Carrying capacity of edge-compressed rectangular plates

1980 ◽  
Vol 7 (1) ◽  
pp. 19-26
Author(s):  
A. N. Sherbourne ◽  
H. M. Haydl
Keyword(s):  
Carrying Capacity ◽  
Ultimate Load ◽  
Compressive Loading ◽  
Effective Width ◽  
Rectangular Plates ◽  
Rigid Plastic ◽  
Simply Supported ◽  
Elastic Loading ◽  
Special Case ◽  
Good Agreement

The carrying capacity of simply supported rectangular plates under uniaxial, in-plane compressive loading is investigated. The ultimate load is determined as the load corresponding to the intersection of an elastic loading line and a rigid–plastic unloading line. An attempt is made to formulate a plastic roof mechanism for the rectangular plate; the square buckle pattern mechanism for long plates is obtained as a special case. The effective width method is re-examined and is shown to give good agreement with experimental evidence. The recommendations of CSA S136-1974 are briefly reviewed in the light of the results obtained.

scholarly journals Vibration of Skew Sandwich Plates With Laminated Facings

1997 ◽  
Author(s):  
C. M. Wang ◽  
K. K. Ang ◽  
C. Wang
Keyword(s):  
Ritz Method ◽  
Composite Plates ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Edge Conditions ◽  
System Vibration ◽  
Special Case ◽  
Length Limitation ◽  
Good Agreement

A Rayleigh-Ritz analysis is presented for the free vibration of skew sandwich plates composed of an orthotropic core and laminated facings. By proposing a set of Ritz functions consisting of the product of mathematically complete polynomial functions and the the boundary equations raised to appropriate powers, the Rayleigh-Ritz method can be automated to handle such composite plates with any combination of edge conditions. For convenience and better accurarcy, the Ritz formulation was derived in the skew coordinate system. Vibration frequencies of rectangular plates (a special case of skew plates) obtained via this method have been found to be in good agreement with previous researchers results. Owing to length limitation, only sample vibration frequencies for skew sandwich plates are presented.

Application of large-deflection theory to normally loaded rectangular plates with clamped edges

1970 ◽  
Vol 5 (2) ◽  
pp. 140-144 ◽  
Author(s):  
A Scholes
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Non Linear ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Clamped Edges ◽  
Clamped Edge ◽  
Good Agreement

A previous paper (1)∗described an analysis for plates that made use of non-linear large-deflection theory. The results of the analysis were compared with measurements of deflections and stresses in simply supported rectangular plates. In this paper the analysis has been used to calculate the stresses and deflections for clamped-edge plates and these have been compared with measurements made on plates of various aspect ratios. Good agreement has been obtained for the maximum values of these stresses and deflections. These maximum values have been plotted in such a form as to be easily usable by the designer of pressure-loaded clamped-edge rectangular plates.

Bending of normally loaded simply supported rectangular plates in the large-deflection range

1969 ◽  
Vol 4 (3) ◽  
pp. 190-198 ◽  
Author(s):  
A Scholes ◽  
E L Bernstein
Keyword(s):  
Linear Equations ◽  
Rectangular Plates ◽  
Algebraic Equations ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Linear Algebraic Equations ◽  
Non Linear ◽  
Out Of Plane ◽  
Linear Differential ◽  
Good Agreement

Means of solving the non-linear differential equations of plate bending are revieweed and a method based on minimizing the corresponding energy integral is selected as offering most advantages. The energy intergral can be approximated either by using finite-difference approximatons or by assuming a form of displacement variation. Two sets of non-linear algebraic equations (in the in-plane and out-of-plane deflections) are thus formed and, by substitution alternately in each set, the resulting linear equations are solved. Results for simply supported rectangular plates have been worked out in some detail; these are compared with tests made on plates of various aspect ratios. Good agreement on maximum values of stress and deflection was obtained.

Closed-Form Solutions for Eigenbuckling of Rectangular Mindlin Plate

2016 ◽  
Vol 16 (08) ◽  
pp. 1550079 ◽  
Author(s):  
Yufeng Xing ◽  
Wei Xiang
Keyword(s):  
Closed Form ◽  
Present Method ◽  
Separation Of Variables ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Major Development ◽  
First Time ◽  
Good Agreement

This paper studies the eigenbuckling of Mindlin plate with two adjacent edges clamped and the remaining edges simply supported or clamped by using the separation of variables method, and the concise and explicit closed-form solutions are obtained for the first time. The cases involving free edges can also be dealt with if there are two opposite edges simply supported. The closed-form solutions are in good agreement with the existing solutions, thus the validity of present method and accuracy of the obtained solutions are verified. This paper proves to be a major development of analytical method since it has long been acknowledged that the eigenbuckling of rectangular plates without two parallel edges simply supported are not amenable to analytical solutions.

Postbuckling Behavior of Rectangular Plates With Small Initial Curvature Loaded in Edge Compression—(continued)

1960 ◽  
Vol 27 (2) ◽  
pp. 335-342 ◽  
Author(s):  
Noboru Yamaki
Keyword(s):  
Stress State ◽  
Boundary Conditions ◽  
Ultimate Load ◽  
Numerical Solutions ◽  
Effective Width ◽  
Rectangular Plates ◽  
Postbuckling Behavior ◽  
Shear Theory ◽  
Title Problem ◽  
Square Plate

In the previous paper [1], the title problem is theoretically treated under eight different boundary conditions and numerical solutions are obtained for the deflection, edge shortening, and effective width of the square plate in edgewise compression. As a continuation of this work, the stress state in the buckled plate is investigated and numerical results for the square plate are given graphically. Further the formulas for the ultimate load of the square plate in each case are derived by using the maximum-shear theory for the beginning of yielding and comparison is made with the previous results and experiments.

Free and Forced Vibration of Stepped Levy Plates

1993 ◽  
Author(s):  
Jinkyo Lee ◽  
Lawrence A. Bergman
Keyword(s):  
High Frequency ◽  
Minimum Weight ◽  
Rectangular Plates ◽  
Uniform Thickness ◽  
Minimum Weight Design ◽  
Simply Supported ◽  
Acoustic Transducers ◽  
Nonuniform Thickness ◽  
Weight Design ◽  
Special Case

Abstract The study of the transverse vibration of thin rectangular plates has been mainly confined to plates of uniform thickness. There are few publications available on the vibration of plates with nonuniform thickness. These plates have application in various fields such as civil engineering and aerospace structures and are often found in high frequency acoustic transducers. Furthermore, it is sometimes possible to achieve minimum weight design of plates by having suitable variations in thickness. For the special case of a plate with two opposite edges simply supported and thickness discontinuities perpendicular to the simply supported edges, an analytical solution is possible using a dynamic flexibility method. Several examples are discussed.

scholarly journals Semi-Analytical Solution Based on Strip Method for Buckling and Vibration of Isotropic Plate

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Mohamed A. El-Sayad ◽  
Ahmed M. Farag
Keyword(s):  
Transition Matrix ◽  
Isotropic Plate ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Analytical Results ◽  
Present Technique ◽  
Benchmark Solutions ◽  
Good Agreement

The present paper achieves a semianalytical solution for the buckling and vibration of isotropic rectangular plates. Two opposite edges of plate are simply supported and others are either free, simply supported, or clamped restrained against rotation. The general Levy type solution and strip technique are employed with transition matrix method to develop a semianalytical approach for analyzing the buckling and vibration of rectangular plates. The present analytical approach depends on reducing the strips number of the decomposed domain of plate without escaping the results accuracy. For this target, the transition matrix is expressed analytically as a series with sufficient truncation numbers. The effect of the uni-axial and bi-axial in-plane forces on the natural frequency parameters and mode shapes of restrained plate is studied. The critical buckling of rectangular plate under compressive in-plane forces is also examined. Analytical results of buckling loads and vibration frequencies are obtained for various types of boundary conditions. The influences of the aspect ratios, buckling forces, and coefficients of restraint on the buckling and vibration behavior of rectangular plates are investigated. The presented analytical results may serve as benchmark solutions for such plates. The convergence and efficiency of the present technique are demonstrated by several numerical examples compared with those available in the published literature. The results show fast convergence and stability in good agreement with compressions.

scholarly journals Strengthening of RCC Beams in Shear by Using SBR Polymer-Modified Ferrocement Jacketing Technique

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Rajinder Ghai ◽  
Prem Pal Bansal ◽  
Maneek Kumar
Keyword(s):  
Carrying Capacity ◽  
Shear Failure ◽  
Ultimate Load ◽  
Load Test ◽  
Wire Mesh ◽  
Styrene Butadiene Rubber ◽  
Shear Load ◽  
Butadiene Rubber ◽  
Load Carrying Capacity ◽  
Load Carrying

There is a common phenomenon of shear failure in RCC beams, especially in old buildings and bridges. Any possible strengthening of such beams is needed to be explored that could strengthen and make them fit for serviceable conditions. The present research has been made to determine the performance of predamaged beams strengthened with three-layered wire mesh polymer-modified ferrocement (PMF) with 15% styrene-butadiene-rubber latex (SBR) polymer. Forty-eight shear-designed and shear-deficient real-size beams were used in this experimental work. Ultimate shear load-carrying capacity of control beams was found at two different shear-span (a/d) ratios 1 and 3. The sets of remaining beams were loaded with different predetermined damage levels of 45%, 75%, and 95% of the ultimate load values and then strengthened with 20 mm thick PMF. The strengthened beams were then again tested for ultimate load-carrying capacity by conducting the shear load test at a/d = 1 and 3. As a result, the PMF-strengthened beams showed restoration and enhancement of ultimate shear load-carrying capacity by 5.90% to 12.03%. The ductility of strengthened beams was improved, and hence, the corresponding deflections were prolonged. On the other hand, the cracking pattern of PMF-strengthened beams was also improved remarkably.

scholarly journals Eigenproblem Versus the Load-Carrying Capacity of Hybrid Thin-Walled Columns with Open Cross-Sections in the Elastic Range

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3468
Author(s):  
Zbigniew Kolakowski ◽  
Andrzej Teter
Keyword(s):  
Cross Sections ◽  
Carrying Capacity ◽  
Ultimate Load ◽  
Equilibrium Path ◽  
Load Carrying Capacity ◽  
Nonlinear Buckling ◽  
Elastic Range ◽  
Load Carrying ◽  
Thin Walled ◽  
Ultimate Load Carrying Capacity

The phenomena that occur during compression of hybrid thin-walled columns with open cross-sections in the elastic range are discussed. Nonlinear buckling problems were solved within Koiter’s approximation theory. A multimodal approach was assumed to investigate an effect of symmetrical and anti-symmetrical buckling modes on the ultimate load-carrying capacity. Detailed simulations were carried out for freely supported columns with a C-section and a top-hat type section of medium lengths. The columns under analysis were made of two layers of isotropic materials characterized by various mechanical properties. The results attained were verified with the finite element method (FEM). The boundary conditions applied in the FEM allowed us to confirm the eigensolutions obtained within Koiter’s theory with very high accuracy. Nonlinear solutions comply within these two approaches for low and medium overloads. To trace the correctness of the solutions, the Riks algorithm, which allows for investigating unsteady paths, was used in the FEM. The results for the ultimate load-carrying capacity obtained within the FEM are higher than those attained with Koiter’s approximation method, but the leap takes place on the identical equilibrium path as the one determined from Koiter’s theory.

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