Correlation Between some Stability Problems for Orthotropic and Isotropic Plates under Bi-Axial and Uni-Axial Direct Stress

1954 ◽  
Vol 4 (1) ◽  
pp. 83-92 ◽  
Author(s):  
W. H. Wittrick
Keyword(s):  
Axial Compression ◽  
Orthotropic Plate ◽  
Isotropic Plate ◽  
List Type ◽  
Simply Supported ◽  
Side Ratio ◽  
Buckling Stress ◽  
Isotropic Plates ◽  
Stress Coefficient ◽  
Rectangular Orthotropic Plate

SummaryFour buckling problems are considered, namely: — (a) A rectangular orthotropic plate, with all edges simply supported, subjected to compression on its ends and a known compression or tension on its sides;(b) the same as (a) but with the ends clamped and sides simply supported;(c) a rectangular orthotropic plate, with the ends simply supported and sides clamped, subjected to compression on its ends; and(d) the same as (c) but with all edges clamped.In each case it is shown that the variables involved can all be combined into such a non-dimensional form that a single curve serves to give the value of the end compression required to cause buckling. This curve is identical with the curve of buckling stress coefficient against side ratio for a corresponding isotropic plate under uni-axial compression.

Buckling of Rectangular Plates under Bi–Axial Compression

1955 ◽  
Vol 59 (536) ◽  
pp. 566-568 ◽  
Author(s):  
J. S. Przemieniecki
Keyword(s):  
Compressive Stress ◽  
Axial Compression ◽  
Rapid Decrease ◽  
Rectangular Plates ◽  
Side Ratio ◽  
Buckling Stress ◽  
Compressive Stresses ◽  
Isotropic Plates ◽  
Stress Coefficient ◽  
Edge Conditions

The problem of the buckling under bi-axial compression is considered for flat rectangular isotropic plates with simple edge conditions and no lateral restraint. The buckling stress coefficient is plotted against the side ratio for various conditions of edge restraint and a known compression or tension on the sides of the plate. It is found that there is some reduction in the buckling stress if the sides of the plate are subjected to compressive stresses and, conversely, there is an increase for tensile stresses. Furthermore, for plates with large side ratios, there is a rapid decrease of the spanwise buckling stress as the chordwise compressive stress approaches its appropriate Euler instability value.

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.

Analysis of an Orthotropic Plate by Maclaurin's Series

1963 ◽  
Vol 67 (626) ◽  
pp. 126-127 ◽  
Author(s):  
N. R. Rajappa ◽  
D. V. Reddy
Keyword(s):  
Cross Section ◽  
Orthotropic Plate ◽  
Practical Applications ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Distributed Load ◽  
Functions Of Two Variables ◽  
Uniformly Distributed Load ◽  
Rectangular Orthotropic Plate

A method is presented for the analysis of a simply-supported rectangular orthotropic plate subjected to a uniformly distributed load by the application of Maclaurin's series. The solutions have practical applications in the design of interconnected beam systems because of the elastic equivalence of the grid framework to an orthotropic plate.The application of Maclaurin's series to the analysis of beams in bending was first described by Hetényi. Recently Reddy and Gangadharan described a modified approach for beams with stepped variations in cross section. Ballesteros has extended the method to functions of two variables in the analysis of isotropic plates in bending.

Buckling of Tapered Rectangular Plates in Compression

1962 ◽  
Vol 13 (4) ◽  
pp. 308-326 ◽  
Author(s):  
W. H. Wittrick ◽  
C. H. Ellen
Keyword(s):  
Boundary Conditions ◽  
Thickness Variation ◽  
Rectangular Plates ◽  
Buckling Mode ◽  
Direction Parallel ◽  
Simply Supported ◽  
Side Ratio ◽  
Buckling Stress ◽  
Stress Coefficient ◽  
Two Sides

SummaryThe problem considered is the buckling of a rectangular plate, tapered in thickness in a direction parallel to two sides, and uniformly compressed in that direction. Curves are presented showing the variation of buckling stress coefficient with the side ratio and the amount of taper, for each of two types of thickness variation, namely exponential and linear, and for each of two sets of boundary conditions, namely all edges simply-supported, and ends clamped and sides simply-supported. It is shown that, unlike the case of a uniform plate, there are no discontinuous changes of buckling mode.

A Reduction Method for Buckling Problems of Orthotropic Plates

1957 ◽  
Vol 8 (2) ◽  
pp. 145-156 ◽  
Author(s):  
P. Shuleshko
Keyword(s):  
Boundary Conditions ◽  
Orthotropic Plate ◽  
Reduction Method ◽  
Isotropic Plate ◽  
Axial Loading ◽  
Orthotropic Plates ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Plate Buckling

SummarySeveral plate buckling problems are solved, using a reduction method. By this method the solution of an orthotropic plate can be reduced to the solution of an isotropic plate and the solution of a plate with bi-axial loading can be reduced to the solution of a plate with uni-axial loading and so on. Plates with simply-supported ends and various boundary conditions at the sides with uni-axial and bi-axial loading are considered and the necessary reduction equations are given.

Compressive Buckling of Infinite Strips with Elastically Restrained Edges

1963 ◽  
Vol 14 (2) ◽  
pp. 158-162 ◽  
Author(s):  
W. H. Wittrick ◽  
W. E. Bodley
Keyword(s):  
Infinite Strip ◽  
Side Ratio ◽  
Buckling Stress ◽  
Stress Coefficient ◽  
Wide Range ◽  
End Conditions ◽  
Compressive Buckling ◽  
Elastically Restrained Edges ◽  
Elastically Restrained ◽  
The Given

SummaryIt has been shown in another paper that the relation between the compressive buckling stress coefficient and side ratio for a rectangular plate with the sides elastically restrained against deflection and rotation can be obtained from the corresponding curve for a plate with the same end conditions but with both sides simply-supported, provided only that the buckling stress coefficient and wavelength of the buckle are known for an infinite strip with the given side conditions. This paper presents these numerical values for infinite strips with a wide range of edge stiffnesses.

scholarly journals The effect of flexural–torsional buckling on the stability of timber members: a case study

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Osama A. B. Hassan
Keyword(s):  
Axial Compression ◽  
Bending Moment ◽  
List Type ◽  
Torsional Buckling ◽  
Solution Methods ◽  
Simplified Solution ◽  
The Stability ◽  
Flexural Torsional Buckling ◽  
Building Engineering

Abstract This study investigates the stability of timber members subjected to simultaneously acting axial compression and bending moment, with possible risk for torsional and flexural–torsional buckling. This situation can occur in laterally supported members where one side of the member is braced but the other side is unbraced. In this case, the free side will buckle out of plane while the braced side will be prevented from torsional and flexural–torsional buckling. This problem can be evident for long members in timber-frame structures, which are subjected to high axial compression combined with bending moments in which the member is not sufficiently braced at both sides. This study is based on the design requirement stated in Eurocode 5. Solution methods discussed in this paper can be of interest within the framework of structural and building Engineering practices and education in which the stability of structural elements is investigated. Article Highlights This case study investigates some design situations where the timber member is not sufficiently braced. In this case, a stability problem associated with combined torsional buckling and flexural buckling can arise. The study shows that the torsional and/or flexural–torsional buckling of timber members can be important to control in order to fulfil the criteria of the stability of the member according to Eurocode 5 and help the structural engineer to achieve safer designs. The study investigates also a simplified solution to check the effect of flexural torsional buckling of laterally braced timber members.

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