Theory of Plastic Buckling of Plates and Application to Simply Supported Plates Subjected to Bending or Eccentric Compression in Their Plane

1956 ◽  
Vol 23 (1) ◽  
pp. 27-34
Author(s):  
P. P. Bijlaard
Keyword(s):  
Reduction Factor ◽  
Elastic Buckling ◽  
Plastic Buckling ◽  
Simply Supported ◽  
Buckling Stress ◽  
Plate Buckling ◽  
Eccentric Compression ◽  
Finite Difference Equations ◽  
Longitudinal Bending ◽  
Plate Width

Abstract After some general considerations on the plastic buckling of plates, the plastic buckling stresses are calculated for long plates, subject to longitudinal bending or eccentric compression in their plane, and simply supported at their unloaded edges. The solutions are based on the author’s theory of plastic plate buckling and are obtained by reducing the governing partial differential equation to ordinary finite-difference equations. Second-order finite differences are used, with a spacing equal to one ninth of the plate width. A simple design formula is presented for the plastic reduction factor with which the elastic buckling stress has to be multiplied for obtaining the plastic buckling stress.

Buckling of Thin Cylindrical Shell Under Hoop Stresses Varying in Axial Direction

1957 ◽  
Vol 24 (3) ◽  
pp. 405-412
Author(s):  
N. J. Hoff
Keyword(s):  
Cylindrical Shell ◽  
Thermal Stresses ◽  
Axial Direction ◽  
Elastic Buckling ◽  
Thin Cylindrical Shell ◽  
Simply Supported ◽  
Buckling Stress ◽  
Compressive Stresses ◽  
Hoop Stresses ◽  
Approximate Formulas

Abstract The buckling of a thin cylindrical shell simply supported along the perimeter of its end sections is analyzed under hoop compressive stresses varying in the axial direction. The thermal stresses arising from a uniform increase in the temperature of the cylinder are determined. It is found that such thermal stresses are not likely to cause elastic buckling. Simple approximate formulas are developed for buckling stress and thermal stress.

CALCULATION OF EFFORTS RIPS FOUNDATION BOLTS IN THE BCALCULATION OF EFFORTS RIPS FOUNDATION BOLTS IN THE BASES OF CENTRAL AND ECCENTRIC COMPRESSION COLUMNASES OF CENTRAL AND ECCENTRIC COMPRESSION COLUMN

2021 ◽  
Vol 295 (2) ◽  
pp. 32-36
Author(s):  
A.E. Svyatoshenko ◽  
◽  
Keyword(s):  
Cross Section ◽  
Software Package ◽  
Calculation Model ◽  
Neutral Axis ◽  
Continuous Section ◽  
Eccentric Compression ◽  
Engineering Technique ◽  
Section Shape ◽  
Longitudinal Bending ◽  
The Stability

An engineering technique for calculating the tearing forces in the foundation bolts in the bases of centrally compressed columns is proposed. The calculation of the forces is based on the calculation of extra-centrally compressed rods, taking into account: the influence of the cross-section shape; the initial curvature of the neutral axis of the column; random eccentricity; nonlinear steel work. The calculation of the attachment forces (Nult and Mfic) of columns on the foundation edge is based on the method of practical calculations of centrally compressed elements using the stability coefficients at central compression φ (longitudinal bending coefficients), which are calculated depending on the flexibility l. The calculation of the attachment forces for rods with different reduced flexibility was performed by FEM in the FEMAP software package, as well as analytically using fictitious forces in centrally compressed rods. To calculate the tearing forces in the foundation bolts, a calculation model is made taking into account the contact interaction of the base and the reinforced concrete base. Graphs of the effect of the flexibility of the centrally compressed rod on the tearing force in the foundation bolts at the stage of exhaustion of the bearing capacity of the column when calculating its stability as an element of a continuous section under central compression are constructed.

Some Observations on the Compressive Buckling of Rectangular Plates

1963 ◽  
Vol 14 (1) ◽  
pp. 17-30 ◽  
Author(s):  
W. H. Wittrick
Keyword(s):  
Rate Of Change ◽  
Infinite Strip ◽  
Rectangular Plates ◽  
Buckling Mode ◽  
Simply Supported ◽  
Side Ratio ◽  
Buckling Stress ◽  
Stress Coefficient ◽  
Wide Range ◽  
Elastically Restrained

SummaryThe problem considered is the buckling of a rectangular plate under uniaxial compression. The ends may be either both clamped, both simply-supported or a mixture of the two. The sides may be elastically restrained against both deflection and rotation with any stiffnesses whatsoever. It is shown that the curve of buckling stress coefficient versus side ratio can be deduced in a simple manner from that of a plate with the same end conditions but with both sides simply-supported, provided only that the buckling stress coefficient and wavelength for an infinite strip with the same side conditions are known. Some correlations between the curves for the three types of end condition are discussed. It is also shown that if, for some given side ratio, the buckling mode is known, then it is always possible to deduce the rate of change of buckling stress coefficient with side ratio at that point. The argument is based upon an assumption which is shown to give very accurate results in a wide range of cases.

The Plastic Buckling of Axially Compressed Square Tubes

1992 ◽  
Vol 59 (2) ◽  
pp. 276-282 ◽  
Author(s):  
S. Li ◽  
S. R. Reid
Keyword(s):  
Deformation Theory ◽  
Buckling Analysis ◽  
Rectangular Plates ◽  
Plastic Buckling ◽  
Buckling Mode ◽  
Important Conclusion ◽  
Simply Supported ◽  
Edge Conditions ◽  
Crushing Behavior ◽  
Incremental Theory Of Plasticity

A plastic buckling analysis for axially compressed square tubes is described in this paper. Deformation theory is used together with the realistic edge conditions for the panels of the tube introduced in our previous paper (Li and Reid, 1990), referred to hereafter as LR. The results obtained further our understanding of a number of problems related to the plastic buckling of axially compressed square tubes and simply supported rectangular plates, which have remained unsolved hitherto and seem rather puzzling. One of these is the discrepancy between experimental results and the results of plastic buckling analysis performed using the incremental theory of plasticity and the unexpected agreement between the results of calculations based on deformation theory for plates and experimental data obtained from tests conducted on tubes. The non-negligible difference between plates and tubes obtained in the present paper suggests that new experiments should be carried out to provide a more accurate assessment of the predictions of the two theories. Discussion of the results herein also advances our understanding of the compact crushing behavior of square tubes beyond that given in LR. An important conclusion reached is that strain hardening cannot be neglected for the plastic buckling analysis of square tubes even if the degree of hardening is small since doing so leads to an unrealistic buckling mode.

Influence of Defects on Elastic Buckling Properties of Single-Layered Graphene Sheets

2014 ◽  
Vol 636 ◽  
pp. 11-14 ◽  
Author(s):  
Bao Long Li ◽  
Li Jun Zhou ◽  
Jian Gao Guo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Vacancy Defect ◽  
Elastic Buckling ◽  
Graphene Sheets ◽  
Effect Factors ◽  
Vacancy Defects ◽  
Size Dependent ◽  
Buckling Stress ◽  
Geometrical Dimensions

Molecular structural mechanics based finite element method has been applied to study the effects of two types of Stone-Wales (SW) defects and vacancy defect on elastic buckling properties of single-layered graphene sheets (SLGSs). The defect effect factors of critical buckling stresses are calculated for the defective SLGSs with different chirality and geometrical dimensions. It is proved that defect effect factors are size-dependent and chirality-dependent. The results show that the vacancy defects will always weaken the SLGSs’ stability, and two types of SW defects have different effects on zigzag and armchair SLGSs. What’s more, the positions of defects also have remarkable influence on the critical buckling stress of SLGSs.

Local buckling of rectangular concrete-filled steel tubular columns with binding bars under eccentric compression

2020 ◽  
Vol 23 (10) ◽  
pp. 2204-2219
Author(s):  
Jun Wan ◽  
Jian Cai ◽  
Yue-Ling Long ◽  
Qing-Jun Chen
Keyword(s):  
Stress Gradient ◽  
Local Buckling ◽  
Steel Plates ◽  
Cross Sectional ◽  
Tubular Columns ◽  
Buckling Stress ◽  
Aspect Ratios ◽  
Eccentric Compression ◽  
Buckling Behavior ◽  
Elastically Restrained

Based on the energy method, this article presents a theoretical study on the elastic local buckling of steel plates in rectangular concrete-filled steel tubular columns with binding bars subjected to eccentric compression. The formulas for elastic local buckling strength of the steel plates in eccentrically loaded rectangular concrete-filled steel tubular columns with binding bars are derived, assuming that the loaded edges are clamped and the unloaded edges of the steel plate are elastically restrained against rotation. Then, the experimental results are compared with these formulas, which exhibits good agreement. Subsequently, the formulas are used to study the elastic local buckling behavior of steel plates in rectangular concrete-filled steel tubular columns with binding bars under eccentric compression. It is found that the local buckling stress of steel plates in eccentrically loaded rectangular concrete-filled steel tubular columns with binding bars is significantly influenced by the stress gradient coefficient, width-to-thickness ratio, and the longitudinal spacing of binding bars. With the decrease of width–thickness ratios or the longitudinal spacing of binding bars or with the increase of the stress gradient coefficient, the local buckling stress increases. Furthermore, the influence of the longitudinal spacing of binding bar is more significant than the stress gradient coefficients. Finally, appropriate limitation for depth-to-thickness ratios ( D/ t), width-to-thickness ratios ( B/ t), and binding bar longitudinal spacing at various stress gradient coefficients ( α0) corresponding to different cross-sectional aspect ratios ( D/ B) are suggested for the design of rectangular concrete-filled steel tubular columns with binding bars under eccentric compression.

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