Discrete-Like Crack Simulation of Reinforced Concrete Incorporated with Analytical Solution of Cyclic Bond Model
Publication: Journal of Structural Engineering
Volume 140, Issue 3
Abstract
This paper presents solutions of second-order ordinary differential equations on bond problems to estimate crack widths of reinforced concrete (RC) members subjected to repeated cyclic loads. Up to now, bond behaviors under repeated cyclic loads have usually been calculated by a difference scheme. In contrast, this research adopts analytical solutions of the differential equations to calculate bond behaviors in finite element models where a number of concrete cracks occur. The conventional differential equation for the bond problem has been available only under monotonic loading conditions. This paper extends the equation to cases where the reinforcement becomes plastic and the bond is subject to unloading/reloading conditions. The bond stress-slip relationship is modeled by a multilinear model that is composed of an envelope made of five lines, unloading/reloading paths, and a negative friction path. The solution of the differential equation is classified into 25 cases when the bond stress-slip relationship is on the envelope and seven cases when on the unloading/reloading paths or the negative friction path. The solutions are implemented into the smeared crack-based finite-element method (FEM) to evaluate the crack widths of a RC beam subject to repeated cyclic flexural/shear loads. The FEM program is incorporated with the discrete-like crack procedure developed by the authors and calculates stress redistributions due to cracking using the solutions of the differential equations. Typical distributions of reinforcement stress, bond stress, and slip along the reinforcement are presented.
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References
Abeles, P. (1937). “Versuche mit Rechteckbalken, bewehrt mit besonders hochwertigem Stahl.” Beton und Eisen, 36(17), 282–287 (in German).
Abrams, D. A. (1913). “Tests of bond between concrete and steel.” Univ. of Illinois Bulletin, 7.
Arnovljević, I. (1909). “Das Verteilungsgesetz der Haftspannung bei axial beanspruchten Verbundstäben.” Zeitschrift für Architektur und Ingenieurwesen, 55(2), 413–418 (in German).
Ayoub, A., and Filippou, F. C. (1999). “Mixed formulation of bond-slip problems under cyclic loads.” J. Struct. Eng., 661–671.
Bach, C., and Graf, O. (1911). “Versuche mit Eisenbeton-Balken zur Ermittlung der Widerstandsfästigkeit verschiedener Bewehrung gegen Schubkräfte. Erster Teil.” Deutscher Ausschuss für Eisenbeton, 10, 1–132 (in German).
Bažant, Z. P., and Oh, B. H. (1983). “Crack band theory for fracture of concrete.” Mater. Struct., 16(3), 155–177.
Bufler, H. (1958). “Ein neuer Ansatz zur Berechnung der Draht- und Haftspannungen im Stahlbeton.” Bauingenieur, 10, 382–388 (in German).
Cervenka, V., and Pukl, R. (1995). “Mesh sensitivity effects in smeared finite element analysis of concrete structures.” Proc. 2nd Int. Conf. on Fracture Mechanics of Concrete Structures (FRAMCOS 2), F. H. Wittman, ed., AEDIFICATIO, Freiburg, Germany, 1387–1396.
Chi, M., and Kirstien, A. F. (1958). “Flexural cracks in reinforced concrete beams.” J. Proc., ACI, 54(4), 865–878.
Ciampi, V., Eligehausen, R., Bertero, V. V., and Popov, E. P. (1982). “Analytical model for concrete anchorages of reinforcing bars under generalized excitations.”, Earthquake Engineering Research Center, Univ. of California, Berkeley, CA.
Darwin, D., and Pecknold, D. A. (1977). “Nonlinear biaxial stress-strain law for concrete.” J. Engrg. Mech. Div., 103(2), 229–241.
Edwards, A. D., and Picard, A. (1972). “Theory of cracking in concrete members.” J. Struct. Div., 98(12), 2687–2700.
Eligehausen, R., Popov, E. P., and Bertero, V. V. (1983). “Local bond stress-slip relationships of deformed bars under generalized excitations.”, Univ. of California, Berkeley, CA.
Emperger, F. (1940). “Die statische Bedeutung des Haftwiderstandes im Tragwerk aus Eisenbeton.” Beton und Eisen, 8, 106–109 (in German).
fib. (2010). fib Model Code 2010, Fédération Internationale de la Précontrainte, Lausanne, Switzerland, 233–239.
Filippou, F. C., Popov, E. P., and Bertero, V. V. (1983). “Modeling of R/C joints under cyclic excitations.” J. Struct. Eng., 2666–2684.
Fukuda, T. (1933). “On some problems connected with the distribution of stresses in reinforced concrete members acted upon by axial forces.” J. JSCE, 19(3), 201–212 (in Japanese).
Haskett, M., Oehlers, D. J., Ali, M. S. M., and Wu, C. (2009). “Yield penetration hinge rotation in reinforced concrete beams.” J. Struct. Eng., 130–138.
Ingraffea, A. R., Gerstk, W. H., Gergely, P., and Saouma, V. (1984). “Fracture mechanics of bond in reinforced concrete.” J. Struct. Eng., 871–890.
Jungwirth, D. (1970). “Elektronische Berechnung des in einem Stalbetonbalken in gerissenen Zustand auftretenden Kräftezustandes unter besonderer Berücksichtigung des Querkraftbereiches.” Deutscher Ausschuss für Stahlbeton, 211, 1–117 (in German).
Kanakubo, T., Sato, Y., Uchida, Y., Watanabe, K., and Shima, H. (2012). “Japan Concrete Institute TC activities on bond behavior and constitutive laws in RC (Part 3. Application of constitutive laws for FEA).” Bond in Concrete 2012—General Aspects of Bond, J. W. Cairns, G. Metelli, and G. A. Plizzari, eds., Creations, Brescia, Italy, 105–112.
Laurencet, P., Jaccoud, J. P., and Favre, R. (1998). “Residual crack widths of RC & PC structures under cyclic actions.” CEB and fib Int. Ph.D. Symp. in Civil Eng., fib, Lausanne, Switzerland, 1–8.
Lee, S. L., Mansur, M. A., Tan, K. H., and Kasiraju, K. (1987). “Cracking behavior of concrete tension members reinforced with welded wire fabric.” ACI Struct. J., 84(6), 481–491.
Leonhardt, F., and Walther, R. (1962). “Beiträge zur Behandlung der Schubprobleme im Stahlbetonbau (1).” Beton- und Stahlbetonbau, 57(2), 32–44 (in German).
Lowes, L. N., Moehle, J. P., and Govindjee, S. (2004). “Concrete-steel bond model for use in finite element modeling of reinforced concrete structures.” ACI Struct. J., 101(4), 501–511.
Morita, S., and Kaku, T. (1973). “Local bond stress-slip relationship under repeated loading.” Proc. IABSE Symp. on the Resistance and Ultimate Deformability of Structures, International Association for Bridge and Structural Engineering, Zürich, 221–226.
Naganuma, K., Yonezawa, K., Kurimoto, O., and Eto, H. (2004). “Simulation of nonlinear dynamic response of reinforced concrete scaled model using three-dimensional finite element method.” Proc. 13th World Conf. on Earthquake Engineering (WCEE 13), Canadian Association for Earthquake Engineering, Ottawa, 586.
Ngo, D., and Scordelis, A. C. (1967). “Finite element analysis of reinforced concrete beams.” J. Proc., ACI, 64(3), 152–163.
Nilson, A. H. (1968). “Nonlinear analysis of reinforced concrete by the finite element method.” J. Proc., ACI, 65(9), 757–766.
Oh, B. H., and Kim, S. H. (2007a). “Realistic models for local bond stress-slip of reinforced concrete under repeated loading.” J. Struct. Eng., 216–224.
Oh, B. H., and Kim, S. H. (2007b). “Advanced crack width analysis of reinforced concrete beams under repeated loads.” J. Struct. Eng., 411–420.
Ottosen, N. S. (1977). “A failure criterion for concrete.” J. Engrg. Mech. Div., 103(4), 527–535.
Rasid, Y. R. (1968). “Ultimate strength analysis of prestressed concrete pressure vessels.” Nucl. Eng. Des., 7(4), 334–344.
Rehm, G. (1961). “Über die Grundlagen des Verbundes zwischen Stahl und Beton.” Deutscher Ausshcuss für Stahlbeton, 138.
Ruiz, M. F., Muttoni, A., and Gambarova, P. G. (2007). “Analytical modeling of the pre- and postyield behavior of bond in reinforced concrete.” J. Struct. Eng., 1364–1372.
Rüsch, H., and Rehm, G. (1963a). “Versuche mit Betonformstählen.” Deutscher Ausschuss für Stahlbeton, 140, 1–182.
Rüsch, H., and Rehm, G. (1963b). “Versuche mit Betonformstählen (Teil II).” Deutscher Ausschuss für Stahlbeton, 160, 1–82.
Rüsch, H., and Rehm, G. (1964). “Versuche mit Betonformstählen (Teil III).” Deutscher Ausschuss für Stahlbeton, 165, 1–52.
Salem, H. M., and Maekawa, K. (2004). “Pre- and postyield finite element method simulation of bond of ribbed reinforcing bars.” J. Struct. Eng., 671–680.
Sato, Y., and Naganuma, K. (2006). “Crack tracing process for smeared crack based nonlinear FEM.” Proc. 3rd Int. Conf. Urban Earthquake Engineering (ICUEE 3), Tokyo Institute of Technology, Tokyo, Japan, 325–332.
Sato, Y., and Naganuma, K. (2007). “Discrete-like crack simulation by smeared crack-based FEM for reinforced concrete.” Earthquake Eng. Struct. Dyn., 36(14), 2137–2152.
Sato, Y., and Naganuma, K. (2010). “Crack width analysis using smeared-crack-based finite element method. Part 7. Strategy to mesh-division dependency.” Summaries of technical papers of Annual Meeting Architectural Institute of Japan, AIJ, Tokyo, Japan, C 2, 17–18.
Sato, Y., and Naganuma, K. (2012). “Discrete-like crack simulation by smeared crack-based FEM—Reinforced concrete wall subjected to shrinkage.” Bond in Concrete 2012—General Aspects of Bond, J. W. Cairns, G. Metelli, and G. A. Plizzari, eds., Creations, Brescia, Italy, Brescia, Italy, 193–200.
Shima, H., Chou, L. L., and Okamura, H. (1987). “Bond-slip-strain relationship of deformed bars embedded in massive concrete.” J. JSCE, 378(6), 165–174 (in Japanese).
Sugimoto, K., Kashiwase, T., Tsuda, K., and Eto, H. (2003). “Evaluation method for the earthquake resistant performance of RC buildings: Part 2.” Summaries of technical papers of Annual Meeting Architectural Institute of Japan, AIJ, Tokyo, Japan, C-2, 143–144 (in Japanese).
Vecchio, F. J. (1989). “Nonlinear finite element analysis of reinforced concrete membranes.” ACI Struct. J., 86(1), 26–35.
Venkateswarlu, B., and Gesund, H. (1972). “Cracking and bond slip in concrete beams.” J. Struct. Div., 98(12), 2663–2686.
Watanabe, H., Katori, K., Shinohara, Y., and Hayashi, S. (2004). “Shear crack control on reinforced concrete column by lateral prestressing.” Proc. 1st Int. Conf. Urban Earthquake Eng. (ICUEE 1), Tokyo Institute of Technology, Tokyo, Japan, 239.
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Published In
Journal of Structural Engineering
Volume 140 • Issue 3 • March 2014
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Feb 23, 2012
Accepted: May 3, 2013
Published online: Nov 14, 2013
Published in print: Mar 1, 2014
Discussion open until: Apr 14, 2014
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