Empirical formulations for estimation of ultimate strength of continuous stiffened aluminium plates under combined in-plane compression and lateral pressure

The present research was undertaken based on the results obtained by the same authors in a sensitivity study on the buckling and ultimate strength of continuous stiffened aluminium plates. Empirical expressions are developed for predicting ultimate compressive strength of welded stiffened aluminium plates used in marine applications under combined in-plane axial compression and different levels of lateral pressure. Existing data of the ultimate compressive strength for stiffened aluminium plates numerically obtained by the authors through the previously performed sensitivity analysis are used for deriving formulations that are expressed as functions of two parameters, namely the plate slenderness ratio and the column (stiffener) slenderness ratio. Regression analysis is used in order to derive the empirical formulations. The formulae implicitly include effects of the weld on initial imperfections, and the heat-affected zone.     

Strengthening of perforated plates under uniaxial compression: Buckling analysis

This paper focuses on the cutout-strengthening of perforated steel plates subjected to uniaxial compressive loads. The square plates considered each has a centrally placed circular hole and four simply supported edges in the out-of-plane direction. Four types of stiffeners named ringed stiffener (RS), flat stiffener (FS), longitudinal stiffener (LS) and transverse stiffener (TS) are mainly discussed. The finite element method (FEM) has been employed to analyse the elastic and elasto-plastic buckling behaviors of strengthened and unstrengthened perforated plates. The results show that the strengthened perforated plates have higher buckling strengths than those of the unstrengthened ones, while the elevations in elastic buckling stress and elasto-plastic ultimate strength are closely related to stiffener types (i.e., RS, FS, LS and TS) as well as plate geometric parameters (i.e., a plate slenderness ratio and a hole diameter ratio). Furthermore, comparisons of strengthening efficiency considering the variations of buckling stress with stiffener weight are carried out, and recommendations on the most efficient cutout-strengthening methods for the uniaxially compressed perforated square plates with centric circular holes are proposed.     

竖向加劲钢板剪力墙门槛刚度研究

为研究设置竖向加劲肋的钢板剪力墙的弹性屈曲性能,采用有限元法对竖向加劲钢板剪力墙弹性屈曲性能进行研究,分析加劲肋的刚度、加劲数量和钢板高宽比等因素的影响。研究表明:设置竖向加劲能有效提高钢板墙剪切临界应力,钢板高宽比、加劲肋数目和加劲肋抗弯刚度均对钢板剪力墙屈曲系数有较大影响。提出加劲肋门槛刚度的判定标准和计算公式,该判定标准考虑了加劲肋扭转刚度的影响。与有限元结果的比较表明,具有较好的精度,且明显优于文献结果。     

两边连接交叉加劲钢板剪力墙弹性屈曲分析

采用ANSYS有限元软件对两边连接交叉加劲钢板剪力墙进行了弹性屈曲分析,重点研究了加劲肋与墙板的刚度比、墙板高厚比、边长比以及加劲肋宽厚比对弹性屈曲系数的影响,并将分析结果与十字加劲板进行了比较.研究表明,交叉加劲肋能够显著提高钢板剪力墙的弹性屈曲荷载,其远大于十字加劲肋;随着墙板边长比和高厚比的增大,屈曲系数趋于减小;而较小的加劲肋宽厚比能使墙板获得较大的屈曲系数;最后给出了两边连接交叉加劲板弹性屈曲系数的计算公式.     

Tests on intermediately stiffened plate elements and beam compression elements

This paper describes an experimental investigation into the behaviour of cold-formed steel intermediately stiffened plates which are subject to pure compression and cold-formed beams with intermediately stiffened compression elements which are subject to bending. Each plate or beam has a central intermediate stiffener. The investigation is concerned with the performance of the intermediately stiffened elements with different degrees of rigidity provided by the stiffener. The ultimate loads are compared with the predictions of BS 5950 Part 5 Code and the first Draft Eurocode 3.     

交叉加劲钢板剪力墙弹性屈曲研究

用有限元方法对交叉加劲钢板剪力墙的弹性屈曲性能进行了研究,重点研究了加劲肋与墙板的刚度比、墙板高厚比、边长比以及加劲肋宽厚比等对弹性屈曲系数k的影响,同时与十字加劲板的抗剪屈曲性能进行了对比。研究结果表明,设置交叉加劲肋能显著提高钢板剪力墙的弹性屈曲荷载;屈曲系数k随着墙板边长比、高厚比以及加劲肋宽厚比的增大而趋于减小;本文给出的交叉加劲板弹性屈曲系数k的计算公式与有限元法的结果较吻合。     

Local buckling and post-local buckling redistribution of stress in slender plates and sections

Cold-formed open steel sections are comprised of component plates termed stiffened elements (webs) and unstiffened elements (flanges). The local buckling and post-local buckling behaviour of sections may be determined from the behaviour of the component plates. Much research effort has documented the theoretical elastic local buckling of plates and sections, however until recently few experimental studies have been reported on the local buckling and post-local buckling behaviour of unstiffened plates. This paper presents experimental and numerical studies of unstiffened plates and sections that contain them in both compression and bending, and in particular analyses the mechanism that provides post-buckling strength. It is shown that, as with stiffened elements, the mechanism is the post-local buckling redistribution of stress, however unlike stiffened elements this redistribution can occur to such an extent that tensile stresses commonly form in axially compressed slender elements. The stress distributions at ultimate are compared with current international cold-formed steel specifications.     

Buckling of thin flat-walled structures by a spline finite strip method

A method of buckling analysis of thin flat-walled structures of finite length subjected to longitudinal compression and bending, transverse compression as well as shear is described. The analysis uses the spline finite strip method and allows for boundary conditions other than simply supported ends as required in the semi-analytical finite strip method of buckling analysis.Convergence studies with increasing numbers of section knots are described for plates in compression, bending and shear, and for long columns with different support conditions subjected to compression. A buckling analysis of a stiffened plate subjected to compression and shear is compared with results from a finite element analysis.     

Influence of longitudinal stiffeners on elastic stability of girder webs

In this paper, linear buckling analyses of plates with longitudinal stiffeners having various shapes and positions and subjected to axial force, in-plane bending and shear are developed. The aim is to give some new practical insights about the shape and optimum position of longitudinal stiffener in webs when axial force, bending moment and shear act. By means of a comprehensive numerical investigation, some practical issues for buckling phenomena in stiffened plates, taking into account (a) dimensions and shape (square and rectangular) of the plate, (b) dimensions and shape of the stiffener (with open and closed cross-sections), (c) location of the stiffener, and (d) load configuration (uniform compression, pure bending, combinations of axial compression and bending, and shear) are developed.     

Buckling of laminated composite stiffened panels subjected to in-plane shear: A parametric study

The presence of in-plane loading may cause buckling of stiffened panels. An accurate knowledge of critical buckling load and mode shapes are essential for reliable and lightweight structural design. This paper presents some parametric studies on simply supported laminated composite blade-stiffened panels subjected to in-plane shear loading. A total of 450 models were analyzed using ANSYS 7.1 and a database is prepared for different plate and stiffener combinations. Studies are carried out by changing the panel orthotropy ratio, stiffener depth, pitch length (number of stiffeners), smeared extensional stiffness ratio of stiffener to that of the plate and extensional stiffness to shear stiffness ratio of the plate. Based on the studies, few important parameters influencing the buckling behaviour are identified and guidelines for better stiffener proportioning are developed, which will be helpful for the designer.     

Optimal stiffener design of moderately thick plates under uniaxial and biaxial compression

In this paper, the optimal stiffener design of moderately thick plates under uniaxial and biaxial compression is investigated on the premise that the plate thickness and the required ultimate strength are given. As the theoretical basis of stiffener design, the ultimate strength formulations of weak stiffened thick panels under in-plane biaxial compression are first developed on the basis of large deflection orthotropic plate theory, in which the post-weld initial deflection is taken into account. The von Mises yield criterion is employed to determine the limit state of the panel, and the Nelder-Mead simplex algorithm is used to obtain the efficient solution of nonlinear differential equations. The optimization method presented is based on the stiffener design principles of the overall instability stress and of the working stress. In the optimization formulation, the numbers and geometric sizes of the stiffeners are defined as design variables; the weight ratio of stiffeners to plate is taken as a single objective function; requirements against overall buckling of the panel, local buckling of the plates between the stiffeners and local buckling of the stiffeners themselves are set as constraint functions. Results of both design examples and parameter studies show that, for moderately thick plates, the stiffener weight given by the proposed optimization method is much lower than the weight determined by the current stiffener design method on the premise of the same requirement of structural safety. Using the present optimization method to obtain the lightest and the most effective stiffener layout for moderately thick plates is proposed.     

全加劲两侧开缝钢板剪力墙弹性屈曲研究

采用有限元方法对全加劲两侧开缝钢板剪力墙在面内水平荷载作用下的弹性屈曲临界荷载、屈曲模态进行了研究。对影响其弹性屈曲性能的参数进行了分析,包括两侧和中部加劲肋与墙板的刚度比、两侧和中部加劲肋宽厚比以及墙板高厚比和边长比。给出了全加劲两侧开缝钢板剪力墙加劲肋的弹性屈曲设计参考公式,为开缝钢板剪力墙的应用提供依据。     

Numerical and experimental investigations on the compression behaviour of stiffened plates

The main objective of this paper is to present the results of the finite element method for non-linear analysis of stiffened plates subjected to axial compression load considering post-buckling behaviour up to collapse. For this purpose two series of well executed experimental data on longitudinally stiffened steel plates with and without transversal stiffeners subjected to uniform axial in-plane load carried out to study the buckling and post-buckling up to final failure have been chosen. The first series are those of Ghavami where the influences of stiffener cross-section of the type rectangular (R), L and T, their spacing and the presence of rigid transversal stiffeners have been studied. The second series of Tanaka & Endo, where the behaviour of stiffened plates having three and two flat bars for longitudinal and transversal stiffeners respectively were analysed. For the purpose a well-established commercially available Finite Element program ANSYS has been chosen. The selected element was SHELL43, which can trace the full-range, elastic-plastic behaviour of the stiffened plates. It is seen that the simulated results of FEM are in good consistency with the test results.     

Elastic web bend-buckling analysis of longitudinally stiffened I-section girders

The linear elastic web bend-buckling behavior of I-section girders with a longitudinal stiffener is investigated by a threedimensional finite element analysis in which the web, top and bottom flanges, and transverse and longitudinal stiffeners are modeled as thin shell elements. After obtaining the bend-buckling moment for an I-section girder by finite element analysis, the buckling stress and subsequently the buckling coefficient of a rectangular web panel with a longitudinal stiffener are calculated and compared with those obtained by AASHTO LRFD and Eurocode 3. To observe the effect of various parameters on the buckling behavior of an I-section girder under pure bending, the following aspects are considered: the non-symmetry of the cross-section, the location of the longitudinal stiffener, the boundary conditions along the transverse and longitudinal stiffeners and flanges, the flexural rigidity of the longitudinal stiffener, the spacing of the transverse web stiffeners, and the slenderness of the web. Based on the numerical results, new design equations for the bend-buckling coefficient of a longitudinally stiffened I-girder are proposed.     

Stability analysis of stiffened plates by finite strips

The stability analysis of stiffened plates by means of the finite strip method is presented. The studies are based on the thin shallow theory, giving nonlinear strain displacement relations, but linear curvature displacement relations. The nonlinear equilibrium equations are obtained by the principle of incremental virtual work, using finite strip discretization. The higher order strip with one internal nodal line is applied. It is shown that considerable improvements can be obtained using this kind of strip. It is especially true for the postbuckling analysis. Numerical examples of the strength of stiffened plates in compression are carried out, covering a range of plate and stiffener slenderness.     

Accurate discrete modelling of stiffened isotropic and orthotropic rectangular plates

An analytical approach is presented here for simply supported blade-stiffened rectangular plates wherein important non-classical effects such as transverse shear deformation and rotary inertia are carefully accounted for. The analysis differs from full three-dimensional modelling of both the plate and the stiffener in that a plane stress idealization is used to model the kinematics of transverse bending of the stiffener while simple one-dimensional classical models are employed for lateral bending and torsion. Parametric studies are used to highlight the importance of non-classical effects in plate and stiffener kinematics and to finally lead to certain recommendations for accurate modelling of stiffened plates.     

Determination of effective breadth and effective width of stiffened plates by finite strip analyses

A finite strip (FS) method is presented for the numerical investigation of two design parameters — effective breadth and effective width — of stiffened plates. For the effective breadth, stiffened plates under bending are studied. Due to the transverse bending loads there is shear transmission through the plate from the stiffener which leads to a non-uniform longitudinal stress distribution across the plate width. This phenomenon, termed as shear lag, can be represented by the ‘effective breadth concept’, and has been extensively studied by analytical methods. A linear FS method is presented which utilizes the advantages of decoupling of Fourier terms on the one hand and, on the other hand, allows the treatment of both webs and flanges using a plate model. A definitely different situation exists for estimating the effectiveness of the plate breadth (or width) of plates in the postbuckling range. The ‘concept of effect width’ is based on the fact that plates with supported longitudinal edges and/or stiffeners can accept additional load after buckling under longitudinal compression, and enables the designer to evaluate the postbuckling strength of plate structures simply by using the design parameter ‘effective width’. Several formulae (most of them empirically derived) exist for an approximative calculation of the load dependent value of the effective width. A nonlinear FS method is developed and applied to the investigation of the postcritical strength of locally buckled structures. An incremental successive iterative procedure is introduced for an effective numerical analysis.     

十字加劲钢板剪力墙的抗剪极限承载力

我国《高层民用建筑钢结构技术规程》规定了钢板墙剪切弹性屈曲不先于剪切屈服,其明显的不足是没有利用板的屈曲后强度,同时弹性屈曲也不能作为结构在弹塑性阶段的设计指标。本文应用板的大挠度弹塑性有限元方法对十字加劲方形钢板剪力墙的屈曲后性能和极限承载力进行了系统的研究,并在大量数值分析的基础上,提出了以板的平均剪切应变相应的剪应力作为钢板剪力墙承载能力的极限状态,以达到利用薄板屈曲后强度的目的,进而提出了钢板剪力墙承载力的设计简化计算公式及钢板墙侧柱刚度阈值的计算公式,供设计参考。数值计算结果表明,影响钢板墙抗剪性能主要有三个参数:板高厚比、肋板刚度比和边柱刚度。     

Compression tests of longitudinally stiffened plates undergoing distortional buckling

This paper describes a series of compression tests performed on longitudinally stiffened plates fabricated from a mild steel plate of thickness of 4.0 mm with nominal yield stress of 235.0 MPa. The stiffened plates with longitudinal stiffeners of a range of rigidities were tested to failure. The ultimate strengths and performances of the longitudinally stiffened plates in compression undergoing distortional buckling or interaction between local and distortional buckling were investigated experimentally and theoretically. The compression tests indicated that the critical buckling mode was dependent mainly on the rigidity of the longitudinal stiffeners and the width-to-thickness ratio of the sub-panels. A noticeable interaction between local and distortional buckling was also observed for some stiffened plates. A significant post-buckling strength reserve was shown for those sections with distortional buckling and for those sections showing interaction between local and distortional buckling. A limiting strength curve for distortional buckling of longitudinally stiffened plates was studied. Simple design strength formulas in the direct strength method are proposed to account for the distortional buckling and the interaction between local and distortional buckling of longitudinally stiffened plates. The strength curves were compared with the test and FE results conducted. The adequacy of the strength curve was confirmed. A set of conclusions on the buckling behavior of longitudinally stiffened plates was drawn from the experimental studies.     

Numerical investigations on dynamic performance of stiffened box steel bridge piers

The aim of this paper is to carry out extensive numerical investigations about the effect of various structural parameters on the dynamic performance of stiffened box steel bridge pier under a strong earthquake ground motion. The considered structural parameters are the local slenderness ratios of stiffener and stiffened wall as well as the global slenderness ratio of the pier. In the present study, all investigated piers are made of high tensile steel with high yield ratio. The non-linear time history analyses are carried out using in-house Finite Element Program DYNAPSS, recently developed by the first author. This program is verified by comparing its results with the results obtained by the general FE program. In this program, the geometrical nonlinearity is considered on the bases of Total Lagrangian formulation, while the non-linearity of structural steel material is considered through implementation of modified multisurface cyclic plasticity model by which real characteristics of high tensile steel material such as, Plateau, Massing type of Bauschinger??s effect, disappearing of Plateau and cyclic strain hardening, are accurately modeled. The results are closely examined in respect with the damage index criterion. From this study, it is found that the increase in slenderness ratios of stiffener does not only increase the damage index, but also may lead to the full collapse. Furthermore, the damage index increases with the increase of local slenderness ratio of stiffened wall and the global slenderness ratio. Also, it is found that when the loacal buckling is not the dominant eigen mode and the pier behave as a single degree of freedom, the natural period has destructive effects when it is close to predominant period of the earthquake. Finally, contour plots of damage index values are presented. These contour plots may be greatly useful for the design of stiffened box steel bridge piers, where, critical values of structural parameters corresponding to certain value of damage index could be determined.