The present paper investigates structural response and buckling of long unstiffened thin-walled cylindrical steel shells, subjected to bending moments, with particular emphasis on stability design. The cylinder response is characterized by cross-sectional ovalization, followed by buckling (bifurcation instability), which occurs on the compression side of the cylinder wall. Using a nonlinear finite element technique, the bifurcation moment is calculated, the post-buckling response is determined, and the imperfection sensitivity with respect to the governing buckling mode is examined. The results show that the buckling moment capacity is affected by cross-sectional ovalization. It is also shown that buckling of bent elastic long cylinders can be described quite accurately through a simple analytical model that considers the ovalized prebuckling configuration and results in very useful closed-form expressions. Using this analytical solution, the incorporation of the ovalization effects in the design of thin-walled cylinders under bending is thoroughly examined and discussed, considering the framework of the provisions of the new European Standard EN1993-1-6.
Issue Section:
Design and Analysis
1.
Brush
, D. O.
, and Almroth
, B. O.
, 1975, Buckling of Bars, Plates and Shells
, McGraw-Hill
, New York
.2.
Von Kármán
, T.
, and Tsien
, H.
, 1941, “The Buckling of Thin Cylindrical Shells Under Axial Compression
,” J. Aeronaut. Sci.
0095-9812, 8
(8
), pp. 303
–312
.3.
Koiter
, W. T.
, 1967, On the Stability of Elastic Equilibrium
(English Translation: NASA Technical Translation F10
), H. J. Paris
, Amsterdam
.4.
Koiter
, W. T.
, 1963, “The Effect of Axisymmetric Imperfections on the Buckling of Cylindrical Shells Under Axial Compression
,” Proc. K. Ned. Akad. Wet., Ser. B: Phys. Sci.
0023-3366, 66
, pp. 265
–279
.5.
Timoshenko
, S.
, 1934, Theory of Elastic Stability
, McGraw-Hill
, New York
.6.
Bijlaard
, P. P.
, 1949, “Theory and Tests on the Plastic Stability of Plates and Shells
,” J. Aeronaut. Sci.
0095-9812, 16
, pp. 405
–408
.7.
Gerard
, G.
, 1956, Compressive and Torsional Buckling of Thin-Walled Cylinders in the Yield Region, NACA Technical Note No. 3726.8.
Batterman
, S. C.
, 1965, “Plastic Buckling of Axially Compressed Cylindrical Shells
,” AIAA J.
0001-1452, 3
, pp. 316
–325
.9.
Teng
, J. G.
, 1996, “Buckling of Thin Shells: Recent Advances and Trends
,” Appl. Mech. Rev.
0003-6900, 49
(4
), pp. 263
–274
.10.
Simitses
, G. J.
, 1986, “Buckling and Postbuckling of Thin Cylindrical Shells
,” Appl. Mech. Rev.
0003-6900, 39
(10
), pp. 1517
–1524
.11.
Yamaki
, N.
, 1984, Elastic Stability of Circular Cylindrical Shells
, North-Holland
, Amsterdam
.12.
Bazant
, Z. P.
, and Cedolin
, L.
, 1991, Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories
, Oxford University Press
, New York
.13.
Seide
, P.
, and Weingarten
, V. I.
, 1961, “On the Buckling of Circular Cylindrical Shells Under Pure Bending
,” ASME J. Appl. Mech.
0021-8936, 28
, pp. 112
–116
.14.
Chen
, Y. N.
, and Kempner
, J.
, 1976, “Buckling of Oval Cylindrical Shells Under Compression and Asymmetric Bending
,” AIAA J.
0001-1452, 14
, pp. 1235
–1240
.15.
Brazier
, L. G.
, 1927, “On the Flexure of Thin Cylindrical Shells and Other “Thin” Sections
,” Proc. R. Soc. London, Ser. A
0950-1207, 116
, pp. 104
–114
.16.
Comité Européen de Normalisation
, 2005, Eurocode 3: Design of Steel Structures, Part 1–6, prEN 1993-1-6, Shell Structures, Brussels, Belgium.17.
Reissner
, E.
, 1959, “On Finite Bending of Pressurized Tubes
,” ASME J. Appl. Mech.
0021-8936, 26
, pp. 386
–392
.18.
Ades
, C. S.
, 1957, “Bending Strength of Tubing in the Plastic Range
,” J. Aeronaut. Sci.
0095-9812, 24
, pp. 605
–610
.19.
Aksel’rad (Axelrad)
, E. L.
, 1962, “Flexure and Instability of Thin-Walled Pressurized Tubes
,” Izvestiya Akademii Nauk SSSR, Otdelenie Tekhnicheskikh Nauk, Mekhanika i Mashinostroenie
, 1
, pp. 98
–114
(in Russian).20.
Boyle
, J. T.
, 1981, “The Finite Bending of Curved Pipes
,” Int. J. Solids Struct.
0020-7683, 17
, pp. 515
–529
.21.
Levyakov
, S. V.
, 2001, “Equations of Finite Bending of Thin-Walled Curvilinear Tubes
,” J. Appl. Mech. Tech. Phys.
0021-8944, 42
(5
), pp. 898
–901
.22.
Kyriakides
, S.
, and Shaw
, P. K.
, 1982, “Response and Stability of Elasto-Plastic Circular Pipes Under Combined Bending and External Pressure
,” Int. J. Solids Struct.
0020-7683, 18
, pp. 957
–973
.23.
Gresnigt
, A. M.
, 1986, “Plastic Design of Buried Steel Pipes in Settlement Areas
,” Heron
0046-7316, 31
(4
), pp. 1
–113
.24.
Corona
, E.
, and Kyriakides
, S.
, 1988, “On the Collapse of Inelastic Tubes Under Combined Bending and Pressure
,” Int. J. Solids Struct.
0020-7683, 24
, pp. 505
–535
.25.
Karamanos
, S. A.
, and Tassoulas
, J. L.
, 1991, “Stability of Inelastic Tubes Under External Pressure and Bending
,” J. Eng. Mech.
0733-9399, 117
(12
), pp. 2845
–2861
.26.
Axelrad
, E. L.
, 1965, “Refinement of Buckling-Load Analysis for Tube Flexure by Way of Considering Precritical Deformation
,” Izvestiya Akademii Nauk SSSR, Otdelenie Tekhnicheskikh Nauk, Mekhanika i Mashinostroenie
, 4
, pp. 133
–139
(in Russian).27.
Stephens
, W. B.
, Starnes
, J. H.
, Jr., and Almroth
, B. O.
, 1975, “Collapse of Long Cylindrical Shells Under Combined Bending and Pressure Loads
,” AIAA J.
0001-1452, 13
(1
), pp. 20
–25
.28.
Fabian
, O.
, 1977, “Collapse of Cylindrical, Elastic Tubes Under Combined Bending, Pressure and Axial Loads
,” Int. J. Solids Struct.
0020-7683, 13
, pp. 1257
–1270
.29.
Karamanos
, S. A.
, 2002, “Bending Instabilities of Elastic Tubes
,” Int. J. Solids Struct.
0020-7683, 39
(8
), pp. 2059
–2085
.30.
Houliara
, S.
, and Karamanos
, S. A.
, 2006, “Buckling and Post-Buckling of Long Pressurized Elastic Thin-Walled Tubes Under In-Plane Bending
,” Int. J. Non-Linear Mech.
0020-7462, 41
(4
), pp. 491
–511
.31.
Sherman
, D. R.
, 1976, “Tests of Circular Steel Tubes in Bending
,” J. Struct. Div.
0044-8001, 102
(ST11), pp. 2181
–2195
.32.
Van Foeken
, R.
, 1994, “Effect of Buckling Deformations on the Burst Pressure of Pipes
,” Interim TNO Report No. 94-CON-R1008/FNR, Rijswijk, The Netherlands.33.
Elchalakani
, M.
, Zhao
, X. -L.
, and Grzedieta
, R.
, 2002, “Bending Tests to Determine Slender Limits for Cold-Formed Circular Hollow Sections
,” J. Constr. Steel Res.
0143-974X, 58
, pp. 1407
–1430
.34.
Dama
, E.
, Karamanos
, S. A.
, and Gresnigt
, A. M.
, 2006, “Failure of Locally-Buckled Pipelines
,” ASME
Paper No. PVP2006-ICPVT11-93510.35.
Kyriakides
, S.
, and Ju
, G. T.
, 1992, “Bifurcation and Localization Instabilities in Cylindrical Shells Under Bending I: Experiments
,” Int. J. Solids Struct.
0020-7683, 29
, pp. 1117
–1142
.36.
Ju
, G. T.
, and Kyriakides
, S.
, 1992, “Bifurcation and Localization Instabilities in Cylindrical Shells Under Bending II: Predictions
,” Int. J. Solids Struct.
0020-7683, 29
, pp. 1143
–1171
.37.
Tvergaard
, V.
, and Needleman
, A.
, 1980, “On the Localization of Buckling Patterns
,” ASME J. Appl. Mech.
0021-8936, 47
, pp. 613
–619
.38.
Hill
, R.
, 1958, “A General Theory of Uniqueness and Stability of Elastic-Elastic Solids
,” J. Mech. Phys. Solids
0022-5096, 6
, pp. 236
–249
.39.
Hutchinson
, J. W.
, 1974, “Plastic Buckling
,” Adv. Appl. Mech.
0065-2156, 14
, pp. 67
–144
.40.
Greiner
, R.
, and Wallner
, S.
, 1997, “The New Part ‘Strength of Shells’ of Eurocode 3
,” Proceedings of the International Conference on Carrying Capacity of Steel Shell Structures
, Brno, Czech Republic, pp. 119
–125
.41.
Rotter
, J. M.
, 1998, “Shell Structures: The New European Standard and Current Research Needs
,” Thin-Walled Struct.
0263-8231, 31
, pp. 3
–23
.42.
Schmidt
, H.
, 2000, “Stability of Steel Shell Structures: General Report
,” J. Constr. Steel Res.
0143-974X, 55
, pp. 159
–181
.43.
Chen
, L.
, Doerich
, C.
, and Rotter
, J. M.
, 2008, “A Study of Cylindrical Shells Under Global Bending in the Elastic-Plastic Range
,” Steel Construction
, 1
(1
), pp. 59
–65
.44.
Rotter
, J. M.
, and Schmidt
, H.
, 2008, Buckling of Steel Shells, European Design Recommendations
(ECCS Publication No. 125
), 5th ed., European Convention for Constructional Steelwork
, Brussels, Belgium
.45.
Karamanos
, S. A.
, and Tassoulas
, J. L.
, 1996, “Tubular Members I: Stability Analysis and Preliminary Results
,” J. Eng. Mech.
0733-9399, 122
(1
), pp. 64
–71
.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.
