Simplified moment-curvature relationship in analytical form for circular RC sections
DOI:
https://doi.org/10.5459/bnzsee.51.3.145-158Abstract
The behaviour of regular multi-span simply-supported bridges is strongly dependent on the behaviour of its piers. The response of a pier is governed, in general, by different mechanisms: flexure, shear, second order effects, lap-splice of longitudinal bars or their buckling. The flexural behaviour is an important part of the problem, and it can be characterised through the equivalent plastic hinge length and the Moment-Curvature law of the fixed end. In this paper, a procedure to calculate the Moment-Curvature relationship of circular RC sections is proposed which is based on defining the position of few characteristic points. The analytical formulation is based on adjusted polynomial functions fitted on a database of fibre-based analyses. The proposed solution is based on three parameters: dimensionless axial force, mechanical ratio of longitudinal reinforcement, geometrical ratio of transverse reinforcement. A benchmark case is presented to compare the solution to a FEM non-linear analysis. Even if it is based on few input data, this solution allows to have good indicators on the material performances (e.g. yielding, spalling, etc). For these reasons, the proposed approach is deemed to be particularly effective in performing quick yet accurate mechanics-based regional-scale assessment of bridges.
References
Palermo A, Liu R, Rais A, McHaffie B, Andisheh K, Pampanin S, Gentile R, Nuzzo I, Graniero M, Loporcaro G, McGann C and Wotherspoon L (2017). “Performance of road bridges during the 14th November 2016 Kaikoura earthquake”. Bulletin of the New Zealand Society for Earthquake Engineering, 50(2): 253-270. DOI: https://doi.org/10.5459/bnzsee.50.2.253-270
Pinho R, Monteiro R, Casarotti C and Delgado R (2009). “Assessment of Continuous Span Bridges through Nonlinear Static Procedures”. Earthquake Spectra, 25(1): 143–159. DOI: https://doi.org/10.1193/1.3050449
Kircher CA, Whitman RV and Holmes WT (2006). “HAZUS Earthquake Loss Estimation Methods”. Natural Hazard Review, 7:45-59. DOI: https://doi.org/10.1061/(ASCE)1527-6988(2006)7:2(45)
Broglio S, Crowley H and Pinho R (2010). “Simplified Capacity Curves for RC Bridges”. Proceedings of 14th European Conference on Earthquake Engineering, Ohrid, Republic of Macedonia, 30/08/2010-03/09/2010.
Fardis MN (2007). “Risk Mitigation for Earthquakes and Landslides. Guidelines for Displacement-Based Design of Buildings and Bridges”. Report No. 5/2007, IUSS Press, Pavia, Italy.
Raffaele D, Porco F, Fiore A and Uva G (2014). “Simplified vulnerability assessment of reinforced concrete circular piers in multi-span simply supported bridges”. Structure and Infrastructure Engineering, 10(8): 950–962. DOI: https://doi.org/10.1080/15732479.2013.772642
Raffaele D, Porco F, Uva G and Fiore A (2014). “Simplified assessment of seismic retrofitting interventions on RC circular piers in multi-span simply sup- ported bridges”. Proceedings of the 7th International Conference on Bridge Maintenance, Safety and Management, Shanghai, China, 07-11/07/14. 2245–2252.
Raffaele D, Uva G, Porco F and Fiore A (2014). “About of seismic capacity of bridge piers: A simplified approach”. Proceedings of the 7th International Conference on Bridge Maintenance, Safety and Management, Shanghai, China, 07-11/07/14. 2245–2252. DOI: https://doi.org/10.1201/b17063-343
Esmaeily A and Peterman RJ (2007). “Performance analysis tool for reinforced concrete members”. Computers and Concrete, 4(5): 331–346. DOI: https://doi.org/10.12989/cac.2007.4.5.331
Montejo LA and Kowalsky MJ (2007). “Set of Codes for the Analysis of Reinforced Concrete Members”. Technical Report No. IS-07-01, North Carolina State University, USA.
Padgett JE, Nielson BG and Desroches R (2008). “Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios”. Earthquake Engineering and Structural Dynamics, 37: 711–725. DOI: https://doi.org/10.1002/eqe.782
Zelaschi C, Monteiro R and Pinho R (2015). “Improved fragility functions for RC bridge populations”. Proceedings of the 5th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete Island, Greece, 25-27 May 2015. DOI: https://doi.org/10.7712/120115.3685.627
Miano A, Fatemeh J, De Risi R, Prota A and Manfredi G (2015). “A Case-Study on scenario based probabilistic seismic loss assessment for a portfolio of bridges”. Proceedings of the 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12, Vancouver, Canada, 12-15/07/2015.
Kowalsky MJ and Priestley MJN (2000). “Improved Analytical Model for Shear Strength of Circular Reinforced Concrete Columns in Seismic Regions”. ACI Structural Journal, 97-S42: 388-396. DOI: https://doi.org/10.14359/4633
Berry MP and Eberhard MO (2005). “Practical Performance Model for Bar Buckling”. Journal of Structural Engineering, 131(7): 1060–1070. DOI: https://doi.org/10.1061/(ASCE)0733-9445(2005)131:7(1060)
Priestley MJN, Seible F and Calvi G (1996). “Seismic Design and Retrofit of Bridges”. John Wiley and Sons, New York, USA, 686 pp. DOI: https://doi.org/10.1002/9780470172858
Priestley MJN, Calvi GM and Kowalsky MJ (2007). “Displacement Based Seismic Design of Structures”. IUSS Press, Pavia, Italy, 721 pp.
Peruš I, Poljanˇsek K and Fajfar P (2006). “Flexural deformation capacity of rectangular RC columns determined by the CAE method”. Earthquake Engineering and Structural Dynamics, 35(12): 1453–1470. DOI: https://doi.org/10.1002/eqe.584
Peruš I and Fajfar P (2007). “Prediction of the force–drift envelope for RC columns in flexure by the CAE method”. Earthquake Engineering and Structural Dynamics, 36(15): 2345–2363. DOI: https://doi.org/10.1002/eqe.735
Mander JB, Priestley MJN and Park R (1988). “Theoretical Stress Strain Model for Confined Concrete”. Journal of Structural Engineering, 114(8): 1804–1826. DOI: https://doi.org/10.1061/(ASCE)0733-9445(1988)114:8(1804)
NTC2008, Ministero delle Infrastrutture e dei Trasporti (2008). “DM 14 gennaio 2008 in materia di “norme tecniche per le costruzioni”. Gazzetta ufficiale n.29 del 4 febbraio 2008, Supplemento ordinario n.30”. Istituto Poligrafico e Zecca dello stato (in Italian).
NZSEE/MBIE (2017). “The Seismic Assessment of Existing Buildings Technical Guidelines for Engineering Assessments”. Final draft, 1 July 2017, New Zealand.
Loporcaro G (2017). “A Least Invasive Method to Estimate the Residual Strain Capacity in Earthquake-damaged Buildings”. PhD Dissertation, University of Canterbury, Christchurch, New Zealand, 250 pp.
Sadowski AJ, Rotter JM, Stafford PJ, Reinke T and Ummenhofer T (2017). “On the gradient of the yield plateau in structural carbon steels”. Journal of Constructional Steel Research, 130: 120-130. DOI: https://doi.org/10.1016/j.jcsr.2016.11.024
King DJ, Priestley MJN and Park R (1986). “Computer Programs for Concrete Column Design”. Research Report 86/12, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand.
Priestley MJN and Park R (1987). “Strength and ductility of concrete bridge columns under seismic loading”. ACI Structural Journal, 84(1): 61–76. DOI: https://doi.org/10.14359/2800
Computer and Structures (2016). “SAP2000 v18. Structural Analysis Program, Manual”. Berkeley, California, USA.
