Membrane Reinforcement in Saddle Shells: Design versus Ultimate Behavior
Publication: Journal of Structural Engineering
Volume 112, Issue 4
Abstract
In current practice, stresses from elastic analysis are used to design reinforcement in concrete shells based on pointwise limit state behavior. This practice may be justified in view of the lower bound theorem of plasticity and the fact that elastic stresses are equilibrium stresses. Reinforced concrete, however, is not a perfectly plastic material, and the lower bound theorem cannot be strictly applied. To verify the adequacy of current practice, therefore, an analytical program was undertaken at North Carolina State Univ. A finite element computer program, which accounts for cracking of concrete and yielding of reinforcement, and that incorporates a cracking model consistent with the limit state design equations, was developed. The program was used to analyze various plane stress and shell problems. Many cases of hyperbolic paraboloid shells were also studied and are reported in this paper. It is shown that in all the saddle shell cases analyzed, the calculated ultimate capacity exceeded the design ultimate capacity. This proves the adequacy of the current practice at least for the saddle shells studied. Other conclusions of the parametric studies performed are also presented.
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References
1.
Akbar, H., and Gupta, A. K., “Membrane Reinforcement in Concrete Shells; Design Versus Nonlinear Behavior,” Report, Department of Civil Engineering, North Carolina State Univ., Jan., 1985. (Also available through University Microfilm International as Ph.D. thesis presented by H. Akbar to North Carolina State Univ. at Raleigh, 1985.)
2.
Akbar, H., and Gupta, A. K., “Ultimate Behavior of an R.C. Nuclear Containment Subjected to Internal Pressure and Earthquake,” Journal of Structural Engineering, ASCE, to be published.
3.
“Building Code Requirements for Reinforced Concrete (ACI 318‐83),” American Concrete Institute, Committee 318, Detroit, MI, 1983.
4.
Brotchie, J. F., Beresford, F. D., and Leicester, R. H., “Design, Construction and Performance of Post‐Tensioned Hyperbolic Paraboloid Shell,” Australian Construction Review, Vol. 44, No. 1, Feb., 1971, pp. 68–74.
5.
“Finite Element Analysis of Reinforced Concrete Structures,” Report, American Society of Civil Engineers, 1982.
6.
Gupta, A. K., “Membrane Reinforcement in Shells,” Journal of the Strucural Engineering Division, ASCE, Vol. 107, No. ST1, Jan., 1981, pp. 41–56.
7.
Gupta, A. K., “Membrane Reinforcement in Concrete Shells: A Review,” Nuclear Engineering and Design, Vol. 82, Oct., 1984, pp. 63–75.
8.
Gupta, A. K., and Akbar, H., “A Finite Element for the Analysis of Reinforced Concrete Structures,” Int. J. Num. Math. Eng., Vol. 19, 1983, pp. 1705–1712.
9.
Gupta, A. K., and Akbar, H., “Cracking in Reinforced Concrete Analysis,” Journal of Structural Engineering, ASCE, Vol. 110, Aug., 1984, pp. 1735–1746.
10.
Gupta, A. K., and Maestrini, S., “An Investigation on the Ultimate Behavior of Hyperbolic Cooling Towers,” Report, Department of Civil Engineering, North Carolina State Univ., Feb., 1985. (To be published in Engineering Structures.)
11.
Lin, C. S., “Nonlinear Analysis of Reinforced Concrete Slabs and Shells,” UC‐SESM Report No. 73‐7, Univ. of California, Berkeley, 1973.
12.
Lin, C. S., and Scordelis, A. C., “Nonlinear Analysis of RC Shells of General Forms,” Journal of the Structural Engineering Division, ASCE, Vol. 101, No. ST3, Mar., 1975, pp. 523–538.
13.
Lo, K. S., and Scordelis, A. C., “Design of a 271 Ft. Span Prestressed HP Shell,” Proceedings, International Colloquium on Progress of Shell Structures in the Last Ten Years (Madrid 1969), International Association for Shell Structures, Madrid, 1970.
14.
Long, J. E., “Experimental Investigation of the Effect of Edge Stiffening on a Square Hyperbolic Paraboloid Shell,” Technical Report TRA 400, Cement and Concrete Association, London, Dec., 1966, pp. 1–48.
15.
Mueller, G., “Nonlinear Analysis of Reinforced Concrete Hyperbolic Paraboloid Shells,” UC‐SESM Report No. 77‐6, Univ. of California, Berkeley, 1977.
16.
Rowe, R. E., “Tests on Four Types of Hyperbolic Paraboloid Shells,” Proceedings, Symposium on Shell Research (Delft, 1961), Wiley Interscience, New York, and North‐Hollarid Publishing Company, Amsterdam, 1961, pp. 16–35.
17.
Shaaban, A., and Ketchum, M. S., “Design of Hipped Hypar Shells,” Journal of the Structural Engineering Division, ASCE, Vol. 102, No. ST11, Paper 2543, Nov., 1976, pp. 2151–2161.
18.
Schnobrich, W. C., “Analysis of Hipped Roof Hyperbolic Paraboloid Structures,” Journal of the Structural Engineering Division, ASCE, Vol. 98, No. ST7, Paper 9052, July, 1972, pp. 1575–1583.
19.
Schnobrich, W. C., Mohraz, B., and Hoebel, J. L., “Influence of Edge Beam Properties on the Stress in Hyperbolic Parabolas,” Proceedings, International Colloquim on Progress of Shell Structures in the Last Ten Years (Madrid 1969), International Association for Shell Structures, Madrid, 1970.
20.
Scordelis, A. C., and Ketchum, M. A., “Structural Behavior and Design of Saddle HP Shells,” Proceedings of IASS World Congress, Madrid, Spain, Vol. 2, Sept., 1979.
21.
Thurman, A. G., and Herman, G. J., “Model Studies of a Concrete Hyperbolic Paraboloid,” Proceedings, ASCE, Vol. 88, No. ST6, Dec., 1962, pp. 161–181.
22.
White, R. N., “Reinforced Concrete Hyperbolic Paraboloid Shells,” Journal of the Structural Engineering Division, ASCE, Vol. 101, No. ST9, Sept., 1975, pp. 1961–1979.
Information & Authors
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Published In
Journal of Structural Engineering
Volume 112 • Issue 4 • April 1986
Pages: 800 - 814
Copyright
Copyright © 1986 ASCE.
History
Published online: Apr 1, 1986
Published in print: Apr 1986
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