Finite Element Elastic Beam‐Column
Publication: Journal of Engineering Mechanics
Volume 109, Issue 5
Abstract
An accurate and unified finite element description is presented, in both stiffness and flexibility formats, of the response of planar elastic beams subject to terminal loads. The stability and bowing functions are inter‐related, their descriptions accounting for the effects of axial deformability and a measure of the shear deformation effects. A perturbation technique is used to solve the non‐linear governing equations. The solutions so derived are cast in four distinct forms: (1) Deformation; (2) incremental; (3) perturbation; and (4) asymptotic forms of structural analysis. A brief comparison between related formulations presented in the literature is included.
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References
1.
Argyris, J. H., “Recent Advances in Matrix Methods of Structural Analysis,” Progress in Aeronautical Sciences, D. Kuchemann and L. H. G. Sterne, eds., MacMillan, 1964.
2.
Baker, J. F., “A Note on the Effective Length of a Pillar Forming Part of a Continuous Member in a Building Frame,” 2nd Report, Steel Structures Research Committee, HMSO, London, England, pB‐43, 200, 1934.
3.
Berry, A., “The Calculation of Stresses in Aeroplane Spars,” Transactions of the Royal Aeronautical Society, No. 1, 1916.
4.
Britvec, S. J., “The Stability of Elastic Systems,” Pergamon Press Inc., New York, N.Y., 1973, p. 139.
5.
Britvec, S. J., and Chilver, A. H., “Elastic Buckling of Rigidly Jointed Braced Frames,” Proceedings, Journal of the Engineering Mechanics Division, ASCE, Vol. 89, 1963, p. 217.
6.
Chu, K. H., “Secondary Moments, End Rotations, Inflection Points and Elastic Buckling Loads of Truss Members,” IABSE, Vol. 19, 1959, p. 17.
7.
Huddleston, J. V., “Effect of Axial Strain on Buckling and Post‐buckling Behaviour of Elastic Columns,” Developments in Theoretical and Applied Mechanics, D. Frederick, ed., Pergamon Press.
8.
James, B. W., “Principal Effects of Axial Loads on Moment Distribution Analysis of Rigid Structures,” NACA TN 534, Washington, D.C., 1935.
9.
Jennings, A., “Frame Analysis Including Change of Geometry,” Journal of the Structural Division, ASCE, Vol. 94, 1968, p. 627.
10.
Livesley, R. K., and Chandler, D. B., “Stability Functions for Structural Frameworks,” Manchester Univ. Press, 1956.
11.
Lundquist, E. E., and Kroll, W. D., “Tables of Stiffness and Carryover Factors for Structural Members under Axial Load,” NACA Tech. Note 652, Washington, D.C., 1938.
12.
Lundquist, E. E., and Kroll, W. D., “Extended Tables of Stiffness and Carryover Factors for Structural Members under Axial Load,” NACA Report 4B24, Washington, D.C., 1944.
13.
Mallet, R. H., and Marcal, P. V., “Finite Element Analysis of Nonlinear Structures,” Journal of the Structural Division, ASCE, Vol. 94, 1968, p. 2081.
14.
Manderla, H., “Die Berechnung der Sekundarspannungen, welche im einfachen Fachwerk infolge starrer Knotenverbindungen auftreten, Allgemeine Bauzeitung, 1880.
15.
Martin, H. C., “On the Derivation of Stiffness Matrices for the Analysis of Large Deflection and Stability Problems,” Conference on Matrix Methods in Structural Mechanics, Wright Patterson Base, Ohio, 1965.
16.
Merchant, W., “Critical Loads of Tall Building Frames,” Structural Engineer, Vol. 33, 1955, p. 85.
17.
Merchant, W., and Brotton, P. M., “A Generalized Method of Analysis of Elastic Plane Frames,” IABSE Symposium, Rio de Janeiro, 1964.
18.
Powell, G. H., “Theory of Nonlinear Elastic Structures,” Journal of the Structural Division, ASCE, Vol. 95, 1969, p. 2687.
19.
Roorda, J., and Chilver, A. H., “Frame Buckling: An Illustration of the Perturbation Technique,” International Journal of Nonlinear Mechanics, Vol. 5, 1970, p. 235.
20.
Saafan, S. A., “Nonlinear Behaviour of Structural Plane Frames,” Journal of the Structural Division, ASCE, Vol. 89, 1963, p. 557.
21.
Sewell, M. J., “The Static Perturbation Technique in Buckling Problems,” Journal of the Mechanics and Physics of Solids, Vol. 13, 1965, p. 247.
22.
Teixeira De Freitas, J. A., “The Elastoplastic Analysis of Planar Frames for Large Displacements by Mathematical Programming,” thesis presented to the University of London, London, England, in 1979, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
23.
Thompson, J. M. T., “Discrete Branching Points in the General Theory of Elastic Stability,” Journal of the Mechanics and Physics of Solids, Vol. 13, 1965, p. 295.
24.
Timoshenko, S. P., and Gere, J. M., “Theory of Elastic Stability,” McGraw‐Hill Book Co. Inc., New York, N.Y., 1961, p. 132.
25.
Turner, M. J., Dill, E. H., Martin, H. C., and Melosh, R. J., “Large Deflections of Structures Subjected to Heating and External Loads,” Journal of the Aerospace Sciences, Vol. 22, 1960, p. 97.
26.
Williams, F. W., “An Approach to the Nonlinear Behaviour of the Members of a Rigid Jointed Plane Framework with Finite Deflections,” Journal of Mechanics and Applied Mathematics, Vol. 17, 1964, p. 451.
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Copyright © 1983 ASCE.
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Published online: Oct 1, 1983
Published in print: Oct 1983
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