Reinforced Concrete Frame Element with Bond Interfaces. I: Displacement-Based, Force-Based, and Mixed Formulations
This article has a reply.
VIEW THE REPLYPublication: Journal of Structural Engineering
Volume 128, Issue 3
Abstract
This is the first of two papers that presents the theory and applications of three different formulations of reinforced concrete frame elements with bond slip in the reinforcing bars. This paper presents the governing differential equations of the problem (strong form) and the three different element formulations (weak forms). The first is the displacement-based formulation, which is derived from the principle of stationary potential energy. The second is the force-based formulation, which is derived from the principle of stationary complementary energy. The third is the two-field mixed formulation, which is derived from the principle of stationary Hellinger–Reissner potential. The selection of the displacement and force shape functions for the different formulations is discussed. Tonti’s diagrams are used to conveniently represent the equations that govern both the strong and the weak forms of the problem. This paper derives the general matrix equations of the three formulations. Implementation of the formulations in a general-purposed nonlinear structural analysis software and a set of applications are discussed in the companion paper.
Get full access to this article
View all available purchase options and get full access to this article.
References
Ayoub, A., and Filippou, F. C.(2000). “Mixed formulation of nonlinear steel-concrete composite beam element.” J. Struct. Eng., 126(3), 371–381.
de Veubeke, B. F. (1965). Stress analysis, O. C. Zienkiewicz and G. S. Holister, eds., Wiley, London, 145–197.
Eligehausen, R., Popov, E. P., and Bertero, V. V. (1983). “Local bond stress-slip relationships of deformed bars under generalized excitations: experimental results and analytical model.” Rep. EERC 83-23, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif.
Felippa, C. A. (2000). ASEN 5367 Course Notes: Advanced Finite Element Methods, Dept. of Aerospace Engineering, Univ. of Colorado, Boulder, http://caswww.colorado.edu/courses.d/AFEM.d/Home.html
Filippou, F. C., D’Ambrisi, A., and Issa, A.(1999). “Effects of reinforcement slip on hysteretic behavior of reinforced concrete frame members.” ACI Struct. J., 96(3), 327–335.
Filippou, F. C., and Issa, A. (1988). “Nonlinear analysis of reinforced concrete frames under cyclic load reversals.” Rep. EERC 88/12, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif.
Kent, D. C., and Park, R.(1971). “Flexural members with confined Concrete.” J. Struct. Div. ASCE, 97(ST7), 1964–1990.
Kwak, H. G., and Filippou, F. C.(1995). “A new reinforcing steel model with bond-slip.” Struct. Eng. Mech., Int. J., 3(4), 299–312.
Limkatanyu, S., and Spacone, E.(2002). “Reinforced concrete frame element with bond interfaces. II: State determinations and numerical validation.” J. Struct. Eng. , 128(3), 356–364.
Lowes, L. N. (1999). “Finite element modeling of reinforced concrete beam-column bridge connections.” PhD thesis, Univ. of California, Berkeley, Calif.
Menegotto, M., and Pinto, P. E. (1973). “Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometry and nonelastic behavior of elements under combined normal force and bending.” Proc., IABSE Symp. on Resistance and Ultimate Deformability of Structures Acted on by Well-Defined Repeated Loads, Lisbon, Portugal, IABSE Edition, Switzerland, 112–123.
Monti, G., Filippou, F. C., and Spacone, E.(1997). “Finite element for anchored bars under cyclic load reversals.” J. Struct. Eng. 123(5), 614–623.
Monti, G., and Spacone, E.(2000). “Reinforced concrete fiber beam element with bond-slip.” J. Struct. Eng. 126(6), 654–661.
Ngo, D., and Scordelis, A. C.(1967). “Finite element analysis of reinforced concrete beams.” ACI Struct. J., 64(3), 152–163.
Nilson, A. H.(1971). “Internal measurement of bond-slip.” ACI Struct. J., 69(7), 439–441.
Rubiano-Benavides, N. R. (1998). “Predictions of the inelastic seismic response of concrete structures including shear deformations and anchorage slip.” PhD thesis, Univ. of Texas, Austin, Tex.
Salari, M. R., Spacone, E., Shing, P. B., and Frangopol, D. M.(1998). “Nonlinear analysis of composite beams with deformable shear connectors.” Ground Water, 124(10), 1148–1158.
Spacone, E., Filippou, F. C., and Taucer, F. F.(1996). “Fibre beam-column model for nonlinear analysis of R/C frames. Part I: formulation.” Earthquake Eng. Struct. Dyn., 25, 711–725.
Spacone, E., and Limkatanyu, S.(2000). “Response of reinforced concrete members including bond-slip effects.” ACI Struct. J., 97(6), 831–839.
Zienkiewicz, O. C., and Taylor, R. L. (1989). The finite element method, 4th Ed., Vol. 1, McGraw-Hill, London.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 128 • Issue 3 • March 2002
Pages: 346 - 355
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Feb 21, 2001
Accepted: Aug 17, 2001
Published online: Mar 1, 2002
Published in print: Mar 2002
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.