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Forty-First Wilbur Wright Memorial Lecture: Buckling and Stability

Published online by Cambridge University Press:  28 July 2016

N. J. Hoff
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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.

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Research Article
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The Aeronautical Journal , Volume 58 , Issue 517 , January 1954, pp. 3 - 52
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Copyright © Royal Aeronautical Society 1954

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References

References

1. SirFletcher, Banister (1950). A History of Architecture, 15th Edition. B. T. Batsford, London, 1950, p. 28.Google Scholar
2. The Architecture of Vitruvius Pollio (1791), translated from the original Latin by Newton, W., Architect, London, 1791; Book the Fourth, Chapter I: Of the Three Kinds of Columns and of their Invention.Google Scholar
3. Vitruvii Pollionis., M. De Architectura (1569). Libri Decem, Cum Commentariis Danielis Barbari, Electi Patriarchae Aquileiensis, Venetiis, 1567, p. 123.Google Scholar
4. Timoshenko, Stephen P. (1953). History of Strength of Materials. McGraw-Hill Book Co., New York, 1953, p. 32.Google Scholar
5. Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici latissimo sensu accepti, Auctore Leonhardo Eulero, Lausanne et Genevae, apud Marcum-Michaelum Bousquet et socios, 1744; Additamentum I: De curvis elasticis, p. 267.Google Scholar
6. Leonhard Euler's “ Elastic Curves,” translated and annotated by Oldfather, W. A., Ellis, C. A., and Brown, D. M.. Reprinted from Isis, Vol. 20, No. 58, November 1933. The Saint Catherine Press, Bruges, Belgium.Google Scholar
7. Considère, M. (1891). Résistance des pieces comprimées, Congrès International des Procédés de Construction, Annexe, Librairie Polytechnique, Paris, 1891, p. 371.Google Scholar
8. Engesser, Fr. (1889). Ueber die Knickfestigkeit gerader Stäbe. Zeitschrift des Architekten und Ingenieurvereins zu Hanover, Vol. 35, No. 4, p. 455, 1889.Google Scholar
Engesser, Fr. (1895). Knickfragen. Schweizerische Bauzeitung, Vol. 25, No. 13, p. 88, March 30, 1895.Google Scholar
9. Jasinski, F. (1895). Noch ein Wort zu den” Knickfragen.“ Schweizerische Bauzeitung, Vol. 25, No. 25, p. 172, June 22, 1895.Google Scholar
10. Engesser, Fr(1895. Ueber Knickfragen. Schweizerische Bauzeitung, Vol. 26, No. 4, p. 24, July 27, 1895.Google Scholar
11. von Tetmajer, L. (1903). Die Gesetze der Knickungsund der zusammengesetzten Druckfestigkeit der technisch wichtigsten Baustoffe, 3rd Edition. Franz Deuticke, Leipzig and Vienna, 1903.Google Scholar
12. Von Tetmajer, L. (1904). Die angewandte Elastizitätsund Festigkeitslehre. Franz Deuticke, Leipzig and Vienna, 1904. Google Scholar
13. Bach, C. (1902). Elastizität und Festigkeit. Julius Springer, Berlin, 1902.CrossRefGoogle Scholar
14. Lilly, W. E. (1908). The Design of Plate Girders, Appendix 1, The Design of Columns and Struts. Chapman &Hall, London, 1908.Google Scholar
15. Morley, Arthur (1908). Strength of Materials. Longmans, Green & Co., London, 1908.Google Scholar
16. Johnson, J. B. C. W., Bryan, and Turneaure, F. E. (1916). The Theory and Practice of Modern Framed Structures. Part III: Design, Ninth Edition. John Wiley & Sons, 1916. Google Scholar
17. Court of Claims of the United States, No. 33852. Montgomery, Regina C., Montgomery, Heir, and Montgomery, Richard J., assignee of Ellen Montgomery, Heir of John J. Montgomery, deceased, v. the United States. U.S. Government Printing Office, Washington, D.C., 1921.Google Scholar
18. Bach, C. (1902). Elastizität und Festigkeit. Julius festigkeit, Mitteilungen über Forschungsarbeiten auf dem Gebiete des Ingenieurwesens, Verein Deutscher Ingenieure, Heft 81, Berlin, 1910.Google Scholar
19. SirRichard, Southwell(1912). The Strength of Struts. Engineering Vol. 94, p. 249, August 23, 1912.Google Scholar
20. Shanley, F. R. (1946). The Column Paradox. Journal of the Aeronautical Sciences, Vol. 13, December 1946.CrossRefGoogle Scholar
Shanley, F. R. (1946). Inelastic Column Theory. Journal of the Aeronautical Sciences, Vol. 14, May 1947.CrossRefGoogle Scholar
21. Salerno, V. L., Frances, Bauer, and James, Sheng (1952). The Behavior of a Simply Supported Column under Constant or Varying End Load with Transverse Displacement of One Point of Support. Proceedings of the First U.S. National Congress of Applied Mechanics, The American Society of Mechanical Engineers, New York, N.Y., 1952, p. 425.Google Scholar
22. Hoff, N. J. (1949). The Process of the Buckling of Elastic Columns. P.I.B.A.L. Report No. 163, Polytechnic Institute of Brooklyn, Brooklyn, N.Y., December 1949.Google Scholar
Hoff, N.J. (1951). The Dynamics of the Buckling of Elastic Columns. Journal of Applied Mechanics, Vol. 18, No. 1, p. 68, March 1951.CrossRefGoogle Scholar
23. Brillouin, L. (1948). A Practical Method of Solving Hill's Equation. Quarterly of Applied Mathematics, Vol. 6, No. 2, p. 167, July 1948.CrossRefGoogle Scholar
24. Hoff, N. J., Nardo, S., and Erickson, Burton (1950). An Experimental Investigation of the Process of Buckling of Columns. P.I.B.A.L. Report No. 170, Polytechnic Institute of Brooklyn, Brooklyn, N.Y., August 1950; also Proceedings of the Society for Experimental Stress Analysis, Vol. 9, No.1, p. 201, 1951.Google Scholar
25. Stoker, James J. (1950). Non-linear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, New York, N.Y., 1950.Google Scholar
26. Burgreen, David(1951). Free Vibrations of Pin-Ended Column with Constant Distance between Pin Ends. Journal of Applied Mechanics, Vol. 18, June 1951.CrossRefGoogle Scholar
27. Romano, Frank J. (1953). Columns Compressed in an Elastic Testing Machine. Dissertation, Polytechnic Institute of Brooklyn, June 1953.Google Scholar
28. Erickson, Burton, Nardo, S. V., and Hoff, N. J. (1953). Deviations from Straightness of Carefully Machined and Centered Columns. P.I.B.A.L. Report No. 224, Polytechnic Institute of Brooklyn, Brooklyn, N .Y., August 1953. To be published in the Proceedings of the Society for Experimental Stress Analysis.Google Scholar
29. Ziegler, Hans (1952). Zum Begriff des konservativen Systems. Elemente der Mathematik, Vol. 7, No. 6, p. 121, 1952.Google Scholar
30. Pflüger, Alf (1950). Stabilitätsprobleme der Elastostatik. Springer, Berlin, 1950, p. 217.Google Scholar
31. Beck, Max (1952). Die Knicklast des einseitig eingespannten, tangential gedrückten Stabes. Zeitschrift für Angewandte Mathematik und Physik, Vol. 3, No. 3, p.225, 1952.CrossRefGoogle Scholar
32. Tsien, H. S. (1942). Buckling of a Column with Non-Linear Lateral Supports. Journal of the Aeronautical Sciences, Vol. 9, No. 4, p. 119, February 1942.CrossRefGoogle Scholar
33. Cox, H. L. (1940). Stress Analysis of Thin Metal Construction. Journal of the Royal Aeronautical Society, Vol. 44, No. 351, p. 231, March 1940.CrossRefGoogle Scholar
34. Hoff, N.J.,Nardo, S. V., and Erickson, Burton (1952). The Maximum Load Supported by an Elastic Column in a Rapid Compression Test. Proceedings of the First U.S. National Congress of Applied Mechanics, The American Society of Mechanical Engineers, New York, N.Y., 1952.Google Scholar
35. Gerard, George and Herbert, Becker(1952). Column Behavior under Conditions of Impact. Journal of the Aeronautical Sciences ,Vol. 19, No. 1, p. 58, January 1952.Google Scholar
36. Chawla, J.P. (1952). Numerical Analysis of the Process of Buckling of Elastic and Inelastic Columns. Proceedings of the First U.S. National Congress of Applied Mechanics, The American Society of Mechanical Engineers, New York, N.Y., 1952, p. 435.Google Scholar
37. Carel, Koning, and Taub, Joseph (1933). Stossartige Knickbeanspruchung schlanker Stäbe im elastischen Bereich bei beiderseits gelänkiger Lagerung. Luftfahrtforschung, Vol. 10, No. 2, p. 17, 1933. See also Part 2, by Joseph Taub, Vol. 10, No. 2, p. 65.Google Scholar
38. Meier, J. H. (1945). On the dynamics of Elastic Buckling. Journal of the Aeronautical Sciences, Vol. 12, No. 4, p. 433, October 1945.CrossRefGoogle Scholar
39. Lubkin, S., and Stoker, J. J. (1943). Stability of Columns and Strings under Periodically Varying Forces. Quarterly of Applied Mathematics, Vol. 1, No. 3, October 1943.CrossRefGoogle Scholar
40. Biezeno, C. B. (1929). Ueber eine Stabilitätsfrage beim gelenkig gelagerten, schwachgekrümmten Stabe. Proceedings of the Academy of Sciences in Amsterdam, Vol. 32, No. 7, 1929, p. 990.Google Scholar
Biezeno, C. B. (1938). Das Durchschlagen eines schwach gekrÜmmten Stabes. Zeitschrift fÜr Angewandte Mathematik und Mechanik, Vol. 18, No. 1, p. 21, February 1938. See also Biezeno-Grammel, Technische Dynamik, Springer, Berlin, 1939 (lithoprinted by Edwards Bros., 1944), p. 526.CrossRefGoogle Scholar
41. Timoshenko, S. (1935). Buckling of Flat Curved Bars and Slightly Curved Plates. Journal of Applied Mechanics, Vol. 2, No. 1, p. A–17, March 1935.CrossRefGoogle Scholar
Timoshenko, S. (1936). Theory of Elastic Stability. McGraw-Hill, New York, 1936, p. 230.Google Scholar
42. Marguerre, K. (1938).Die Durchschlagkraft eines schwach gekrümmten Balkens. Sitzungsberichte der Berliner Mathematischen Gesellschaft, Vol. 37, 1938.Google Scholar
Marguerre, K. (1950). Neuere Festigkeitsprobleme des Ingenieurs. Springer, Berlin, Chapter 5, 1950.Google Scholar
43. Hoff, N. J.,and Bruce, Victor G. (1951). Dynamic Analysis of the Buckling of Laterally Loaded Flat Arches. P.I.B.A.L. Report No. 191, Polytechnic Institute of Brooklyn, Brooklyn, N.Y., October 1951.Google Scholar
44. Bruce, Victor G. (1952). Further Investigations on the Problem of the Buckling of a Laterally Loaded Flat Arch. P.I.B.A.L. Report No. 199, Polytechnic Institute of Brooklyn, Brooklyn, N.Y., May 1952.Google Scholar
45. Hoff, N. J., and Bruce, Victor G. (1952).Dynamic Analysis of the Buckling of Laterally Loaded Flat Arches. Paper presented before the Eighth International Congress on Theoretical and Applied Mechanics, Istanbul, Turkey, August 20-28, 1952 (to be published in the Journal of Mathemmics and Physics).Google Scholar
46. Fung, Yuan-Cheng, and Kaplan, A.(1952). Buckling of Low Arches and Curved Beams of Small Curvature. National Advisory Committee for Aeronautics, Technical Note No. 2840, Washington, D.C., December 1952.Google Scholar
47. Nádai, A. (1950). Theory of Flow and Fracture of Solids. McGraw-Hill, New York, N.Y., Second Edition, 1950.Google Scholar
48. Smith, Gilbert V. (1950). Properties of Metals at Elevated Temperatures. McGraw-Hill, New York, N.Y., 1950.Google Scholar
49. Orowan, E. (1952). Creep in Metallic and Non-Metallic Materials. Proceedings of the First U.S. National Congress of Applied Mechanics, The American Society of Mechanical Engineers, New York, N.Y., 1952, p. 453.Google Scholar
50. Hoff, N. J. (1953). Necking and Rupture of Rods under Tensile Loads. Journal of Applied Mechanics, Vol. 20 No 1, p. 105, March 1953.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
54. Hoff, N. J. (1949). Dynamic Criteria of Buckling. Research, Engineering Structures Supplement, Butterworths Scientific Publications, London, and Academic Press, New York, N.Y., 1949, p. 121.Google Scholar
55. Kempner, Joseph (1952). Creep Bending and Buckling of Linear Viscoelastic Columns. P.I.B.A.L. Report No. 195, March 1952.Google Scholar
Kempner, Joseph (1952). Creep Bending and Buckling of Non-Linear Viscoelastic Columns. P.I.B.A.L. Report No. 200, May 1952.Google Scholar
Kempner, Joseph, and Patel, Sharad A. (1952). Creep Buckling of Columns. P.I.B.A.L. Report No. 205, November 1952.Google Scholar
Ness, Nathan (1951). Time Dependent Buckling of a Uniformly Heated Column. P.l.B.A.L. Report No. 192, October 1951. (These four reports are to be published as N.A.C.A. Technical Notes.)Google Scholar
56. Ross, A. D. (1946). The Effects of Creep on Instability and Indeterminacy Investigated by Plastic Models. The Structural Engineer, Vol. 24, No. 8, p. 413, August 1946.Google Scholar
Ross, A. D. (1947). The Effects of Creep on Instability and Indeterminacy Investigated by Plastic Models. The Structural Engineer, Vol. 25, No. 5, p. 179, May 1947.Google Scholar
Prentis, J. M., and Ross, A. D. (1948). Slender Reinforced Concrete Columns. Concrete and Constructional Engineering, Vol. 43, No. 9, p.261, September 1948.Google Scholar
57. Marin, Joseph (1947). Creep Deflection in Columns. Journal of Applied Physics, Vol.18, January 1947.CrossRefGoogle Scholar
58. Jackson, L. R., Schwope, A. D., and Shober, F. R. (1949). Information on the Plastic Properties of Aircraft Materials and Plastic Stability of Aircraft Structures at High Temperatures. Batelle Memorial Institute, December 15, 1949.Google Scholar
59. Libove, Charles (1952). Creep Buckling of Columns. Journal of the Aeronautical Sciences,Vol. 19, No. 7, p. 459, July 1952 CrossRefGoogle Scholar
60. Gerard, George (1952). Note on Creep Buckling of Columns. Journal of the Aeronautical Sciences, Vol. 19, No. 10, p. 714, October 1952.CrossRefGoogle Scholar
61. Shanley, F. R. (1952). Weight-Strength Analysis of Aircraft Structures. McGraw-Hill, 1952, p. 343.Google Scholar
62. Higgins, T. P. Jr. Effect of Creep on Column Deflection, p. 359 of book by F. R. Shanley cited as Reference 61.Google Scholar
63. Rosenthal, D., and Baer, H. W. (1952). An Elementary Theory of Creep Buckling of Columns. Proceedings of the First U.S. National Congress of Applied Mechanics, The American Society of Mechanical Engineers, New York, N.Y., 1952, p. 603.Google Scholar
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.Google Scholar
65. Hoff, N. J. (1953). Approximate Analysis of Structures in the Presence of Moderately Large Creep Deformations. P.I.B.A.L. Report No. 223, June 1953, to be published in the Quarterly of Applied Mathematics.Google Scholar
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. Google Scholar
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.Google Scholar
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.Google Scholar
Levy, Samuel (1942). Bending of Rectangular Plates with Large Deflections. National Advisory Committee for Aeronautics, Technical Report No. 737, 1942.Google Scholar
Hu, Pai C., Lundquist, E. E., and Batdorf, S. B. (1946).Google Scholar
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.Google Scholar
Cox, H. L. (1933). Buckling of Thin Plates in Compression. Aeronautical Research Council Reports and Memoranda No. 1554, 1933.Google Scholar
Lahde, R., and Wagner, H. (1936). Versuche zur Ermittlung der mittragenden Breite von verbeulten Blechen. Luftfahrtforschung, Vol. 13, No. 8, p. 262, August 1936.Google Scholar
Trefftz, E., and Marguerre, K. (1937). Ueber die Tragfähigkeit eines längsbelasteten Plattenstreifens nach Ueberschritt der Beullast. Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 17, No.2, p. 85, April 1937.Google Scholar
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.Google Scholar
70. Lorenz, R. (1908). Achsensymmetrische Verzerrungen in dünnwandigen Hohlzylindern. Zeitschrift des Vereins Deutscher Ingenieure, Vol. 52, No. 43, p. 1706, Oct. 1908.Google Scholar
Lorenz, R. (1911). Die nicht achsensymmetrische Knickung dünnwandiger Hohlzylinder. Physikalische Zeitschrift, Vol. 12, No. 7, p. 241, April 1911.Google Scholar
71. Timoshenko, S. (1910). Einige Stabilitätsprobleme der Elastizitätstheorie. Zeitschrift für Mathematik und Physik, Vol. 58, No. 4, p. 337, June 1910.Google Scholar
72. Southwell, R. V. (1913). On the General Theory of Elastic Stability. Philosophical Transactions of the Royal Society, London, Series A, Vol. 213, No. A501, p. 187, August 1913.Google Scholar
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.Google Scholar
73. Robertson, Andrew (1928). The Strength of Tubular Struts. Proceedings of the Royal Society, London, Vol. 121, No. 788, p. 558, December 1. 1928.Google Scholar
74. Lundquist, E. E. (1933). Strength Tests of Thin-Walled Duralumin Cylinders in Compression. National Advisory Committee for Aeronautics, Technical Report No. 473, Washington, D.C., 1933.Google Scholar
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.CrossRefGoogle Scholar
76. Flügge, W. (1932). Die Stabilitat der Kreiszylinderschale. lngenieur-Archiv, Vol. 3, No. 5, p. 463, December 1932.CrossRefGoogle Scholar
77. von Kármán, Th., and Tsien, Hsue-Shen (1939). The Buckling of Spherical Shells by External Pressure. Journal of the Aeronautical Sciences, Vol. 7, December 1939.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
81. Leggett, D. M. A., and JoNES, R. P. N. (1946). The Behaviour of a Cylindrical Shell under Axial Compression when the Buckling Load has been Exceeded. Aeronautical Research Council Reports and Memoranda No. 2190, August 1942; this paper was first presented publicly at the International Congress for Theoretical and Applied Mechanics, Paris, France, 1946.Google Scholar
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. CrossRefGoogle Scholar
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. Google Scholar
84. Kotter, W. T. (1945). Over de Stabiliteit van het elastisch Evenwicht. H.J. Paris, Amsterdam, Holland, 1945.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
88. Hoff, N. J. (1950). Plastic Column Behavior. Journal of the Aeronautical Sciences, Vol. 17, No. 11, p. 743, Nov. 1950.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
93. Lin, Tung-Hua (1950). Inelastic Column Buckling. Journal of the Aeronautical Sciences, Vol. 17, No. 3, p. 159, March 1950.CrossRefGoogle Scholar
94. Cicala, P. (1950). Column Buckling in the Elastoplastic Range. Journal of the Aeronautical Sciences, Vol. 17, No. 8, p. 508, August 1950.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
97. Ziegler, Hans (1952). Die Stabilitätskriterien der Elastomechanik. Ingenieur-Archiv, Vol. 20, No. 1, p. 49, 1952.CrossRefGoogle Scholar
98. Rayleigh, Lord (1945). The Theory of Sound. First American Edition. Dover Publications, New York, N.Y., 1945, Vol. 1, pp. 245 and 297.Google Scholar
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:Google Scholar
100. Tyler, C. M. Jr. (1951). Dynamic Buckling of Columns. Journal of Applied Mechanics, Vol. 18, No. 3, p. 317. September 1951.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
106. Imachi, Isamu. On the Axial Impact on a Thin Strut Considering its Lateral Stability. Library of Congress Reproduction PB 94940.Google Scholar