考虑单侧翼缘受载腹板屈曲的不锈钢钢管设计

本文给出了冷成型不锈钢方钢管和矩形钢管在腹板屈曲时的设计公式。研究了两种单翼缘加载的情况,一种是端部单翼缘加载,另一种是内部单翼缘加载,此外还研究了内部加载的情况。采用屈服线理论预测了不锈钢管截面的腹板屈曲强度。屈服线理论模型是在试验中观察到的破坏模式的基础上发展起来的。在屈服线模型基础上采用不同的假定,给出了计算冷成型不锈钢方钢管和矩形钢管的腹板屈曲强度的三种设计方法。其中两种腹板屈曲设计方法是完全采用屈服线分析理论推导出来的,另外一种设计方法是综合理论分析和经验分析得到的。将试验得到的腹板屈曲强度和这三种设计方法得到的屈曲强度进行了对比。结果表明采用纯理论推导得到的设计方法计算得到的腹板屈曲设计强度偏于保守,而综合了理论分析和经验分析得到的设计方法其计算的腹板屈曲设计强度值比较合理,可以用于单翼缘受载时冷成型不锈钢管的设计。     

第五届钢结构进展国际会议（ICASS2007）2007年12月5～7日，新加坡

主办单位：新加坡国立大学 新加坡钢结构协会 钢结构进展国际会议是举办了多年的盛会，第一次到第三次会议在中国香港召开，第四次会议于2005年在中国上海召开。大会旨在为钢结构的科研工作者和工程师们提供一个平台，使他们能够就钢结构、铝结构和组合结构的分析、性能、设计以及施工等方面的最新进展互相交流探讨。     

Aluminum tubular sections subjected to web crippling—Part II: Proposed design equations

The web crippling design rules in the current American Aluminum Design Manual, Australian/New Zealand Standard, and European code for aluminum structures are assessed. Test strengths of aluminum square and rectangular hollow sections under end-two-flange (ETF) and interior-two-flange (ITF) loading conditions are compared with the design strengths (capacities) obtained using the aforementioned specifications. Furthermore, the test strengths are also compared with the design strengths obtained using the unified web crippling equation as specified in the North American Specification for cold-formed steel structural members. It is shown that the design strengths predicted by the aforementioned specifications are either quite conservative or unconservative, but in general the predictions are unreliable resulting from reliability analysis. Hence, two different unified web crippling equations for aluminum square and rectangular hollow sections under ETF and ITF loading conditions are proposed. The proposed unified design equation (A) uses the same technique as the North American Specification for the unified web crippling equation with new coefficients of C, C_N and C_h determined based on the test results obtained in this study. The proposed unified design equation (B) is similar to the unified web crippling equation in the NAS Specification, and the effect of the ratio N/h is also considered, where N is bearing length and h is the depth of the flat portion of web. Generally, it is shown that the proposed unified web crippling equation (B) compares well with the test results.     

Web crippling behaviour of laterally restrained cold-formed steel re-entrant profiled deckings

Web crippling failure is often found to be critical in cold-formed steel profiled deckings during construction of composite slabs. Therefore, accurate prediction to the web crippling resistances of profiled deckings over internal supports under hogging moment is highly desirable. This paper presents an extensive experimental investigation into the structural behaviour of laterally restrained re-entrant profiled deckings under concentrated loads. A total of 104 web crippling tests on fully supported re-entrant profiled deckings with nominal yield strengths at 235 and 550 N/mm² are carried out to provide data for direct comparison with design resistances obtained from codified design rules. It should be noted that in the past, little attention has been paid to establish the lateral restraint condition of profiled deckings under concentrated loads in tests. Hence, local section distortion or ‘section spreading’ is often observed in tests but seldom dealt with rigorously during design development. In the present study, effective lateral restraints are provided to the test specimens in order to fully mobilize the web crippling resistances of the profiled deckings. It is found that the measured web crippling resistances are typically 20%–40% higher than those obtained from the codified design rules given in BS5950: Part 6, Eurocode 3: Part 1.3 and the North America Specification, depending on the steel grades and thicknesses, the load bearing lengths as well as the loading conditions.

In general, both BS5950 and Eurocode 3 give conservative web crippling resistances for re-entrant profiled deckings with both low and high strength steel under internal and end loading conditions. Moreover, the corresponding resistance factors determined according to a codified reliability analysis are considerably larger than the required values. Thus, the design rules are reliable and conservative, although they tend to be very conservative for profiled deckings under end loading condition. However, an examination on the design rules given in the NAS shows that only some of them are applicable to predict the web crippling resistances of low and high strength steel re-entrant profiled steel deckings. The design rule for IOF condition always gives both conservative and reliable resistances for both low and high strength steel profiled deckings, compared to the measured values. The design rule for EOF condition is also found to be both conservative and reliable for low strength steel profiled deckings only, but not for high strength steel profiled deckings. The design rules for ITF and ETF conditions are not applicable for both low and high strength steel profiled deckings according to the reliability analyses.

It is demonstrated that a set of new design rules specifically for re-entrant profiled deckings is needed for both improved efficiency and reliability. Moreover, the comprehensive set of test data is readily adopted to calibrate both finite element models and design expressions in subsequent studies.     

Web crippling behaviour of thin-walled lipped channel beams

This paper presents the results of an investigation into web crippling behaviour—conducted on cold-formed thin-walled steel lipped channel beams subjected to Interior-One-Flange (IOF), Interior-Two-Flange (ITF), End-One-Flange (EOF) and End-Two-Flange (ETF) loading conditions as defined by the American Iron and Steel Institute (AISI). An experimental program was designed to obtain the load-deformation characteristics of beam members with varying cross-sectional and loading parameters under the three web crippling loading conditions. The results obtained from the experiments comprised of the ultimate web crippling strength values and displacements of the thirty-six beam specimens tested. Nonlinear finite element models were developed to simulate web crippling failure of the two loading conditions considered in the experimental program. Also, a combination of elastic analysis with a plastic mechanism approach was employed to investigate the load-deformation characteristics of lipped channel members subjected to the IOF loading condition. The comparison of experimental, finite element and plastic mechanism approach results revealed that the nonlinear finite element models were best capable of closely simulating the web crippling failure behaviour observed in the experiments for all ranges of displacement. Web crippling strength predicted from the Eurocode 3, Part 1.3 [1], and the Polish PN-B-0327 [2] design specifications were also compared with the experimental results and the comparisons indicated considerable underestimations for the range of specimens under EOF and ETF loading conditions.     

Experimental and numerical investigations of cold-formed stainless steel tubular sections subjected to concentrated bearing load

Experimental and numerical investigations of cold-formed stainless steel square and rectangular hollow sections subjected to concentrated bearing load are presented in this paper. A total of 124 data are presented that include 64 test results and 60 numerical results. The tests were performed on austenitic stainless steel type 304, high strength austenitic and duplex material. The measured web slenderness value of the tubular sections ranged from comparatively stocky webs of 6.2 to relatively more slender webs of 61.4. The tests were carried out under end and interior loading conditions. A non-linear finite element model is developed and verified against experimental results. Geometric and material non-linearities were included in the finite element model. The material nonlinearity of the flat and corner portions of the specimen sections were carefully incorporated in the model. It was shown that the finite element model closely predicted the web crippling strengths and failure modes of the tested specimens. Hence, the model was used for an extensive parametric study of cross-section geometries, and the web slenderness value ranged from 52.0 to 206.7. The test results and the web crippling strengths predicted from the finite element analysis were compared with the design strengths obtained using the American, Australian/New Zealand and European specifications for stainless steel structures. A unified web crippling equation with new coefficients for cold-formed stainless steel square and rectangular hollow sections subjected to concentrated bearing load is proposed. It is demonstrated that the proposed web crippling equation is safe and reliable using reliability analysis.     

双翼缘荷载作用下腹板开洞冷弯型钢截面的腹板压屈(2):参数研究和设计公式

采用有限元法对开洞腹板压屈冷弯型钢截面进行参数研究,在内部双翼缘(ITF)受荷和端部双翼缘(ETF)受荷工况下,验证腹板开洞和截面尺寸对承受腹板压屈的槽形截面腹板的压屈强度的影响。在这2种荷载工况下,开洞位于承重板下方中部。研究证实,影响腹板压屈强度的主要因素是开孔深度与腹板厚度的比值及承重板长度与腹板厚度的比值。与试验及有限元结果相比,该文以腹板压屈强度折减系数的形式给出的设计建议较保守。     

Web crippling of cold-formed unlipped channels with flanges restrained

The paper describes a series of web crippling tests on cold-formed unlipped channels with flanges restrained (fastened) as well as channels with flanges unrestrained (unfastened). The tests were performed under end and interior two-flange loading conditions specified in the North American Specification and Australian/New Zealand Standard for cold-formed steel structures, namely end-two-flange and interior-two-flange loading conditions. The concentrated load was applied by a bearing plate at the top flange of the channels, and the reaction force applied by an identical bearing plate at the bottom flange of the channels. The bearing plates acted across the full flange widths of the channels. The flanges of the channels were either bolted to one or two bearing plates for the specimens with flanges restrained. The web crippling test strengths are compared with the design strengths obtained using the North American Specification, Australian/New Zealand Standard and American Iron and Steel Institute Specification for cold-formed steel structures. It is shown that the design strengths predicted by the North American Specification using the unfastened design rules are generally conservative, but unconservatively predicted using the fastened design rules, even when the flanges of the specimens were restrained. The design strengths predicted by the Australian/New Zealand Standard and American Iron and Steel Institute Specification are unconservative.     

Shear buckling in foam-filled web core sandwich panels using a Pasternak foundation model

Web core panels, foam-filled sandwich panels with interior webs, are a structurally efficient option for transverse load bearing applications. In web core panels, the interaction between the webs and core material can have a substantial impact on web shear buckling strength and is a key element of lightweight structural design. The present work is an investigation of web buckling behavior in web core panels under a distributed load. To solve this problem, web shear buckling was analyzed for the case of pure shear loading with foam support, and this analytic model was extended to the case of panels with a transverse distributed load. The webs are modeled as simply supported plates resting on a Pasternak elastic foundation. To that end, a buckling model for plates on a Pasternak foundation is presented, along with closed-form approximations of the solution for square and infinitely long plates. An accurate model for the foundation constants is developed using energy methods. Applicability of the plate buckling model to web core panels with transverse loads is presented via a finite element study. In panels, the slenderness and spacing of the webs have a slight effect on the boundary conditions between the webs and face sheets. The effect is relatively small, however, and the model presented in this work underpredicts buckling strength by less than 25%. The model in this work is thus a reasonable approach to the practical design of web core panels.     

Design rules for web crippling of CFRP strengthened aluminium rectangular hollow sections

Web crippling failure (web buckling and web yielding) is critical for thin-walled members when subjected to concentrated load. Carbon fibre reinforced polymer (CFRP) is attracting increasing research interest as a strengthening material for metallic structural members. Improved web crippling capacity of aluminium rectangular hollow sections has been achieved with CFRP being attached to the exterior and/or interior of the webs from a series of tests conducted by the authors. This paper focuses on developing design rules for predicting the nominal crippling strength of CFRP strengthened sharp-corner aluminium tubular sections: rectangular hollow section (RHS) and square hollow section (SHS), under end bearing load. The existing design rules for bare sections without CFRP strengthening are firstly reviewed and assessed, including design rules for both cold-formed steel structural members (Australian/New Zealand standard (AS 4100-1998) and North American Specification) and aluminium structures (Australian/New Zealand standard (AS 1664-1997) and American aluminium design manual). They are modified to take account of the improved capacity due to CFRP strengthening. The proposed design rules are calibrated against test results.     

Effect of pitting corrosion on strength of web plates subjected to patch loading

Pitting corrosion is typical corrosion observed on coated hold frames in way of cargo holds of bulk carriers, which exclusively carry coal and iron ore. Extensive survey on the effect of pitting corrosion on structural strength under a wide variety of loading conditions is necessary to clarify the relationship between pitting intensity and residual strength in detail. In the present study, a series of tests has been conducted on structural models which consist of web, shell and face plates to investigate the effect of pitting corrosion on strength of web plates subjected to patch loading. In these tests, artificial pitting was made on the web plates and two equal concentrated loads have been applied vertically at the one third points of simply supported models. It was found that web crippling behavior is strongly affected by the pit distribution on the web plates. According to the FE-analyses following the experiment, ultimate strength of the web plates with pitting under patch loading is a little smaller than or almost the same as that of the web plates with uniform corrosion in terms of average thickness loss.     

A design rule for web crippling of cold-formed steel lipped channel beams based on nonlinear FEA

This paper presents the details of a research study conducted with the aim of developing an alternative design rule to predict the web crippling strength of cold-formed steel lipped channel beams. Current empirical web crippling design rules are perceived to be only accurate for the type of sections and the section dimensions that have been tested. A large number of experiments are often necessary to validate these design rules for a wider range of section types and dimensions, and these experiments are often expensive and impractical. Hence, a design rule which is based on a theoretical or numerical model has been attempted through this work.Four series of tests, replicating the four web crippling loading conditions namely: Interior-One-Flange (IOF), Interior-Two-Flange (ITF), End-One-Flange (EOF) and End-Two-Flange (ETF), were performed to predict the ultimate strength of one hundred and eight specimens. The test specimens were manufactured to include three distinct corner radii and two different web heights, and the specimens were tested using three different lengths of load bearing plates. Two additional loading scenarios which could arise due to the loading flange restraint namely—fixed-flange and free-flange were also examined. Finite element models were developed to numerically simulate the tests performed in the experimental investigations. Load-deformation curves were obtained from both the tests and FE models, and the FE models were validated using the test results. The validation showed a close agreement of FE results with the test results which provided the confidence of using the FE model for a parametric study beyond the limits of the experiments. Based on the results of the parametric study, a design rule was developed which is much more flexible to adapt for new types of sections and ranges of dimensions.     

A new slenderness-based approach for the web crippling design of plain channel steel beams

In this paper, the web crippling strength of cold-formed steel plain channel beams subjected to concentrated loads is evaluated on the basis of numerical models and available test results. The design equations existing in current steel codes display many coefficients, have not theoretical background and overlook the slenderness concept, which is a trademark of safety checking rules related with other failure modes such as column flexural-torsional buckling, web shear buckling and plate buckling. The main objective is to show that such slenderness-based approach is possible for web crippling design. Firstly, some considerations about the web crippling of cold-formed steel beams are drawn and a brief review is made. Secondly, the equations for web crippling design available in current Eurocode 3 and AISI steel codes are described. Then, the numerical model is explained in detail. On the basis of numerical and experimental results, it is shown that an approach based on the slenderness concept leads to fairly good estimates of web crippling load. Finally, some conclusions are drawn.     

不锈钢薄腹梁受剪性能试验研究

通过对7根不锈钢薄腹梁进行受剪性能试验研究,分析了梁腹板的剪切屈曲和屈曲后强度。结果表明：所有梁均发生剪切屈曲破坏,薄腹板中形成拉力带,上翼缘和横向加劲肋中出现塑性铰;根据腹板表面应变和侧向鼓曲变形测得的剪切屈曲应力均低于理论计算的弹性剪切屈曲应力;梁的受剪承载力显著高于腹板剪切屈曲时的荷载,具有较高的屈曲后强度;梁端设置封头肋板可以提高梁的受剪承载力。基于得出的试验结果及现有其他试验数据,对两种考虑腹板屈曲后强度的受剪承载力计算方法进行评估,我国GB 50017—2017《钢结构设计标准》中的公式仅考虑了腹板的受剪承载力,其计算结果总体偏于保守,但是对腹板高厚比较小(λs<1.5)的不锈钢薄腹梁,受剪承载力计算偏于不安全,且计算结果离散性较大;EN 1993-1-4中的计算公式中同时考虑了腹板和翼缘的受剪承载力,其计算结果偏于保守且离散性较小。     

Experimental study of web crippling behaviour of hollow flange channel beams under two flange load cases

This paper presents the details of an experimental study of a cold-formed steel hollow flange channel beam known as LiteSteel beam (LSB) subject to web crippling under End Two Flange (ETF) and Interior Two Flange (ITF) load cases. The LSB sections with two rectangular hollow flanges are made using a simultaneous cold-forming and electric resistance welding process. Due to the geometry of the LSB, and its unique residual stress characteristics and initial geometric imperfections, much of the existing research for common cold-formed steel sections is not directly applicable to LSB. Experimental and numerical studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending, predominant shear and combined actions. To date, however, no investigation has been conducted on the web crippling behaviour and strength of LSB sections. Hence an experimental study was conducted to investigate the web crippling behaviour and capacities of LSBs. Twenty-eight web crippling tests were conducted under ETF and ITF load cases, and the ultimate web crippling capacities were compared with the predictions from the design equations in AS/NZS 4600 and AISI S100. This comparison showed that AS/NZS 4600 and AISI S100 web crippling design equations are unconservative for LSB sections under ETF and ITF load cases. Hence new equations were proposed to determine the web crippling capacities of LSBs based on experimental results. Suitable design rules were also developed under the direct strength method (DSM) format.     

Shear buckling characteristics of cold-formed steel channel beams

Cold-formed steel members are increasingly used as primary structural elements in the building industries around the world due to the availability of thin and high strength steels and advanced cold-forming technologies. Cold-formed lipped channel beams (LCB) are commonly used as flexural members such as floor joists and bearers. However, their shear capacities are determined based on conservative design rules. For the shear design of LCB web panels, their elastic shear buckling strength must be determined accurately including the potential post-buckling strength. Currently the elastic shear buckling coefficients of LCB web panels are determined by assuming conservatively that the web panels are simply supported at the junction between their flange and web elements. Hence finite element analyses were conducted to investigate the elastic shear buckling behavior of LCBs. An improved equation for the higher elastic shear buckling coefficient of LCBs was proposed based on finite element analysis results and included in the ultimate shear capacity equations of the North American cold-formed steel codes. Finite element analyses show that relatively short span LCBs without flange restraints are subjected to a new combined shear and flange distortion action due to the unbalanced shear flow. They also show that significant post-buckling strength is available for LCBs subjected to shear. New equations were also proposed in which post-buckling strength of LCBs was included.     

Prediction of web crippling strength of cold-formed steel sheetings using neural networks

This study considers the use of neural networks (NNs) to predict the web crippling strength of cold-formed steel decks. Web crippling is critical for slender webs as in the case of trapezoidal sheetings which are widely used in roofing applications. The elastoplastic behaviour of web crippling is quite complex and difficult to handle. There is no well established analytical solution due to complex plastic behaviour. This leads to significant errors in various design codes. The objective of this study is to provide a fast and accurate method of predicting the web crippling strength of cold-formed steel sheetings and to introduce this in a closed-form solution which has not been obtained so far. The training and testing patterns of the proposed NN are based on well established experimental results from literature. The trained NN results are compared with the experimental results and current design codes (NAS 2001) and found to be considerably more accurate. Moreover, a trained neural network gives the results significantly more quickly than the design codes and finite element (FE) models. The web crippling strength is also introduced in closed-form solution based on the parameters of the trained NN. Extensive parametric studies are also performed and presented graphically to examine the effect of geometric and mechanical properties on web crippling strength.     

A new formulation for web crippling strength of cold-formed steel sheeting using genetic programming

This study presents Genetic programming (GP) as a new tool for the formulation of web crippling strength of cold-formed steel decks for various loading cases. There is no well established analytical solution of the problem due to complex plastic behaviour. The objective of this study is to provide an alternative robust formulation to related design codes and to verify the robustness of GP for the formulation of such structural engineering problems. The training and testing patterns of the proposed GP formulation are based on well established experimental results from the literature. The GP based formulation results are compared with experimental results and current design codes and found to be more accurate.