Use of Regression Analysis in Determining the Length of Plastic Hinge in Reinforced Concrete Columns

Basic objective of this study is to create a regression
analysis method that can estimate the length of a plastic hinge which
is an important design parameter, by making use of the outcomes of
(lateral load-lateral displacement hysteretic curves) the experimental
studies conducted for the reinforced square concrete columns. For
this aim, 170 different square reinforced concrete column tests results
have been collected from the existing literature. The parameters
which are thought affecting the plastic hinge length such as crosssection
properties, features of material used, axial loading level,
confinement of the column, longitudinal reinforcement bars in the
columns etc. have been obtained from these 170 different square
reinforced concrete column tests. In the study, when determining the
length of plastic hinge, using the experimental test results, a
regression analysis have been separately tested and compared with
each other. In addition, the outcome of mentioned methods on
determination of plastic hinge length of the reinforced concrete
columns has been compared to other methods available in the
literature.

• Mehmet Alpaslan Köroğlu
• Musa Hakan Arslan
• Muslu Kazım Körez

• Columns
• plastic hinge length
• regression analysis
• reinforced concrete.

[1] Sawyer H.A. (1964), "Design of Concrete Frames for Two Failure
States”, Proc. of the International Symposium on the Flexural Mechanics
of Reinforced Concrete. ASCE-ACI, Miami, pp.405-431.
[2] Corley, W.G. ‘‘Rotational capacity of reinforced concrete beams’’,
Journal of Structural Division ASCE, 92(ST5), pp. 121–146 (1966).
[3] Mattock, A.H. ‘‘Rotational capacity of hinging regions in reinforced
concrete beams’’, Journal of Structural Division ASCE, 93(ST2), pp.
519–522 (1967).
[4] Park, R.,Priestley, M.J. andGill, W.D., Ductility of Square Confined
Concrete Columns, Journal of the Structural Division, ASCE, Vol.108,
No. ST4, pp. 929- 950, 1982.
[5] Priestley, M.J.N. and Park, R. ‘‘Strength and ductility of concrete bridge
columns under seismic loading’’, ACI Structural Journal, 84(1), pp. 61–
76 (1987).
[6] Paulay, T. and Priestley, M.J.N., Seismic Design of Reinforced Concrete
and Masonry Buildings, John Wiley and Sons, New York (1992).
[7] Sheikh, S.A. and Khoury, S.S. ‘‘Confined concrete columns with
stubs’’, ACI Structural Journal, 90(4), pp. 414–431 (1993).
[8] Sheikh, S.A., Shah, D.V. and Khoury, S.S. ‘‘Confinement of highstrength
concrete columns’’, ACI Structural Journal, 91(1), pp. 100–111
(1994).
[9] Bayrak, O. and Sheikh, S.A. ‘‘Confinement reinforcement design
considerations for ductile HSC columns’’, Journal of Structural Division
ASCE, 124(9), pp. 999–1010 (1998).
[10] Panagiotakos TB, Fardis MN. 2001. Deformations of reinforced
concrete members at yielding and ultimate. ACI Structural Journal.
98:135-148.
[11] Berry, M.P., Lehman, D.E. and Lowes, L.N. ‘‘Lumped-plasticity models
for performance simulation of bridge columns’’, ACI Structural Journal,
105(3), pp. 270–279 (2008).
[12] Bae, S. and Bayrak, O. ‘‘Plastic hinge length of reinforced concrete
columns’’, ACI Structural Journal, 105(3), pp. 290–300 (2008).
[13] Arakawa, Takashi; Arai, Yasuyuki; Egashira, Keiichi; and Fujita,
Yutaka, "Effects of the Rate of Cyclic Loading on the Load-Carrying
Capacity and Inelastic Behavior of Reinforced Concrete Columns,"
Transactions of the Japan Concrete Institute, Vol. 4, 198, (1982)
[14] Amitsu, Shigeyuki; Shirai, Nobuaki; Adachi, Hiromi; and Ono, Arata,
"Deformation of Reinforced Concrete Column with High or Fluctuating
Axial Force,” Transactions of the Japan Concrete Institute, Vol. 13,
1991, pp. 355-362.
[15] Atalay, M.B.; and Penzien, J. "The Seismic Behavior of Critical Regions
of Reinforced Concrete Components as Influenced by Moment, Shear
and Axial Force,” Report No. EERC 75-19, University of California,
Berkeley, December 1975, 226 pages.
[16] Azizinamini, Atorod; Johal, Lakhpal S.; Hanson, Norman W.; Musser,
Donald W.; and Corley, William G.; "Effects of Transverse
Reinforcement on Seismic Performance of Columns – A Partial
Parametric Investigation,” Project No. CR-9617, Construction
Technology Laboratories, Skokie, Illinois, Sept. 1988.
[17] Bousias S.N., Triantafilluo T.C., Fardis M.N., Spathis l., O Regan B.A.,
Fiber-Reinforced Polymer Retrofitting of Rectangular Reinforced
Concrete Columns with or without Corrosions, ACI Structural Journal,
101(4),512-520, 2004.
[18] Bett, Bart J.; Klingner, Richard E.; and Jirsa, James O., "Behavior of
Strengthened and Repaired Reinforced Concrete Columns Under Cyclic
Deformations,” PMFSEL Report No. 85-3 Department of Civil
Engineering, University of Texas at Austin, Austin, Texas, December
1985
[19] Building Research Institute. A list of experimental results on
deformation ability of reinforced concrete columns under large
deflection.(No. 3). Report no. 21. Ministry of Construction. Japan: 1978.
[20] Gill, Wayne Douglas; Park, R.; and Priestley, M.J.N., "Ductility of
Rectangular Reinforced Concrete Columns With Axial Load,” Report
79-1, Department of Civil Engineering, University of Canterbury,
Christchurch, New Zealand, February 1979, 136 pages.
[21] Iacobucci, R.D., Sheikh S.A., Bayrak O, Retrofit of Square Concrete
Columns with Carbon Fiber-Reinforced Polymer for Seismic Resistance,
ACI Structure Journal, 100(6), 785-794, 2003.
[22] Kanda, Makoto; Shirai, Nobuaki; Adachi, Hiromi; and Sato, Toshio,
"Analytical Study on Elasto-Plastic Hysteretic Behaviors of Reinforced
Concrete Members,” Transactions of the Japan Concrete Institute,
Vol.10, 1988, pp. 257-264.
[23] Kawashima, K., Shoji, G., &Sakakibara, Y. (2000). A Cyclic Loading
Test for Clarifying the Plastic Hinge Length of Reinforced Concrete
Piers.Journal of Structural Engineering, 46A, 767-776.
[24] Lynn, Abraham; "Seismic Evaluation of Existing Reinforced Concrete
Building Colums,” Ph.D. Thesis, University of California at Berkeley,
Berkley, California, 1999, 284 pages.
[25] Mander J.B., Seismic Design of Bridge Piers. Research report 84-2.
Christ church (New Zealand): Department of Civil Engineering,
University of Canterbury, 1984.
[26] Mo YL,Wang SJ. Seismic behaviour of reinforced concrete columns
with various tie configurations.Journal of Structural Engineering ASCE
2000; 126:1122–30.
[27] Nagasaka, Tomoya, "Effectiveness of Steel Fiber as Web Reinforcement
in Reinforced Concrete Columns,” Transactions of the Japan Concrete
Institute, Vol. 4, 1982, pp. 493-500.
[28] Ohno, Tomonori; and Nishioka, Takashi, "An Experimental Study on
Energy Absorption Capacity of Columns in Reinforced Concrete
Structures," Proceedings of the JSCE, Structural
Engineering/Earthquake Engineering, Vol. 1, No 2., October 1984, pp.
137-147.
[29] Ohue, Minoru; Morimoto, Hisao, Fujii, Shigeru; and Morita, Shiro, "The
Behavior of R.C. Short Columns Failing in Splitting Bond-Shear Under
Dynamic Lateral Loading,” Transactions of the Japan Concrete Institute,
Vol. 7, 1985, pp. 293-300.
[30] Ono, Arata; Shirai, Nobuaki; Adachi, Hiromi; and Sakamaki, Yoshio,
"Elasto-Plastic Behavior of Reinforced Concrete Column With
Fluctuating Axial Force,” Transactions of the Japan Concrete Institute,
Vol. 11, 1989, pp. 239-246.
[31] Ozcan, O., Binici B., Ozcebe G., Improving Seismic Performance of
Deficient Reinforced Concrete Columns Using Fiber-Reinforced
Polymers, Engineering Structures, 30,1632-1646, 2008.
[32] Saatcioglu, M. and Grira, M. "Confinement of R/C Columns with
Welded Reinforcement Grids," ACI Structural Journal, Vol. 96, No. 1,
1999
[33] Sakai, Yuuki; Hibi, Junichi; Otani, Shunsuke; and Aoyama, Hiroyuki,
"Experimental Study on Flexural Behavior of Reinforced Concrete
Columns Using High-Strength Concrete,” Transactions of the Japan
Concrete Institute, Vol. 12, 1990, pp. 323-330.
[34] Sezen H., Seismic Behavior and Modeling of Reinforced Concrete
Building Columns, Ph.D. Dissertation, Department of Civil and
Environmental Engineering, University of California, Berkeley,
December 2002.
[35] Soesianawati, M.T.; Park, R; and Priestley, M.J.N., "Limited Ductility
Design of Reinforced Concrete Columns,” Report 86-10, Department of
Civil Engineering, University of Canterbury, Christchurch, New
Zealand, March 1986, 208 pages.
[36] S. A. Sheikh, D. V. Shah and S. S. Khoury, "Confinement of High-
Strength Concrete Columns,” ACI Structural Journal, v. 91, n. 1, Jan.-
Feb. 1994, p. 100-111.
[37] Takemura, H.; Kawashima, K.; "Effect of loading hysteresis on ductility
capacity of bridge piers," Journal of Structural Engineering, Vol. 43A,
pp. 849-858, Japan
[38] Tanaka, H.; and Park, R., "Effect of Lateral Confining Reinforcement on
the Ductile Behavior of Reinforced Concrete Columns,” Report 90-2,
Department of Civil Engineering, University of Canterbury, June 1990,
458 pages.
[39] Vintzileou, E., T. P. Tassios, et al. (2007). "Experimental validation of
seismic code provisions for RC columns." Engineering Structures 29(6):
1153-1164.
[40] Watson, Soesianawati; and Park, R., "Design of Reinforced Concrete
Frames of Limited Ductility,” Report 89-4, Department of Civil
Engineering, University of Canterbury, Christchurch, New Zealand,
January 1989, 232 pages.
[41] http://seismic.cv.titech.ac.jp/en/titdata.html (Kawashima et al.).
[42] Park, R., Kent, D. C. and Sampson, R. A.,"Reinforced concrete member
with cyclic loading,” Journal of Struct. Div., ASCE, Vol. 98, No. 7, pp.
1341-1360, 1972.
[43] Mander, J.B., Priestley, M.J.N ve Park, R., "Theoretical Stress-Strain
Model for Confined Concrete”, Journal of Structural Engineering.,
ASCE, Vol. 114, pp.1804-1826, 1988.