Practical Performance Model for Bar Buckling
Publication: Journal of Structural Engineering
Volume 131, Issue 7
Abstract
A practical model has been developed to predict, for a given level of lateral deformation, the likelihood that longitudinal bars in a reinforced concrete column will have begun to buckle. Three relationships linking plastic rotation, drift ratio, and displacement ductility with the onset of bar buckling were derived based on the results of plastic-hinge analysis, moment-curvature analysis, and the expected influence of the confinement reinforcement. These relationships, which account for the effective confinement ratio, axial-load ratio, aspect ratio, and longitudinal bar diameter, were calibrated using observations of bar buckling from cyclic tests of 62 rectangular-reinforced and 42 spiral-reinforced concrete columns. A version of the drift ratio relationship is proposed for earthquake engineering applications. The ratios of the measured displacements at bar buckling to the displacements calculated with the proposed model had a mean of 1.01 and a coefficient of variation of 25% for rectangular-reinforced concrete columns. The corresponding mean and coefficient of variation for spiral-reinforced columns were 0.97 and 24%, respectively.
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Acknowledgments
The writers thank Amit Mookerjee and Myles Parrish, who assembled much of the column data as part of their MSCE research. Support of this work was provided primarily by the Earthquake Engineering Research Centers Program of the National Science Foundation, under Award Number NSFEEC-9701568 through the Pacific Earthquake Engineering Research Center (PEER).
References
American Concrete Institute (ACI). (2002). “Building code requirements for structural concrete.” ACI 318-02, Detroit.
Atalay, M. B., and Penzien, J. (1975). “The seismic behavior of critical regions of reinforced concrete components as influenced by moment, shear and axial force.” Rep. No. EERC 75-19, Univ. of California, Berkeley, Calif.
Bayrak, O. (1998). “Seismic performance of rectilinearly confined high strength concrete columns.” Doctoral Dissertation, Dept. of Civil Engineering, Univ. of Toronto, Canada.
Bayrak, O., and Sheikh, S. (1996). “Confinement steel requirements for high strength concrete columns.” Proc., 11th World Conf. on Earthquake Engineering, Aculpulco, Mexico, Paper No. 463.
Bayrak, O., and Sheikh, S. (2001). “Plastic hinge analysis.” J. Struct. Eng., 127(9), 1092–1100.
Berry, M. P. (2003). “Estimating flexural damage in reinforced concrete columns.” Master’s thesis, Dept. of Civil and Environmental Engineering, Univ. of Washington, Seattle.
Berry, M. P., and Eberhard, M. O. (2003). “Performance models for flexural damage in reinforced concrete columns.” Pacific Earthquake Engineering Research Center Report 2003, Univ. of California, Berkeley, Calif.
Berry, M. P., and Eberhard, M. O. (2004) “PEER structural performance database user’s manual.” Pacific Earthquake Engineering Research Center Report 2004 ⟨www.ce.washington.edu/~peeral⟩, Univ. of California, Berkeley, Calif.
Bresler, B., and Gilbert, P. H. (1961). “Tie requirements for reinforced concrete columns.” ACI J., 58(5), 555–570.
Calderone, A. J., Lehman, D. E., and Moehle, J. P. (2000). “Behavior of reinforced concrete bridge columns having varying aspect ratios and varying lengths of confinement.” Pacific Earthquake Engineering Research Center Rep. 2000/08, Univ. of California, Berkeley, Calif.
Cheok, G. S., and Stone, W. C. (1986). “Behavior of -scale model bridge columns subjected to cycle inelastic loading.” NBSIR 86-3494, U.S. National Institute of Standards and Technology, Gaithersburg, Md.
Corley, W. G. (1966). “Rotational capacity of reinforced concrete beams.” J. Struct. Div. ASCE, 92(5), 121–146.
Davey, B. E. (1975). “Reinforced concrete bridge piers under seismic loading.” Master of Engineering Report, Civil Engineering Dept., Univ. of Canterbury, Christchurch, New Zealand.
Dhakal, R., and Maekawa, K. (2002). “Reinforcement stability and fracture of cover concrete in reinforced concrete members.” J. Struct. Eng.,, 128(10), 1253–1262.
Eberhard, M. O. (2000). “Consequences of bridge damage on functionality.” Proc., PEER Invitational Workshop on Performance-Based Engineering Concepts for Bridges, Palo Alto, Calif.
Ghee, A. B., Priestley, M. J. N., and Park, R. (1981). “Ductility of reinforced concrete bridge piers under seismic loading.” Rep. 81-3, Dept. of Civil Engineering, Univ. of Canterbury, Christchurch, New Zealand.
Gomes, A., and Appleton, J. (1997). “Nonlinear cyclic stress-strain relationship of reinforcing bars including buckling.” Eng. Struct.,, 19(10), 822–826.
Henry, L., and Mahin, S. A. (1999). “Study of buckling of longitudinal bars in reinforced concrete bridge columns.” Report to the California Dept. of Transportation.
Hose, Y. D. (2001). “Seismic performance and failure behavior of plastic hinge regions in flexural bridge columns.” PhD dissertation, Dept. of Structural Engineering, Univ. of California, San Diego.
Hose, Y. D., Seible, F., and Priestley, M. J. N. (1997). “Strategic relocation of plastic hinges in bridge columns.” Structural Systems Research Project, 97/05, University of California, San Diego.
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.
Kunnath, S., El-Bahy, A., Taylor, A., and Stone, W. (1997). “Cumulative seismic damage of reinforced concrete bridge piers.” Technical Rep. NCEER-97-0006, National Center for Earthquake Engineering Research, Buffalo, N.Y.
Lehman, D. E., Gookin, S. E., Nacamuli, A. M., and Moehle, J. P. (2001). “Repair of earthquake-damaged bridge columns.” ACI Struct. J., 98(2), 233–242.
Lehman, D. E., and Moehle, J. P. (2000). “Seismic performance of well-confined concrete bridge columns.” Pacific Earthquake Engineering Research Center Rep. 1998/01, Univ. of California, Berkeley, Calif.
Mattock, A. H. (1967). “Discussion of ‘Rotational capacity of reinforced concrete beams,’ by W. G. Corley.” J. Struct. Div. ASCE, 93(2), 519–522.
Monti, G., and Nuti, C. (1992). “Nonlinear cyclic behavior of reinforcing bars including buckling.” J. Struct. Eng., 118(12), 3268–3284.
Moyer, M., and Kowalsky, M. (2001). “Influence of tension strain on buckling of reinforcement in RC bridge columns.” Dept. of Civil Engineering, North Carolina State Univ., Raleigh, N.C.
Nelson, J. M. (2000). “Damage model calibration for reinforced concrete columns.” Master’s thesis, Dept. of Civil and Environmental Engineering, Univ. of Washington, Seattle.
Pantazopoulou, S. J. (1998). “Detailing for reinforcement stability in reinforced concrete members.” J. Struct. Eng.,, 124(6), 623–632.
Papia, M., and Russo, G. (1989). “Compressive concrete strain at buckling of longitudinal reinforcement.” J. Struct. Eng., 115(2), 382–397.
Park, R., and Paulay, T. (1990). “Use of interlocking spirals for transverse reinforcement in bridge columns.” Strength and ductility of concrete substructures of bridges, RRU (Road Research Unit) Bulletin 84, 1, 77–92.
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.
Priestley, M. J. N., Seible, F., and Calvi, G. M. (1996). Seismic design and retrofit of bridges, Wiley, New York.
Ranf, R. T., Nelson, J., Price, Z., Eberhard, M. O., and Stanton, J. F. (2003). “Accumulation of flexural damage in lightly reinforced concrete columns.” Pacific Earthquake Engineering Research Center Report PEER-2003, Univ. of California, Berkeley, Calif.
Rodriguez, M., Botero, J., and Villa, J. (1999). “Cyclic stress-strain behavior of reinforcing steel including effect of buckling.” J. Struct. Eng.,, 125(6), 605–612.
Saatcioglu, M., and Baingo, D. (1999). “Circular high-strength concrete columns under simulated seismic loading.” J. Struct. Eng.,, 125(3), 272–280.
Saatcioglu, M., and Grira, M. (1999). “Confinement of reinforced concrete columns with welded reinforcement grids.” ACI Struct. J., 96(1), 29–39.
Saatcioglu, M., and Razvi, S. R. (1994). “Behavior of high strength columns subjected to axial load.” Proc., 5th National Conf. on Earthquake Engineering Research Inst., 2, Oakland, Calif.
Sawyer, H. A. (1964). “Design of concrete frames for two failure states.” Proc., Int. Symposium on the Flexural Mechanics of Reinforced Concrete, ASCE-ACI, Miami, 405–431.
Scribner, C. F. (1986). “Reinforcement buckling in reinforced concrete flexural members.” ACI J., 83(6), 966–973.
Soesianawati, M. T., Park, R., and Priestley, M. J. N. (1986). “Limited ductility design of reinforced concrete columns.” Rep. 86-10, Dept. of Civil Engineering, Univ. of Canterbury, Christchurch, New Zealand.
Stone, W. C., and Cheok, G. S. (1989). “Inelastic behavior of full-scale bridge columns subjected to cyclic loading.” NIST Building Science Series 166, U.S. National Institute of Standards and Technology, Gaithersburg, Md.
Tanaka, H., and Park, R. (1990). “Effect of lateral confining reinforcement on the ductile behavior of reinforced concrete columns.” Rep. 90-2, Dept. of Civil Engineering, Univ. of Canterbury, Christchurch, New Zealand.
Thomsen, J., and Wallace, J. (1994). “Lateral load behavior of reinforced concrete columns constructed using high-strength materials.” ACI Struct. J., 91(5), 605–615.
Vu, N. D., Priestley, M. J. N., Seible, F., and Benzoni, G. (1998). “Seismic response of well confined circular reinforced concrete columns with low aspect ratios.” Proc., 5th Caltrans Seismic Research Workshop, Sacramento, Calif.
Watson, S. (1989). “Design of reinforced concrete frames of limited ductility.” Rep. 89-4, Dept. of Civil Engineering, Univ. of Canterbury, Christchurch, New Zealand.
Wehbe, N., and Saiidi, M. S., and Sanders, D. (1998). “Confinement of rectangular bridge columns for moderate seismic areas.” National Center for Earthquake Engineering Research (NCEER) Bulletin, 12(1).
Wong, Y. L., Paulay, T., and Priestley, M. J. N. (1990). “Squat circular bridge piers under multi-directional seismic attack.” Rep. 90-4, Dept. of Civil Engineering, Univ. of Canterbury, Christchurch, New Zealand.
Xiao, Y., and Martirossyan, A. (1998). “Seismic performance of high-strength concrete columns.” J. Struct. Eng., 124(3), 241–251.
Xiao, Y., and Yun, H. W. (2002). “Experimental studies on full-scale high-strength concrete columns.” ACI Struct. J., 99(2), 199–207.
Zahn, F. A., Park, R., and Priestley, M. J. N. (1986). “Design of reinforced bridge columns for strength and ductility.”Rep. 86-7, Dept. of Civil Engineering, Univ. of Canterbury, Christchurch, New Zealand.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 131 • Issue 7 • July 2005
Pages: 1060 - 1070
Copyright
© 2005 ASCE.
History
Received: Oct 16, 2003
Accepted: Sep 7, 2004
Published online: Jul 1, 2005
Published in print: Jul 2005
Notes
Note. Associate Editor: Rob Y. H. Chai
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