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Chart prepared by Leslaw Kwasniewski
sigma = applied stress.
sigma-sub-E = elastic Euler buckling stress.
sigma-sub-y = material yield stress.
P-sub-cr = critical buckling load.
Delta-l = end axial shortening.
Delta-l-sub-cr = end axial shortening correspnding to critical elastic buckling of the most slender column.
P-sub-cr minus P-sub-crD = abrupt drop in load exhibited during a test in which the axial end shortening is controlled.
P-sub-12 and P-sub-23 are defined in the paper cited below.
NOTICE: The column with intermediate slenderness experiences a sudden change in state whether the axial force or the axial end shortening is controlled. Qualitatively, this behavior is typical of an axially compressed cylindrical shell or an externally pressurized spherical shell. It is called “Finite Disturbance Buckling” (FDB) and “snap-down” in the paper cited below.
From:
Leslaw Kwasniewski (1) and Andrzej Ziolkowski (2)
(1) Warsaw University of Technology, Al. Armii Ludowej 16, 00-637 Warsaw, Poland
(2) Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawinskiego 5B, 02-106 Warsaw, Poland
“Simplified analytical model and numerical simulations of finite-disturbance buckling of columns”, International Journal of Non-Linear Mechanics, Vol. 51, pp 121-131, 2013
ABSTRACT: Phenomenon of finite-disturbance buckling (FDB) is commonly attributed to thin elastic cylindrical and spherical shells and it has been rarely associated with columns. Ziolkowski and Imielowski’s, Experimental Mechanics 51(8), (2011) 1335–1345, recent experimental study, revealing appearance of FDB in aluminum columns with slenderness remaining within specific range only, raises questions about its physical sources and mechanism. The main objective of the presented work is to provide a theoretical explanation and quantitative evaluation on the phenomenon of finite-disturbance buckling of columns undergoing elasto-plastic deformation and expressing itself in the form of critical load drop. Elucidation of the issue may have some implications to the hitherto design procedures. The paper presents a coherent analytical model of the phenomenon supported by comprehensive finite element results, compared with experimental data.
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