Rheological Model for Cyclic Loading of Concrete
Publication: Journal of Structural Engineering
Volume 110, Issue 9
Abstract
A rheological stochastic model to predict the cyclic stress‐strain behavior of concrete subjected to uniaxial compressive loading is proposed. The model consists of rheological elements with random state variables with exponential distributions. The model has 3 parameters and can be calibrated by experimental data from only the monotonically increasing loading. It simulates well the main known characteristics of concrete response to cyclic loading, such as strain softening, path dependency, stiffness degradation, and the concept of envelope curve. The formulation is of the total strain type and all formulas are derived in closed form. The model is computationally efficient for predicting response to any arbitrary strain history. A flow chart for computer implementation is presented.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ahmad, S. H., and Shah, S. P., “Stress‐Strain Curves of Concrete Confined by Spiral Reinforcement,” ACI Journal, Vol. 79, No. 6, Nov.–Dec., 1982, pp. 484–490.
2.
Aoyama, H., and Noguchi, H., “Mechanical Properties of Steel and Concrete Under Load Cycles Idealizing Seismic Actions,” AICAP‐CEB Symposium on Structural Concrete under Seismic Actions, Rome, Italy, May 25–28, 1979, p. 33.
3.
Aoyama, H., et al., “Moment‐Curvature Relations of Reinforced Concrete Sections Obtained from Material Characteristics,” Proceedings of the Annual Convention of AIJ, Oct., 1973, pp. 1261–1262.
4.
Bazant, Z. P., and Bhat, P. D., “Endochronic Theory of Inelasticity and Failure of Concrete,” Journal of the Engineering Mechanics Division, ASCE, Vol. 102, No. EM4, Aug., 1976, pp. 701–722.
5.
Blakeley, R. W. G., and Park, R., “Seismic Resistance of Prestressed Concrete Beam‐Column Assemblies,” ACI Journal, Vol. 68, No. 9, Sept., 1971, pp. 677–692.
6.
Blakeley, R. W. G., and Park, R., “Prestressed Concrete Sections with Cyclic Flexure,” Journal of the Structural Engineering Division, ASCE, Vol. 99, No. ST8, Aug., 1973, pp. 1717–1742.
7.
Desayi, P., Iyengar, K. T. S. R., and Reddy, T. S., “Stress‐Strain Characteristics of Concrete Confined in Steel Under Repeated Loading,” Materiaux et Constructions, Vol. 12, No. 71, pp. 375–383.
8.
Dougill, J. W., “On Stable Progressively Fracturing Solids,” Journal of Applied Mechanics and Physics, Vol. 27, 1976, pp. 423–437.
9.
Iwan, W. D., “A Distributed‐Element Model for Hysteresis and its Steady‐State Dynamic Response,” ASME Journal of Applied Mechanics, Dec., 1966, pp. 893–900.
10.
Iwan, W. D., “On A Class of Models for the Yielding Behavior of Continuous and Composite Systems,” ASME Journal of Applied Mechanics, Sept., 1967, pp. 612–617.
11.
Karsan, I. D., and Jirsa, O., “Behavior of Concrete Under Compressive Loadings,” Journal of the Structural Engineering Division, ASCE, Vol. 95, No. ST12, Dec., 1969, pp. 2543–2563.
12.
Kobayashi, S., et al., “Failure Criterion of Concrete Subjected to Multiaxial Compression,” Journal of the Society of Materials Science, Japan, Vol. 16, No. 170, Nov., 1967, pp. 897–902.
13.
Lippmann, H., “Ductility Caused by Progressive Formation of Shear Cracks,” Three‐Dimensional Constitutive Relations and Ductility Fracture, S. Nemat‐Nasser, ed., North‐Holland Publishing Co., Amsterdam, Holland, 1981, pp. 389–404.
14.
Maher, A., and Darwin, D., “Mortar Constituent of Concrete Under Cyclic Compression,” Structural Engineering and Engineering Materials, SM Report No. 5, The University of Kansas Center for Research, Oct., 1980, p. 165.
15.
Maher, A., and Darwin, D., “Mortar Constituent of Concrete in Compression,” ACI Journal, Mar.–Apr., 1982, pp. 100–109.
16.
Okamoto, S., et al., “Earthquake Resistance of Prestressed Concrete Structures,” Annual Report of BRI, Japan, 1971, pp. 314–323.
17.
Omote, Y., et al., “Hyeteretic Characteristics of Reinforced Concrete Cylindrical Sections Subjected to Cyclic Loading,” Proceedings of the Annual Convention of AIJ, Oct., 1974, pp. 1265–1266.
18.
Shah, S. P., and Chandra, S., “Critical Stress, Volume Change and Microcracking of Concrete,” ACI Journal, Sept., 1968, pp. 770–781.
19.
Shah, S. P., Fafitis, A., and Arnold, R., “Envelope Curves for Spirally Reinforced Concrete Subjected to Cyclic Loading,” Journal of Structural Engineering, ASCE, Vol. 109, No. ST7, July, 1983, pp. 1695–1710.
20.
Sinha, B. P., Gerstle, K. H., and Tulin, L. G., “Stress‐Strain Relations for Concrete Under Cyclic Loadings,” ACI Journal, Feb., 1964, pp. 195–210.
21.
Taylor, M. A., “Theory for the Deformation and Failure of Cement Pastes, Mortars and Concrete Under General States of Stress,” thesis presented to the University of California, at Berkeley, Calif., in 1969, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
22.
Timoshenko, S. P., “Strength of Materials,” Part 2, D. Van Nostrand Co., New York, N.Y., 1930, pp. 679–680.
Information & Authors
Information
Published In
Copyright
Copyright © 1984 ASCE.
History
Published online: Sep 1, 1984
Published in print: Sep 1984
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.