Ductility demand for uni-directional and reversing plastic hinges in ductile moment resisting frames
DOI:
https://doi.org/10.5459/bnzsee.32.1.1-12Abstract
In a major earthquake the beams in moment resisting frames may develop either reversing or unidirectional plastic hinges. The form of plastic hinge depends upon the ratio of the moments induced by the gravity loading to those induced by the seismic actions. Where this ratio is low the plastic hinges form at the ends of the beams and the sign of the inelastic rotation changes with the direction of sway. These are reversing plastic hinges, and the magnitude of the rotation that they sustained is closely related to the inter-storey displacement. However, when the moment ratio exceeds a certain critical value, unidirectional plastic hinges may form. In this case negative moment plastic hinges develop at the column faces and the positive moment plastic hinges form in the beam spans. As the earthquake progresses the positive and negative inelastic rotations accumulate in their respective zones so that peak values are always sustained at the end of the earthquake. With this type of plastic hinge no simple relationship exists between inter-storey drift and inelastic rotation.
Several series of time history analyses have been made to assess the relative magnitudes of inelastic rotation that are imposed on the two forms of plastic hinge. It is found that with design level earthquakes typically the unidirectional plastic hinge is required to sustain 21/ 2 to 4 times the rotation imposed on reversing plastic hinges, with the curvature ductilities ranging up to 140. These values are appreciably in excess of the values measured in tests using standard details. This indicates that in structures where unidirectional plastic hinges may form, the design displacement ductility and or the allowable inter-storey drift should be reduced below the maximum values currently permitted in the New Zealand codes. The problems associated with the formation of unidirectional plastic hinges can be avoided by adding positive moment flexural reinforcement in the mid regions of the beams. By this means the potential positive moment plastic hinges can be restricted to the beam ends.
References
Fenwick, R. C. and Davidson, B. J. (1987), "Moment redistribution in seismic resistant concrete frames", Proceeding Pacific conference on Earthquake Engineering, Wairakei, New Zealand, Vol.1. pp. 95-106
Davidson, B. J. and Fenwick, R. C. (1993), "Seismic response of ductile reinforced concrete frames with unidirectional plastic hinges", University of Auckland School of Engineering Report, No. 527, January, pp. 59
Megget, L.M. and Fenwick, R.C. (1989), "Seismic behaviour o f a reinforced concrete portal frame sustaining gravity loads", Bulletin of NZ National Society for Earthquake Engineering, Vol. 22, No. 1, March, pp. 39-49. DOI: https://doi.org/10.5459/bnzsee.22.1.39-49
Abrams, D. P. (1991), "Laboratory definitions of behaviour for structural components and building systems", SP 127, American Concrete Institute, pp. 91-152
Dely, R. (1998), "Ductility demands for reversing and unidirectional plastic hinges in ductile concrete frames", Master of Engineering Studies Report, Department of Civil and Resource Engineering, University of Auckland, March, pp. 57.
Davidson, B. J. and Fenwick, R. C. (1997), "Ductility demands for reversing and unidirectional plastic hinges in ductile concrete frame structures", Proceedings NZNSEE Technical Conference, Wairakei, March, pp. 190-197.
Standards New Zealand (1992), "Code of practice for general structural design and design loadings for buildings, NZS4203-1992", Wellington N.Z.
Fenwick, R.C. (1991), "The behaviour of plastic hinge zones in seismic resistant concrete structures". SECED Conference Proceedings - Earthquake, Blast and Impact, Published Elsevier Applied Science, London, September, pp. 221-230.
Anaganostopoulas, S. A. and Roesset, J. M. (1974), "Ductility requirements for some non-linear systems subjected to earthquakes", Proceedings 5th_ WCEE, Rome, Vol. 2, pp. 1748-1751.
Fenwick, R. C., Davidson, B. J. and Megget, L. M. (1987), "Inelastic response of concrete structures", Technical report TR7, NZ Concrete Society, pp.95-104
Standards New Zealand, (1995) "Concrete Structures Standard, design of concrete structures, NZS3101- 1995", Wellington, NZ.
Park, R. and Paula, T. (1975), "Design of Concrete Structures", Wiley Interscience, pp. 769
Kemp, A. R. (1998), "The achievement of ductility in reinforced concrete beams", Magazine of Concrete Research, Vol. 50, No. 2, June, pp. 123-132. DOI: https://doi.org/10.1680/macr.1998.50.2.123
Mander, J. B., Priestley, M. J. N. and Park, R. (1988), "Theoretical stress-strain model for confined concrete", ASCE Journal of Structural Engineering, Vol. 114, No.8, pp. 1804-1826. DOI: https://doi.org/10.1061/(ASCE)0733-9445(1988)114:8(1804)
