Nonlinear Analysis of Prestressed Concrete Slabs
Publication: Journal of Structural Engineering
Volume 109, Issue 7
Abstract
An efficient numerical procedure for the material and geometric nonlinear analysis of reinforced and prestressed concrete slabs and panels including the time‐dependent effects due to load history, temperature history, creep, shrinkage and aging of the concrete and relaxation of prestress is developed. The procedure, based on the finite element method, is capable of predicting the response of these structures throughout their service load history as well as throughout elastic, cracking, inelastic and ultimate load ranges. An updated Lagrangian formulation is employed to take the effects of changing structural geometry on the response of planar structures into account. Slabs or panels having an arbitrary tendon layout with either pretensioned, or bonded or unbonded post‐tensioned tendons can be analyzed. Two numerical examples are presented to study the validity and applicability of the present method. The results obtained are compared with experimental and/or analytical results obtained by other investigators.
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References
1.
Aoyama, H., and Noguchi, H., “Mechanical Properties of Steel and Concrete under Load Cycles Idealizing Seismic Actions. Studies of Bond between Concrete and Steel: b) Concrete,” AICAP‐CEB Symposium, Rome, May, 1979.
2.
Agryris, J. H., et al., “Analysis of Prestressed Concrete Reactor Vessels,” Paper H1/1, 2nd International Conference on Structural Mechanics in Reactor Technology, Berlin, West Germany, Sept., 1973.
3.
Arnesen, A., Sorenson, S. I., and Bergan, P. G., “Nonlinear Analysis of Reinforced Concrete,” International Conference on Engineering Application of the Finite Element Method, Oslo, Norway, May, 1979.
4.
Aroni, S., “Slender Prestressed Concrete Columns,” Journal of the Structural Division, ASCE, Vol. 94, No. ST4, Apr., 1968.
5.
Bell, J. C., and Elms, D., “Partially Cracked Finite Elements,” Journal of the Structural Division, ASCE, Vol. 97, No. ST7, July, 1971.
6.
Bell, J. C., and Elms, D. G., “A Finite Element Post Elastic Analysis of Reinforced Concrete Shells,” Bulletin of the International Association for Shell and Spatial Structures, No. 54, Apr., 1974.
7.
Berg, S., “Nonlinear Finite Element Analysis of Reinforced Concrete Plates,” Report No. 73‐1, Institutt for Statikk, Division of Structural Mechanics, University of Trondheim, Norway, Feb., 1973.
8.
Branson, D. E., and Christiason, M. L., “Time‐Dependent Concrete Properties Related to Design—Strength and Elastic Properties, Creep and Shrinkage,” Symposium on Creep, Shrinkage and Temperature Effects, ACI Special Publication SP‐27, Detroit, Mich., 1971, pp. 257–277.
9.
Darwin, D., and Pecknold, D. A., “Analysis of Reinforced Concrete Shear Panels under Cyclic Loading,” Journal of the Structural Division, ASCE, Vol. 102, No. ST2, Feb., 1976, pp. 355–369.
10.
Darwin, D., and Pecknold, D. A., “Nonlinear Biaxial Stress‐Strain Law for Concrete,” Journal of the Engineering Mechanics Division, ASCE, Vol. 103, No. EM2, Apr., 1977, pp. 229–241.
11.
Dotroppe, J. C., Schnobrich, W. C., and Pecknold, D. A., “Layered Finite Element Procedure for Inelastic Analysis of Reinforced Concrete Slabs,” IABSE Publication 33‐11, 1973.
12.
Hand, F. R., Pecknold, D. A., and Schnobrich, W. C., “Nonlinear Layered Analysis of Reinforced Concrete Plates and Shells,” Journal of the Structural Division, ASCE, Vol. 99, No. ST7, July, 1973.
13.
Hawkins, N. M., and Mitchell, D., “Progressive Collapse of Flat Plate Structures,” ACI Journal, Vol. 76, No. 7, July, 1979, pp. 775–808.
14.
Horrigmoe, G., “Finite Element Instability Analysis of Free‐Form Shells,” thesis presented to the University of Trondheim, Norway, in 1977, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
15.
Huang, T., “Anchorage Take‐up Loss in Post‐Tensioned Members,” PCI Journal, Vol. 14, No. 4, Aug., 1969, pp. 30–35.
16.
Irons, B. M., and Razzaque, A., “Shape Function Formulation for Elements other than Displacements Models,” Proceedings of the International Conference on Variational Methods of Engineering, Southhampton, 1972, pp. 4/59–4/72.
17.
Jofriet, J. C., and McNeice, G. M., “Finite Element Analysis of Reinforced Concrete Slabs,” Journal of the Structural Division, ASCE, Vol. 97, No. ST3, Mar., 1971.
18.
Kabir, A. F., “Nonlinear Analysis of Reinforced Concrete Panels, Slabs and Shells for Time Dependent Effects,” US‐SESM Report No. 76‐6, Division of Structural Engineering and Structural Mechanics, University of California, Berkeley, Calif., Dec., 1976.
19.
Kabir, A. F., and Scordelis, A. C., “Analysis of RC Shells for Time Dependent Effects,” Bulletin of the International Association for Shell and Spatial Structures, Vol. XXI, No. 69, Apr., 1979.
20.
Kang, Y. J., “Nonlinear Geometric, Material and Time Dependent Analysis of Reinforced and Prestressed Concrete Frames,” UC‐SESM Report No. 77‐1, Division of Structural Engineering and Structural Mechanics, University of California, Berkeley, Calif., Jan., 1977.
21.
Kang, Y. J., and Scordelis, A. C., “Nonlinear Analysis of Prestressed Concrete Frames,” Journal of the Structural Division, ASCE, Vol. 106, No. ST2, Feb., 1980.
22.
Kristjansson, R., “Physikalisch and Geometrisce nichtlineare Berechnung von Stahlbetonplatten mit Hilfe Finiter Elemente,” thesis presented to the University of Darmstadt, at Darmstadt, West Germany, in 1977, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
23.
Lin, C. S., and Scordelis, A. C., “Nonlinear Analysis of Reinforced Concrete Shells of General Form,” Journal of the Structural Division, ASCE, Vol. 101, No. ST3, Mar., 1975.
24.
Lin, T. Y., Design of Prestressed Concrete Structures, 2nd ed., John Wiley and Sons, New York, N.Y., 1963.
25.
Magura, D. D., Sozen, M. A., and Siess, C. P., “A Study of Stress Relaxation in Prestressing Reinforcement,” PCI Journal, Vol. 9, No. 2, Apr., 1964.
26.
Murray, D. W., and Wilson, E. L., “Finite Element Large Deflection Analysis of Plates,” Journal of the Engineering Mechanics Division, ASCE, Vol. 95, No. EM1, Feb., 1969, pp. 143–165.
27.
“Prediction of Creep, Shrinkage and Temperature Effects in Concrete Structures,” ACI Committee 209, Paper SP 27‐3, ACI Special Publications SP‐27, American Concrete Institute, Detroit, Mich., Apr., 1970.
28.
Razzaque, A., “Program for Triangular Bending Elements with Derivative Smoothing,” International Journal of Numerical Methods of Engineering, Vol. 6, 1973, pp. 333–343.
29.
Scanlon, A., and Murray, D. W., “Time Dependent Reinforced Concrete Slab Deflections,” Journal of the Structural Division, ASCE, Vol. 100, No. ST9, Sept., 1974.
30.
Schnobrich, W. C., “Behavior of Reinforced Concrete Predicted by Finite Element Method,” Proceedings of the Second National Symposium on Computerized Structural Analysis and Design, George Washington University, Washington, D.C., Mar., 1976.
31.
Scordelis, A. C., “Finite Element Analysis of Reinforced Concrete Structures,” Proceedings of the Specialty Conference, on Finite Element Methods in Civil Engineering, Montreal, June, 1972.
32.
Scordelis, A. C., “General Report—Basic Problems,” Proceedings, IASS Symposium on Nonlinear Behavior of Reinforced Concrete Spatial Structures, Darmstadt, West Germany, July, 1978.
33.
Scordelis, A. C., Lin, T. Y., and Itaya, R., “Behavior of a Continuous Slab Prestressed in Two Directions,” ACI Journal, Vol. 56, No. 6, Dec., 1959, pp. 441–459.
34.
“Shear in Reinforced Concrete,” ACI Special Publication SP‐42, American Concrete Institute, Detroit, Mich., 1974.
35.
Van Greunen, J., “Nonlinear Geometric Material and Time‐Dependent Analysis of Reinforced and Prestressed Concrete Slabs and Panels,” UC‐SESM Report No. 79‐3, Division of Structural Engineering and Structural Mechanics, University of California, Berkeley, Calif., Oct., 1979.
36.
Van Zyl, S. F., “Analysis of Curved Segmentally Erected Prestressed Concrete Box Girder Bridges,” Report No. UC‐SESM 78‐2, Division of Structural Engineering and Structural Mechanics, University of California, Berkeley Calif., Jan., 1978.
37.
Van Zyl, S. F., and Scordelis, A. C., “Analysis of Curved Prestressed Segmental Bridges,” Journal of the Structural Division, ASCE, Vol. 105, No. ST11, Nov., 1979.
38.
Wegner, R., “Finite Element Models for Reinforced Concrete,” Proceedings of the U.S.‐Germany Symposium on Formulations and Computational Methods in Finite Element Analysis, Massachusetts Institute of Technology, Cambridge, Mass., Aug., 1976.
39.
Wegner, R., and Duddeck, H., “Der Gerissenen Zustand Zweisetig Elagerter Platten unter Einzellasten—Nichtlineare Berechnung mit Finiter Elementen,” Beton and Stahlbetonbau, 70, 1975.
40.
Zienkiewicz, O. C., Owen, D. R. J., and Phillips, D. W., “Finite Element Method in Analysis of Reinforced and Concrete Structures,” Paper M1/1, 1st International Conference on Structural Mechanics in Reactor Technology, Berlin, West Germany, Sept., 1971.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 109 • Issue 7 • July 1983
Pages: 1742 - 1760
Copyright
Copyright © 1983 ASCE.
History
Published online: Jul 1, 1983
Published in print: Jul 1983
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