Elastic Buckling Coefficients Research Articles

Performance of vertically-placed stiffened corrugated panels in steel plate shear walls: Shear elastic buckling analysis

Adding horizontal stiffeners to vertically-placed corrugated panels is an effective way to improve their shear buckling strength. Since the shear elastic buckling loads (Ncr) of vertically-placed stiffened corrugated steel walls (VSCSWs) are related to their practical design, this study investigates the VSCSWs' shear elastic buckling behaviors and aims to determine the formulas for predicting the Ncr of VSCSWs. Firstly, the number of horizontal stiffeners required by VSCSWs is discussed utilizing the calculation model of VSCSWs’ shear elastic buckling load established based on the minimum potential energy and the Ritz method. Then, the shear elastic buckling behaviors of VSCSWs with one pair and two pairs of horizontal stiffeners are analyzed, and formulas for predicting their shear elastic buckling coefficients are proposed. Lastly, finite element shear elastic buckling analyses are conducted to verify the accuracy of the proposed formulas. It is found that the shear elastic buckling coefficient of VSCSWs first grows and then almost remains unchanged with the increased rigidity ratio of the stiffening system. It has been observed that the equations proposed are in good agreement with the numerical results and can be applied to the design of the VSCSWs.

Elastic buckling analysis of horizontally-placed trapezoidally-corrugated steel shear walls stiffened with vertical steel strips

By simply adding vertical steel strips evenly spaced on both sides of horizontally-placed trapezoidally-corrugated steel shear walls (TCSPSWs), the ultimate shear resistance and ductility of the TCSPSWs can be effectively improved, particularly for embedded corrugated steel plate with a width greater than the height. Because the shear elastic global buckling loads of steel-strip-stiffened TCSPSWs (STCSPSWs) are critical to the design of their ultimate shear resistance, this study investigates the elastic buckling behaviors of TCSPSWs stiffened with one pair (STCSPSWs-1) and two pairs (STCSPSWs-2) of vertical steel strips. To begin, the elastic buckling loads of the STCSPSWs can be theoretically solved using the theorem of minimum potential energy and the Ritz method based on orthotropic plate theory. It is discovered that as the bending stiffness of the steel strip increases, the elastic buckling coefficients of the STCSPSWs initially increase and then almost remain unchanged. Then, formulas which are more accurate than the existing ones are provided for estimating the elastic shear buckling loads of STCSPSWs-1, and formulas for predicting the elastic buckling load of STCSPSWs-2 are also proposed. Finally, the proposed formulas are validated further by performing finite element elastic buckling analyses. The analytical results of this paper show that the proposed formulas are accurate and can be used to design STCSPSWs in practice.

Local and distortional buckling of extruded aluminium alloy lipped angle columns

The outstand flanges of aluminium alloy angles are sensitive to local buckling due to the low elastic modulus of material. To improve the sectional buckling stress, lips could be introduced to improve the stability behaviour of the outstand flanges. This paper presents an equilibrium approach and a simplified energy method for the local and distortional buckling of extruded aluminium alloy lipped angle columns. Closed form solutions for local buckling and distortional buckling are proposed. The equivalent flexural rigidity and torsional rigidity of the lip are two main factors affecting the sectional buckling behaviour. As distinct from double-sided symmetrical edge stiffeners, the bending of a single-sided edge stiffener can lead to in-plane compressive deformation of the adjacent flange. Based on the edge-stiffened flange model, the equivalent flexural rigidity of the lip is obtained from finite element (FE) analysis. To validate the proposed analytical methods, the elastic buckling coefficients of lipped angles with varying dimensions are obtained from eigenvalue buckling analysis. Lips of different thicknesses are considered to study the effect of torsional rigidity. Comparing with FE results, the proposed equilibrium approach shows excellent accuracy for both local and distortional buckling stresses. The closed form solution given by energy method can also well predict the sectional buckling stress. Finally, parametric studies are carried out to further investigate the effects of flexural and torsional rigidities of lips and the slenderness ratios of flanges on the elastic buckling behaviour. Some design remarks are concluded to provide valuable reference for the application of extruded aluminium alloy lipped angles in practice.

Elastic buckling analysis of rectangular longitudinally profiled (LP) steel plates under uniform compression

Longitudinally profiled (LP) steel plates are plates rolled to variable thickness along the rolling direction in order to suit practical loading distributions in construction applications. The elastic buckling load of LP steel plates is different to normal flat plates due to the change in thickness and it is hard to find analytical solutions to the governing equation. In this paper, the elastic buckling coefficients of rectangular LP plates were calculated using the Galerkin and Rayleigh-Ritz method (GRM). The plates were under uniform compression and four typical boundary conditions were considered. The element expression of the feature matrix was obtained by theoretical derivation and the elastic buckling coefficients were obtained by calculating the eigenvalues of the feature matrix numerically with MATLAB. Numerical models of LP plates were developed to validate the derivation. Upon validation it was further found that the elastic buckling coefficients of LP plates can be approximately expressed by those of constant thickness steel plates together with variable thickness coefficients. A series of approximation formulae of elastic buckling coefficients of LP rectangular steel plates were proposed. Simplified design formulae of elastic buckling coefficients of LP plates were proposed for the first time to promote the application of LP plates in engineering practice.

Stiffness Demand on Stiffeners of Vertically Stiffened Steel Plate Shear Wall

Elastic buckling of steel plate shear walls (SPSWs) vertically stiffened by either flat-bar or closed-section stiffeners is studied first to determine the required bending stiffness on stiffeners. The torsional stiffness of the stiffener is found to increase the buckling stress and reduce the required bending stiffness. The proposed equation for the elastic threshold stiffness is related to the increment of the elastic buckling stress of stiffened SPSWs over that of unstiffened SPSWs. Comparisons with previous research on stiffened plates are presented. For moderately thick and stocky plates, elastic-plastic buckling stress is used to define the threshold stiffness. It is found that the threshold stiffness based on elastic-plastic buckling stress is less than that based on elastic buckling stress. Replacing the elastic buckling coefficients with elastic-plastic buckling coefficients, the proposed equation gives good predictions for elastic-plastic threshold stiffness. The findings of this study may be helpful in understanding the real demand on stiffeners in stiffened SPSWs.

Local Buckling Coefficient Calculation Method of Thin Plates with Round Holes

ABSTRACTWhen slender parts of plated structural members are under compression the local buckling may govern resistance of the whole structure. In addition to that, holes in those slender parts may reduce the resistance even more. Knowing that holes in different positions of steel structural members are very common, a simple but as precise as possible calculation method of critical buckling force would be beneficial for engineers. In order to create such a method, which would take the influence of the holes into account, an extensive analysis campaign of elastic buckling of thin plates with holes has been carried out. The finite element method was used for the calculations, and analysis of the obtained results derived to a simple calculation expression.The influence of different positioning and diameters of holes on elastic local buckling force is analyzed in the paper, and the developed calculation equation is presented. The proposed calculation method/ equation can be used by engineers in order to easily predict the elastic buckling coefficients and the critical forces of plates with round holes under compression. In order to add more value for engineers, the factors which have influence on the critical buckling force are commented. Also, recommendations for further development and possible extensions of the method are given in the paper.

07.04: Web crippling design of hollow flange channel beams under one flange load cases

ABSTRACTThe advantage of having no unstiffened elements coupled with material located away from the neutral axis makes hollow flange channel (HFC) beam sections structurally efficient in bending when compared with other commonly used open cold‐formed steel sections. This concept is similar to hot‐rolled steel sections such as the universal beam and channel beam sections, which are very efficient in bending. However, the hot‐rolled sections are heavier, torsionally weak, and have low resistance to flexural‐torsional buckling. The two hollow flanges in HFC beams make them torsionally strong and also eliminate the occurrence of distortional and local flange buckling modes in most cases. However, HFC beams have slender webs, making them vulnerable to web crippling failure modes. To understand the web crippling behaviour of HFC beams and develop accurate design rules, finite element models of HFC beams were developed and validated using available experimental results under End One Flange (EOF) and Interior One Flange (IOF) load cases. Using the validated finite element models, a detailed parametric study was conducted for many HFC sections. Finite element analyses provided the required elastic buckling and ultimate loads of HFC beams in web crippling (EOF and IOF load cases). New predictive equations were proposed to determine the elastic buckling coefficients of HFC beams, followed by Direct Strength Method (DSM) based design rules using the test, elastic buckling and nonlinear analysis results from finite element analyses. This paper presents the details of the web crippling design rules developed based on the detailed numerical study on the web crippling behaviour of hollow flange channel beams under one flange load cases.

A unified analysis for distortional and lateral buckling of C-purlins in flexure

This paper developed a unified model for the distortional and lateral buckling of cold-formed C-purlins subjected to bending in the plane of symmetry. It can study not only the distortional buckling, but also the global lateral buckling. Different from Hancock's model, the new model includes two interactive springs between lateral and rotational restraints provided by the web to the flange-lip section. A closed-form solution is acquired by the Ritz method. And the elastic buckling coefficients of 20 purlin sections predicted by the solution are compared with those from Finite Element Method (FEM), showing excellent agreement between them. Comparison is also provided with Hancock's method. The closed form solutions are also substituted into the Direct Strength Method to obtain nominal flexure strength of the purlins, and it is found that the proposed model predicted almost the same strength as the software Schafer's CUFSM with differences less than 1%. A good correlation is observed between test results and the proposed method.

Elastic buckling behavior of steel trapezoidal corrugated shear walls with vertical stiffeners

This paper investigates the elastic buckling behavior of steel trapezoidal corrugated shear walls (STCSWs) with vertical stiffeners. On the basis of an orthotropic plate model, by utilizing the theorem of minimum potential energy and the Ritz method, the buckling loads of stiffened STCSWs can be precisely calculated using MATLAB. Then, a value of transition rigidity of stiffener is suggested and, hence formulas of elastic buckling coefficients of stiffened STCSWs are proposed. Finally, the verification of proposed formulas using a FE model shows that the formulas are validated and applicable in estimating the elastic buckling loads of stiffened STCSWs.

Local elastic buckling coefficients of steel plates in composite steel plate shear walls

The system of a steel plate bolted to a Reinforced Concrete (RC) shear wall goes by the name of a ‘Composite Steel Plate Shear Wall’ (CSPSW), which is used as the lateral resisting system in tall buildings. In this system, the steel plate buckles under medium-strong earthquakes, which may lead to instability. However, the buckling load of steel plates is usually a limited criterion for the design of CSPSW. This paper reports a series of experiments on CSPSW. The experiments were used to investigate the buckling load of a steel plate bolted to one side of a high strength reinforced concrete panel. Furthermore, theoretical modeling, based on energy methods, was used to obtain the elastic buckling coefficients of steel plates with various aspect ratios under shear loading. The results were presented in graphical and tabular forms showing good agreement of theoretical modeling with experimental results. The elastic buckling coefficients can be used for determination of the number of bolts or the spacing between the bolts.

Elastic buckling of web plates in I-girders under patch and wheel loading

This paper makes a brief review of the earlier research on the elastic buckling of rectangular plates with simply supported and clamped boundary conditions, as well as the buckling of web plates in I-girders subjected to patch load. New investigation has been carried out to simulate the realistic load and the restraining conditions of the web plates in I-girders. The buckling of a large number of models under patch load was analyzed with ANSYS and formulae were proposed to predict the elastic buckling coefficients of webs in I-girders. The rotational restraints provided to the web plates by the flanges are considered accurately in the suggested formulae. The wheel load is another kind of patch load rarely touched in the literature. This paper suggests a simple model to determine the bearing stresses on the top edge of the web plates in I-girders where the effect of the crane rail rigidity is considered. Based on this model, the buckling of the web plate is analyzed and formulae with excellent accuracy are suggested to predict the buckling load.

Elastic Buckling Coefficients for Long, Unstiffened Plates

Long, unstiffened plates are thin plates stiffened at only one edge parallel to the direction of stress. These occur in various shapes, including a T-shaped section. For modeling purposes, the plates can be assumed to be simply supported along the stiffened edge parallel to the applied stress and along the transverse edges at the ends of the plates. The plates can be subjected to a range of linear stress gradients. For plates subjected to linear stress gradients with maximum compression at the simply supported edge and maximum tension at the free edge, elastic buckling coefficients are determined. A finite difference approach is taken, since an assumption of a simple geometric buckled shape (for use in a method such as the Galerkin method) cannot be made. The results from the finite difference solution and an equation that approximates the solution are presented, along with available elastic buckling coefficients for other linear stress gradients.

Buckling of Axially Compressed Cylinders

The results of buckling tests on 41 small-scale ring stiffened steel cylinders and one large radius fabricated ring stiffened steel cylinder under axial compression are presented. These results are compared with those of many other investigators on both stiffened and unstiffened cylinders. Elastic buckling coefficients are determined for both small scale and fabricated cylinders. A plasticity factor is determined from test data on cylinders which failed inelastically. Design equations are recommended for fabricated metal cylinders.