Rebar Anchorage Slip Macromodel Considering Bond Stress Distribution: Monotonic Loading and Model Application
Publication: Journal of Structural Engineering
Volume 144, Issue 8
Abstract
This study presents a modified macromodel for calculating the anchorage slip of rebar under monotonic loading and its application to the fiber beam–column element model. The proposed macromodel reflects bond stress distribution along rebar and hence captures slip responses over the entire rebar stress range. The anchorage slip problem is formulated using three governing equations among four bond fields, namely, bond stress, rebar stress and strain, and slip. The general framework for macromodels with a given bond stress distribution and micromodels with a given bond–slip relationship is established. Then, the proposed macromodel is developed using a refined bond stress distribution function, which is established by solving a validated micromodel. Available experimental results are used to calibrate the bond stress parameter and to investigate the validity of the proposed model. Comparisons indicate considerably improved accuracy of the proposed macromodel over the conventional macromodel for capturing stress-slip relationships and bond field distributions. Finally, the proposed macromodel is implemented into a conventional fiber beam–column model. The modified fiber model is applied to simulate a bridge column shake-table test, and shows success in capturing anchorage slip contributions. Therefore, the model is validated for both slip responses and model applications.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers gratefully acknowledge the financial support provided by the National Key Research Program of China (Grant No. 2017YFC0703405). The writers also express their sincere appreciation to the reviewers of this paper for their constructive comments and suggestions.
References
Alsiwat, J. M., and M. Saatcioglu. 1992. “Reinforcement anchorage slip under monotonic loading.” J. Struct. Eng. 118 (9): 2421–2438. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:9(2421).
Baber, T. T., and M. N. Noori. 1985. “Random vibration of degrading, pinching systems.” J. Eng. Mech. 111 (8): 1010–1026. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:8(1010).
CEB-FIP (Comité Euro-International du Béton-Fédération International de la Précontrainte). 1991. CEB-FIP model code 1990: Design code. London, UK: CEB-FIP.
Eligehausen, R., E. P. Popov, and V. V. Bertero. 1983. Local bond stress-slip relationships of deformed bars under generalized excitations. Berkeley, CA: Univ. of California.
Esmaeily, A., and Y. Xiao. 2005. “Behavior of reinforced concrete columns under variable axial loads: Analysis.” ACI Struct. J. 102 (5): 736–744.
Filippou, F. C., E. P. Popov, and V. V. Bertero. 1983. Effects of bond deterioration on hysteretic behavior of reinforced concrete joints. Berkeley, CA: Univ. of California.
Ibarra, L. F., R. A. Medina, and H. Krawinkler. 2005. “Hysteretic models that incorporate strength and stiffness deterioration.” Earthquake Eng. Struct. Dyn. 34 (12): 1489–1511. https://doi.org/10.1002/eqe.495.
Lehman, D. E. 1998. “Seismic performance of well-confined concrete bridge columns.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of California.
Lynn, A. C., J. P. Moehle, S. A. Mahin, and W. T. Holmes. 1996. “Seismic evaluation of existing reinforced concrete building columns.” Earthquake Spectra 12 (4): 715–739. https://doi.org/10.1193/1.1585907.
Maekawa, K., A. Pimanmas, and H. Okamura. 2003. Nonlinear mechanics of reinforced concrete. London, UK: Spon.
Mathey, R. G., and D. Watstein. 1961. “Investigation of bond in beam and pull-out specimens with high-yield-strength deformed bars.” ACI J. Proc. 57 (3): 1071–1090.
Monti, G., F. C. Filippou, and E. Spacone. 1997. “Finite element for anchored bars under cyclic load reversals.” J. Struct. Eng. 123 (5): 614–623. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:5(614).
Monti, G., and E. Spacone. 2000. “Reinforced concrete fiber beam element with bond–slip.” J. Struct. Eng. 126 (6): 654–661. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:6(654).
Murcia-Delso, J., and P. B. Shing. 2015. “Bond–slip model for detailed finite-element analysis of reinforced concrete structures.” J. Struct. Eng. 141 (4): 04014125. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001070.
Nie, J. G., W. H. Pan, M. X. Tao, and Y. Z. Zhu. 2017. “Experimental and numerical investigations of composite frames with innovative composite transfer beams.” J. Struct. Eng. 143 (7): 0401704. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001776.
Nie, J. G., M. X. Tao, C. S. Cai, and G. Chen. 2011. “Modeling and investigation of elasto-plastic behavior of steel-concrete composite frame systems.” J. Constr. Steel Res. 67 (12): 1973–1984. https://doi.org/10.1016/j.jcsr.2011.06.016.
OSU (Oregon State University). 1996. “Solution techniques for problems of the form .” Accessed January 1, 2018. http://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/ode/second/reduc1/reduc1.html.
Otani, S., and M. A. Sozen. 1972. Behavior of multistory reinforced concrete frames during earthquakes. UILU-ENG-72-2018. Urbana, IL: Univ. of Illinois.
Pan, W. H., M. R. Eatherton, M. X. Tao, Y. Yang, and X. Nie. 2017a. “Design of single-level guyed towers considering interrelationship between bracing strength and rigidity requirements.” J. Struct. Eng. 143 (9): 04017128. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001857.
Pan, W. H., M. X. Tao, and J. G. Nie. 2017b. “Fiber beam–column element model considering reinforcement anchorage slip in the footing.” Bull. Earthquake Eng. 15 (3): 991–1018. https://doi.org/10.1007/s10518-016-9987-3.
Park, Y. J., A. M. Reinhorn, and S. K. Kunnath. 1987. IDARC: Inelastic damage analysis of reinforced concrete frame-shear-wall structures. Buffalo, NY: State Univ. of New York.
Ray, T., and A. Reinhorn. 2012. “Enhanced smooth hysteretic model with degrading properties.” J. Struct. Eng. 140 (1): 04013028. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000798.
Saatcioglu, M., J. M. Alsiwat, and G. Ozcebe. 1992. “Hysteretic behavior of anchorage slip in R/C members.” J. Struct. Eng. 118 (9): 2439–2458. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:9(2439).
Santos, J., and A. A. Henriques. 2015. “New finite element to model bond–slip with steel strain effect for the analysis of reinforced concrete structures.” Eng. Struct. 86 (1): 72–83. https://doi.org/10.1016/j.engstruct.2014.12.036.
Schoettler, M. J., J. I. Restrepo, G. Guerrini, D. E. Duck, and F. Carrea. 2015. A full-scale, single-column bridge bent tested by shake-table excitation. Berkeley, CA: Univ. of California.
Sezen, H., and T. Chowdhury. 2009. “Hysteretic model for reinforced concrete columns including the effect of shear and axial load failure.” J. Struct. Eng. 135 (2): 139–146. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:2(139).
Sezen, H., and J. P. Moehle. 2006. “Seismic tests of concrete columns with light transverse reinforcement.” ACI Struct. J. 103 (6): 842–849.
Sezen, H., and E. J. Setzler. 2008. “Reinforcement slip in reinforced concrete columns.” ACI Struct. J. 105 (3): 280–289.
Shima, H., L. L. Chou, and H. Okamura. 1987a. “Bond characteristics in post-yield range of deformed bars.” Proc. Jpn. Soc. Civ. Eng. 1987 (378): 213–220.
Shima, H., L. L. Chou, and H. Okamura. 1987b. “Bond–slip–strain relationship of deformed bars embedded in massive concrete.” Proc. Jpn. Soc. Civ. Eng. 1987 (378): 165–174.
Terzic, V., M. J. Schoettler, J. I. Restrepo, and S. A. Mahin. 2015. Concrete column blind prediction contest 2010: Outcomes and observations. Berkeley, CA: Univ. of California.
Ueda, T., I. Lin, and N. M. Hawkins. 1986. “Beam bar anchorage in exterior column-beam connections.” ACI J. Proc. 83 (3): 412–422.
Viwathanatepa, S., E. Popov, and V. V. Bertero. 1979. Effects of generalized loadings on bond of reinforcing bars embedded in confined concrete blocks. Berkeley, CA: Univ. of California.
Yamao, Y., L. L. Chou, and J. Niwa. 1984. “Experimental study of local bond–slip relationship.” Proc. Jpn. Soc. Civ. Eng. 1984 (343): 219–228. https://doi.org/10.2208/jscej1969.1984.343_219.
Zhao, J., and S. Sritharan. 2007. “Modeling of strain penetration effects in fiber-based analysis of reinforced concrete structures.” ACI Struct. J. 104 (2): 133–141.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 144 • Issue 8 • August 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Mar 11, 2017
Accepted: Jan 30, 2018
Published online: May 18, 2018
Published in print: Aug 1, 2018
Discussion open until: Oct 18, 2018
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.