DOI QR코드

DOI QR Code

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

  • 투고 : 2024.05.18
  • 심사 : 2024.07.01
  • 발행 : 2024.08.25

초록

This work aims to show a model to estimate the minimum cost (Thickness and area of steel in X and Y directions) for design a circular isolated footing with eccentric column that considers that the surface in contact with the ground works partially under compression. The formulation is shown by integration to find the moments, the bending shears and the punching shear using the pressure volume under the footing. Some researchers show the minimum cost design for circular isolated footings for an eccentric column assuming that the contact area works completely in compression, others consider the contact surface with the ground working partially in compression for a column in the center of the base. Three numerical examples are developed to obtain the complete design, which are: Example 1 for a column in the center of the base,Example 2 for a column at a distance of 1.50 m from the center of the base in the X direction, Example 3 for a column at a distance of 1.50 m from the center of the base in both directions. Also, a comparison of the new model against the model proposed by other authors is presented. The comparison shows that the new model generates a great saving of up to 43.74% for minimum area and 48.44% for minimum cost design in a column located in the center of the base, and when the column is located at a distance of radius/2 starting from the center of the base in the X direction generates great savings of up to 45.24% for minimum area and 31.80% for minimum cost design. Therefore, it is advisable to use the model presented in this study.

키워드

과제정보

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

참고문헌

  1. ACI 318S-14 (American Concrete Institute) (2014), Building Code Requirements for Structural Concrete and Commentary, Committee 318.
  2. 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.
  3. 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.
  4. Al-Ansari, M.S. (2013), "Structural cost of optimized reinforced concrete isolated footing", Int. Scholar. Sci. Res. Innov., 7(4), 193-200.
  5. Al-Ansari, M.S. (2014), "Cost of reinforced concrete paraboloid shell footing", J. Struct. Anal. Des., 1(3), 111-119.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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://doi.org/10.13053/cys-26-4-4080.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. 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.
  31. Lopez-Chavarria, S., Luevanos-Rojas, A. and Medina-Elizondo, M. (2017c), "A new mathematical model for design of square isolated footings for general case", Int. J. Innov. Comput. I., 13(4), 1149-1168.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. Luevanos-Rojas, A. (2014c), "Design of boundary combined footings of rectangular shape using a new model", Dyna, 81(188), 199-208. https://doi.org/10.15446/dyna.v81n188.41800.
  37. 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.
  38. 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.
  39. 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.
  40. 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.
  41. Luevanos-Rojas, A. (2016c), "A new model for the design of rectangular combined boundary footings with two restricted opposite sides", Revista ALCONPAT, 6(2), 172-187. https://doi.org/10.21041/ra.v6i2.137.
  42. 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.
  43. 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.
  44. 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.
  45. 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.
  46. Luevanos-Rojas, A., Barquero-Cabrero, J.D., Lopez-Chavarria, S., Medina-Elizondo, M., Vela-Moreno, V.B. and Barraza-Saucedo, R. (2022), "Costo minimo para zapatas combinadas trapezoidales de concreto reforzado apoyadas sobre el terreno", Revista Internacional de Investigacion e Innovacion Tecnologica, 10(56), 62-85.
  47. Luevanos-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", Int. J. Innov. Comput. I., 9(10), 4001-4022.
  48. Luevanos-Rojas, A., Lopez-Chavarria, S. and Medina-Elizondo, M. (2017a), "Optimal design for rectangular isolated footings using the real soil pressure", Ing. Invest., 37(2), 25-33. https://doi.org/10.15446/ing.investig.v37n2.61447.
  49. 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.
  50. 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.
  51. 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.
  52. Luevanos-Rojas, A., Moreno-Landeros, V.M., Santiago-Hurtado, G., Olguin-Coca, F.J., Lopez-Leon, L.D., Baltazar-Zamora, M.A. and Diaz-Gurrola, E.R. (2024b), "Mathematical modeling of the optimal cost for the design of circular isolated footings with eccentric column", Math., 12(5), 1-19. https://doi.org/10.3390/math12050733.
  53. Luevanos-Rojas, A., Santiago-Hurtado, G., Moreno-Landeros, V.M., Olguin-Coca, F.J., Lopez-Leon, L.D. and Diaz-Gurrola, E.R. (2024a), "Mathematical modeling of the optimal cost for the design of strap combined footings", Math., 12(2), 1-20. https://doi.org/10.3390/math12020294.
  54. Luevanos-Soto, I., Luevanos-Rojas, A., Moreno-Landeros, V.M. and Santiago-Hurtado, G. (2024), "Minimum area for circular isolated footings with eccentric column taking into account that the surface in contact with the ground works partially in compression", Couple. Syst. Mech., 13(3), 201-217. https://doi.org/10.12989/csm.2024.13.3.201.
  55. 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.
  56. 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.
  57. 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.
  58. 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.
  59. Pasillas-Orona, A.I., Luevanos-Rojas, A., Lopez-Chavarria, S., Medina-Elizondo, M. and Aguilera-Mancilla, 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.
  60. 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.
  61. 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.
  62. 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.
  63. 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.
  64. Rizwan, M., Alam, B., Rehman, F.U., Masud, N., Shahzada, K., Masud, T. (2012), "Cost optimization of combined footings using modified complex method of box", Int. J. Adv. Struct. Geotech. Eng., 1(1), 24-28.
  65. 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.
  66. 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.
  67. 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.
  68. 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.
  69. 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.