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Forty-First Wilbur Wright Memorial Lecture: Buckling and Stability

  • N. J. Hoff
Extract

Although columns built almost 5,000 years ago still stand in Egypt, the first theoretical calculation of the load-carrying capacity of columns was published by Euler only 209 years ago. The classical theory established in this publication is still the foundation of all stability analyses and is likely to remain so in the future. It was derived for perfectly elastic columns and for specific end conditions. These end conditions are not realised in the ordinary column test nor do they correspond exactly to the conditions prevailing in an aeroplane wing when it is subjected to a gust or to the shock of landing. They are not the same as the end conditions of a column in a building when it collapses during a tornado or an earthquake.

Copyright
COPYRIGHT: © Royal Aeronautical Society 1954
References
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51. Kempner, Joseph, and Hoff, N. J. (1952). Behaviour of a Linear Visco-Elastic Column, Appendix 2, p. 110, of N. J. Hoff, Structural Problems of Future Aircraft. Third Anglo-American Aeronautical Conference, The Royal Aeronautical Society, London, 1952.
52. Freudenthal, A. M. (1946). Some Time Effects in Structural Analysis. Sixth International Congress of Applied Mechanics, Paris, France, 1946, unpublished; see also Freudenhal, A. M., The inelastic Behavior of Engineering Materials and Structures, John Wiley & Sons, New York, N.Y., 1950, p. 518.
53. Kempner, Joseph, and Pohle, Frederick V.(1953). On the Non-Existence of a Finite Critical Time for Linear Viscoelastic Columns. Journal of the Aeronautical Sciences, August 1953.
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55. Kempner, Joseph (1952). Creep Bending and Buckling of Linear Viscoelastic Columns. P.I.B.A.L. Report No. 195, March 1952.
Kempner, Joseph (1952). Creep Bending and Buckling of Non-Linear Viscoelastic Columns. P.I.B.A.L. Report No. 200, May 1952.
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61. Shanley, F. R. (1952). Weight-Strength Analysis of Aircraft Structures. McGraw-Hill, 1952, p. 343.
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64. Libove, Charles (1953). Creep Buckling Analysis of Rectangular Section Columns. National Advisory Committee for Aeronautics, Technical Note No. 2956, Washington, D.C., June 1953.
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66. Schuman, L., and Back, G. (1930). Strength of Rectangular Flat Plates under Edge Compression. National Advisory Committee for Aeronautics, Technical Report No. 356, 1930.
67. Von Kármán, Th., Sechler, E. E., and Donnell, L. H.(1932). The Strength of Thin Plates in Compression, Transactions of the American Society of Mechanical Engineers, Paper APM-54-5, Vol. 54, No. 2, p. 53, January 1932.
68. Coan, John (1951). Large Deflection Theory for Plates with Small Initial Curvature Loaded in Edge Compression. Journal of Applied Mechanics, Vol. 18, June 1951.

The theory is a refinement of the following earlier analyses:

Levy, Samuel (1942). Bending of Rectangular Plates with Large Deflections. National Advisory Committee for Aeronautics, Technical Report No. 737, 1942.
Hu, Pai C., Lundquist, E. E., and Batdorf, S. B. (1946).
Effect of Small Deviations from Flatness on Effective Width and Buckling of Plates in Compression. National Advisory Committee for Aeronautics, Technical Note No. 1124, September 1946.

The effective width concept was also discussed in the following publications:

Cox, H. L. (1933). Buckling of Thin Plates in Compression. Aeronautical Research Council Reports and Memoranda No. 1554, 1933.
Lahde, R., and Wagner, H. (1936). Versuche zur Ermittlung der mittragenden Breite von verbeulten Blechen. Luftfahrtforschung, Vol. 13, No. 8, p. 262, August 1936.
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69. Hoff, N. J., Boley, B. A., and Coan, J. M. (1948). The Development of a Technique for Testing Stiff Panels in Edgewise Compression. Proceedings of the Society for Experimental Stress Analysis, Vol. 5, No.2, p. 14, 1948.
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Lorenz, R. (1911). Die nicht achsensymmetrische Knickung dünnwandiger Hohlzylinder. Physikalische Zeitschrift, Vol. 12, No. 7, p. 241, April 1911.
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A comprehensive presentation of the subject can be found in Timoshenko, S. (1936). Theory of Elastic Stability. McGraw-Hill Book Co., New York, N.Y., 1936, p. 439.
73. Robertson, Andrew (1928). The Strength of Tubular Struts. Proceedings of the Royal Society, London, Vol. 121, No. 788, p. 558, December 1. 1928.
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75. Donnell, L. H. (1934). A New Theory for the Buckling of Thin Cylinder under Axial Compression and Bending. Transactions of the American Society of Mechanical Engineers, Paper AER-56-12, Vol. 56, No. 11, p. 795, November 1934.
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78. von Kármán, Th., Dunn, Louis G., and Hsue-Shen Tsien, (1940). The Influence of Curvature on the Buckling Characteristics of Structures. Journal of the Aeronautical Sciences, Vol.7, No. 7, p. 276, May 1940.
79. Von Kármán, Th., and Hsue-Shen, Tsien (1941). The Buckling of Thin Cylindrical Shells under Axial Compression. Journal of the Aeronautical Sciences, Vol. 8, No.8, p. 303, June 1941.
80. Tsien, Hsue-Shen (1942). A Theory for the Buckling of Thin Shells. Journal of the Aeronautical Sciences, Vol. 9, No. 10, p. 373, August 1942.
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82. Michielsen, Herman F. (1948). The Behavior of Thin Cylindrical Shells after Buckling under Axial Compression. Journal of the Aeronautical Sciences, Vol. 15, No. 12, p 738, December 1948.
83. Kempner, Joseph (1952). Post-Buckling Behavior of Axially Compressed Circular Cylindrical Shells. P.I.B.A.L. Report No. 212, Polytechnic Institute of Brooklyn, Brooklyn, N.Y., December 1952; to be published in the Journal of the Aeronautical Sciences.
84. Kotter, W. T. (1945). Over de Stabiliteit van het elastisch Evenwicht. H.J. Paris, Amsterdam, Holland, 1945.
85. Friedrichs, K. O. (1941). On the Minimum Buckling Load for Spherical Shells. Theodore von Kármán Anniversary Volume, p. 258, California Institute of Technology, Pasadena, 1941.
86. Donnell, H. L., and Wan, C. C. (1950). Effect of Imperfections on Buckling of Thin Cylinders and Columns under Axial Compression. Journal of Applied Mechanics, Vol. 17, No. 1, p. 73, March 1950.
87. Duberg, John E., and Wilder, Thomas W. III (1950). Column Behavior in the Plastic Stress Range. Journal of the Aeronautical Sciences, Vol. 17, No. 6, p. 324, June 1950.
Duberg, John E., and Wilder, Thomas W. III (1951). Inelastic Column Behavior. National Advisory Committee for Aeronautics, Technical Note No. 2267, Washington, D.C., January 1951.
88. Hoff, N. J. (1950). Plastic Column Behavior. Journal of the Aeronautical Sciences, Vol. 17, No. 11, p. 743, Nov. 1950.
89. Wilder, Thomas W. III, Brooks, William A. Jr., and Mathauser, Eldon E. (1953). The Effect of Initial Curvature on the Strength of an Inelastic Column. National Advisory Committee for Aeronautics, Technical Note No. 2872, Washington, D.C., January 1953.
90. Ramberg, Walter, and Osgood, William R. (1943). Description of Stress-Strain Curves by Three Parameters. National Advisory Committee for Aeronautics, Technical Note No. 902, Washington, D.C., July 1943.
91. Pearson, C. E. (1950). Bifurcation Criterion and Plastic Buckling of Plates and Columns. Journal of the Aeronautical Sciences, Vol. 17, No. 7, p.417, July 1950.
92. Wang, Chi-Teh (1948). Inelastic Column Theories and an Analysis of Experimental Observations. Journal of the Aeronautical Sciences, Vol. 15, No. 5, p. 283, May 1948.
93. Lin, Tung-Hua (1950). Inelastic Column Buckling. Journal of the Aeronautical Sciences, Vol. 17, No. 3, p. 159, March 1950.
94. Cicala, P. (1950). Column Buckling in the Elastoplastic Range. Journal of the Aeronautical Sciences, Vol. 17, No. 8, p. 508, August 1950.
95. Templin, R. L., Hartman, E. C., and Paul, D. A. (1942). Typical Tensile and Compressive Stress-Strain Curves for Aluminum Alloy 24S-T, Alclad 24S-T, 24S-RT, and Alclad 24S-RT Products. Aluminum Research Laboratories Research Paper No. 6, Aluminum Company of America, Pittsburgh, Pennsylvania, 1942, p. 14.
96. Hoff, N. J. (1949). Dynamic Criteria of Buckling. Research, Engineering Structures Supplement, Butterworths Scientific Publications, London, England, and Academic Press, New York, N.Y., 1949, p. 121.
97. Ziegler, Hans (1952). Die Stabilitätskriterien der Elastomechanik. Ingenieur-Archiv, Vol. 20, No. 1, p. 49, 1952.
98. Rayleigh, Lord (1945). The Theory of Sound. First American Edition. Dover Publications, New York, N.Y., 1945, Vol. 1, pp. 245 and 297.
99. Jeffreys, Harold, and Jeffreys, Bertha Swirles (1950). Methods of Mathematical Physics. Cambridge University Press, Cambridge, England, 2nd Ed., 1950, p. 523. Suggestions for an alternative solution of the linearised equations of Reference 22 were made in the following publication:
100. Tyler, C. M. Jr. (1951). Dynamic Buckling of Columns. Journal of Applied Mechanics, Vol. 18, No. 3, p. 317. September 1951.

The dynamics of the buckling process of thin rectangular panels is treated in:

101. Zizicas, G. A. (1952). Dynamic Buckling of Thin Elastic Plates. Transactions of the American Society of Mechanical Engineers, Vol. 74, No. 7, p. 1257, Oct. 1952.

After this paper was completed the following publications, dealing with dynamic buckling under loads increasing linearly with time, have come to the author's attention:

102. Katsuta, Chitoshi (1947). On Buckling of an Elastic Long Column under High-Speed Loading. Paper read before a meeting of the Architectural Institute of Japan, 23rd November 1947. Library of Congress reproduction PB 94937.
103. Suhara, Jirô (1948). Dynamic Stability of Column Compressed by Axial Load Increasing with Time. Paper read before the Research Committee on Applied Mechanics, Faculty of Engineering, University of Kyushu, May 1948. Library of Congress reproduction PB 94945.
104. Katsuta, Chitoshi (1952). High-Speed Buckling of Mild Steel Columns. Proceedings of the First Japan National Congress for Applied Mechanics, Japan National Committee for Theoretical and Applied Mechanics, Science Council of Japan, p. 65, May 1952.

Creep buckling is discussed in :

105. Matvo, Miyagawa (1952). On Buckling Rupture of Columns Caused by Creep. Proceedings of the First Japan National Congress for Applied Mechanics, Japan National Committee for Theoretical and Applied Mechanics, Science Council of Japan, p. 47, May 1952.

The buckling of a column hit axially by a mass is analysed in:

106. Imachi, Isamu. On the Axial Impact on a Thin Strut Considering its Lateral Stability. Library of Congress Reproduction PB 94940.
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The Aeronautical Journal
  • ISSN: 0001-9240
  • EISSN: 2059-6464
  • URL: /core/journals/aeronautical-journal
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