Warping Moment Distribution
Publication: Journal of Structural Engineering
Volume 111, Issue 2
Abstract
Presented here is an iterative procedure for the calculation of continuous structures subjected to torsional loads and experiencing both the St. Venant and warping torsion. The procedure is entirely analogous to the wellknown moment distribution method. Structures to which it applies include crane girders, box‐girder bridges, and vertical shear elements of high‐rise buildings with prismatic, thin‐walled, open sections. The formulas for the necessary constants including warping stiffness, warping carry‐over factors and fixed‐end warping moments are given, and the procedure is illustrated with the aid of an example of a continuous crane girder which demonstrates its efficiency. In order to make the paper self‐contained, the equations of mixed torsion are summarized in Appendix I.
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References
1.
Blaszkowiak, S., and Kaczkowski, Z., The Cross Method, (in Polish), Polish Academy of Sciences, Warsaw, Poland, 1959.
Translation into English published under the title Iterative Methods in Structural Analysis, Pergamon Press, New York, N.Y., 1966.
2.
Bleich, F., Buckling Strength of Metal Structures, Second ed., McGraw‐Hill Book Co., Inc., New York, N.Y., 1952.
3.
Chilver, A. H., ed., Thin‐Walled Structures, John Wiley and Sons, Inc., New York, N.Y., 1967.
4.
Gere, J. M., Moment Distribution, D. Van Nostrand Company, Inc., Princeton, N.J., 1963.
5.
Goodier, J. N., “Torsional and Flexural Buckling of Bars of Thin‐Walled Open Section under Compressive and Bending Loads,” Journal of Applied Mechanics, Vol. 9, 1942, p. A‐103.
6.
Heins, C. P., Jr., and Seaburg, P. A., “Torsion Analysis of Rolled Steel Sections,” AIA File No. 13‐A‐1, Bethlehem Steel Corporation, Bethlehem, Pa., 1963.
7.
Kollbrunner, C. F., and Easier, K., Torsion in Structures—An Engineering Approach, (English translation from the German, with annotations and an appendix by B. G. Johnston), Springer‐Verlag, New York, N.Y., 1969.
8.
Kollbrunner, C. F., and Hajdin, N., “Warping Torsion of Thin‐walled Beams with Open Section,” (in German), Schweizer Stahlbau‐Vereinigung, Report, Part 1, Vol. 29, Zurich, Germany, 1964.
9.
Lightfoot, E., Moment Distribution, John Wiley and Sons, Inc., New York, N.Y., 1961.
10.
Lundquist, E. E., “Principles of Moment Distribution Applied to Stability of Structural Members,” Proceedings of the Fifth International Congress of Applied Mechanics, John Wiley and Sons, Inc., New York, N.Y., 1938, pp. 145–150.
11.
Lyse, I., and Johnston, B. G., “Structural Beams in Torsion,” Transactions, ASCE, Vol. 101, Paper No. 1941, 1936, pp. 857–929.
12.
Manual of Steel Construction, Eighth ed., American Institute of Steel Construction, Inc., Chicago, Ill., 1980.
13.
Oden, J. T., and Rippberger, E. A., Mechanics of Elastic Structures, Second ed., McGraw‐Hill Book Co., Inc., New York, N.Y., 1981.
14.
Pilkey, W. D., and Chang, P. Y., Modern Formulas for Statics and Dynamics, McGraw‐Hill Book Co., Inc., New York, N.Y., 1978.
15.
Popov, E. P., Introduction to Mechanics of Solids, Prentice‐Hall, Inc., Englewood Cliffs, N.J., 1968.
16.
Reilly, R. J., “Stiffness Analysis of Grids Including Warping,” Journal of the Structural Division, ASCE, Vol. 98, No. ST7, July, 1972, pp. 1511–1523.
17.
Timoshenko, S. P., “Theory of Bending, Torsion and Buckling of Thin‐Walled Members of Open Cross‐Section,” Journal of the Franklin Institute, Philadelphia, Pa., Mar.–May, 1945.
18.
Vlasov, V. Z., Thin‐Walled Elastic Beams, Moscow, USSR, 1959,
(English translation from the Russian), ATS 61‐11400, National Science Foundation, Washington, D.C., 1961.
19.
Wagner, H., “Torsion and Buckling of Open Sections,” Technical Memorandum No. 807, National Advisory Committee for Aeronautics, Washington, D.C., 1936.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 111 • Issue 2 • February 1985
Pages: 453 - 466
Copyright
Copyright © 1985 ASCE.
History
Published online: Feb 1, 1985
Published in print: Feb 1985
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