×

zbMATH — the first resource for mathematics

Nonlinear analysis of spatial framed structures by a lumped plasticity model based on the Haar-Kàrmàn principle. (English) Zbl 1398.74369
Summary: A lumped plasticity model is proposed for the nonlinear static and dynamic analyses of three-dimensional reinforced concrete (r.c.) frames. A bilinear moment-curvature law and an interaction surface axial force-biaxial bending moment are considered. The nonlinear dynamic analysis is performed using a two-parameter implicit integration scheme and an initial-stress like iterative strategy, adopting the Haar-Kàrmàn principle. As a preliminary, two cantilever steel beams, one with box-section and one with tubular section, are used for validating the proposed model under monotonic and cyclic loadings. Moreover single-storey r.c. three-dimensional frames, with square and rectangular cross-sections, subjected to bi-directional ground motions, are assumed as test structures for studying the sensitivity of the model to changes in strength and stiffness input parameters. Comparisons with more refined fibre models prove the reliability of the proposed model.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74E30 Composite and mixture properties
74S15 Boundary element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
Software:
SeismoStruct
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bousias SN, Verzeletti G, Fardis MN, Gutierrez E (1995) Load-path effects in column biaxial bending with axial force. J Eng Mech 121(5): 596–605 · doi:10.1061/(ASCE)0733-9399(1995)121:5(596)
[2] Magliulo G, Ramasco R (2007) Seismic response of three- dimensional r/c multi-storey frame building under uni- and bi-directional input ground motion. Earthquake Eng Struct Dyn 36: 1641–1657 · doi:10.1002/eqe.709
[3] ASCE (1982) The State-of-the-art report on finite element analysis of reinforced concrete. ASCE Task Committee, New York
[4] FIB (2008) Practitioners’ guide to finite element modeling of reinforced concrete structures. State-of-art report. Fib Bulletin No. 45
[5] Kwon M, Spacone E (2002) Three-dimensional finite element analyses of reinforced concrete columns. Comput Struct 80: 199–212 · doi:10.1016/S0045-7949(01)00155-9
[6] Ameen M, Raghu Prasad BK, Gopalakrishnan AR (2009) Boundary element analysis of reinforced concrete structural elements. Eng Anal Boundary Elem 33(6): 263–270 · Zbl 1244.74136 · doi:10.1016/j.enganabound.2008.08.014
[7] Spacone E, Ciampi V, Filippou FC (1996) Mixed formulation of nonlinear beam finite element. Comput Struct 58(I): 71–83 · Zbl 0918.73154 · doi:10.1016/0045-7949(95)00103-N
[8] Izzudin BA, Siyam AAFM, Lloyd Smith D (2002) An efficient beam-column formulation for 3D reinforced concrete frames. Comput Struct 80: 659–676 · doi:10.1016/S0045-7949(02)00033-0
[9] Marmo F (2007) A fiber-free approach to the inelastic analysis of reinforced concrete structures. Ph.D. Thesis, University of Naples-Federico II, Italy
[10] Marmo F, Rosati L, Sessa S (2008) Exact integration of uniaxial elasto-plastic laws for nonlinear structural analysis. In: Proceedings of the 2008 seismic engineering conference commemorating the 1908 Messina and Reggio Calabria earthquake, Reggio Calabria, II, pp 1219–1226
[11] Mazza F (1998) Damage models for the nonlinear seismic analysis of r.c. framed structures (in italian). Ph.D. Thesis, University of Calabria, Italy
[12] Powell GH, Chen PF-S (1986) 3D beam-column element with generalized plastic hinges. J Eng Mech 112(7): 627–641 · doi:10.1061/(ASCE)0733-9399(1986)112:7(627)
[13] Lai S-S, Will GT, Otani S (1984) Model for inelastic biaxial bending of concrete members. J Struct Eng 110(11): 2563–2584 · doi:10.1061/(ASCE)0733-9445(1984)110:11(2563)
[14] Filippou F, Issa A (1988) Nonlinear analysis of reinforced concrete frames under cyclic load reversals. Report No. UCB/EERC-88/12, Earthquake Engineering Research Center, University of California, Berkeley, California
[15] Ricles JM, Yang Y-S, Priestley JN (1998) Modeling nonductile of r/c columns for seismic analysis of bridge. J Struct Eng 124(4): 415–425 · doi:10.1061/(ASCE)0733-9445(1998)124:4(415)
[16] Marante ME, Flórez-López J (2003) Three-dimensional analysis of reinforced concrete frames based on lumped damage mechanics. Int J Solids Struct 40: 5109–5123 · Zbl 1060.74615 · doi:10.1016/S0020-7683(03)00258-0
[17] Sfakianakis MG, Fardis MN (1991) Nonlinear finite element for modeling reinforced concrete columns in three-dimensional dynamic analysis. Comput Struct 40: 1405–1419 · doi:10.1016/0045-7949(91)90411-E
[18] Mazza F, Mazza M (2008) A numerical model for the nonlinear seismic analysis of three-dimensional r.c. frames. In: Proceedings of the 14th world conference on earthquake engineering, Beijing, China · Zbl 1165.20016
[19] Dides MA, de la Llera JC (2005) A comparative study of concentrated plasticity models in dynamic analysis of building structures. Earthquake Eng Struct Dyn 34: 1005–1026 · doi:10.1002/eqe.468
[20] Aristodemo M, Casciaro R, Vulcano A (1982) Earthquake response of plane frames exhibiting degrading hysteretic capacity. In: Proceedings of the 7th European conference on earthquake engineering, Athens, Greece, pp 35–42
[21] Haar A, von Kàrmàn T (1909) Zur Theorie der Spannungzustande in Plastischen und Sandartingen Medien, Gottinger Nachrichten
[22] Ponter ARS, Martin GB (1972) Some extremal properties and energy theorems for inelastic materials and their relationship to the deformation theory of plasticity. Int J Mech Phys Solids 20/5: 281–300 · Zbl 0241.73003 · doi:10.1016/0022-5096(72)90024-5
[23] SeismoStruct–A computer program for static and dynamic nonlinear analysis of framed structures. SeismoSoft 2008. Available from URL: http://www.seismosoft.com
[24] Eurocode 8 (2003) Design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings. C.E.N., European Committee for Standardisation
[25] Eurocode 2 (2004) Design of concrete structures. Part 1-1: general rules and rules for buildings. C.E.N., European Committee for Standardization
[26] Argyris GH, Balmer H, Doltsinis JS, Dunne PC, Haase M, Kleiber M, Malejannakis GA, Mlejnek H-P, Muller M, Scharpf DW (1979) Finite element method–the natural approach. Comput Methods Appl Mech Eng 17/18: 1–106 · Zbl 0407.73058 · doi:10.1016/0045-7825(79)90083-5
[27] Ortiz M, Popov EP (1985) Accuracy and stability of integration algorithms for elastoplastic constitutive relations. Int J Numer Methods Eng 21: 1561–1576 · Zbl 0585.73057 · doi:10.1002/nme.1620210902
[28] Casciaro R (1975) Time evolutional analysis of nonlinear structures. Meccanica 3(X): 156–167 · Zbl 0374.73069 · doi:10.1007/BF02149027
[29] Eurocode 3 (2003) Design of steel structures. Part 1-1: general rules. C.E.N., European Committee for Standardization
[30] Mander JB, Priestley MJN, Park R (1988) Theoretical stress–strain model for confined concrete. J Struct Eng 114(8): 1804–1825 · doi:10.1061/(ASCE)0733-9445(1988)114:8(1804)
[31] Montejo LA, Kowalsky MJ (2007) Set of codes for the analysis of reinforced concrete members. North Carolina State University. Technical report no. IS-07-01
[32] King DJ, Priestley MJN, Park R (1986) Computer Programs for Concrete Column Design. Research Report 86/12, Department of Civil Engineering, University of Canterbury, New Zealand
[33] Gasparini D, Vanmarcke E (1976) Simulated earthquake motions compatible with prescribed response spectra. Massachusetts Institute of Technology, Department of Civil Engineering
[34] Ahmed M, Dad Khan MK, Wamiq M (2008) Effect of concrete cracking on the lateral response of rcc buildings. Asian J Civ Eng (Building and Housing) 9(1): 25–34
[35] Menegotto M, Pinto PE (1973) Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometry and nonelastic behavior of elements under combined normal force and bending. In: IABSE Symposium on Resistance and Ultimate Deformability of Structures Acted on by Well Defined Repeated Loads, Lisbon, pp 15–22
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.