Effect of Longitudinal Stress Gradients on Elastic Buckling of Thin Plates
Publication: Journal of Engineering Mechanics
Volume 133, Issue 4
Abstract
This paper analyzes the effect of longitudinal stress gradients on the elastic buckling of thin isotropic plates. Two types of thin plates are considered: (1) a plate simply supported on all four edges and rotationally restrained on two longitudinal edges; and (2) a plate simply supported on three edges with one longitudinal edge free and the opposite longitudinal edge rotationally restrained. These two cases illustrate the influence of longitudinal stress gradient on stiffened and unstiffened elements, respectively. A semianalytical method is derived and presented herein to calculate the elastic-buckling stress of both types of rectangular thin plates subjected to nonuniform applied longitudinal stresses. Finite-element analysis using ABAQUS is employed to validate the semianalytical model for plates with fixed and/or simple supports. Empirical formulas are produced to calculate the buckling coefficients of plates with fixed and/or simple supports under longitudinal stress gradients. The results help establish a better understanding of the effect of longitudinal stress gradients on the elastic buckling of thin plates and are intended to aid in the development of design provisions to include these effects in the strength prediction of thin-walled beams under moment gradients.
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Acknowledgments
The sponsorship of the American Iron and Steel Institute is gratefully acknowledged.
References
ABAQUS. (2001). ABAQUS version 6.2, Pawtucket, R.I.
Libove, C., Ferdman, S., and Reusch, J. (1949). “Elastic buckling of a simply supported plate under a compressive stress that varies linearly in the direction of loading.” NACA Technical Note No. 1891, National Advisory Committee for Aeronautics, Washington, D.C.
Lundquist, E., and Stowell, E. (1942a). “Critical compressive stress for flat rectangular plates supported along all edges and elastically restrained against rotation along the unloaded edges.” NACA Rep. No. 733, National Advisory Committee for Aeronautics, Washington, D.C.
Lundquist, E., and Stowell, E. (1942b). “Critical compressive stress for outstanding flanges.” NACA Rep. No. 734, National Advisory Committee for Aeronautics, Washington, D.C.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability, 2nd Ed., McGraw-Hill, Columbus, Ohio.
Yu, C. (2005). “Distortional buckling of cold-formed steel members in bending.” Ph.D. thesis, Johns Hopkins Univ., Baltimore.
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Copyright
© 2007 ASCE.
History
Received: Mar 29, 2005
Accepted: Aug 15, 2006
Published online: Apr 1, 2007
Published in print: Apr 2007
Notes
Note. Associate Editor: Hayder A. Rasheed
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