TECHNICAL PAPERS
May 1, 1986

Time‐Dependent Cyclic Deflections in R/C Beams

Publication: Journal of Structural Engineering
Volume 112, Issue 5

Abstract

A numerical integration method to predict the time‐related deflections of reinforced concrete beams, which includes cyclic loading and unloading, is presented. It requires little computer storage capacity. The major aspects of this method include the time‐dependent strains in the stress‐strain relationships for concrete compression and tension in terms of the creep coefficient, the creep‐moment‐curvature relationships, the deflection‐creep coefficient diagrams, and shrinkage deflections. Variations in the flexural stiffness caused by cracking are accounted for in the tension stress‐strain relationship in terms of maximum tensile stress. By applying the principle of strain superposition, the effect of loading history on the beam is incorporated into the creep coefficient for the specific concrete age at which deflection is desired. Deflections are determined from the deflection‐creep coefficient diagrams. The procedure eliminates the inconsistency in the zero strain surface location caused by superimposing deflection components from loading and unloading. Comparisons between the calculated deflections and test data from beams under cyclic loading and unloading are very good.

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References

1.
Bažant, Z., and Kim, S. S., “Nonlinear Creep of Concrete—Adaptation and Flow,” Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM3, June, 1979, pp. 429–446.
2.
Bažant, Z. P., and Panula, L., “Practical Prediction of Time‐Dependent Deformations of Concrete,” Materials and Structures, Vol. 11, No. 65, 1978, pp. 307–328, 415–434,
Vol. 12, No. 69, 1979, pp. 169–183.
3.
Branson, D. E., “Instantaneous and Time‐Dependent Deflections of Simple and Continuous Reinforced Concrete Beams,” Report No. 7, Part I, Alabama Highway Research Department, Bureau of Public Roads, Aug., 1965, pp. 1–78.
4.
Branson, D. E., Deformation of Concrete Structures, McGraw‐Hill Book Company, New York, 1977.
5.
“Building Code Requirements for Reinforced Concrete,” ACI 318‐83, American Concrete Institute, Committee 318, Detroit, Mich., 1983.
6.
Carreira, D. J., and Chu, K.‐H., “Stress‐Strain Relationship for Plain Concrete in Compression.” ACI Journal, Proceedings Vol. 82, No. 6, Nov.–Dec. 1985, pp. 797–804.
7.
Carreira, D. J., and Chu, K.‐H., “The Moment‐Curvature Relationship of Reinforced Concrete Members,” ACI Journal, Proceedings Vol. 83, No. 2, Mar.–Apr. 1986, pp. 191–198.
8.
Carreira, D. J., and Chu, K.‐H., “Stress‐Strain Relationship for Reinforced Concrete in Tension,” ACI Journal, Proceedings Vol. 83, No. 1, Jan.–Feb. 1986, pp. 21–28.
9.
Helgason, T., “Time Dependent Deformation in Plain Concrete and in Reinforced Concrete Beams,” thesis, presented to Illinois Institute of Technology, in Chicago, Ill., in 1973, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
10.
McHenry, D., “A New Aspect of Creep in Concrete and Its Application to Design,” Proceedings, American Society for Testing and Materials, Vol. 43, 1943, pp. 1069–1084.
11.
“Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures,” ACI 209R‐82 Report, ACI SP‐76, Designing for Creep and Shrinkage in Concrete Structures, American Concrete Institute, Committee 209, Detroit, Mich., 1982, pp. 199–300.

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 112Issue 5May 1986
Pages: 943 - 959

History

Published online: May 1, 1986
Published in print: May 1986

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Kuang‐Han Chu, F. ASCE
Prof. Emeritus of Civ. Engrg., Illinois Inst. of Tech., Chicago, IL 60616
Domingo J. Carreira, M. ASCE
Engrg. Specialist, Sargent and Lundy Engrs., Chicago, IL 60603; and Adjunct Assoc. Prof., Illinois Inst. of Tech., Chicago, IL 60616

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