A generalised effective width method for plates loaded in compression

In recent years there have been a number of notable theoretical studies which have provided extensive load-shortening curves for rectangular plates loaded in compression along their transverse edges. These studies have provided engineers with a clear understanding of the effects which initial out-of-plane deformations and residual stresses have upon the behaviour of plates loaded in compression. The present paper shows how the information provided by these load-shortening curves can be utilised to provide effective width expressions. This will enable this latest research information to be incorporated in those existing design methods which utilise an effective width approach.One important benefit of the present study is that whereas earlier effective width formulae only provided information on the load-carrying capacity of a plate up to its peak load, the proposed method enables the post peak load behaviour of a compressed plate to be readily calculated.     

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.     

Simplified calculation of effective flange width for shear walls with flange

The shear lag effect of shear walls with flange is normally analyzed by introducing the concept of effective flange width. Therefore, it is crucial to accurately evaluate the effective flange width for tall buildings design. In this paper, based on the energy variational method, the normal stress distribution in the flange of shear walls is deduced, and the analytical solution of effective flange width in elastic stage is obtained according to the stress equivalent principle. For simplification, a parametric study on a serial T‐shaped cross‐section shear walls was conducted using finite element method in order to clarify the characteristic of effective flange width along with the loading history and the variations of shear lag effect with different parameters accordingly. Based on the numerical results, simplified formulas of the effective flange width in different loading stages are deduced for practical structure design. Moreover, the rationality of the values derived from different design codes is evaluated by comparing with simplified formulas. Copyright © 2015 John Wiley & Sons, Ltd.     

The in-plane shear failure of transversely stiffened thin plates

This paper examines the response of stiffened plates with plain flat outstands when subjected to in-plane shear loading in the form of applied in-plane shear displacement. The buckling and post-buckling failure capabilities of thin plates subjected to in-plane shear, can, of course, be improved through the introduction of stiffening elements whose flexural and torsional rigidities can contribute significantly towards a more stabilised structural system. This paper details appropriate suitable finite element modelling strategies and procedures to enable the determination of the post-buckled failure response of the stiffened shear panels and to highlight the significant influence of the stiffeners. The modelling procedures are able to describe the complete loading history of the stiffened panel structures from the onset of initial buckling through the elastic post-buckling phase of behaviour involving the considerable interaction between plate and stiffener and then through initial material yielding and yield propagation to ultimate conditions and elasto-plastic unloading.     

Plastic shear buckling of unstiffened stocky plates

A number of moderate to stocky steel and aluminum plates, with various slenderness ratios and boundary conditions are numerically analyzed under the action of pure in-plane shear and the results are validated against available analytical methods. Numerical non-linear finite element analyses are performed to assess different theoretical approaches and to picture buckling behaviors of moderate stocky plates. It is observed that while thick stocky plates possess some post-yield capacity during the hardening stage prior to plastic buckling, moderately thick plates yield and buckle concurrently followed by softening due to sudden loss of stiffness. It is also concluded that changes in the modulus of elasticity and shear modulus should be considered in the analysis and that the secondary bending stresses induced by initial out-of-plane curvature can cause significant reduction in the post-yield capacity and ultimate resistance of stocky plates.     

Elastic buckling of perforated plates under shear

Finite element studies aimed at computing the buckling coefficient for plates containing cut-outs and subjected to shear are reported. The cases considered are:

1. 1. Square and rectangular plates with central circular cut-outs.

2. 2. Square plates with centrally placed rectangular cut-outs.

3. 3. Square plates with eccentrically placed circular cut-outs.

4. 4. Square plates with reinforced circular cut-outs.

5. 5. Square plates with reinforced rectangular cut-outs.

Simply supported plates as well as clamped plates have been studied and approximate formulae for the use of designers have been suggested for the practical cases where the hole dimension is generally not greater than half the width of the plate.     

Effective width estimation of flanged reinforced concrete shear walls

The present study deals with introducing a novel approach toward estimating the effective width of flanged reinforced concrete shear walls (FRCSWs). Due to the paucity of studies in assessing the effective width of nonrectangular sections, this paper aims at proposing efficacious formulations for the effective width estimation of short, squat, and slender T- and U-shaped reinforced concrete (RC) shear walls subjected to the simultaneous action of the axial and lateral loading. To this end, at first, FRCSWs are simulated in the flanged shear wall numerical laboratory (FlashLab) program, which utilizes the finite element Abaqus software to analyze the walls. Thereafter, employing the developed numerical models, an extensive parametric investigation is conducted for a wide range of the key parameters. General expressions have then been developed to estimate the effective width of flanged RC shear walls invoking the evolutionary polynomial regression (EPR) analysis in conjunction with the genetic algorithm (GA). To assess the capability of the established equations in predicting the effective width of flanged sections, R-factors have been calculated for all the cases examined in this study, which ranged between 0.78 and 0.94. Furthermore, a comparison has been made among the results attained through the proposed methodology and those obtained using the conventional design codes. It was revealed that the relative error obtained employing the proposed formulations is less than that of the corresponding values of the design codes by approximately 30% on average. The superiority of the established framework stems from consideration of the following: (1) influential parameters, (2) effective width variations at different performance levels, (3) loading direction, and (4) type of the wall in the effective width calculation process.     

混凝土梁有效翼缘宽度取值研究

指出了我国《混凝土结构设计规范》中混凝土梁有效翼缘宽度取值的问题。采用能量变分法,推导弹性状态下有效翼缘宽度的计算公式,考虑不同的支座条件下,跨度、梁肋净距、翼缘相对刚度对取值的影响,并验证了公式的准确性。提出了在不同状态下,受拉区和受压区的混凝土梁有效翼缘宽度取值的建议。     

斜拉桥宽幅扁平钢箱梁有效宽度的探讨

针对斜拉桥宽幅扁平钢箱梁,研究其受力特性对剪力滞效应的影响,通过计算某钢斜拉桥主梁翼缘的有效宽度,探讨考虑翼缘有效宽度的必要性,为斜拉桥宽幅扁平钢箱梁断面的设计提供了指导。     

Slenderness classification of unstiffened metal plates under shear loading

Buckling behavior of slender and compact carbon steel, stainless steel and aluminum plates under the action of in-plane shear is investigated. Unstiffened shear plates with respect to their slenderness parameter and buckling behavior are qualitatively and quantitatively divided into slender, moderate and stocky categories. Accordingly, slender plates have a low buckling capacity, followed by a large postbuckling reserve. Their ultimate load coincides with the formation of inclined yield bands. Stocky plates yield before buckling. They have some post-yield capacity, buckle plastically and their ultimate and critical loads are equivalent. Moderate plates have concurrent material yielding and geometrical buckling followed by a sudden loss of stiffness. They neither have post-yield nor postbuckling reserves. Since the proportional limit stress is observed to be the cause of bifurcation in stocky plates, it is suggested that in dealing with the slenderness parameter, the yield stress be replaced by the proportional limit stress.     

The transition from thin plates to moderately thick plates by using finite element analysis and the shear locking problem

Two simple plate bending elements, based on Mindlin theory for analysis of both moderately thick and thin plates, are presented in this paper. These elements have either four nodes or eight nodes with 12 and 24 DOF, respectively. To illustrate the accuracy of these finite elements named as TURE12 and TURE24, several numerical examples of displacements and stresses for both thin and moderately thick plate bending problems are presented and discussed with a range of finite element meshes and thickness-to-plate length ratios. In addition, the bending and shearing behaviours of a Mindlin plate are analyzed with respect to shear locking. In order to test the shear locking, the results obtained from the Mindlin plate analysis using 4- or 8-noded elements with full, reduced, and selective reduced integration are compared with the exact classical thin plate solution.     

连续箱梁翼缘有效宽度的概念及应用

阐述了剪力滞的基本概念，分析了影响箱梁翼缘有效宽度的因素，探讨了工程中箱梁翼缘有效宽度的计算及应用，以完善箱梁翼缘有效宽度的计算，从而做出更好的设计。     

Refined Mindlin-Reissner theory of forced vibrations of shear deformable plates

Two theories of shear deformable plate vibrations that account for the influence of the transverse normal stress component are derived. The first is a slightly modified Mindlin theory, including a shear correction factor, while in the second the use of the shear correction factor is replaced by stress components that exactly satisfy elasticity motion equations and plate face boundary conditions. A comparison with the exact 3D solution for a sinusoidally loaded rectangular plate and infinite strip is made. It is found that the refined theories significantly increase the accuracy of results compared to the original Mindlin theory.     

Critical shear stress of flat rectangular plates with free edges

A numerical investigation is carried out by means of a finite element buckling analysis to determine the critical shear stress of flat rectangular plates with two opposite edges free. Plate sizes and the boundary conditions at the two edges loaded in shear are the parameters considered in this study. Results of the investigation show a considerable difference in the buckling strength of plates if the in-plane displacement normal to the loaded edges is restrained either at one or at both of those edges. The in-plane flexibility of the supports is, therefore, an important parameter to be accounted for in the structural design of such plates. Finally, the numerical investigation is also extended to the shear buckling strength of flat rectangular plates with only one free edge.     

Ultimate strength of dented steel plates under edge shear loads

The aims of this paper are to investigate the ultimate shear strength reduction characteristics of steel plates due to local impacts, and also to develop the ultimate shear strength design formulae of dented steel plates. The ANSYS nonlinear finite element code is used to investigate the effects of shape, size (depth, diameter), and location of the denting on the ultimate strength behavior of simply supported steel plates under edge shear loads. A closed-form expression for predicting the ultimate shear strength of dented steel plates is derived by the regression analysis based on the computed results. The results and insights developed from the present study will be very useful for damage tolerant design of steel plated structures with local denting.     

Ultimate strength of perforated steel plates under edge shear loading

The aim of the present study is to investigate the ultimate strength characteristics of perforated steel plates under edge shear loading, which is a primary action type arising from cargo weight and water pressure in ships and ship-shaped offshore structures. The plates are considered to be simply supported along all (four) edges and kept straight. The cutout is circular and located at the center of the plate. A series of ANSYS nonlinear finite element analyses (FEA) are undertaken with varying the cutout size (diameter) as well as plate dimensions (plate aspect ratio and thickness). By the regression analysis of the FEA results obtained, a closed-form empirical formula for predicting the ultimate shear strength of perforated plates, which can be useful for first-cut strength estimations in reliability analyses or code calibrations, is derived. The accuracy of the ultimate strength formula developed is verified by a comparison with more refined nonlinear FEA results.     

Experimental and numerical analysis of a multi-stiffened pure aluminium shear panel

The current paper deals with a detailed numerical study carried out on a pure aluminium shear panel and implemented through a FEM numerical model calibrated on the results obtained by an experimental test. The comparison between experimental and numerical data, in terms of dissipative capacity, maximum hardening ratio, secant shear stiffness and equivalent viscous damping factor, is carried out in order to show that the proposed model is reliable enough to well interpret the actual behaviour of the specimen, which exhibits many buckling phenomena and large plastic deformations. The proposed model is therefore profitably used to detect the exact displacement levels corresponding to the activation of the main buckling phenomena, as well as the stresses acting on the boundary bolted connections, which may result the weak point of the system. Moreover, the main outcomes of a parametrical study, which are implemented on the basis of the calibrated numerical model, are critically discussed and properly analysed, in order to define the erosion factor of the shear strength due to buckling.     

部分剪力连接简支组合梁的混凝土翼缘有效宽度有限元分析

采用ANSYS有限元软件对部分剪力连接简支组合梁混凝土翼缘的有效宽度进行了系统的研究,探讨了荷载类型、剪力连接度、组合梁的宽跨比、混凝土板厚度等因素对组合梁有效宽度的影响,以及有效宽度沿组合梁跨度方向的变化关系。结果表明,组合梁中混凝土板有效宽度随着剪力连接程度的提高而增大,随着宽跨比的增加而减小。最后,拟合出了混凝土有效宽度的计算公式,为有关组合梁的进一步研究提供了依据。     

空间连续组合桁梁桥有效分布宽度分析

通过对某两跨空间连续组合桁架梁桥的有限元模拟,分析了均布荷载和集中荷载作用下该桥面有效分布宽度,继而探讨了宽跨比、桥面板厚度、高跨比,以及节点纵、横桥向间距等参数变化对桥面板有效分布宽度的影响,最后与各国规范进行有效分布宽度系数的对比,得出空间连续组合桁架梁有效分布宽度的规律。     

钢筋混凝土剪力墙剪切刚度计算的斜向腹筋桁架-拱模型

钢筋混凝土剪力墙构件腹板为双向配筋,其剪切刚度的传统计算方法忽略竖向钢筋的作用,低估了剪力墙构件的剪切刚度和受剪承载力。为考虑双向配筋对剪力墙剪切刚度的影响,提出等效斜向腹筋桁架-拱模型,与传统桁架-拱模型不同,模型中桁架作用的腹杆由斜向等效受拉钢筋及斜裂缝间的混凝土斜压杆构成,斜向等效钢筋的方向与裂缝处两个方向钢筋的合力方向一致。采用最小能量原理推导了斜向压杆倾角的理论算式,在已有试验数据的基础上,对压杆角度理论算式进行简化,提出了便于工程应用的简化算式。斜向开裂后剪力墙的有效剪切刚度为斜向腹筋桁架模型剪切刚度与拱模型剪切刚度的叠加,采用该模型分别对现有的剪力墙试件进行计算,并将计算值与实测值进行了比较,结果表明,提出的斜向腹筋桁架-拱模型可以较为准确地计算钢筋混凝土剪力墙构件斜向开裂后的有效剪切刚度。