Keywords: seismic, design, yield, curvature, displacement, performance.

Given the inherent limitations of traditional force-based (FB) procedures [1,2,3], innovative and transparent displacement-based (DB) procedures [4] have been proposed in recent years. In the DB procedures, design force levels are based on the estimate of yield displacement of the structure. The ultimate displacement demand is first compared with yield displacement to estimate section ductility demand. Section ductility demand can be used to calculate effective damping level [4,5], which is then used to calculate the inelastic displacement demand and effective period from the elastic displacement response spectrum.

The intended mechanism for the majority of bridge piers and columns involves the formation of plastic hinges at critical locations (plastic hinge regions). The yield displacement of concrete columns can be estimated using simple expressions that account for the flexural deformation of the column [4]. Such expressions can be developed based on yield curvature of the column at the critical location (plastic hinge region)

Previous studies on effective yield curvature [4,6,7] have limitations of not properly incorporating all the influential parameters. This paper presents simple expressions to estimate effective yield curvature for normal- and high-strength circular reinforced concrete columns based on moment-curvature analyses [8] of 200 column sections. Such expressions can be programmed into an excel spreadsheet and can be used for the DB design of columns and also for the performance evaluation of existing columns. Effective yield curvature is presented in terms of the gross diameter of the section and the yield strain of longitudinal reinforcement together with three modification factors that take into account the effect of the strength of concrete, axial load ratio and the amount of longitudinal reinforcement.

A DB procedure for the design of a bridge column has been presented based on the substitute structure approach using the developed expressions for estimating effective yield curvature.

1

R. Park, T. Paulay, "Reinforced concrete structures", Wiley, USA, 1975.

2

T. Paulay, M.J.N. Priestley, "Seismic design of reinforced concrete and masonry buildings", Wiley Interscience, New York, USA, 1992.

3

R. Park, "A static force-based procedure for the seismic assessment of existing reinforced concrete moment resisting frames", Bulletin of New Zealand Society for Earthquake Engineering, 30(3), 213-226, 1997.

4

M.J.N. Priestley, M.C. Calvi, M.J. Kowalsky, "Displacement-based seismic design of structures", IUSS Press, Pavia, 2007.

5

E. Miranda, J.R. Garcia, "Evaluation of approximate methods to estimate maximum inelastic displacement demand", Earthquake Engineering and Structural Dynamics, 31, 539-560, 2002. doi:doi:10.1002/eqe.143

6

M.J.N. Priestley, J. Ranzo, G. Benzoni, M.J. Kowalsky, "Yield displacement of circular bridge columns", Proceedings of the Fourth Caltrans Research Workshop, California Department of Transportation, Sacramento, 1996.

7

E.H. Montes, M. Aschleim, "Estimates of yield curvature for the design of reinforced concrete columns", Magazine of Concrete Research, 55(4), 373-383, 2003. doi:10.1680/macr.55.4.373.37581

8

M.N.Sheikh, F. Legeron, C. Guiziou, "Optimal target performance for cost effective seismic design of bridges", Proceedings: Ninth Canadian Conference on Earthquake Engineering, Ottawa, Ontario, Canada, 26-29 June, 2007.

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