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Modeling for the strap combined footings Part I: Optimal dimensioning

  • Received : 2018.05.03
  • Accepted : 2019.01.16
  • Published : 2019.01.25

Abstract

This paper presents a new model for the strap combined footings to obtain the most economical contact surface on the soil (optimal dimensioning) to support an axial load and moment in two directions to each column. The new model considers the soil real pressure, i.e., the pressure varies linearly. Research presented in this paper shows that can be applied to the T-shaped combined footings and the rectangular combined footings. The classical model uses the technique of test and error, i.e., a dimension is proposed, and subsequently, the equation of the biaxial bending is used to obtain the stresses acting on each vertex of the strap combined footing, which must meet the conditions following: The minimum stress should be equal or greater than zero, and maximum stress must be equal or less than the allowable capacity that can withstand the soil. Numerical examples are presented to obtain the optimal area of the contact surface on the soil for the strap combined footings subjected to an axial load and moments in two directions applied to each column. Appendix shows the Tables 4 and 5 for the strap combined footings, the Table 6 for the T-shaped combined footings, and the Table 7 for the rectangular combined footings.

Keywords

References

  1. Abbasnia, R., Shayanfar, M. and Khodam, A. (2014), "Reliabilitybased design Optimization of structural systems using a hybrid genetic algorithm", Struct. Eng. Mech., Int. J., 52(6), 1099-1120. https://doi.org/10.12989/sem.2014.52.6.1099
  2. Al-Ansari, M.S. (2013), "Structural cost of optimized reinforced concrete isolated footing", Int. Schol. Sci. Res. Innov., 7(4), 193-200.
  3. Aschheim, M., Hernandez-Montes, E. and Gil-Martin, L.M. (2008), "Design of optimally reinforced RC beam, column, and wall sections", J. Struct. Eng., 134(2), 231-239. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:2(231)
  4. Awad, Z.K. (2013), "Optimization of a sandwich beam design: analytical and numerical solutions", Struct. Eng. Mech., Int. J., 48(1), 93-102. https://doi.org/10.12989/sem.2013.48.1.093
  5. Barros, M.H.F.M., Martins, R.A.F. and Barros, A.F.M. (2005), "Cost optimization of singly and doubly reinforced concrete beams with EC2-2001", Struct. Multidiscip. O., 30(3), 236-242. https://doi.org/10.1007/s00158-005-0516-2
  6. Bordignon, R. and Kripka, M. (2012), "Optimum design of reinforced concrete columns subjected to uniaxial flexural compression", Compos. Concrete, 9(5), 327-340. https://doi.org/10.12989/cac.2012.9.5.327
  7. Ceranic, B. and Fryer, C. (2000), "Sensitivity analysis and optimum design curves for the minimum cost design of singly and doubly reinforced concrete beams", Struct. Multidiscip. O., 20(4), 260-268. https://doi.org/10.1007/s001580050156
  8. Fleith de Medeiros, G. and Kripka, M. (2013), "Structural Optimization and proposition of pre-sizing parameters for beams in reinforced concrete buildings", Compos. Concrete, 11(3), 253-270. https://doi.org/10.12989/cac.2013.11.3.253
  9. Gao, Q., Yang, M.G. and Qiao, J.D. (2017), "A multiparameter optimization technique for prestressed concrete cable-stayed bridges considering prestress in girder", Struct. Eng. Mech., Int. J., 64(5), 557-566.
  10. Gharehbaghi, S. (2018), "Damage controlled optimum seismic design of reinforced concrete framed structures", Struct. Eng. Mech., Int. j., 65(1), 53-68.
  11. Ha, T. (1993), "Optimum Design of Unstiffened Built-up Girders", J. Struct. Eng., 119(9), 2784-2792. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:9(2784)
  12. Hans, G. (1985), "Flexural limit design of column footing", J. Struct. Eng., 111(11), 2273-2287. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:11(2273)
  13. Hwang, Y., Jin, S.S., Jung, H.Y., Kim, S.H., Lee, J.J. and Jung, H.J. (2018), "Experimental validation of FE model updating based on multi-objective optimization using the surrogate model", Struct. Eng. Mech., Int. J., 65(2), 173-181.
  14. Jarmai, K., Snyman, J.A., Farkas, J. and Gondos, G. (2003), "Optimal design of a welded I-section frame using four conceptually different optimization algorithms", Struct. Multidiscip. O., 25(1), 54-61. https://doi.org/10.1007/s00158-002-0272-5
  15. Jiang, D. (1983), "Flexural Strength of Square Spread Footing", J. Struct. Eng., 109(8), 1812-1819. https://doi.org/10.1061/(ASCE)0733-9445(1983)109:8(1812)
  16. Jiang, D. (1984), "Closure to "Flexural Strength of Square Spread Footing" by Da Hua Jiang (August, 1983)", J. Struct. Eng., 110(8), 1926-1926. https://doi.org/10.1061/(ASCE)0733-9445(1984)110:8(1926)
  17. Kao, CH-S. and Yeh, I-CH. (2014), "Optimal design of plane frame structures using artificial neural networks and ratio variables", Struct. Eng. Mech., Int. J., 52(4), 739-753. https://doi.org/10.12989/sem.2014.52.4.739
  18. Kaveh, A. and Bijari, S. (2018), "Simultaneous analysis, design and Optimization of trusses via force method", Struct. Eng. Mech., Int. J., 65(3), 233-241.
  19. Kaveh, A. and Mahdavi Dahoei, V.R. (2016), "Optimal design of truss structures using a new optimization algorithm based on global sensitivity analysis", Struct. Eng. Mech., Int. J., 60(6), 1093-1117. https://doi.org/10.12989/sem.2016.60.6.1093
  20. Kaveh, A. and Talatahari, S. (2012), "A hybrid CSS and PSO algorithm for optimal design of structures", Struct. Eng. Mech., Int. J., 42(6), 783-797. https://doi.org/10.12989/sem.2012.42.6.783
  21. Khajehzadeh, M., Taha M.R. and Eslami, M. (2014), "Multiobjective optimization of foundation using global-local gravitational search algorithm", Struct. Eng. Mech., Int. J., 50(3), 257-273. https://doi.org/10.12989/sem.2014.50.3.257
  22. Kripka, M. and Chamberlain Pravia, Z.M. (2013), "Cold-formed steel channel columns optimization with simulated annealing method", Struct. Eng. Mech., Int. J., 48(3), 383-394. https://doi.org/10.12989/sem.2013.48.3.383
  23. Leps, M. and Sejnoha, M. (2003), "New approach to optimization of reinforced concrete beams", Comput. Struct., 81(18-19), 1957-1966. https://doi.org/10.1016/S0045-7949(03)00215-3
  24. Lopez-Chavarria, S., Luevanos-Rojas, A. and Medina-Elizondo, M. (2017a), "A mathematical model for dimensioning of square isolated footings using optimization techniques: general case", Int. J. Innov. Comput. I., 13(1), 67-74.
  25. Lopez-Chavarria, S., Luevanos-Rojas, A. and Medina-Elizondo, M. (2017b), "Optimal dimensioning for the corner combined footings", Adv. Comput. Des., 2(2), 169-183. https://doi.org/10.12989/ACD.2017.2.2.169
  26. Luevanos-Rojas, A. (2012a), "A mathematical model for dimensioning of footings square", I.RE.C.E., 3(4), 346-350.
  27. Luevanos-Rojas, A. (2012b), "A mathematical model for the dimensioning of circular footings", Far East J. Math. Sci., 71(2), 357-367.
  28. Luevanos-Rojas, A. (2013), "A mathematical model for dimensioning of footings rectangular", ICIC Expr. Lett. Part B: Appl., 4(2), 269-274.
  29. Luevanos-Rojas, A. (2015), "A new mathematical model for dimensioning of the boundary trapezoidal combined footings", Int. J. Innov. Comput. I., 11(4), 1269-1279.
  30. Luevanos-Rojas, A. (2016), "A mathematical model for the dimensioning of combined footings of rectangular shape", Rev. Tec. Fac. Ing. Univ., 39(1), 3-9.
  31. Luevanos-Rojas, A., Lopez-Chavarria, S. and Medina-Elizondo, M. (2017), "Optimal design for rectangular isolated footings using the real soil pressure", Ing. Invest., 37(2), 25-33.
  32. Luevanos-Rojas, A., Lopez-Chavarria, S. and Medina-Elizondo, M. (2018), "A new model for T-shaped combined footings Part I: Optimal dimensioning", Geomech. Eng., Int. J., 14(1), 51-60.
  33. Ozturk, H.T. and Durmus, A. (2013), "Optimum cost design of RC columns using artificial bee colony algorithm", Struct. Eng. Mech., Int. J., 45(5), 643-654. https://doi.org/10.12989/sem.2013.45.5.643
  34. Rath, D.P., Ahlawat, A.S. and Ramaswamy, A. (1999), "Shape optimization of RC flexural members", J. Struct. Eng., 125(12), 1439-1445. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:12(1439)
  35. Sahab, M.G., Ashour, A.F. and Toropov, V.V. (2005), "Cost optimisation of reinforced concrete flat slab buildings", Eng. Struct., 27(3), 313-322. https://doi.org/10.1016/j.engstruct.2004.10.002
  36. Tiliouine, B. and Fedghouche, F. (2014), "Cost Optimization of reinforced high strength concrete T-sections in flexure", Struct. Eng. Mech., Int. J., 49(1), 65-80. https://doi.org/10.12989/sem.2014.49.1.065
  37. Uzuner, B.A. (2016), Introduction to Foundation Engineering, Derya Bookstore, Trabzon, Turkey.
  38. 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
  39. Wang, Y. (2009), "Reliability-based economic design optimization of spread foundations", J. Geotech. Geoenviron., 135(7), 954-959. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000013
  40. Wang, Y. and Kulhawy, F.H. (2008), "Economic design optimization of foundations", J. Geotech. Geoenviron., 134(8), 1097-1105. https://doi.org/10.1061/(ASCE)1090-0241(2008)134:8(1097)
  41. Zhang, H.Z., Liu, X., Yi, W.J. and Deng, Y.H. (2018), "Performance comparison of shear walls with openings designed using elastic stress and genetic evolutionary structural Optimization methods", Struct. Eng. Mech., Int. J., 65(3), 303-314.
  42. Zou, X., Chan, C., Li, G. and Wang, Q. (2007), "Multiobjective optimization for performance-based design of reinforced concrete frames", J. Struct. Eng., 133(10), 1462-1474. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:10(1462)