Reciprocal Conjugate Method for Space Curved Bars
Publication: Journal of Structural Engineering
Volume 115, Issue 3
Abstract
By means of a correspondence between two systems, each consisting of a space curved bar resting on an external medium, a complete reciprocal formulation of the conjugate structure method is herein presented. The method allows us to transform (internal and external) forces and deformations of one of the two systems into deformations and forces respectively of the conjugate one. This can be done by interchanging the field equilibrium and the mechanical boundary conditions in the two systems with the field compatibility equations and the kinematical boundary conditions and vice versa. The reciprocal correspondence descends from the Principle of Virtual Work and it can be regarded as a particular form of this principle. The Culmann and Ricci ellipse theories and the Cross column analogy are shown as particular aspects of the unified method. The equilibrium, compatibility equations and constitutive laws of the one‐dimensional space member supported on an external medium are derived in a suitable form. An application to influence lines of circular bridge, also taking into account the shear deformation effect, is developed.
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References
1.
Arici, M. (1985). “Analogy for beam‐foundation elastic systems.” J. Struct. Engrg., ASCE, 111(8), 1691–1702.
2.
Baron, F. (1961). “Matrix analysis of structures curved in space.” J. Struct. Div., ASCE, 87(3), 17–38.
3.
Bažant, Z. P. (1966). “Conjugate analogy for space structures.” J. Struct. Div., ASCE, 92(3), 137–159.
4.
Cross, H., Morgan, N. (1932). Continuous frames of reinforced concrete. John Wiley and Sons, Inc., New York, N.Y.
5.
Culmann, K. (1875). Die graphiske statik. Meyer‐Zeller, Zürich, Switzerland, S4, Cap. II.
6.
Den Hartog, J. P. (1949). Strength of material. Dover Publication, New York, N.Y.
7.
Greene, C. E. (1869). Michigan technic.
8.
Hjelmstad, K. D. (1986). “Conjugate structure method.” J. Struct. Engrg., ASCE, 112(6), 1413–1427.
9.
Mohr, O. (1868). “Beitrag zun theorie der holz‐und eisenconstruktionen,” Z. Architekten‐Ingenieur, Hannover, Germany, 19.
10.
Oden, J. T. (1967). “Linear and nonlinear analysis by conjugate analogy.” J. Struct. Div., ASCE, 93(4), 27–44.
11.
Ricci, C. L. (1911). “L'ellisse di elasticità trasversale,” Rend. Acc. Scienze, Torino.
12.
Ritter, W. (1886). Der Elastische Bogen, Zürich, Switzerland.
13.
Rizzo, S. (1981). “L'Analogia generalizzata di mohr nella costruzione delle linee di influenza,” Giornale del Genio Civile, 6, Roma, Italy, 159–168.
14.
Timoshenko, S. P. (1930). Strength of materials, D. Van Nostrand, New York, N.Y.
15.
Washizu, K. (1968). Variational method in elasticity and plasticity, Pergamon Press, Oxford.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 115 • Issue 3 • March 1989
Pages: 560 - 575
Copyright
Copyright © 1989 ASCE.
History
Published online: Mar 1, 1989
Published in print: Mar 1989
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