Buckling Of Plates Research Articles

Experimental and computational study on local buckling of standard and improved cold-formed square hollow sections under static and dynamic loading

Because of aesthetics, economic advantages, easy composite member production and design, and a wide range of standard sizes, hollow sections are commonly utilized in various construction industry applications worldwide, including conventional and unique free-form structures. However, the sections must fulfill more restricted circumstances to avoid early local buckling. The behavior of cold-formed square hollow sections with different wall thicknesses under static and dynamic transverse impact loading was investigated experimentally and numerically in this study. A method that uses rivet nuts is proposed to improve the dominant local buckling behavior, which is observed in the experimental studies and causes a relatively low bending strength, for providing convenience in field applications. The effectiveness of the proposed method is demonstrated experimentally and numerically using finite-element analysis. In addition to conventional measurement techniques, motion analysis is performed using digital image correlation to measure the displacements during static and dynamic tests. With the proposed technique, the local buckling strength of the square hollow sections is increased by 64% under static loading and by approximately 40–85% under dynamic loading compared with standard square hollow sections, respectively. This is due to the internal stiffness plate, steel threaded rods, and rivet nut configuration connecting the flanges and webs of the square hollow section, which ensures load sharing between the section parts. Additionally, steel threaded rods prevent early buckling of the internal stiffness plate. In addition, parametric analysis results show that the thickness of the internal stiffness plate has a negligible effect on the local buckling strength, although the presence of an internal stiffness plate increased the strength. The numerical analysis results indicate that the local buckling behavior of both conventional and improved square hollow specimens can be predicted with acceptable errors in terms of their strength and damage modes using finite-element analysis models.

Nonlinear Buckling and Postbuckling of Circular Plates Reinforced with Graphene Platelets Using the Shooting Method

The buckling and postbuckling behaviors of functionally graded graphene platelets-reinforced composite (FG-GPLRC) circular plates are studied based on the classical nonlinear von Karman plate theory. The effective Young’s modulus of the composite is estimated using the modified Halpin–Tsai micromechanical model, and the effective Poisson’s ratio is estimated by the rule of mixtures. Governing equations of the problem are derived based on the Hamilton principle and the numerical solutions of critical loads and postbuckling deflection–load relationships are calculated using the shooting method. Different from the existing linear buckling analysis based on the Terriftz criterion, the study with considering the global deformation of the plates, we analyze the influencing factors of the critical buckling loads and postbuckling paths of the FG-GPLRC circular plates subjected to uniformly distributed radial pressure. The results show that the content, geometric parameters and distribution pattern of GPL have great influences on the critical buckling loads and the post-buckling bearing capacities of the circular FG-GPLRC plates.

Local buckling resistance of bamboo scrimber plates in compression

This paper describes experimental and theoretical investigations on behaviour of short bamboo scrimber box columns under compression. In the experimental programme, six groups of short columns with different width-to-thickness ratios of plates were tested and the load capacity and failure modes of the columns were determined. Test results indicated that when the width-to-thickness ratio of plates was less than or equal to 10, box columns exhibited compression failure and the ultimate compressive strength of bamboo scrimber was reached at failure. However, local buckling of bamboo scrimber plates was observed instead of compression failure once the width-to-thickness ratio of plates exceeded 11, and the ultimate compressive stress decreased with increasing width-to-thickness ratio. Based on the experimental data, theoretical analyses were also performed by considering the nonlinear stress-strain relationship to quantify the buckling stress of bamboo scrimber plates with four simply-supported edges. Comparisons between experimental and theoretical results suggest that when the theoretical equation yields reasonably good estimations of the local buckling stress of columns with the width-to-thickness ratio of plates greater than 10.

Experimental and analytical investigation on the compressive behavior of double-skin steel-concrete composite tube walls

An innovative structural wall named double-skin steel-concrete composite tube(DSCCT) wall is proposed in this paper. The proposed wall is composed of rectangular steel composite tube, in-filled concrete, external concrete and stud-tie bar connectors. Sixteen full-scaled DSCCT wall specimens and two reinforced concrete walls (RCW) specimens were tested under axial monotonic compression to investigate their load bearing capacity. Parameters included are the double-skin steel plates thickness, steel plate slenderness ratio (the distance to thickness ratio of the stud-tie bars), stud-tie bar arrangement etc. The vertical load-displacement responses of the test specimens are discussed along with their stiffness, strength, and deformation capacity. Experimental results indicate that the DSCCT specimens exhibited a fairly good bearing capacity, the external concrete, steel composite tube and in-filled concrete could work together well. The greater the thickness of the double-skin steel plate, the greater the buckling wavelength; The smaller steel plate slenderness ratio, the later the local buckling of the double-skin steel plate occurred, and the higher the bearing capacity of the DSCCT wall specimens. The displacement ductility coefficient of the DSCCT wall specimens was higher than that of RCW specimen. Considering the local buckling of the double-skin steel plates and the confinement effect of the steel composite tube on the internal concrete, a theoretical calculation formula of the axial compression bearing capacity of DSCCT wall was proposed. The proposed calculation values were in good agreement with the test values, and had higher calculation accuracy and stability in predicting the axial compression bearing capacity of DSCCT walls.

Mechanisms of plasticity development and energy dissipation on concrete-encased steel plate shear wall with boundary steel frame under cyclic loading

Steel frame infilled with composite plate shear wall (SF-CPSW) is an efficient lateral load resisting structure with significant ductility and energy dissipation capacity. In this paper, CPSW comprises the infill steel plate, encased concrete panel and headed studs. The steel frames (SFs) are expected to sustain the vertical load, while as the boundary members of the CPSW, they also influence the lateral behaviors of structure. However, the research on the interactions or plasticity development of SF-CPSW is limited. Thus, its energy dissipation mechanism is unclear to date. This paper conducts finite element analyses on the hysteresis performance and energy dissipation mechanism of SF-CPSW structure under cyclic loading. The hysteresis and skeleton of lateral load-drift ratio responses, distributions and developments of internal forces, stresses and strains and the energy assignments are studied to reveal the mechanisms of lateral load-resisting and plasticity development of SF-CPSW. The effects of steel plate thickness, beam cross-section, column cross-section and concrete panel thickness on the hysteresis performance and energy assignment are investigated to propose the energy dissipation mechanism and associated design methods. The results indicate that the energy dissipation of SF-CPSW is governed by the plastic shearing of infill steel plate and beam web due to the shear force transfers and bending restraints from CPSW to the steel frame. Besides, the columns resist portions of lateral load under such interactions. The structural energy dissipation should develop successively by the shear yielding of steel plate, the shear yielding of beam and column, the flexural yielding of beam, the plastic buckling of steel plate and the flexural yielding of column. As the major members for energy dissipation, the yield shear strength of beam should be higher than 27.5% yield shear strength of infill steel plate.

Experimental Investigation on Bonded and Screwed Carbon Fiber-Reinforced Plastic Plates on Timber Column–Sill Joints

In this study, timber column–sill joints strengthened with carbon fiber-reinforced plastic (CFRP) plates using bonds and screws were subjected to loading tests. Twelve joint specifications were considered depending on different combinations of the CFRP plate surface finish and thickness and the type of bond, and the corresponding effects on the load–displacement behavior of the joints were investigated. Three failure modes were observed in addition to the peeling of the CFRP plate. The specimens that failed owing to screw tear out and screw head pull-through in the CFRP plate or splitting of the sill showed load–displacement curves of a similar shape. Those that failed owing to buckling of the CFRP plate showed a rapid and substantial load decrease due to failure. This failure mode was only observed in 0.50 mm thick CFRP plate specimens. When a peel-ply CFRP plate was installed in the column–sill joint specimens, similar secant stiffnesses were observed in the silicon and epoxy resin-bonded specimens, both with high shear strength. Although the specimens with bonds with a high shear strength showed lower deformation performance, the specimens' maximum load increased with the bond's shear strength. The maximum load improved for a 0.75 mm thick peel-ply silicon- or epoxy-bonded CFRP plate. The load's maximum value after peeling the CFRP plate was 0.79–1.23 times as large as the maximum load of the no-bond specimens and did not change significantly.

Re-examination of thermo-mechanical buckling and postbuckling responses of sandwich plates with porous FG-GPLRC core

The current study re-examines compressive postbuckling and thermal postbuckling responses of porous sandwich plates resting on an elastic foundation. The core of the sandwich plates is made of porous graphene platelets reinforced composite (GPLRC). Compressive postbuckling of the porous sandwich plates under uniaxial compression at elevated temperature and thermal postbuckling of the same plates under uniform thermal loading are studied. The GPLRC core is made of multilayers, and each layer may have different values of porosity coefficient to obtain a piecewise functionally graded (FG) pattern. The Young’s moduli along with the shear modulus of the porous GPLRC core are estimated through a generic Halpin–Tsai model in which the porous nature of the material is taken into consideration. The material properties of the metal face sheets and the porous GPLRC core are assumed to be temperature dependent. The governing equations for the postbuckling of the porous sandwich plates reinforced by GPLs are established based on the Reddy’s third order shear deformation theory (TSDT). In the modeling, we also consider the von Kármán nonlinear strain–displacement relationships, the plate-foundation interaction and the thermal effect. A two-step perturbation approach is utilized in solving the postbuckling problem. Numerical studies are performed to compare the results obtained from the present model and the equivalent isotropic model (EIM). The results confirm that the EIM is not suitable for analyzing buckling and postbuckling of porous plates.

Composite Cold-Formed Steel Beams with Diagonal Rebars for Earthquake-Resistant Buildings.

The construction industry is on the lookout for cost-effective structural members that are also environmentally friendly. Built-up cold-formed steel (CFS) sections with minimal thickness can be used to make beams at a lower cost. Plate buckling in CFS beams with thin webs can be avoided by using thick webs, adding stiffeners, or strengthening the web with diagonal rebars. When CFS beams are designed to carry heavy loads, their depth logically increases, resulting in an increase in building floor height. The experimental and numerical investigation of CFS composite beams reinforced with diagonal web rebars is presented in this paper. A total of twelve built-up CFS beams were used for testing, with the first six designed without web encasement and the remaining six designed with web encasement. The first six were constructed with diagonal rebars in the shear and flexure zones, while the other two with diagonal rebars in the shear zone, and the last two without diagonal rebars. The next set of six beams was constructed in the same manner, but with a concrete encasement of the web, and all the beams were then tested. Fly ash, a pozzolanic waste byproduct of thermal power plants, was used as a 40% replacement for cement in making the test specimens. CFS beam failure characteristics, load-deflection behavior, ductility, load-strain relationship, moment-curvature relationship, and lateral stiffness were all investigated. The results of the experimental tests and the nonlinear finite element analysis performed in ANSYS software were found to be in good agreement. It was discovered that CFS beams with fly ash concrete encased webs have twice the moment resisting capacity of plain CFS beams, resulting in a reduction in building floor height. The results also confirmed that the composite CFS beams have high ductility, making them a reliable choice for earthquake-resistant structures.

A Novel Analytical Approach for Nonlinear Thermo-Mechanical Buckling of Higher-Order Shear Deformable Porous Circular Plates and Spherical Caps with FGM Face Sheets

A novel analytical approach for nonlinear thermo-mechanical buckling of higher-order shear deformable porous circular plates and spherical caps with functionally graded material (FGM) face sheets resting on Pasternak elastic foundation is presented in this paper. The circular plates and spherical caps are assumed to be subjected to uniformly distributed external pressure and/or uniformly distributed thermal loads, and the nonlinear higher-order shear deformation theory (HSDT) is used for largely thick plates and caps with the shell-foundation interaction modeled by Pasternak elastic foundation. The caps are assumed to be shallow with clamped boundary conditions. The total potential energy expression of structures is established and the Ritz energy method is used to solve the problem directly from the total potential energy expression. The expressions between external pressure–deflection, thermal load–deflection, and thermo-mechanical combined load–defection can be obtained using the iterative algorithms. The critical buckling loads and postbuckling behavior of plates/caps are investigated numerically. Significant effects of foundation, porosity, structure parameters on the nonlinear thermo-mechanical responses of circular plates and spherical caps are numerically investigated and discussed, and the complex tendencies of postbuckling strength of plates and caps are obtained.

Axial compressive behavior of middle partially encased composite brace

To prevent the buckling and unbalanced tensile-compressive behavior of steel braces, a middle partially encased composite brace (MPEC) is proposed in this paper. In this composite brace, concrete is encased in the middle section of the H-shaped steel, and stiffeners are welded in the steel section for reinforcement. Axial compressive tests were implemented on four MPEC braces and one comparison specimen with considering the flange thickness, longitudinal reinforcement ratio, stirrup spacing and slenderness. The test results revealed that the failure of all composite braces was due to local buckling of the flange plates and separation from the concrete. The presence of concrete within the steel flange effectively limited the buckling of the H-shaped steel and improved the stiffness and compressive capacity. The compressive capacity of the composite braces was primarily influenced by the sectional dimension of the H-shaped steel, while the contribution of the reinforced concrete was limited. Additionally, a higher longitudinal reinforcement ratio improved the ductility of the composite braces, while larger stirrup spacing reduced both the compressive capacity and ductility. The specimen with large slenderness demonstrated poor mechanical properties and experienced a more abrupt failure. The axial compressive capacity of MPEC braces was calculated based on the critical buckling stress of steel plate and the confinement of concrete in partially encased composite columns (PEC). The calculated results showed good accuracy compared to the experimental data, and thus, the formula proposed in this study can be applied in design applications to predict the axial compressive capacity of MPEC braces.

Test on Shear Behavior of Double-Sided Thin Steel Plate Shear Wall Filled with Rigid Polyurethane Foam

A double-sided thin steel plate shear wall filled with rigid polyurethane foam (SWR) is proposed. A quasi-static monotonic loading test and quasi-static cycling loading test on shear behavior and the energy dissipation capacity of the SWR were carried out. Four kinds of test specimens, including the pure steel frames, the steel frame with double-sided thin steel plates, the SWR, and the SWR with an open hole, were tested. The results showed that compared with the pure steel frame, the erection of thin steel plates on both sides enhances the shear bearing capacity, initial shear stiffness, and energy consumption capacity. It turns out that the rigid foam polyurethane (RPUF) significantly increases the shear performance of the thin steel plate shear wall. The main reason for this is that the bond effect and support effect of the RPUF delay the out-of-plane buckling of thin steel plates and improve shear performance and energy dissipation capacity.

О ЕСТЕСТВЕННЫХ ГРАНИЧНЫХ УСЛОВИЯХ В ЗАДАЧЕ О ПОТЕРЕ УСТОЙЧИВОСТИ ПЛАСТИНЫ С ЭЛЛИПТИЧЕСКОЙ ВСТАВКОЙ ПРИ РАСТЯЖЕНИИ

This paper studies the issue of determination and influence of natural boundary conditions in the problem of buckling of a thin plate with an elliptical inclusion under tension. First, the naturalness of the boundary conditions of the “free edge” type for a plate with a hole is proved. Then a plate with welded inclusion is considered and natural boundary conditions are derived. The limit cases are checked for an absolutely soft inclusion and for an absolutely rigid one. It is shown that the first case leads to a problem with a hole and the corresponding natural boundary conditions, and in the second case, to the absence of natural conditions, since a problem with a clamped edge occurs. The authors conclude that the use of additional restrictions will lead to the construction of a basis that will rapid up the convergence of the method. Variational methods are widely used in all fields of mechanics, including in the field of machine, aircraft, and rocket engineering. An exact solution to the problems of elasticity theory and structural mechanics is not always possible to construct, therefore, in practice, great importance is attached to various approximate methods. Among them a special place is occupied by variational methods based on the direct minimization of the corresponding energy of the body and making it possible to build approximate analytical solutions in the form of a functional series. The goal of variational methods is to construct a partial sum of this series, which, with a sufficient number of terms, will be maximum close to the solution. However, the issue of convergence is influenced by many factors, and one of them is the natural boundary conditions, which are derived in this paper for the problem of the stability loss of the plate with the elliptical inclusion under tension.

Buckling of a Vertically Mounted Cantilevered Plate Under Static Torsional Corner Loads—Experiment and Theory

AbstractThe results of an experimental study on the buckling of a vertically cantilevered plate under corner twisting forces are reported. In this configuration, an interesting and somewhat counter-intuitive behavior is observed in which a laterally loaded slender panel exhibits a subtle instability characterized by nonlinear out-of-plane corner deflections. This is one of the few studies in the literature that investigates the buckling of cantilevered plates and appears to be the only experimental study of buckling under twisting loads, i.e., loading the plate with point loads at the free corners and in opposite directions. This paper discusses the practical aspects of experimental verification and methodology and evaluates the effect of the plate aspect ratio (AR) on the nondimensional buckling load in this configuration. In addition, experimental results are compared to finite element analysis (FEA) simulations performed on accessible software. There is generally good agreement between the experiment and the finite element simulation for the change of buckling load with plate aspect ratio. The nondimensional buckling load appears to decrease asymptotically with increasing aspect ratio, though the correlation between experiment and computation is less consistent as aspect ratio increases due to experimental and computational limitations.

Study on the load-end shortening formulae of structural elements including hard corner element considering collapse modes based on test and numerical modelling

This paper focus on improving the load-end shortening formulae of structural elements considering collapse modes and steel grades through experimental and numerical methods. The existing load-end shortening formulae in CSR-H is derived from the buckling theoretical formulae of plates and stiffeners. Stiffener elements deform in different collapse modes under compressive loads, while hard corner elements are assumed as elasto-plastic behaviours, which may obviously overestimate the ultimate load carrying capacity due to the local buckling of plates. Beam–column buckling, torsional buckling and web local buckling for stiffener elements and hard corner elements were designed with different sizes of test specimens in compression tests. After compassion, the minimum and appropriate modelling technology with three stiffener elements and four hard corner elements were proposed to verify the load-end shortening curves of structural elements. A new load-end shortening curve for hard corner elements was developed to calculate the ultimate strength, which could reflect the realistic progressive collapse behaviours under longitudinal compression.

Thermal-Hydraulic Analysis of Inward and Outward Fuel Plate Buckling in a Typical MTR Reactor

In the present work, a numerical study of inward and outward buckling of two successive fuel plates of a typical material testing reactor is investigated using computational fluid dynamics code. Fuel plate buckling results in partial blockage of the hot channel. Both buckling toward the inside and outside are considered. Simulations are conducted for different blockage levels of the nominal flow area, i.e., 0%, 20%, 40%, 50%, 60%, and 70% for inward buckling. Blockage levels of 0%, 20%, 40%, 50%, 60%, 70%, 80%, and 90% are considered for outward buckling. The impact of the flow field redistribution in four successive channels on the cooling capacity of each channel is investigated. The obtained results show that for an inward buckling ratio greater than 50%, critical phenomena will occur that could affect the clad integrity. Moreover, for inward buckling of 70%, the maximum clad temperature in the blocked channel reaches the value associated with the onset of nucleate boiling at the operating pressure. On the other hand, for outward buckling of 90%, critical phenomena that could affect the clad integrity will occur.

Effect of openings on lateral behaviors of corrugated plate module walls and high-rise modular buildings

In modular buildings with container-like modules, the corrugated plates and the opening conditions were proven to have significant influence on the module rigidity. But the effect of openings on failure modes of modules and lateral sway performance of modular buildings were rarely considered. In this paper, shear performance of long modules with different kinds of openings and different beam sections were investigated. A simplified analytical model of perforated module sidewalls was proposed and was applied to the seismic structural analyses of high-rise modular frames. Results indicated that the opening subdivided the corrugated plate sidewalls, which mechanism led to the postponement of plate buckling and the increased elastic shear strengths comparing to intact walls. High stress concentrations and regional plate buckling firstly occurred around the opening, and then the buckled regions expanded toward two side columns as the increase of shear drifts. The frame beams and regional corrugated plates above or below the opening behaved like a kind of coupling beams that channeled short corrugated sidewalls at two sides of the opening. The bending rigidity of the coupling beam system determined the composition effect of short corrugated plates at two sides of the opening, and then directly influenced the drift performance of individual modules and the whole modular buildings.

Decision tree for local + global imperfection combinations in double‐symmetric prismatic members – Practical recommendations in the framework of advanced analysis

AbstractBetter and simpler possibilities of structural optimization due to increasing computational power but also for reasons of environmental sustainability, the use of materials and their reusability lead to greater acceptance towards more advanced numerically intensive, so‐called ‘design by analysis' methods like geometrically and materially non‐linear analyses with imperfections (GMNIA). The general choice of imperfections and their combination in such models, especially for slender cross sections of intermediate length prone to an interaction between a global and local plate buckling, is crucial in terms of the reached load‐bearing capacity. Annex C of EN 1993‐1‐5:2010 makes use of the ‘70 %‐rule' for the combination of imperfection modes and amplitudes. This rule postulates that two GMNIA calculations should be conducted when local and global interactive buckling may be dominant; one with 100 % + 70 % of the maximum specified amplitude in either case. In addition, extended information is provided on the choice and combination of imperfections in the newly introduced and currently available draft of the prEN 1993‐1‐14:2020 (design assisted by finite element analysis). Although information is provided on how the local and global imperfections should be combined, it is not stated when it is relevant to consider those. Based on conducted GMNIA simulations on SHS/RHS (square and rectangular hollow sections) and I‐shaped sections, this article presents general decision support on the choice of equivalent imperfections. On the basis of numerical analysis, the developed flow chart and design routine allow for the decision whether the consideration of the interaction of local and global imperfections is required or not.

Experimental and numerical investigation of 800 MPa HSS welded T-section column strengthened with CFRP

Carbon Fiber Reinforcement Polymer (CFRP) has been widely utilized in repairing and retrofitting engineering. The purpose of this work is to study the buckling behavior of high strength steel (HSS) welded T-section column strengthened with CFRP using experimental and numerical method. The experiment of six specimens of 800 MPa HSS welded T-section column strengthened with CFRP under axial compression is performed. The influences of three main parameters (i.e., the number of CFRP layers, the slenderness of columns, and the width-to-thickness of plates) are observed in this work. All columns fail by the debonding of CFRP layers and the flexural–torsional buckling of specimens. CFRP layer can effectively delay the local buckling of plate or the torsional buckling of specimen. CFRP layer and slenderness has significant influences on the bearing capacity of specimens. The flexural and torsional displacement of columns strengthened with CFRP is much smaller than that of columns without CFRP. A finite element (FE) method for estimating the bearing capacity of HSS welded T-section column strengthened with CFRP is developed using ANSYS software. It is found that the confining effect of CFRP is more effective for stub columns. A more accurate model modified from Cadei et al.’s model for estimating the bearing capacity of 800 MPa HSS welded T-section column strengthened with CFRP under compression is proposed.

A high-order finite element continuation for buckling analysis of porous FGM plates

This work presents an effective approach to investigating the buckling and post-buckling behavior of porous FGM plates. The main objective of the present analysis is to use a High Order Continuation based on the Asymptotic Numerical Method with the Finite Element Method for nonlinear behaviors of a Porous Functionally Graded Material plate (PFGM) with different porosity distributions under various types of transverse loads. In our study, we will take into account the lack of uniform and non-uniform porosity using a Higher-order Shear Deformation Theory (HSDT). The adapted solver proves to be more effective for analyzing non-linear mechanical phenomena and more precisely the post-buckling analysis of the PFGM plates. Indeed, this numerical high order algorithm presents an adaptive step length to the local nonlinearity of the solution branch and to detect easily the bifurcation points and bifurcated branches. When compared to iterative techniques like Newton–Raphson, the proposed high-order algorithm has the benefit of speeding up the resolution of nonlinear problems. The mathematical formulation is based on the higher-order shear deformation plate theory taking into consideration geometrical nonlinearity and initial imperfections. Numerical results of a parametric study on the effect of various types of load, porosity distribution, grading index, porosity index and different span-to-thickness ratios will be investigated.

Theoretical analysis of shear buckling stress in torsion of thin-walled square cross-section beams

Thin high-strength steel sheets are increasingly being applied to vehicle frames in order to increase the strength and reduce the weight. The thinner the plate, the more likely it is to occur buckling. So it is important to understand the structural properties based on buckling theory in order to efficiently design for buckling in the early stages of vehicle development. The authors have addressed the issue of theoretically determining the shear buckling stresses in torsion of thin-walled square cross-section beams. In the previous paper (Budiansky, et al., 1948) for determining shear buckling stresses in torsion of infinitely long thin-walled square beams, two adjacent plates were treated collectively, the buckling modes were expressed as an infinite series in the width direction and a single sinusoidal wave in the infinite length direction, then, the method of Lagrange multiplier was used to consider the constraint condition in the center line, finally the shear buckling stress was obtained by the energy method. However, this process cannot be applied to finite-length beams because a single sinusoidal wave cannot satisfy the boundary conditions at both ends in the longitudinal direction. So, the purpose of this paper is to theoretically determine the shear buckling stress in torsion of a thin-walled square beam of finite length. First, based on the previous process, two adjacent plates are considered to be a single plate, and the buckling mode is represented by an infinite Fourier series as in the shear buckling of a single plate. The shear buckling stress in torsion is obtained by the energy method, taking into account the constraint condition in the center line of the width direction of the plate by the method of Lagrange multiplier. The validity of the derived values is compared with the FEM results, and the results are in good agreement.