Membrane Behavior of R/C Shell Element and Limits on Reinforcement
Publication: Journal of Structural Engineering
Volume 114, Issue 2
Abstract
The behavior of reinforced concrete (R/C) shell elements subjected to membrane stresses is examined. The governing equations are derived from equilibrium, compatibility, and the constitutive law of reinforced concrete under biaxial stress states. Using these equations, load‐deformation relations of membrane elements are traced up to and past the ultimate load. There are three types of failure modes: (1) Yielding of reinforcement in both directions; (2) yielding of reinforcement in only one direction combined with the compressional failure of concrete; and (3) the failure of concrete without the yielding of any reinforcement. Using an analogy with beams in flexure, it is shown that the element behavior is ductile for the first two modes and brittle for the last mode. One of the major factors that influences the failure mode is the amount of reinforcement. Two sets of boundaries that separate the three different failure modes are identified in terms of reinforcement ratios. One set of boundaries separates the first two failure modes. This set defines the limit of reinforcement beyond which a commonly used strength formula based on the yielding of reinforcement alone is not valid. The other set, which separates the last two failure modes, defines the limit beyond which the element behavior is brittle. These boundaries are presented in a form suitable for use as design guides.
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References
1.
Akbar, H., and Gupta, A. K. (1986a). “Membrane reinforcement in saddle shells: Design versus ultimate behavior.” J. Struct. Engrg., ASCE, 112(4), 800–814.
2.
Akbar, H., and Gupta, A. K. (1986b). “Ultimate behavior of an R. C. nuclear containment subjected to internal pressure and earthquake.” J. Struct. Engrg., ASCE, 112(6), 1280–1295.
3.
Brondum‐Nielsen, T. (1974). “Optimum design of reinforced concrete shells and slabs.” Report No. R44, Structural Research Laboratory, University of Denmark, Copenhagen, Denmark.
4.
Building code requirements for reinforced concrete. (1983). Committee 318, American Concrete Institute, Detroit, Mich.
5.
Collins, M. P. (1978). “Toward a rational theory for RC members in shear.” J. Struct. Div., ASCE, 104(4), 649–666.
6.
“Concrete shell structures—Practice and commentary.” (1964). ACI J., Committee 334, 61(9), 1091–1108.
7.
Fialkow, M. N. (1983). “Strength design of shell membrane reinforcement.” J. Struct. Engrg., ASCE, 109(4), 891–908.
8.
Fialkow, M. N. (1985). “Design and capacity evaluation of reinforced concrete shell membranes.” ACI J., 82(6), 844–852.
9.
Grob, J., and Thurliman, B. (1976). “Ultimate strength and design of reinforced concrete beams under bending and shear.” IABSE Publication, 36(11), 105–120.
10.
Gupta, A. K., “Discussion on proposed addition to proposed ACI standard; code requirements for nuclear safety related concrete structures.” ACI J., 37(7), 431–432.
11.
Gupta, A. K. (1978). “Skew reinforcement in slabs.” J. Struct. Div., ASCE, 104(8), 1317–1321.
12.
Gupta, A. K. (1981). “Membrane reinforcement in shells.” J. Struct. Div., ASCE, 107(1), 41–56.
13.
Gupta, A. K. (1984). “Membrane reinforcement in concrete shells: A review.” Nuclear Engrg. and Design, 82, Oct., 63–75.
14.
Gupta, A. K., and Sen, S. (1977). “Design of flexural reinforcement in concrete slabs.” J. Struct. Div., ASCE, 103(4), 793–804.
15.
Hsu, T. T. C. (1984). Torsion of reinforced concrete, Van Nostrand Reinhold Company, New York, N.Y.
16.
Hsu, T. T. C., and Mo, Y. L. (1985). “Softening of concrete in torsional members—Theory and tests.” ACI J., 81(3), 290–303.
17.
Hsu, T. T. C., Mau, S. T., and Chen, B. (1987). “Theory of shear transfer strength of reinforced concrete.” ACI J., 84(2), 149–160.
18.
Lin, C. S., and Scordelis, A. C. (1975). “Nonlinear analysis of RC shells of general form.” J. Struct. Div., ASCE, 101(3), 523–538.
19.
Mau, S. T., and Hsu, T. T. C. (1986). “Shear design and analysis of low‐rise structural walls.” ACI J., 83(2), 306–315.
20.
Nielsen, M. P., Braestrup, M. W., and Bach, F. (1978). “Rational analysis of shear in reinforced concrete beams.” IABSE Proc., P‐15, May.
21.
“Reinforced concrete cooling tower shells—Practice and commentary.” 1984. ACI J., Committee 334, 81(6), 623–631.
22.
Vecchio, F., and Collins, M. P. (1981). “Stress‐strain characteristics of reinforced concrete in pure shear.” Final Report, IABSE Colloquim on Advanced Mechanics of Reinforced Concrete, Delft, Netherlands, 211–225.
23.
Vecchio, F., and Collins, M. P. (1982). “The response of reinforced concrete to in‐plane shear and normal stresses.” Publication No. 82‐03, University of Toronto, Department of Civil Engineering, Toronto, Canada, Mar.
24.
Vecchio, F., and Collins, M. P. (1986). “The modified compression‐field theory for reinforced concrete elements subjected to shear.” ACI J., 83(2), 219–231.
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Copyright © 1988 ASCE.
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Published online: Feb 1, 1988
Published in print: Feb 1988
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