Elastic Critical Loads on Multistory Rigid Frames
Publication: Journal of Structural Engineering
Volume 109, Issue 5
Abstract
A direct matrix method for the calculation of the elastic critical loads on rigid frames is presented. The effect of the secondary axial forces in columns is readily included. The procedure leads to a linear eigenvalue problem where the smallest root from a product matrix represents the critical load. The computational aspects of the method are considered, and the analysis is reduced to the setting up of two main matrixes. The first matrix is directly evaluated from the geometrical and loading properties, and the second is the linear elastic stiffness matrix under a fictitious system of transverse forces. Economy in the setting up of the stiffness matrix is achieved by treating individual columns as substructures. The method is applied to three example frames, and the numerical results are compared with those obtained from stability‐function solutions.
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References
1.
Awadalla, E. S., “Elastic Stability Analysis of Struts and Plates by the Matrix Displacement Method,” thesis presented to the University of Leeds, at Leeds, England, in 1968, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
2.
Awadalla, E. S., “A Direct Matrix Method for the Elastic Stability Analysis of Deep Circular Arches,” International Journal for Numerical Methods in Engineering, Vol. 8, No. 1, 1974, pp. 119–138.
3.
Awadalla, E. S., and Yettram, A. L., “A Direct Numerical Method for Elastic Stability Analysis,” presented at the September, 1977, International Conference on the Behaviour of Slender Structures, held at the City University, London, England.
4.
Da Deppo, D. A., and Schmidt, R., “Nonlinear Analysis of Buckling and Postbuckling Behaviour of Circular Arches,” Journal of Applied Mathematics and Physics, Vol. 20, No. 6, 1969, pp. 847–857.
5.
Edmonds, F. D., and Medland, I. C., “Approximate Determination of Frame Critical Loads,” Journal of the Structural Division, ASCE, Vol. 98, No. ST3, Proc. Paper 8771, Mar., 1972, pp. 695–711.
6.
Horne, M. R., “An Approximate Method for Calculating the Elastic Critical Loads of Multi‐Storey Plane Frames,” The Structural Engineer, Vol. 53, No. 6, June, 1975, pp. 242–248.
7.
Korn, A., “Bounding of Frame Buckling Loads,” Journal of the Structural Division, ASCE, Vol. 96, No. ST8, Proc. Paper 7452, Aug., 1970, pp. 1639–1655.
8.
McMinn, S. J., Matrices for Structural Analysis, Spon, London, England, 1962.
9.
Merchant, W., “The Failure Load of Rigid Jointed Frameworks as Influenced by Stability,” The Structural Engineer, Vol. 32, No. 7, July, 1954, pp. 185–190.
10.
Przemieniecki, J. S., “Matrix Structural Analysis of Substructures,” Journal of the American Institute of Aeronautics and Astronautics, Vol. 1, No. 1, Jan., 1963, pp. 138–147.
11.
Salem, A. H., “Stability of Unbraced Single‐Bay Multistorey Frames,” Journal of the Structural Division, ASCE, Vol. 99, No. ST2, Proc. Paper 9552, Feb., 1973, pp. 223–242.
12.
Williams, F. W., and Howson, W. P., “Compact Computation of Natural Frequencies and Buckling Loads for Plane Frames,” International Journal for Numerical Methods in Engineering, Vol. 11, 1977, pp. 1067–1081.
13.
Wood, R. H., “Effective Lengths of Columns in Multi‐Storey Buildings,” Parts 1, 2 and 3, The Structural Engineer, Vol. 52, Nos. 7, 8, and 9, July, Aug., and Sept., 1974, pp. 235, 295, and 341.
14.
Yettram, A. L., and Husain, H. M., “Generalised Matrix Force and Displacement Methods of Linear Structural Analysis,” Journal of the American Institute of Aeronautics and Astronautics, Technical Notes, Vol. 3, No. 6, June, 1965, pp. 1154–1156.
15.
Yettram, A. L., and Awadalla, E. S., “A Direct Matrix Method for the Elastic Stability Analysis of Struts,” International Journal of Mechanical Sciences, Vol. 9, No. 5, May, 1967, pp. 315–321.
16.
Yettram, A. L., and Awadalla, E. S., “A Direct Matrix Method for the Elastic Stability Analysis of Plates,” International Journal of Mechanical Sciences, Vol. 10, 1968, pp. 887–901.
17.
Yettram, A. L., and Awadalla, E. S., “The Distribution of Transverse Reactive Forces at the Edges of a Rectangular Plate at the Buckling Load,” International Journal of Mechanical Sciences, Vol. 12, 1970, pp. 669–674.
Information & Authors
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Published In
Journal of Structural Engineering
Volume 109 • Issue 5 • May 1983
Pages: 1091 - 1106
Copyright
Copyright © 1983 ASCE.
History
Published online: May 1, 1983
Published in print: May 1983
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