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http://dx.doi.org/10.12989/acd.2017.2.2.169

Optimal dimensioning for the corner combined footings  

Lopez-Chavarria, Sandra (Institute of Multidisciplinary Researches, Autonomous University of Coahuila)
Luevanos-Rojas, Arnulfo (Institute of Multidisciplinary Researches, Autonomous University of Coahuila)
Medina-Elizondo, Manuel (Institute of Multidisciplinary Researches, Autonomous University of Coahuila)
Publication Information
Advances in Computational Design / v.2, no.2, 2017 , pp. 169-183 More about this Journal
Abstract
This paper shows optimal dimensioning for the corner combined footings to obtain the most economical contact surface on the soil (optimal area), due to an axial load, moment around of the axis "X" and moment around of the axis "Y" applied to each column. The proposed model considers soil real pressure, i.e., the pressure varies linearly. The classical model is developed by trial and error, i.e., a dimension is proposed, and after, using the equation of the biaxial bending is obtained the stress acting on each vertex of the corner combined footing, which must meet the conditions following: 1) Minimum stress should be equal or greater than zero, because the soil is not withstand tensile. 2) Maximum stress must be equal or less than the allowable capacity that can be capable of withstand the soil. Numerical examples are presented to illustrate the validity of the optimization techniques to obtain the minimum area of corner combined footings under an axial load and moments in two directions applied to each column.
Keywords
corners combined footings; optimization techniques; contact surface; more economical dimension; optimal area;
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Times Cited By KSCI : 10  (Citation Analysis)
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1 Jiang, D. (1983), "Flexural strength of square spread footing", J. Struct. Eng., 109(8), 1812-1819.   DOI
2 Jiang, D. (1984), "Flexural strength of square spread footing", J. Struct. Eng., 110(8), 1926-1926.
3 Kao, C.H.S. and Yeh, I.C.H. (2014), "Optimal design of plane frame structures using artificial neural networks and ratio variables", Struct. Eng. Mech., 52(4), 739-753.   DOI
4 Kaveh, A. and Talatahari, S. (2012), "A hybrid CSS and PSO algorithm for optimal design of structures", Struct. Eng. Mech., 42(6), 783-797.   DOI
5 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.   DOI
6 Kripka, M. and Chamberlain, P.Z.M. (2013), "Cold-formed steel channel columns optimization with simulated annealing method", Struct. Eng. Mech., 48(3), 383-394.   DOI
7 Kurian, N.P. (2005), Design of Foundation Systems, Alpha Science Int'l Ltd, New York, U.S.A.
8 Leps, M. and Sejnoha, M. (2003), "New approach to optimization of reinforced concrete beams", Comput. Struct., 81(18-19), 1957-1966.   DOI
9 Luevanos-Rojas, A. (2012a), "A mathematical model for dimensioning of footings square", I.RE.C.E., 3(4), 346-350.
10 Luevanos-Rojas, A. (2012b), "A mathematical model for the dimensioning of circular footings", Far East J. Math. Sci., 71(2), 357-367.
11 Luevanos-Rojas, A. (2013), "A mathematical model for dimensioning of footings rectangular", ICIC Expr. Lett. Part B: Appl., 4(2), 269-274.
12 Luevanos-Rojas, A. (2015), "A new mathematical model for dimensioning of the boundary trapezoidal combined footings", J. Innovat. Comput. I, 11(4), 1269-1279.
13 Ozturk, H.T. and Durmus, A. (2013), "Optimum cost design of RC columns using artificial bee colony algorithm", Struct. Eng. Mech., 45(5), 643-654.   DOI
14 Luevanos-Rojas, A. (2016a), "Numerical experimentation for the optimal design of reinforced rectangular concrete beams for singly reinforced sections", Dyn., 83(196), 134-142.
15 Luevanos-Rojas, A. (2016b), "A mathematical model for the dimensioning of combined footings of rectangular shape", Rev. Tec. Fac. Ing. Univ., 39(1), 3-9.
16 McCormac, J.C. and Brown, R.H. (2013), Design of Reinforced Concrete, John Wiley & Sons, Inc., Mexico.
17 Punmia, B.C., Ashok, K.J. and Arun, K.J. (2007), Limit State Design of Reinforced Concrete, Laxmi Publications (P) Limited, New York, U.S.A.
18 Rath, D.P., Ahlawat, A.S. and Ramaswamy, A. (1999), "Shape optimization of RC flexural members", J. Struct. Eng., 125(12), 1439-1445.   DOI
19 Sahab, M.G., Ashour, A.F. and Toropov, V.V. (2005), "Cost optimization of reinforced concrete flat slab buildings", Eng. Struct., 27(3), 313-322.   DOI
20 Tiliouine, B. and Fedghouche, F. (2014), "Cost optimization of reinforced high strength concrete T-sections in flexure", Struct. Eng. Mech., 49(1), 65-80.   DOI
21 Tomlinson, M.J. (2008), Cimentaciones, Diseno y Construccion, Trillas, Mexico.
22 Varghese, P.C. (2009), Design of Reinforced Concrete Foundations, PHI Learning Pvt. Ltd., New York, U.S.A.
23 Wang, Y. (2009), "Reliability-based economic design optimization of spread foundation", J. Geotech. Geoenviron., 135(7), 954-959.   DOI
24 Wang, Y. and Kulhawy, F.H. (2008), "Economic design optimization of foundation", J. Geotech. Geoenviron., 134(8), 1097-1105.   DOI
25 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. Optim., 30(3), 236-242.   DOI
26 Zou, X., Chan, C., Li, G. and Wang, Q. (2007), "Multi objective optimization for performance-based design of reinforced concrete frames", J. Struct. Eng., 133(10), 1462-1474.   DOI
27 Abbasnia, R., Shayanfar, M. and Khodam, A. (2014), "Reliability-based design optimization of structural systems using a hybrid genetic algorithm", Struct. Eng. Mech., 52(6), 1099-1120.   DOI
28 Al-Ansari, M.S. (2013), "Structural cost of optimized reinforced concrete isolated footing", Schol. Sci. Res. Innovat., 7(4), 193-200.
29 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.   DOI
30 Awad, Z.K. (2013), "Optimization of a sandwich beam design: Analytical and numerical solutions", Struct. Eng. Mech., 48(1), 93-102.   DOI
31 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. Optim., 20(4), 260-268.   DOI
32 Bordignon, R. and Kripka, M. (2012), "Optimum design of reinforced concrete columns subjected to uniaxial flexural compression", Comput. Concrete, 9(5), 327-340.   DOI
33 Bowles, J.E. (2001), Foundation Analysis and Design, McGraw-Hill, New York, U.S.A.
34 Calabera-Ruiz, J. (2000), Calculo de Estructuras de Cimentacion, Intemac Ediciones, Mexico.
35 Das, B.M., Sordo-Zabay, E. and Arrioja-Juarez, R. (2006), Principios de Ingeniería de Cimentaciones, Cengage Learning Latin America, Mexico.
36 Fleith de Medeiros, G. and Kripka, M. (2013), "Structural optimization and proposition of pre-sizing parameters for beams in reinforced concrete buildings", Comput. Concrete, 11(3), 253-270.   DOI
37 Gere, J.M. and Goodno, B.J. (2009), Mechanics of Materials, Cengage Learning, New York, U.S.A.
38 Gonzalez-Cuevas, O.M. and Robles-Fernandez-Villegas, F. (2005), Aspectos Fundamentales del Concreto Reforzado, Limusa, Mexico.
39 Ha, T. (1993), "Optimum design of unstiffened built-up girders", J. Struct. Eng., 119(9), 2784-2792.   DOI
40 Hans, G. (1985), "Flexural limit design of column footing", J. Struct. Eng., 111(11), 2273-2287.   DOI
41 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. Optim., 25(1), 54-61.   DOI