Abstract
A highly accurate nonlinear analytical algorithm to simulate the behavior of reinforced concrete (RC) columns under monotonic biaxial bending moment and axial loading is proposed. In the proposed algorithm, the nonlinear behavior of confined and unconfined concrete elements as well as steel elements is considered, and the column is discretized into two macro-elements located between the pseudo-plastic hinges at critical sections and the inflection point. The critical sections of the column are discretized into a number of rotary oblique fiber elements (ROFEs) and the neutral axis (N.A.) position of each section in each step of loading is searched automatically using a proposed “4-rotations and 2-translations” search model. The ROFEs remain always parallel to the N.A. of the sections and make a uniform stress distribution along each ROFE in each section. Consequently, the variations of stress across each fiber are quite small which increase the accuracy of the calculation, while the number of elements (fibers) is relatively small compared to those of the fixed rectangular finite element (FRFE). This research shows that there is a better agreement between the simulated results using ROFE discretization and experimental results performed in the full-scale RC columns than when the FRFE discretization model is employed. The application of the component effect combination method is also compared with the proposed simultaneous direct method.
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Rofooei FR, Mirjalili MR, Attari NKA (2012) Modal Spectra combination method for pushover analysis of special steel moment resisting frames. Int J Civ Eng 10(4):245–252
Brondum-Nielsen T (1985) Ultimate flexural capacity of cracked polygonal concrete sections under biaxial bending. J ACI Tech Pap 82(7):863–869
Yen JYR (1991) Quasi-Newton method for reinforced concrete column analysis and design. J Struct Div ASCE 117(3):657–666
Yau CY, Chan SL, So AKW (1993) Biaxial bending of arbitrarily shaped reinforced concrete columns of arbitrary shape. Struct J ACI Tech Pap 90(3):269–273
Zak L (1993) Computer analysis of reinforced concrete sections under biaxial bending and longitudinal load. Struct J ACI 90(2):163–169
Bonet JL, Barros MHFM, Romero ML (2006) Comparative study of analytical and numerical algorithms for designing reinforced concrete sections under biaxial bending. Comput Struct 84(31–32):2184–2193
Barros MHFM, Barros A, Ferreira C (2004) Closed form solution of optimal design of rectangular reinforced concrete sections. Eng Comput 21(7):761–776
Bonet JL, Romero ML, Miguel PF, Fernandez MA (2004) A fast stress integration algorithm for reinforced concrete sections with axial loads and biaxial bending. Comput Struct 82(2–3):213–225
Amziane S, Dubé JF (2008) Global RC structural damage index based on the assessment of local material damage. J Adv Concr Technol 6(3):459–468
Dias Da Silva, V, Barros MHFM, Julio EN BS, Ferreira CC (2009) Closed form ultimate strength of multi-rectangle reinforced concrete sections under axial load and biaxial bending. Computer Concrete 6(6):505–521
Dundar C, Tokgoz S (2012) Strength of biaxially loaded high strength reinforced concrete columns. Struct Eng Mech 44(5):649–661
Barrera AC, Bonet JL, Romero ML, Fernandez MA (2012) Ductility of slender reinforced concrete columns under monotonic flexure and constant axial load. Eng Struct 40:398–412
Melo J, Varum H, Rossetto T (2015) Experimental cyclic behaviour of RC columns with plain bars and proposal for Eurocode 8 formula improvement. Eng Struct 88:22–36
Shirmohammadi F, Esmaeily A (2015) Performance of reinforced concrete columns under bi-axial lateral force/displacement and axial load. Eng Struct 99:63–77
Rodrigues H, Furtado A, Arêde A (2016) Behavior of rectangular reinforced-concrete columns under biaxial cyclic loading and variable axial loads. J Struct Eng ASCE. doi:10.1061/(ASCE)ST.1943-541X.0001345
Furtado A, Rodrigues H, Arêde A (2017) Load-path influence in the response of RC buildings subjected to biaxial horizontal loadings: numerical study. Int J Civ Eng. doi: 10.1007/s40999-017-0215-6
Sadeghi K (2017) Nonlinear numerical simulation of reinforced concrete columns under cyclic biaxial bending moment and axial loading. Int J Civ Eng 15(1):113–124
Lam N, Wilson J, Lumantarna E (2011) Force-deformation behaviour modeling of cracked reinforced concrete by EXCEL spreadsheets. Comput Concrete 8(1):43–57 43
Abbasnia R, Mirzadeh N, Kildashti K (2011) Assessment of axial force effect on improved damage index of confined RC beam-column members. Int J Civ Eng 9(3):237–246
Code CEB-FIP, Model Code (2010) First complete draft, vol 1. International Federation for Structural Concrete (fib), Lausanne
Sheikh SA, Khoury SS (1993) Confined concrete columns with stubs. ACI Struct J 90(4):414–431
Sadeghi K (2014) Analytical stress-strain model and damage index for confined and unconfined concretes to simulate RC structures under cyclic loading. Int J Civ Eng 12(4):333–343
Park R, Kent DC, Sampson RA (1972) Reinforced concrete members with cyclic loading. J Struct Div Proc Am Soc Civil Eng ASCE 98(ST7):1341–1359
Lamirault J (1984) Contribution á l’étude du comportement des ossatures en béton armé sous cisaillement normales: Simulation par analyse non linéaire globale. Ph.D. Dissertation, University of Nantes, Nantes
Priestley MJN, Park R (1991) Strength and durability of concrete bridge columns under seismic loading. Struct J ACI 84(4):61–76
Priestley MJN, Calvi GM, Kowalsky MJN (2007) Displacement-based seismic design of structures. IUSS, Pavia
Ou YC, Kurniawan RA, Kurniawan DP, Nguyen ND (2012) Plastic hinge length of circular reinforced concrete columns. Comput Concrete 10(6):663–681
Sadeghi K (2017) Global and local cumulative damage models for reinforced concrete structures subjected to monotonic, cyclic, or fatigue loading. Int J Civ Eng. doi:10.1007/s40999-017-0171-1
Sadeghi K, Lamirault J, Sieffert JG (1993) Damage indicator improvement applied on R/C structures subjected to cyclic loading, vol 1. Structural Dynamics, Eurodyn’93, Balkema, Rotterdam, pp 129–136
Sadeghi K (2011) Energy based structural damage index based on nonlinear numerical simulation of structures subjected to oriented lateral cyclic loading. Int J Civ Eng 9(3):155–164
Sieffert JG, Lamirault J, Garcia JJ (1990) Behavior of R/C columns under static compression and lateral cyclic displacement applied out of symmetrical planes. In: Proceedings of the 1st European conference on structural dynamics (Eurodyn 90), Bochum, Structural Dynamics, Kratzig et al., Balkema, Rotterdam, vol 1, pp 543–550
Sadeghi K (1995) Simulation numérique du comportement de poteaux en béton armé sous cisaillement dévié alterné. Ph.D. dissertation. Ecole Centrale de Nantes/University of Nantes, Nantes, France
AFPS90 (1990) Combinaison des effets des composantes du mouvement sismique, Recommandations AFPS90 pour la rédaction de règles relative aux ouvrages et installations à réaliser dans les régions sujettes aux séismes. AFPS, Paris, pp 101–105
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The financial and technical support of the University of Nantes/Ecole Centrale de Nantes and the Near East University are appreciated.
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Sadeghi, K., Nouban, F. A Highly Accurate Algorithm for Nonlinear Numerical Simulation of RC Columns Under Biaxial Bending Moment and Axial Loading Applying Rotary Oblique Fiber-Element Discretization. Int J Civ Eng 15, 1117–1129 (2017). https://doi.org/10.1007/s40999-017-0260-1
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DOI: https://doi.org/10.1007/s40999-017-0260-1