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Abstract

The governing differential equation for buckling of a non-uniform column is expressed in the form of bending moment. The special solutions for 14 types of non-uniform columns are derived from the governing equation. Using a rotational spring and a hinge connection to describe the local flexibility induced by a crack in the column yields the eigenvalue equation for buckling. The main advantage of the proposed method is that the eigenvalue equation for buckling of a non-uniform column with an arbitrary number of cracks, any kind of two end supports, and an arbitrary number of rotational and translational spring supports at intermediate points can be conveniently determined from a second-order determinant based on the fundamental solutions and recurrence formula developed in this paper. As a consequence, the decrease in the determinant order as compared with previously developed procedures simplifies the analysis. A numerical example is given to illustrate the application of the proposed method and to study the effect of cracks on the critical buckling force of a non-uniform column.

Keywords

buckling stability crack column

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References

Dimarogonas

A. D.

Vibration of cracked structures: A state of the art review. J. Eng. Fract. Mech., 1996, 55, 831–857.

Anifantis

Dimarogonas

Stability and columns with a single crack subjected follower and vertical loads. Int. J. Solid Struct., 1983, 19, 281–291.

Chen

L. W.

Chen

C. U.

Vibration and stability of cracked thick rotating blades. Comput. Struct., 1988, 28, 67–74.

Yang

X. Y.

W. J.

Xie

Y. M.

Eigenvalue sensitivity of cracked beam structures. Adv. Struct. Eng., 1999, 2 (3), 199–204.

Rozos

P. F.

Aspragatos

Dimarogonas

A. D.

Identification of crack location and magnitude in a cantilever beam from the vibration mode. J. Sound Vib., 1990, 138, 381–388.

Shifrin

E. I.

Ruotolo

Natural frequencies of a beam with arbitrary number of cracks. J. Sound Vib., 1999, 222 (3), 409–423.

Takahashi

Vibration and stability of non-uniform cracked Timoshenko beam subjected to follower force. Compu. Struct., 1999, 71, 585–591.

Qian

G. L.

S. N.

Jiang

J. S.

The dynamic behaviour and crack detection of a beam with a crack. J. Sound Vib., 1990, 138, 233–243.

Liang

R. H.

Choy

Theoretical study of crack-induced eigenfrequency changes on beam structures. J. Eng. Mech. ASCE, 1992, 118 (2), 384–396.

10.

Q. S.

Cao

G. Q.

Stability analysis of a bar with multi-segment varying cross-section. Comput. Struct., 1994, 35 (5), 1085–1089.

11.

Q. S.

Buckling analysis of multi-step non-uniform beams. Adv. Struct. Eng., 2000, 3 (2), 139–144.

12.

Q. S.

Buckling of multi-step non-uniform beams with elastically restrained boundary conditions. J. Constr. Steel Res., 2001, 57 (7), 753–777.

13.

Q. S.

Classes of exact solutions for several static and dynamic problems of non-uniform beams. Struct. Eng. Mech., 2001, 12 (1), 85–100.

14.

Q. S.

Buckling of multi-step cracked columns with shear deformation. Eng. Struct., 2001, 23 (4), 356–364.

Buckling of Non-Uniform Columns with an Arbitrary Number of Cracks

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