Stability of plane Frames Omitting Axial Strains
Publication: Journal of Structural Engineering
Volume 111, Issue 10
Abstract
The number of degrees of freedom for the stability analysis of plane frames may be considerably reduced by introducing axial constraints. Determination of the rank and basis of the constraint matrix by Gauss-Jordan elimination with pivoting leads to automatic selection of the best set of dependent and independent joint translations. Then a transformation of the buckling equations produces a reduced set of equations, that may be solved for the buckling loads of frames. This technique can be applied in conjunction with the elimination of joint rotations, thereby accomplishing a double reduction without significant loss of accuracy. The procedure described has been programmed on a digital computer.
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References
1.
Eisenberger, M., “Constraints for Axial Strains in Plane Frames,” thesis presented to Stanford University, at Stanford, Calif., in 1979, in partial fulfillment of the requirements for the degree of Civil Engineer.
2.
Eisenberger, M., “Static and Dynamic Analysis of Plane and Space Frames with Axial Constraints,” Technical Report 48, J. A. Blume Earthquake Engineering Center, Stanford, Calif., Oct., 1980.
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Guyan, R. J., “Reduction of Stiffness and Mass Matrices,” AIAA Journal, Vol. 3, No. 2, 1965, p. 380.
4.
Weaver, W., Jr., “Constraints for Axial Strains in Frames,” Journal of the Structural Division, ASCE, Vol. 106, No. ST1, Proc. Paper 15121, Jan., 1980, pp. 199–209.
5.
Weaver, W., Jr., and Eisenberger, M., “Dynamics of Frames with Axial Constraints,” Journal of the Structural Division, ASCE, Vol. 109, No. ST3, Proc. Paper 17818, Mar., 1983, pp. 773–784.
6.
Weaver, W., Jr., and Yoshida, D. M., “The Eigenvalue Problem for Banded Matrices,” Computers and Structures, Vol. 1, 1971, pp. 651–664.
Information & Authors
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Published In
Journal of Structural Engineering
Volume 111 • Issue 10 • October 1985
Pages: 2261 - 2265
Copyright
Copyright © ASCE.
History
Published online: Oct 1, 1985
Published in print: Oct 1985
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