Modeling of Collapse Mechanisms of Thin Reinforced Concrete Shells
Publication: Journal of Structural Engineering
Volume 121, Issue 1
Abstract
A numerical model based on an elasto-plastic–fracturing formulation is presented to predict the ultimate strength as well as the related mode of failure of thin reinforced concrete (RC) shells. The model defines a safe domain within which the shell would not collapse under the applied load. It predicts two possible modes of failure, which may be broadly classified into bending-type failure and buckling-type failure. Important issues are considered in the model: the effects of holes, reinforcing members, and concentrated loads; and shape deviations due to construction or modeling imperfections. By comparison with analytical solutions as well as experimental observations, the model is shown to lead to reasonably accurate predictions of the main events leading to the failure of RC shells, including the loading path relating the downward vertical displacement to the applied load. From detailed investigations, the relations between the actual mode of failure and the level of the bending force are explained. To provide a shell with the maximum ultimate strength can be dangerous if an inadequately safe domain results.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Basar, Y. (1986). “Zur Struktur konsistenter inkrementeller Theorien für geometrisch-nichtlineare Flächentragwerke und deren Operatordarstellung.”Ingenieurarchiv 56, Int. Report, IKIB IV, N. 122-3; Ruhr Univ., Bochum, West Germany, 209–220 (in German).
2.
Bažant, Z. P.(1978). “Endocronic inelasticity and incremental plasticity.”Int. J. Solid Struct., 9(3), 691–714.
3.
Bažant, Z. P.(1980). “Work inequalities for plastic fracturing materials.”Int. J. Solid Struct., 10(5), 873–901.
4.
Bažant, Z. P., and Kim, S. S.(1979). “Plastic fracturing theory for concrete.”J. Engrg. Mech. Div., ASCE, 105(3), 407–428.
5.
Bažant, Z. P., and Krizek, R. J.(1976). “Endocronic constitutive law for liquefaction of sand.”J. Engrg. Mech. Div., ASCE, 102(1), 701–722.
6.
Bažant, Z. P., and Shieh, C. L.(1980). “Hysteretic fracturing endocronic theory for concrete.”J. Engrg. Mech. Div., ASCE, 106(5), 929–950.
7.
Beem, H., Harte, R., Krätzig, W. B., Ramm, E., and Zhuang, Y. (1981). Finite element models for general structures (Finite Element Moduln Algemeiner Strukturen—FEMAS ). Institut für Konstruktiven Ingenieurbau, Ruhr Univ., Bochum, West Germany (in German).
8.
Bergan, P. G., Horrigmoe, G., Krakeland, B., and Soreide, T. H.(1978). “Solution techniques for nonlinear finite element problems.”Int. J. Numerical Methods in Engrg., 12(3), 1677–1696.
9.
Borri, C., Chiarugi, A., and Foraboschi, P. (1995). “Structural analysis and rehabilitation of reinforced concrete shells.”ACI Struct. J., 92(Mar.-Apr.).
10.
Darwin, D., and Pecknold, D. A.(1977). “Non-linear biaxial stress-strain law for concrete.”J. Engrg. Mech. Div., ASCE, 103(2), 229–241.
11.
Drucker, D. C., and Prager, W.(1952). “Soil mechanics and plastic analysis limit design.”Quart. Appl. Math., 10(1), 157–165.
12.
Gilbert, R. I., and Warner, R. F.(1978). “Tension stiffening in R.C. slabs.”J. Struct. Div., ASCE, 104, 1885–1900.
13.
Harte, R. (1982). “Doppelt gekrümmte finite Dreieckelemente für die lineare und geometrisch nichtlineare Berechnung allgemeiner Flächentragwerke,” PhD thesis, Institute für Konstruktiven Ingenieurbau, Ruhr Univ., Bochum, West Germany.
14.
Harte, R. (1985). “Non-linear arbitrarily curved shell elements.”Int. Report, IKIB III, N. 85-1, Ruhr Univ., Bochum, West Germany.
15.
Harte, R., and Eckstein, U.(1986). “Derivation of geometrically non-linear finite shell elements via tensor notation.”Int. J. Numer. Meth. in Engrg., 23(5), 367–384.
16.
Korn, E., and Korn, H. (1968). Mathematic handbook for scientists and engineers, McGraw-Hill, New York, N.Y.
17.
Krätzig, W. B., and Zahlten, W. (1991). “The application of plastic-fracturing theory to finite element analysis of general reinforced shells.”Communication No. 70-3, Institut für Konstruktiven Ingenieurbau, Ruhr Univ., Bochum, West Germany.
18.
Krätzig, W. B., and Zhuang, Y. (1989). “Non-linear physical and geometrical collapse analysis of cooling towers.”Proc. 3rd Int. Conf. on Nat. Draught Cooling Towers, Paris, France.
19.
Kupfer, H., Hilsdorf, H. K., and Rüsch, H.(1969). “Behavior of concrete under bi-axial stresses.”ACI J., 8(66), 656–666.
20.
Lin, C. S., and Scordelis, A. C.(1975). “Non-linear analysis of reinforced concrete shells of general form.”J. Struct. Div., ASCE, 101(3), 523–538.
21.
Muc, A.(1992). “Buckling and post-buckling behavior of laminated shallow spherical shells subjected to external pressure.”Int. J. Nonlinear Mech., 27(3), 465–476.
22.
Ngo, D., and Scordelis, A.(1967). “Finite element analysis of reinforced concrete beams.”ACI J., 64(3), 152–163.
23.
Prager, W. (1959. An introduction to plasticity . Adison Wesley, New York, N.Y.
24.
Prager, W., and Hodge, P. (1951). Theory of perfect plastic solid . John Wiley, New York, N.Y.
25.
Ramm, E. (1980). “Strategies for tracing nonlinear response near limit points.”Proc. Europe-U.S.A. Workshop on Nonlinear F.E. analysis in Struct. Mech., Springer Verlag, 123–132.
26.
Rashid, Y. R.(1968). “Analysis of prestressed concrete pressure vessels.”Nuclear Engrg. and Design J., 7(4), 334–355.
27.
Risk, E.(1970). “An incremental approach to the solution of snapping and buckling problems.”Int. J. Solid Struct., 15(12), 529–551.
28.
Runge, W., and Kutta, W. (1979). “A contribution to the non-linear computer analysis of cooling towers.”Communication No. 71-4, Institut für Knstruktiven Ingenieurbau, Ruhr Univ., Bochum, West Germany.
29.
Scanlon, A. (1971). “Time dependent deflection of reinforced concrete slabs.”Report No. 22-6, Univ. of Alberta, Edmonton, Alberta.
30.
Schimmels, S. A., and Palazotto, A. N.(1994). “Nonlinear geometric and material behavior of shell structures with large strains.”J. Engrg. Mech., ASCE, 120(2), 320–345.
31.
Singer, J. (1980). Elements of numerical analysis . Academic Press, New York, N.Y., 189.
32.
Sörenson, S. I. (1978). “Endochronic theory in non-linear finite element analysis of reinforced concrete.”Report No. 78-1, Div. of Struct. Mech., Norwegian Inst. of Techn., Univ. of Trondheim, Trondheim, Norway.
33.
Timoshenko, S. (1936). Theory of elastic stability . McGraw-Hill, New York, N.Y.
34.
Wempner, G. A.(1971). “Discrete approximations related to nonlinear theories of solid.”Int. J. Solid Struct., 7(10), 1581–1599.
35.
Wessels, M., (1977). “Das statische und dynamische Durchschlags-problem der imperfekten, flachen Kugelschale.”Mitteilung (Communication) Inst. für Static, T. U. Hannover; No. 23, 11–32.
36.
Yang, H. T. Y., and Wu, Y. C.(1989). “A geometrical nonlinear tensorial formulation of a skewed quadrilateral thin shell element.”Int. J. Numer. Meth. in Engrg., 28(12), 2855–2875.
37.
Yuan, K. Y., and Liang, C. C.(1989). “Nonlinear analysis of an axisymmetric shell using three nodes degenerated isoparametric shell elements.”Comput. & Struct., 32(6), 1225–1239.
38.
Zahlten, W. (1990). “A contribution to the physically and geometrically nonlinear computer analysis of general reinforced concrete shells.”Communication No. 90-2, Institut für Konstruktiven Ingenieurbau, Ruhr Univ., Bochum, West Germany.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 121 • Issue 1 • January 1995
Pages: 15 - 27
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Jan 1, 1995
Published in print: Jan 1995
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.