Non linear modeling of three-dimensional reinforced and fiber concrete structures

Abstract

Under the effect of the ascending loading, the behavior of reinforced concrete structures is rather non linear. Research in industry and science aims to extend forward the use of non-linear calculation of fiber concrete for structural parts such as columns, veils and pious, as the fiber concrete is more ductile behavior then the classical concrete behavior. The formulation of the element has been established for modeling the nonlinear behavior of elastic structures in three dimensions, based on the displacement method. For the behavior of concrete and fiber concrete compressive and tensile strength (stress-strain) the uniaxial formulation is used. For steel bi-linear relationship is used. The approach is based on the discretization of the cross section trapezoidal tables. Forming the stiffness matrix of the section, the integral of the surface is calculated as the sum of the integrals on each of the cutting trapezoids. To integrate on the trapeze we have adopted the type of Simpson integration scheme.

Keywords

numerical modeling / column and beam / nonlinear analysis / fibers / pious / reinforcement / 3D formulation / response load-deflection

References

[1] Bažant Z P, Bhat P D. Endochronic theory of inelasticity and failure of concrete. Journal of the Engineering Mechanics Division, 1976, 102: 701–722

[2] Bažant Z P, Bhat P D. Prediction of hysteresis of reinforced concrete members. American Society of Civil Engineers, 1977, 103: 153–167

[3] Bažant Z P. On endochronic inelasticity and incremental plasticity. Structural Engineering Rep. No. 76- 12/259. Northwestern University, Evanston, Illinois, 1976

[4] Bažant Z P. Endochronic inelasticity and incremental plasticity. International Journal of Solids and Structures, 1978, 14(9): 691–714

[5] Bažant Z P, Oh B H. Crack band theory for fracture of concrete. Materials and Structures, 1983, 16(3): 155–177

[6] Bažant Z P, Belytschko T, Chang T P. Continuum theory for strain softening. Journal of Engineering Mechanics, 1984, 111: 381–389

[7] Bažant Z P, Prat P. Microplane model for brittle plastic materials I: Theory, II: verification. Journal of Engineering Mechanics, 1988, 114(10): 1672–1702

[8] Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455

[9] Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343

[10] Rabczuk T, Belytschko T. A three dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29-30): 2777–2799

[11] Rabczuk T, Belytschko T. Application of particle methods to static fracture of reinforced concrete structures. International Journal of Fracture, 2006, 137(1–4): 19–49

[12] Rabczuk T, Akkermann J, Eibl J. A numerical model for reinforced concrete structures. International Journal of Solids and Structures, 2005, 42(5–6): 1327–1354

[13] Bouafia Y, Kachi M S, Fouré B. Stress strain relation in tensile of steel fiber reinforced concrete. The building and the public works Annals, 2002 (in French)

[14] Izzuddin B A, Siyam A A F M, Smith D L. An efficient beam–column formulation for 3D reinforced concrete frames. Computers & Structures, 2002, 80(7–8): 659–676

[15] Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758

[16] Izzuddin B A. Conceptual issues in geometricaly nonlinear analysis of 3D framed structures. Computer Methods in Applied Mechanics and Engineering, 2001, 191(8–10): 1029–1053

[17] Adjrad A, Kachi M, Bouafia Y, Iguetoulene F. Nonlinear modeling structures on 3D. In: Proc. 4th Annu.icsaam 2011. Structural Analysis of Advanced Materials, Romania, 2011, 1–9

[18] Fang C, Izzuddin B A, Elghazouli A Y, Nethercot D A. Modeling of semi-rigid beam-to-column steel joints under extreme loading. Frontiers of Structural and Civil Engineering, 2013, 7(3): 245–263

[19] Marante M E, Flórez-López J. Three-dimensional analysis of reinforced concrete frames based on lumped damage mechanics. International Journal of Solids and Structures, 2003, 40(19): 5109–5123

[20] Bouafia Y, Kachi M S, Fouré B. Numerical modeling of the behavior of steel fiber reinforced concrete. II. International Symposium on Cement and Concrete Technology in the 2000s. Turkish Cement Manufacturers’ Association – European Cement Association. Sept. 6–10, 2000, Istanbul- Turkiye, 2: 582–591

[21] Park S H, Kim D J, Ryu G S, Koh K T. Tensile behavior of ultra high performance hybrid fiber reinforced concrete. Cement and Concrete Composites, 2012, 34(2): 172–184

[22] Rehder B, Banh K, Neithalath N. Fracture behavior of pervious concretes: the effects of pore structure and fibers. Engineering Fracture Mechanics, 2014, 118: 1–16

[23] Mohamed N, Soliman A M, Nehdi M L. Full-scale pipes using dry-cast steel fibre- reinforced concrete. Construction & Building Materials, 2014, 72: 411–422

[24] Teng T L, Chu Y A, Chang F A, Shen B C, Cheng D S. Development and validation of numerical model of steel fiber reinforced concrete for high-velocity impact. Computational Materials Science, 2008, 42(1): 90–99

[25] Park K, Paulino G H, Roesler J. Cohesive fracture model for functionally graded fiber reinforced concrete. Cement and Concrete Research, 2010, 40(6): 956–965

[26] Felippa C A. Nonlinear Finite Element Methods. University of Colorado Boulder, Colorado 80309-0429, USA. 2001

[27] Vasudevan G, Kothandaraman S, Azhagarsamy S. Study on non-linear flexural behavior of reinforced concrete beam using ANSYS by discrete reinforcement modeling. Strength of Materials, 2013, 45(2): 231–241

[28] Grelat A. Nonlinear analysis of hyperstatic reinforced concrete frames. Thesis of Doctor Engineer. University Paris VI, 1978 (in French)

[29] Rules B A E L. 91 modified 99, technical design rules and calculation of reinforced concrete structures and constructions, according to the method of limit states.Edition EYROLLES, 2000 (in French)

[30] Nait-Rabah. Numerical simulation of space frames. Dissertation for Ph.D. degree. Central School of Paris 1990 (in French)

[31] Kachi M S. Modeling the behavior at break of outer prestressed beams. Dissertation for Ph.D. degree. University Mouloud MAMMERI of Tizi-Ouzou, November, 2000 (in French)

[32] Vecchio F J, Emara M B. Shear deformations in reinforced concrete frames. ACI Structural Journal, 1992, 89(1): 46–56 (American Concrete Institute)

[33] Zhan Z. Contribution to the dimensioning of the fiber concrete piles. Dissertation for Ph.D. degree. Universitéd’Orléans, Laboratoire CEBTP, 1991 (in French)

[34] Fourré B. High strength concrete. Internal report OG3, C.E.B.T.P., Nov. 1985 (in French)

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