Probabilistic Approach for Estimating Plastic Hinge Length of Reinforced Concrete Columns
Publication: Journal of Structural Engineering
Volume 142, Issue 3
Abstract
Given the importance of the plastic hinge length in predicting the displacement ductility of reinforced concrete (RC) structures, it is crucial to be able to accurately determine it without a large scatter. However, given the large number of model parameters with significant uncertainty, a deterministic prediction of plastic hinge length is extremely difficult. Therefore, this paper seeks to provide a method to determine the plastic hinge length by a probabilistic approach. Existing plastic hinge length models are collected from the literature to form a comprehensive database. Then, a probabilistic plastic hinge length model is proposed by discussing the plastic hinge mechanism separately to include the missing design variables. The generalized likelihood uncertainty estimation (GLUE) method is used to assess the unknown model parameters with those experimental data. The cumulative distribution functions (CDF) of four model parameters are estimated for the proposed model. It was found that almost all of the observational results fell within the 90% confidence interval of predicted lengths, indicating the strength of the proposed model in predicting the plastic hinge length of RC columns from the prospective of probability. For facilitating use in engineering practice, a deterministic expression is also provided by using the mean value of four model parameters to predict this quantity of interest for the nonlinear analysis of RC structures.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bae, S., and Bayrak, O. (2008). “Plastic hinge length of reinforced concrete columns.” ACI Struct. J., 105(3), 290–300.
Barrera, A. C., Bonet, J. L., Romero, M. L., and Miguel, P. F. (2011). “Experimental tests of slender reinforced concrete columns under combined axial load and lateral force.” Eng. Struct., 33(12), 3676–3689.
Bayrak, O. (1998). “Seismic performance of rectilinearly confined high strength concrete columns.” Ph.D. thesis, Univ. of Toronto, Toronto.
Bayrak, O., and Sheikh, S. A. (2004). “Seismic performance of high strength concrete columns confined with high strength steel.” Proc., 13th World Conf. on Earthquake Engineering, Vancouver, BC, Canada.
Berry, M. P., Lehman, D. E., and Lowes, L. N. (2008). “Lumped-plasticity models for performance simulation of bridge columns.” ACI Struct. J., 105(3), 270–279.
Beven, K., and Binley, A. (1992). “The future of distributed models: Model calibration and uncertainty prediction.” Hydrol. Processes, 6(3), 279–298.
Elmenshawi, A., Brown, T., and El-Metwally, S. (2012). “Plastic hinge length considering shear reversal in reinforced concrete elements.” J. Earthquake Eng., 16(2), 188–210.
Fugard, A. J. B., and Potts, H. W. W. (2015). “Supporting thinking on sample sizes for thematic analyses: A quantitative tool.” Int. J. Soc. Res. Method., 18(6), 669–684.
Gardoni, P., Der Kiureghian, A., and Mosalam, K. M. (2002). “Probabilistic capacity models and fragility estimates for reinforced concrete columns based on experimental observations.” J. Eng. Mech., 1024–1038.
Ghobarah, A. (2001). “Performance-based design in earthquake engineering: State of development.” Eng. Struct., 23(8), 878–884.
Ho, J. C. M., and Pam, H. J. (2003). “Inelastic design of low-axially loaded high-strength reinforced concrete columns.” Eng. Struct., 25(8), 1083–1096.
Hua, L. K., and Wang, Y. (1981). Applications of number theory to numerical analysis, Springer, Berlin.
Kowalsky, M. J., Priestley, M. J. N., and Seible, F. (1999). “Shear and flexural behavior of lightweight concrete bridge columns in seismic regions.” ACI Struct. J., 96(1), 136–148.
Legeron, F., and Paultre, P. (2000). “Behavior of high-strength concrete columns under cyclic flexure and constant axial load.” ACI Struct. J., 97(4), 591–601.
Li, B., and Park, R. (2004). “Confining reinforcement for high-strength concrete columns.” ACI Struct. J., 101(3), 314–324.
Li, B., Wu, Y., and Pan, T. C. (2002). “Seismic behavior of nonseismically detailed interior beam-wide column joints—Part I: Experimental results and observed behavior.” ACI Struct. J., 99(6), 791–802.
Li, B., Wu, Y., and Pan, T. C. (2003). “Seismic behavior of nonseismically detailed interior beam-wide column joints—Part II: Theoretical comparisons and analytical studies.” ACI Struct. J., 100(1), 56–65.
Lu, Y., Gu, X., and Guan, J. (2005). “Probabilistic drift limits and performance evaluation of reinforced concrete columns.” J. Earthquake Eng., 131(6), 966–978.
Mendis, P. (2001). “Plastic hinge lengths of normal and high-strength concrete in flexure.” Adv. Struct. Eng., 4(4), 189–195.
Mundfrom, D. J., Shaw, D. G., and Ke, T. L. (2005). “Minimum sample size recommendations for conducting factor analyses.” Int. J. Test., 5(2), 159–168.
Nash, J. E., and Sutcliffe, J. V. (1970). “River flow forecasting through conceptual models. Part I—A discussion of principles.” J. Hydrol., 10(3), 282–290.
Ohno, T., and Nishioka, T. (1984). “An experimental study on energy absorption capacity of columns in reinforced concrete structures.” Proc. JSCE, Struct. Eng./Earthquake Eng., 1(1), 137–147.
Onwuegbuzie, A. J., and Leech, N. L. (2007). “A call for qualitative power analyses.” Qual. Quantity, 41(1), 105–121.
Pam, H. J., and Ho, J. C. M. (2009). “Length of critical region for confinement steel in limited ductility high-strength reinforced concrete columns.” Eng. Struct., 31(12), 2896–2908.
Pan, Z., and Li, B. (2013). “Truss-arch model for shear strength of shear-critical reinforced concrete columns.” J. Struct. Eng., 548–560.
Panagiotakos, T. B., and Fardis, M. N. (2001). “Deformations of reinforced concrete members at yielding and ultimate.” ACI Struct. J., 98(2), 135–148.
Park, R., and Paulay, T. (1975). Reinforced concrete structures, Wiley, New York.
Park, R., Priestley, M. J. N., and Gill, W. D. (1982). “Ductility of square-confined concrete columns.” J. Struct. Div., 108(4), 929–950.
Paulay, T., and Priestley, M. J. N. (1992). Seismic design of reinforced concrete and masonry buildings, Wiley, New York.
Paultre, P., Legeron, F., and Mongeau, D. (2001). “Influence of concrete strength and transverse reinforcement yield strength on behavior of high-strength concrete columns.” ACI Struct. J., 98(4), 490–501.
Pham, T. P., and Li, B. (2013). “Seismic behaviour of RC columns with light transverse reinforcement under different loading directions.” ACI Struct. J., 110(5), 833–844.
Pham, T. P., and Li, B. (2014). “Evaluating the seismic performance of reinforced concrete columns with plain and deformed longitudinal reinforcing bars.” ACI Struct J., 111(3), 561–574.
Priestley, M. J. N., and Park, R. (1987). “Strength and ductility of concrete bridge columns under seismic loading.” ACI Struct. J., 84(1), 61–76.
Sheikh, S. A., and Khoury, S. S. (1993). “Confined concrete columns with stubs.” ACI Struct. J., 90(4), 414–431.
Sheikh, S. A., Shah, D. V., and Khoury, S. S. (1994). “Confinement of high-strength concrete columns.” ACI Struct. J., 91(1), 100–111.
Tanaka, H. (1990). “Effect of lateral confining reinforcement on the ductile behaviour of reinforced concrete columns.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Canterbury, Christchurch, New Zealand.
Thanh Ngoc Tran, C., and Li, B. (2013). “Ultimate displacement of reinforced concrete columns with light transverse reinforcement.” J. Earthquake Eng., 17(2), 282–300.
Tran, C. T. N., and Li, B. (2012). “Initial stiffness of reinforced concrete columns with moderate aspect ratios.” Adv. Struct. Eng., 15 (2), 265–276.
Yang, K., Shi, Q. X., and Zhao, J. H. (2013). “Plastic hinge length of high strength concrete columns confined by high strength stirrups.” Eng. Mech., 30(2), 254–259 (in Chinese).
Zhao, J., and Sritharan, S. (2007). “Modeling of strain penetration effects in fiber-based analysis of reinforced concrete structures concrete structures.” ACI Struct. J., 104(2), 133–141.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 142 • Issue 3 • March 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Sep 20, 2014
Accepted: Sep 11, 2015
Published online: Nov 9, 2015
Published in print: Mar 1, 2016
Discussion open until: Apr 9, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.