Ultimate Strain Criteria for RC Members in Monotonic or Cyclic Flexure
Publication: Journal of Structural Engineering
Volume 142, Issue 9
Abstract
A large number of experimental curvatures in plastic hinges of concrete members are used alongside analytical moment-curvature relations to backestimate strains in the bars, the extreme concrete fibers of a section, or its confined core at the ultimate conditions of concrete sections in flexure with axial loads. Strain limits derived from these ultimate strains can support fiber models for prismatic members or models with finite-length plastic hinges at the ends. The measurements come from circular or rectangular columns (some tested diagonally), walls, or beams. The ultimate strains derived for steel bars and concrete are not local material properties (especially for cyclic loading): they depend on the geometric features of the section as a whole and of the immediate vicinity of the most critical point in the section. The size effects are clear: (1) concrete ultimate strains increase in a small compression zone, (2) the monotonic ultimate strain of tension bars increases with decreasing number of bars in the tension zone, (3) the ultimate strain of steel in cyclic tests increases with the increasing number of bars in the compression zone, and (4) the ultimate strain of confined concrete is larger at a section corner in biaxial bending than along the full side of a rectangular compression zone in uniaxial flexure, while at the perimeter of a circular section, it is in between these two extremes. The cyclic ultimate strain of steel in tension increases as the bar diameter–to–stirrup spacing ratio increases, thanks to the delay of bar buckling in previous compression half-cycles. The ultimate strains derived apply both as mean values in a plastic hinge and at the end section of prismatic members. Compared to experimental ultimate curvatures, those computed from the proposed ultimate strains do not have bias and exhibit much less scatter than those obtained from arbitrary ultimate strains specified in some codes. These code predictions are, in general, unsafe.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The research leading to these results received funding from the General Secretariat for Research and Technology, grant ERC-12 of the Operational Program “Education and Lifelong Learning,” cofunded by the European Union (European Social Fund) and national resources.
References
ASCE. (2007). “Seismic rehabilitation of existing buildings.” ASCE/SEI 41-06, Reston, VA.
Benjamin, J. R., and Cornell, C. A. (1970). Probability, statistics, and decision for civil engineers, McGraw-Hill, New York.
Biskinis, D., and Fardis, M. N. (2010a). “Deformations at flexural yielding of members with continuous or lap-spliced bars.” Struct. Concr., 11(3), 127–138.
Biskinis, D., and Fardis, M. N. (2010b). “Flexure-controlled ultimate deformations of members with continuous or lap-spliced bars.” Struct. Concr., 11(2), 93–108.
Biskinis, D., and Fardis, M. N. (2013). “Stiffness and cyclic deformation capacity of circular RC columns with or without lap-splices and FRP wrapping.” Bull. Earthquake Eng., 11(5), 1447–1466.
Caltrans. (2006). Seismic design criteria version 1.4, Sacramento, CA.
CEN (European Committee for Standardization). (2004). “Design of concrete structures. Part 1-1: General rules and rules for buildings.” Eurocode 2, EN 1992-1-1:2004, Comite Europeen de Normalisation, Brussels, Belgium.
CEN (European Committee for Standardization). (2005a). “Design of structures for earthquake resistance. Part 2: Bridges.” Eurocode 8, EN 1998-2:2005, Comite Europeen de Normalisation, Brussels, Belgium.
CEN (European Committee for Standardization). (2005b). “Design of structures for earthquake resistance. Part 3: Assessment and retrofitting of buildings.” Eurocode 8, EN 1998-3:2005, Comite Europeen de Normalisation, Brussels, Belgium.
Fardis, M. N. (2013). “Performance- and displacement-based seismic design and assessment of concrete structures in the Model Code 2010.” Struct. Concr., 14(3), 215–229.
Fenwick, R., and Dhakal, R. (2007). “Material strain limits for seismic design of concrete structures.” J. Struct. Eng. Soc. N. Z., 20(1), 14–28.
fib. (2012). “Model Code 2010, final draft.”, Federation Internationale du Beton, Lausanne, Switzerland.
French, C. W., and Schultz, A. E. (1991). Minimum available deformation capacity of reinforced concrete beams, S. K. Ghosh, ed, American Concrete Institute (ACI), Detroit, 363–410.
Goodnight, J. C., Kowalsky, M. J., and Nau, J. M. (2014). “A new look at strain limits and plastic hinge lengths for reinforced concrete bridge columns.” Proc., 10th U.S. National Conf. on Earthquake Engineering: Frontiers of Earthquake Engineering, Earthquake Engineering Research Institute.
Grammatikou, S., Biskinis, D., and Fardis, M. N. (2015). “Strength, deformation capacity, and failure modes of RC walls under cyclic loading.” Bull. Earthquake Eng., 13(11), 3277–3300.
Kazaz, I., Gülkan, P., and Yakut, A. (2012). “Performance limits for structural walls: An analytical perspective.” Eng. Struct., 43, 105–119.
Kowalsky, M. J. (2000). “Deformation limit states for circular reinforced concrete bridge columns.” J. Struct. Eng., 869–878.
Mander, J. B., Priestley, M. J. N., and Park, R. (1988). “Theoretical stress-strain model for confined concrete.” J. Struct. Eng., 1804–1826.
Ministry Public Works and Resettlement. (2007). “Turkish seismic design code for buildings: Specification for structures to be built in disaster areas.”, Ankara, Turkey.
Newman, K., and Newman, J. B. (1971). “Failure theories and design criteria for plain concrete.” Structure, solid mechanics and engineering design, M. Te’eni, ed., Wiley, New York.
Panagiotakos, T. B., and Fardis, M. N. (2001). “Deformations of RC members at yielding and ultimate.” ACI Struct. J., 98(2), 135–148.
Paulay, T., and Priestley, M. J. N. (1992). Seismic design of reinforced concrete and masonry buildings, Wiley, New York.
Richart, F. E., Brandtzaeg, A., and Brown, R. L. (1928). “A study of the failure of concrete under combined compressive stresses.”, Univ. of Illinois, Engineering Experiment Station, Champaign, IL.
Saatcioglu, M. (1991). Deformability of reinforced concrete columns, S. K. Ghosh, ed., American Concrete Institute (ACI), Detroit, 421–452.
Sheikh, S. A., and Uzumeri, S. M. (1982). “Analytical model for concrete confinement in tied columns.” J. Struct. Eng., 108(ST12), 2703–2722.
Standards New Zealand. (2006). “Concrete structures standard NZS 3101.” Wellington, New Zealand.
Walker, A. F., and Dhakal, R. P. (2009). “Assessment of material strain limits for defining plastic regions in concrete structures.” Bull. N. Z. Soc. Earthquake Eng., 42(2), 86–95.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 142 • Issue 9 • September 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jul 28, 2015
Accepted: Dec 17, 2015
Published online: Mar 22, 2016
Discussion open until: Aug 22, 2016
Published in print: Sep 1, 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.