Creep in Continuous Beam Built Span‐by‐Span
Publication: Journal of Structural Engineering
Volume 109, Issue 7
Abstract
The long‐term variation of bending moment distribution caused by creep in a continuous beam erected sequentially in span‐length sections with overhangs is analyzed. A linear aging creep law is assumed. The problem involves changes of the structural system from statically determinate to indeterminate, a gradual increase in the number of redundant moments, and age differences between various cross sections. A system of Volterra integral equations for the history of support bending moments is derived. By considering infinitely many equal spans, which is good enough whenever there are more than a few spans, one can take advantage of a periodicity condition for the construction cycle; this reduces the problem to a single equation which is of a novel type in creep theory—an integral‐difference equation involving time lags in the integrated unknown. The solution exhibits sudden jumps at times equal to multiples of the construction cycle. The jumps decay with time roughly in a geometric progression. Approximation of time integrals with finite sums yields a large system of simultaneous linear algebraic equations. These equations cannot be solved recurrently, step‐by‐step. By solving the large equation system with a computer, the effects of the duration of the construction cycle, of concrete age at assembly of span from segments, and of the overhang length are studied numerically.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Anderson, C. A., “Numerical Creep Analysis of Structures,” Creep and Shrinkage in Concrete Structures, Z. P. Bažant and F. H. Wittmann, eds., J. Wiley & Sons, London, England, 1982, pp. 259–304.
2.
Anderson, C. A., Smith, P. D., and Carruthers, L. M., “NONSAP‐C‐A Nonlinear Stress Analysis Program for Concrete Containments under Static, Dynamic and Long‐Term Loadings,” Report NUREG/CR‐0416, LA‐7496‐MS, rev. 1, R7 and R8, Los Alamos National Laboratory, Los Alamos, New Mexico, Jan., 1982 (available from NTIS, Springfield, Va.).
3.
Bažant, Z. P., “Mathematical Modeling of Creep and Shrinkage in Concrete,” Creep and Shrinkage in Concrete Structures, Z. P. Bažant and F. H. Wittmann, eds., J. Wiley & Sons, London, England, 1982, pp. 163–256.
4.
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.
5.
Bažant, Z. P., and Chern, J. C., “Log Double Power Law for Concrete Creep,” Center for Concrete and Geomaterials, Northwestern University, Evanston, Ill., 1983.
6.
Bažant, Z. P., and Kim, S. S., “Approximate Relaxation Function for Concrete,” Journal of the Structural Division, Proceedings, ASCE, Vol. 105, 1979, pp. 2697–2705.
7.
Bažant, Z. P., and Najjar, L. J., “Comparison of Approximate Linear Methods for Concrete Creep,” Journal of the Structural Division, Proceedings, Vol. 99, No. ST9, 1973, pp. 1851–1874.
8.
Bažant, Z. P., and Ong, J. S., “Numerical Analysis of Creep Effects in Infinitely Long Continuous Beam Constructed Span‐By‐Span,” Report 81‐12/665n, Center for Concrete and Geomaterials, Northwestern University, Evanston, Ill., Dec., 1981.
9.
Bažant, Z. P., and Osman, E., “Double Power Law for Basic Creep of Concrete,” Materials and Structures, Vol. 9, No. 49, 1976, pp. 3–11.
10.
Bažant, Z. P., and Panula, L., “Creep and Shrinkage Characterization for Analyzing Prestressed Concrete Structures,” Prestressed Concrete Institute Journal, Vol. 25, No. 3, May–June, 1980, pp. 86–122.
11.
Bažant, Z. P., and Panula, L., “Practical Prediction of Time‐Dependent Deformation of Concrete,” Materials and Structures, Parts I and II: Vol. 11, No. 65, 1978, pp. 307–328;
Parts III and IV: Vol. 11, No. 66, 1978, pp. 415–434;
Parts V and VI: Vol. 12, No. 69, 1979, pp. 169–183.
12.
Bažant, Z. P., Rossow, E. C., and Horrigmoe, G., “Finite Element Program for Creep Analysis of Concrete Structures,” Proceedings, 6th International Conference on Structural Mechanics in Reactor Technology (SMiRT6), Paris, Aug., 1981, also program “CREEP80,” Report to Oak Ridge National Laboratory, Aug., 1981, available from National Technical Information Service, Springfield, Va.
13.
Dilger, W. H., “Method of Structural Creep Analysis,” Creep and Shrinkage in Concrete Structures, Z. P. Bažant and F. H. Wittmann, eds., J. Wiley & Sons, London, England, 1982, pp. 305–340.
14.
“Finite Element Analysis of Reinforced Concrete,” Time Dependent Effects, ASCE, New York, N.Y., 1982, pp. 309–400.
15.
Gallway, T. M., “Design Feature and Prestress Aspect of Long Key Bridge,” Prestressed Concrete Institute Journal, Vol. 25, No. 6, 1980, pp. 84–96.
16.
Huet, C., “Application of Bažant's Algorithm to the Analysis of Viscoelastic Composite Structures,” Materials and Structures, (RILEM, Paris), Vol. 13, No. 74, 1980, pp. 91–98.
17.
Kang, Y. J., “Nonlinear Geometric, Material and Time Dependent Analysis of Reinforced and Prestressed Concrete Frames,” Report No. UC‐SESM77‐1, Division of Structural Engineering and Structural Mechanics, University of California at Berkeley, Calif., Jan., 1977.
18.
Kang, Y. J., and Scordelis, A. C., “Nonlinear Analysis of Prestressed Concrete Frames,” Proceedings, ASCE, Journal of the Structural Division, Vol. 106, No. ST2, Feb., 1980.
19.
Marshall, V., and Gamble, W. L., “Time‐Dependent Deformations in Sequential Prestressed Concrete Bridges,” Report No. UILU‐EMG‐81‐2014, SRS‐495 (to Illinois Department of Transportation, No. FHWA/IL/UI‐192), Contract IHR‐307), Department of Civil Engineering, University of Illinois, Urbana, Ill., Oct., 1981.
20.
Muller, J., “Construction of Long Key Bridge,” Prestressed Concrete Institute Journal, Vol. 25, No. 6, 1980, pp. 97–111.
21.
Neville, A. M., and Dilger, W., Creep of Concrete: Plain, Reinforced and Prestressed, North‐Holland Publication Co., Amsterdam, 1970.
22.
“Prediction of Creep, Shrinkage and Temperature Effects in Concrete Structures,” ACI‐SP27, Designing for Effects of Creep, Shrinkage and Temperature, American Concrete Institute, Detroit, Mich., 1971, pp. 51–93.
23.
Reference 2, revised ed., ACI Committee 209/II, “Designing for Creep and Shrinkage in Concrete Structures,” American Concrete Institute, SP‐76, Detroit, Mich., 1982.
24.
Schade, D., and Haas, W., “Electronische Berechnung der Auswirkungen von Kriechen und Schwinden bei abschnittsweise hergestellten Verbundstabwerken,” Dentscher Ausschuss für Stahlbeton, Heft 244, W. Ernst & Sohn, Berlin, 1975.
25.
Trost, H., and Wolff, H. J., Zur Wirklichkeitsnahen Ermittlung der Beauspruchungen in abschnittsweise hergestellten Spannbetontragwerken, Der Bauingenieur, Vol. 45, May, 1970, pp. 155–169.
26.
VanZyl, S. F., “Analysis of Curved Segmentary Erected Prestressed Con‐crete Box Girder Bridges,” Report No. UC‐SESM 78‐2, Division of Structural Engineering and Structural Mechanics, University of California, Berkeley, Calif., Jan., 1978.
27.
VanZyl, S. F., and Scordelis, A. C., “Analysis of Curved Prestressed Segmental Bridges,” Journal of the Structural Division, Proceedings, Vol. 105, No. ST11, Nov., 1979.
Information & Authors
Information
Published In
Copyright
Copyright © 1983 ASCE.
History
Published online: Jul 1, 1983
Published in print: Jul 1983
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.