12989/csm.2017.6.4.417.
  42. Luevanos-Rojas, A., Lopez-Chavarria, S. and Medina-Elizondo, M. (2017a), "Optimal design for rectangular isolated footings using the real soil pressure", Ingenieria e Investigacion, 37(2), 25-33. https://doi.org/10.15446/ing.investig.v37n2.61447.
  43. Luevanos-Rojas, A., Lopez-Chavarria, S. and Medina-Elizondo, M. (2018a), "A new model for T-shaped combined footings Part I: Optimal dimensioning", Geomech. Eng., 14(1), 51-60. https://doi.org/10.12989/gae.2018.14.1.051.
  44. Luevanos-Rojas, A., Lopez-Chavarria, S. and Medina-Elizondo, M. (2018b), "A new model for T-shaped combined footings Part II: Mathematical model for design", Geomech. Eng., 14(1), 61-69. https://doi.org/10.12989/gae.2018.14.1.061.
  45. Luevanos-Rojas, A., Lopez-Chavarria, S., Medina-Elizondo, M., Sandoval-Rivas, R. and Farias-Montemayor, O.M. (2020), "An analytical model for the design of corner combined footings", Revista ALCONPAT, 10(3), 317-335. https://doi.org/10.21041/ra.v10i3.432.
  46. Malapur, M.M., Cholappanavar, P. and Fernandes, R.J. (2018), "Optimization of RC column and footings using genetic algorithm", Int. Res. J. Eng. Technol. (IRJET), 5(8), 546-552.
  47. Mohebkhah, A. (2017), "Bearing capacity of stripfootingson a stone masonry trench in clay", Geomech. Eng., 13(2), 255-267. https://doi.org/10.12989/gae.2017.13.2.255.
  48. Montes-Paramo, P., Luevanos-Rojas, A., Lopez-Chavarria, S., Medina-Elizondo, M. and Sandoval-Rivas, R. (2023), "Optimal area for rectangular combined footings assuming that the contact surface with the soil works partially to compression", Ingenieria Investigacion y Tecnologia, 24(02), 1-15. https://doi.org/10.22201/fi.25940732e.2023.24.2.012.
  49. Moreno-Hernandez, M.A., Luevanos-Rojas, A., Lopez-Chavarria, S. and Medina-Elizondo, M. (2022), "Mathematical modeling for corner strap combined footings resting on the ground: Part 1", Computacion y Sistemas, 26(3), 1259-1272. http://doi.org/10.13053/cys-26-3-4079.
  50. Pasillas-Orona, A.I., Luevanos-Rojas, A., Lopez-Chavarria, S., Medina-Elizondo, M. and AguileraMancilla, G. (2020), "Un modelo optimizado para zapatas combinadas trapezoidales apoyadas sobre el terreno: Superficie optima", Acta Universitaria, 30, 1-18. http://doi.org/10.15174/au.2020.2973.
  51. Rad, A.B. (2012), "Static response of 2-D functionally graded circular plate with gradient thickness and elastic foundations to compound loads", Struct. Eng. Mech., 44(2), 139-161. https://doi.org/10.12989/sem.2012.44.2.139.
  52. Ramu, K. and Madhav, M.R. (2010), "Response of rigid footing on reinforced granular fill over soft soil", Geomech. Eng., 2(4), 281-302. https://doi.org/10.12989/gae.2010.2.4.281.
  53. Rawat, S. and Mittal, R.K. (2018), "Optimization of eccentrically loaded reinforced-concrete isolated footings", Pract. Period. Struct. Des. Constr., 23(2), 06018002. https://doi.org/10.1061/(ASCE)SC.1943-5576.0000366.
  54. Rivera-Mendoza, J.B., Luevanos-Rojas, A., Lopez-Chavarria, S., Medina-Elizondo, M. and Garcia-Galvan, M. (2022), "general model for rectangular footings Part II: Modeling for design", Dyna, 89(223), 9-18. https://doi.org/10.15446/dyna.v89n223.100030.
  55. Rizwan, M., Alam, B., Rehman, F.U., Masud, N., Shahzada, K. and Masud, T. (2012), "Cost optimization of combined footings using modified complex method of box", Int. J. Adv. Struct. Geotech. Eng., 1(1), 24-28.
  56. Soto-Garcia, S., Luevanos-Rojas, A., Barquero-Cabrero, J.D., Lopez-Chavarria, 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", Int. J. Innov. Comput. I., 18(4), 1103-1116.
  57. Turedi, Y., Emirler, B., Ornek, M. and Yildiz, A. (2019), "Determination of the bearing capacity of model ring footings: Experimental and numerical investigations", Geomech. Eng., 18(1), 29-39. https://doi.org/10.12989/gae.2019.18.1.029.
  58. Vela-Moreno, V.B., Luevanos-Rojas, A., Lopez-Chavarria, 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", Struct. Eng. Mech., 84(4), 561-573. https://doi.org/10.12989/sem.2022.84.4.561.
  59. Velazquez-Santillan, F., Luevanos-Rojas, A., Lopez-Chavarria, S., Medina-Elizondo, M. and Sandoval-Rivas, R. (2018), "Numerical experimentation for the optimal design for reinforced concrete rectangular combined footings", Adv. Comput. Des., 3(1), 49-69. https://doi.org/10.12989/acd.2018.3.1.049.
  60. Yanez-Palafox, J.A., Luevanos-Rojas, A., Lopez-Chavarria, S. and Medina-Elizondo, M. (2019), "Modeling for the strap combined footings Part II: Mathematical model for design", Steel Compos. Struct., 30(2), 109-121. https://doi.org/10.12989/scs.2019.30.2.109.