Spectral Analysis of Random Shrinkage Stresses in Concrete
Publication: Journal of Engineering Mechanics
Volume 110, Issue 2
Abstract
Random variation of environmental humidity is characterized by its power spectrum, and random variation of pore humidity and stresses in a half‐space is analyzed under the assumption that the problem is linear (or linearized). The diffusion equation and the superposition integral for stress relaxation are used. The dependence of both the creep properties and the drying diffusivity on age is taken into account. Complex variable expressions for the frequency response functions of humidity and stress are obtained and are evaluated numerically. In contrast to nonaging structures, these functions depend on both the current age of concrete and the age when drying starts. The standard deviations of pore humidity and of stress exhibit oscillations about a drifting mean. For typical diffusivities of concrete, the solution is nonstationary for at least 5O yr, and for environmental fluctuations whose period does not exceed one year, the fluctuations are not felt at depths over 20 cm below the surface. Since, even for aging structures, the spectral densities of input and response are related algebraically, the spectral method is computationally more efficient than the impulse response function method, in which the autocorrelation functions of the input and the response are related by integrals.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bažant, Z. P., “Theory of Creep and Shrinkage in Concrete Structures: A Précis of Recent Developments,” Mechanics Today, Vol. 2, Pergamon Press, New York, N.Y., 1975, pp. 1–93.
2.
Bažant, Z. P., “Mathematical Models for Creep and Shrinkage of Concrete,” Chpt. 7 in Creep and Shrinkage in Concrete Structures, Z. P. Bažant and F. H. Wittmann, eds., J. Wiley, London, 1982, pp. 163–256.
3.
Bažant, Z. P., “Response of Aging Linear Systems to Random Input,” Concrete and Geomaterials Report No. 82‐12/665r, Northwestern University, Evanston, Ill., Dec., 1982.
4.
Bažant, Z. P., “Probabilistic Problems in Prediction of Creep and Shrinkage Effects in Structures,” Proceedings, 4th International Conference on Application of Statistics and Probability in Soil and Structural Engineering, Florence, Italy, June, 1983, pp. 325–356.
5.
Bažant, Z. P., and Asghari, A., “Computation of Age‐Dependent Relaxation Spectra,” Cement & Concrete Research, Vol. 4, 1974, pp. 567–579.
6.
Bažant, Z. P., and Najjar, L. J., “Nonlinear Water Diffucion in Nonsaturated Concrete,” Materials and Structures, Paris, France, Vol. 5, 1972, pp. 3–20.
7.
Bažant, Z. P., and Wu, S. T., “Creep and Shrinkage Law for Concrete at Variable Humidity,” Journal of the Engineering Mechanics Division, ASCE, Vol. 100, No. EM6, Dec., 1974, pp. 1183–1207.
8.
Bažant, Z. P., and Wu, S. T., “Rate‐Type Creep Law of Aging Concrete Based on Maxwell Chain,” Materials and Structures, Paris, France, Vol. 7, No. 37, 1974, pp. 45–60.
9.
Bažant, Z. P., Carreira, D., and Walser, A., “Creep and Shrinkage in Reactor Containment Shells,” Journal of the Structural Division, ASCE, Vol. 101, 1975, pp. 1997–2004.
10.
Carslaw, H. S., and Jaeger, J. C., Conduction of Heat in Solids, 2nd ed., Clarendon Press, Oxford, 1959.
11.
Crandall, S. H., Random Vibration in Mechanical Systems, Academic Press, New York, N.Y., 1963.
12.
“Finite Element Analysis of Reinforced Concrete,” State‐of‐the‐Art Report by ASCE Structural Division Task Committee, chaired by A. Nilson, ASCE, New York, 1982, pp. 309–400.
13.
Heller, R. A., “Temperature Response of an Infinitely Thick Slab to Random Surface Temperatures,” Mechanics Research Communication, Vol. 3, 1976, pp. 379–385.
14.
Heller, R. A., “Thermal Stress as a Narrow‐Band Random Load,” Journal of the Engineering Mechanics Division, ASCE, Vol. 102, No. EMS, Oct., 1976, pp. 787–805.
15.
Papoulis, A., Probability, Random Variables and Stochastic Processes, McGraw‐Hill, New York, N.Y., 1965.
16.
Tsubaki, T., and Bažant, Z. P., “Random Shrinkage Stresses in Aging Viscoelastic Vessel,” Journal of the Engineering Mechanics Division, ASCE, Vol. 108, No. EM3, June, 1982, pp. 527–545.
17.
Wierig, H. J., “Die Wasserdampfdurchlässigheit von Zementmörtel und Beton,” Zement‐Kalk‐Gips, Nov., 1965, No. 9, pp. 47–482.
18.
Zhu, B. F., Wang, T. S., et al., “Temperature Stresses and Temperature Control in Hydraulic Concrete Structures,” Water Power Press, Beijing, China, 1976 (in Chinese).
Information & Authors
Information
Published In
Copyright
Copyright © 1984 ASCE.
History
Published online: Feb 1, 1984
Published in print: Feb 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.