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.     

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。     

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。     

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.     

Combined flexure and web crippling strength of a low-ductility high strength steel decking: experiment and a finite element model

Profiled decking or sheeting of high strength low-ductility steel (ASTM611 Grade E) is a relatively new development in building construction industry. Due to inadequate information, the major international codes of design practices are yet to include this steel, and apply additional restrictions on their design and use. This type of decking shows high sensitivity to distortional as well as local buckling. Strength of such decking under combined flexure and web crippling as well as moment–rotation capacity are of principal concern if such decking is to be designed as a continuous structure to achieve better economy. This paper describes an experimental study of the behaviour of re-entrant decking of low-ductility steel under combined web crippling and flexure. Based on this experimental study, a nonlinear finite element model has been proposed which can predict the moment–rotation characteristics of such decking with reasonable accuracy.     

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.     

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.     

瞬态和稳态条件下G550冷弯型钢力学性能

冷弯型钢高温下的力学性能是防火安全设计和数值分析的重要因素。现多采用稳态试验方法研究高温下材料的力学性能。然而,瞬态试验方法能更好地反应火灾的真实情况。采用瞬态和稳态两种方法对厚度为1mm的G550钢材进行试验,并对两种方法的试验结果进行讨论。结果显示,G550钢材的稳态试验结果不同于瞬态试验结果。G550钢材的稳态试验结果高估了冷弯型钢结构的耐火性。此外,将试验结果与其他研究人员的研究结果以及现有设计规范的计算结果进行比较,结果显示,采用BS5950计算的G550钢材屈服强度与瞬态试验结果相一致,比稳态试验结果保守。然而,其他情况下BS5950,AS4100和EC3的计算结果并不保守。最后,采用拟合法给出高温下考虑G550钢材的屈服强度、弹性模量、极限强度等折减因素的统一方程。基于Ramberg-Osgood模型给出G550钢材的应力-应变方程。该方程的计算结果与试验结果相符,能够满足实际工程的需要。     

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.     

Analysis and design of cold-formed steel channels subjected to combined bending and web crippling

The channel failures due to combined bending and web crippling may occur at the highly concentrated interior loading when there is no load stiffener in cold-formed thin-walled steel beams. This paper presents accurate finite element models to predict the behavior and ultimate strengths of cold-formed steel channels subjected to pure bending as well as combined bending and web crippling. Both geometric and material nonlinearities are considered in the finite element analysis. The nonlinear finite element models are verified against experimental results of cold-formed steel channels subjected to pure bending as well as combined bending and web crippling. The finite element analytical results show a good agreement with the experimental results in terms of the ultimate loads and moments, failure modes and web load-deformation curves thus validating the accuracy of the finite element models. The verified finite element models are then used for an extensive parametric study of different channel dimensions. The channel strengths predicted from the parametric study are compared with the design strengths calculated from the North American Specification for cold-formed steel structures. It is shown that the design rules in the North American Specification are generally conservative for channel sections with unstiffened flanges having the web slenderness ranged from 7.8 to 108.5 subjected to combined bending and web crippling. It is demonstrated that the nonlinear finite element analysis by using the verified finite element models against test results is an effective way to predict the ultimate strengths of cold-formed thin-walled steel members.     

冷弯薄壁钢短柱在均匀高温下的性能

本篇章对常温及均匀高温条件下的冷成型薄壁短槽钢的轴向强度进行了初步研究。对常温及均匀高温下的一系列卷边的或非卷边的槽钢进行了试验研究。应用一系列的设计方法和商业化的有限元软件ABAQUS(1998)对试验进行了分析。本中涉及的设计方法包括：英国规范BS5950(1987)、欧洲规范Eurocode3Part1．3(CENl996)和美国规范AISI(1996)，在有限元分析中，考虑了几何非线性和材料非线性。高温下钢材的应力一应变曲线根据欧洲规范Eurocode3Part1．2(CENl995)和Qutinen(2001)采用。在某些试验中发现扭转屈曲，为了扩展针对这种破坏模式的设计方法，在这些规范中引用了Yong和Hancock(1992)考虑扭转屈曲的方法。对设计规范BS5950Part5(1987)、欧洲规范Eurocode3Part1．3(CENl996)和美国规范AISI(1996)中常温下薄壁柱的设计方法加以修改，来考虑钢材高温下的强度和刚度的变化。从试验结果、规范预期的结果和数值分析的比较可见，可很容易的通过上述修正当前规范的方法来分析薄壁型钢短柱高温下的性能。     

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.     

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。     

冷弯槽钢承受集中荷载时腹板压屈的数值分析

引用国际上最新的试验结果,对集中荷载作用下的冷弯薄壁非卷边槽钢进行数值模拟,数值计算结果与试验数据吻合良好。利用有限元软件进行多参数的数值分析,得出影响槽钢腹板压屈的主要参数,并对其影响程度进行定量分析。在试验研究和数值分析的基础上,给出计算槽钢腹板压屈荷载的建议公式,公式计算的结果与试验数据吻合良好,说明建议公式是合理且偏于安全的。     

各国规范高强度螺栓抗剪连接设计方法比较分析

高强度螺栓抗剪连接作为钢结构连接的一种有效方法得到了广泛的应用,而各国规范对高强度螺栓抗剪连接设计方法的规定有所差异。尤其是随着高强度钢材在实际工程中的推广和应用,各国规范规定的适用性有待进行深入探讨。本文对中国钢结构设计规范GB50017-2003、欧洲钢结构设计规范Eurocode 3、美国钢结构设计规范ANSI/AISC360-05、英国钢结构设计规范BS5950和澳大利亚钢结构设计规范AS4100中高强度螺栓抗剪连接设计方法进行对比,其中包括承压型连接和摩擦型连接,并给出了相关实例计算。     

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.     

Web crippling strength of a steel sandwich panel with V-shaped webs

Steel sandwich panels with V-shaped web flutes (V-core panels) serve the structural functions of a proposed energy-efficient roof system for residential construction. Due to its intended use as a flexural member spanning between a ridge beam and a structural wall, and required slender webs for weight considerations, web crippling under end one-flange loading is a critical strength limit state for the V-core panels. Although the 2001 North American Specification for the Design of Cold-Formed Steel Structural Members provides a design procedure to address web crippling, those design rules were developed for members whose cross sections are different from that of V-core panels. Consequently, nine specimens were tested to collect data on V-core panels subjected to end one-flange loading. Test observations suggested that V-core panels behave very similarly to multi-web decks that are strapped and unfastened to the supports. Experimental data reported in the literature was used to modify the web crippling strength equation in the Specification to reflect these particular conditions. The modified equation was found to adequately predict the measured web crippling strength of V-core panels.     

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.