Rate‐Type Concrete Creep Law with Reduced Time
Publication: Journal of Engineering Mechanics
Volume 110, Issue 3
Abstract
For creep analysis of large structural systems, the linear aging integral‐type creep law needs to be converted to a rate‐type form which consists of a system of first‐order linear differential equations with age‐dependent coefficients. The system may be visualized by the Kelvin chain model with age‐dependent elastic moduli and viscosities. In the existing formulation, the independent variable is actual time. It is shown that, by using as the independent variable a certain reduced time which increases with time at a gradually declining rate, one reduces the number of differential equations needed to describe creep within the given time range, thereby making numerical structural analysis more efficient. An algorithm for identifying the material parameters from given creep data, based on minimization of a sum of squared deviations, is also presented. Thermodynamic restrictions on the material coefficients are analyzed. Finally, the capability of closely approximating available creep data is demonstrated.
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References
1.
Anderson, C. A., “Numerical Creep Analysis of Structures,” Los Alamos Scientific Laboratory Report LA‐UR‐80‐2585, Los Alamos, N.M., 1980;
also “Creep and Shrinkage in Concrete Structures,” Z. P. Bažant, and F. H. Wittmann, eds., John Wiley & Sons, Inc., New York, N.Y., 1982, pp. 259–304.
2.
Bažant, Z. P., “Phenomenological Theories for Creep of Concrete Based on Rheological Models,” Acta Technica ČSAV, Prague 11, 1966, pp. 82–109.
3.
Bažant, Z. P., “Theory of Creep and Shrinkage in Concrete Structures: A Precis of Recent Developments,” Mechanics Today, Vol. 2, Pergamon Press, Inc., New York, N.Y., 1975, pp. 1–93.
4.
Bažant, Z. P., “Viscoelasticity of Porous Solidifying Material—Concrete,” Journal of the Engineering Mechanics Division, ASCE, Vol. 102, 1977, pp. 1049–1067.
5.
Bažant, Z. P., “Input of Creep and Shrinkage Characteristics for a Structural Analysis Program,” Materials and Structures, RILEM, Paris, Vol. 15, No. 88, 1982, p. 283; with Errata 1983, 1984.
6.
Bažant, Z. P., “Mathematical Models for Creep and Shrinkage of Concrete,” Chapter 7, Creep and Shrinkage in Concrete Structures, Z. P. Bažant, and F. H. Wittmann, eds., John Wiley & Sons, Inc., New York, N.Y., 1982, pp. 163–258.
7.
Bažant, Z. P., and Asghari, A., “Computation of Age‐Dependent Relaxation Spectra,” Cement and Concrete Research, Vol. 4, pp. 567–579;
Also see “Computation of Kelvin‐Chain Retardation Spectra,” Cement and Concrete Research, Vol. 4, 1974, pp. 797–806.
8.
Bažant, Z. P., and Chern, J. C., “Double Power Logarithmic Law for Basic Creep of Concrete,” Center for Concrete and Geomaterials, Northwestern University, Evanston, Ill., Dec., 1983 (also: submitted to Cement and Concrete Research).
9.
Bažant, Z. P., Rossow, E. C., and Horrigmoe, G., “Finite Element Program for Creep Analysis of Concrete Structures,” Proceedings of the 6th International Conference on Structural Mechanics in Reactor Technology (SMiRT6), Paris, France, Paper H2/1.
10.
Bažant, Z. P., and Wu, S. T., “Dirichlet Series Creep Function for Aging Concrete,” Journal of the Engineering Mechanics Division, ASCE, Vol. 99, No. EM2, Proc. Paper 9645, 1973.
11.
Bažant, Z. P., and Wu, S. T., “Rate‐Type Creep Law of Aging Concrete Based on Maxwell Chain,” Materials and Structures, RILEM, 7, 1974, pp. 45–60.
12.
Cost, T. M., “Approximate Laplace Transform Inversions in Viscoelastic Stress Analysis,” American Institute of Aeronautics and Astronautics, Vol. 2, 1964, pp. 2157–2166.
13.
Gamble, B. R., and Thomass, L. H., “The Creep of Concrete Subject to Varying Stress,” Proceedings of the Australian Conference on the Mechanics of Structures and Materials, Adelaide, Australia, Paper No. 24, Aug., 1969.
14.
Hanson, J. A., “A Ten‐Year Study of Creep Properties of Concrete,” Concrete Lab., Report No. SP‐38, U.S. Dept. of the Interior, Bureau of Reclamation, Denver, Colo., July, 1953.
15.
Harboe, E. M., et al., “A Comparison of the Instantaneous and the Sustained Modulus of Elasticity of Concrete,” Concrete Lab. Report No. C‐854, Div. of Engrg. Lab., U.S. Dept. of the Interior, Bureau of Reclamation, Denver, Colo., Mar., 1958.
16.
Hardy, G. M., and Riesz, M., “The General Theory of Dirichlet Series,” Cambridge Tracts in Mathematics and Mathematical Physics, Cambridge University Press, 18, 1915.
17.
Lanczos, C., “Applied Analysis,” Prentice‐Hall, Englewood Cliffs, N.J., 1964, pp. 272–280.
18.
L'Hermite, R. G., Mamillan, M., and Lefèvre, C., “Nouveaux résultats de recherches sur la déformation et la rupture du béton,” Annales de l'Institut Techn. du Bâtiment et des Travaux Publics, Vol. 18, No. 207–208, 1965, pp. 323–360 (
see also International Conference on the Structure of Concrete, Cement and Concrete Association, London, England, 1968, pp. 423–433).
19.
“Prediction of Creep, Shrinkage and Temperature Effects in Concrete Structures,” Report No. ACI 209 R‐82 by ACI Committee 209, Subcommittee II, chaired by D. J. Carreira, ACI Special Publication SP‐76, “Designing for the Effects of Creep, Shrinkage and Temperature,” Proceedings, A. Pauw Symposium held at ACI Convention, Houston, 1978, American Concrete Institute, Detroit, Mich., 1982, pp. 193–300.
20.
Rostasy, F. S., Teichen, K. Th., and Engelke, H., “Beitrag zur Klärung der Zusammenhanges von Kriechen und Relaxation bei Normal‐beton,” Amtliche Forschungs‐und Materialprüfungsanstalt für das Bauwesen, Otto‐Graf‐Institut, Universität Stuttgart, Strassenbau und Strassenverkehrstechnik, Heft 139, 1972.
21.
Schapery, R. A., “Approximate Methods of Transform Inversion for Viscoelastic Stress Analysis,” Proceedings of the 4th U.S. National Congress of Applied Mechanics, (held at Berkeley, Calif.), Vol. 2, American Society of Mechanical Engineers, 1962, pp. 1075–1085.
22.
Taylor, R. L., Pister, K. S., and Goudreau, G. L., “Thermomechanical Analysis of Viscoelastic Solids,” International Journal of Numerical Methods in Engineering, Vol. 2, 1970, pp. 45–60.
23.
Williams, M. L., “The Structural Analysis of Viscoelastic Materials,” American Institute of Aeronautics and Astronautics, Vol. 2, 1964, pp. 785–808.
24.
Zienkiewicz, O. C., Watson, M., and King, I. P., “A Numerical Method of Viscoelastic Stress Analysis,” International Journal of Mechanical Science, Vol. 10, 1968, pp. 807–827.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 110 • Issue 3 • March 1984
Pages: 329 - 340
Copyright
Copyright © 1984 ASCE.
History
Published online: Mar 1, 1984
Published in print: Mar 1984
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