Plastic strength of thin-walled plated members—Alternative solutions review

The paper presents results of the comparative theoretical study into plastic strength of thin-walled plated structures (plates and columns) using two different approaches: energy method and equilibrium strip method. Two types of members, a thin plate and a channel section column subjected to compression, were under investigation. Numerical results obtained using both methods, together with FE simulation are presented in load-deformation diagrams. Experimental verification of theoretical analysis (using two methods under investigation together with standards strength predictions) focused on stub columns (lipped channel sections) is presented.     

Web crippling of thin-walled cold formed steel cassettes

The resistance of cold-formed thin-walled steel cassettes against local transverse forces, i.e. the web crippling capacity, was investigated both experimentally and numerically using finite element analysis. Both unreinforced (flat) cassette webs and webs with longitudinal stiffeners situated on only one side of the web mid-line were studied. The calculation of the web crippling capacity of this type of stiffened webs is not included in current design codes. However, if cassettes are designed as continuous over two or more spans, the resistance against local transverse forces has to be verified. The study included a total of 52 structural tests. Finite element models were developed and validated on the basis of the test results and very good agreement was achieved. This was followed by an extensive parametric study of the influence of different cross-sectional parameters on the resistance against local transverse forces of longitudinally stiffened webs. Recommendations concerning the design of the cassette web section are given based on the results.     

Distortional buckling of thin-walled inclined lipped channel beams bending about the minor axis

Based on the Generalised Beam Theory (GBT), two computing models are presented to analyse the distortional critical stress of cold-formed thin-walled inclined lipped channel beams bending about the minor axis. The computing model of rigid-body motion ignores the transverse bending deformation of the flange. However, the bending deformation of the flange is accounted for in the transverse bending computing model. Based on the transverse bending computing model, this paper puts up a simple method to take into account the in-plane bending of the flange. The results given by the rigid-body motion computing model does not correlate as well as those given by the transverse bending computing model with the results available in the literature. The accuracy of the transverse bending computing model is verified through comparison of its results with the known results. The comparisons demonstrate the importance of the bending deformation of the flange on the distortional buckling of cold-formed thin-walled channel beams bending about the minor axis.     

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.     

Distortional buckling of thin-walled inclined lipped channel beams bending about the minor axis

Based on the Generalised Beam Theory (GBT), two computing models are presented to analyse the distortional critical stress of cold-formed thin-walled inclined lipped channel beams bending about the minor axis. The computing model of rigid-body motion ignores the transverse bending deformation of the flange. However, the bending deformation of the flange is accounted for in the transverse bending computing model. Based on the transverse bending computing model, this paper puts up a simple method to take into account the in-plane bending of the flange. The results given by the rigid-body motion computing model does not correlate as well as those given by the transverse bending computing model with the results available in the literature. The accuracy of the transverse bending computing model is verified through comparison of its results with the known results. The comparisons demonstrate the importance of the bending deformation of the flange on the distortional buckling of cold-formed thin-walled channel beams bending about the minor axis.     

Distortion of thin-walled beams

First order Generalized Beam Theory (GBT) describes the behaviour of prismatic thin-walled structural members by using system of ordinary differential equations. Solution can lead to separation of the load components and then to subsequent combination of the stresses and deformations. Application of GBT to a steel, cold-formed, thin-walled cantilever beam with complex non-symmetrical open cross section is presented. Theoretical values are compared with experimental ones.     

Experimental studies of the shear behaviour and strength of lipped channel beams with web openings

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. Current practice in flooring systems is to include openings in the web element of floor joists or bearers so that building services can be located within them. Shear behaviour of LCBs with web openings is more complicated while their shear strengths are considerably reduced by the presence of web openings. However, limited research has been undertaken on the shear behaviour and strength of LCBs with web openings. Hence a detailed experimental study involving 40 shear tests was undertaken to investigate the shear behaviour and strength of LCBs with web openings. Simply supported test specimens of LCBs with aspect ratios of 1.0 and 1.5 were loaded at mid-span until failure. This paper presents the details of this experimental study and the results of their shear capacities and behavioural characteristics. Experimental results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LCBs with web openings. Improved design equations have been proposed for the shear strength of LCBs with web openings based on the experimental results from this study.     

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.     

冷弯薄壁型钢卷边槽形截面构件畸变屈曲控制研究

基于部分加劲板件的畸变屈曲和局部屈曲的稳定系数比较,提出了冷弯薄壁型钢卷边槽形截面构件畸变屈曲发生于局部屈曲之后或畸变屈曲不发生的临界控制条件;给出了通过构件畸变屈曲计算长度控制畸变屈曲的临界条件;提出一种控制畸变屈曲的构造措施,即在卷边间加设缀板,并通过已有试验对其有效性进行验证,同时推导了卷边间缀板的刚度需求。结果表明：通过构件截面尺寸控制畸变屈曲不发生或发生在局部屈曲之后,可以不考虑构件畸变屈曲的影响,简化冷弯薄壁型钢卷边槽形截面构件承载力的计算;计算长度小于畸变屈曲半波长一半的构件不发生畸变屈曲;通过在卷边间加设缀板的构造措施能有效阻止部分加劲板件的转动,构件的畸变屈曲荷载和承载力都有很大的提高,缀板布置间距不同,构件承载力的提高幅度也不同,缀板间距越小,构件承载力提高幅度越大。算例分析表明,满足一定间距和刚度需求的缀板能够提高构件的畸变屈曲承载力或避免畸变屈曲的发生。     

高强冷弯薄壁型钢卷边槽形截面轴压构件畸变屈曲性能研究

建立了考虑材料和几何双重非线性的550MPa高强冷弯薄壁型钢卷边槽形截面轴压构件畸变屈曲性能分析的有限元模型,并通过对两种厚度高强冷弯薄壁型钢轴压构件畸变屈曲试验已有结果的分析比较验证了其有效性;采用该模型进一步分析了厚度、长度、初始缺陷模式及幅值等参数对畸变屈曲轴压构件承载力的影响,并对轴压构件畸变屈曲发生机理进行了探讨。结果表明：厚度、长度和初始缺陷模式是影响畸变屈曲轴压构件承载力的主要因素,且卷边面内屈曲是槽形截面轴压构件发生畸变屈曲的主要原因。通过理论计算与试验结果的对比分析,表明可以采用建议方法计算此类复杂截面轴压构件的畸变屈曲承载力。     

Equivalent thickness of cold-formed thin-walled channel sections with perforated webs under compression

Cold-formed thin-walled channel sections with perforated webs (thermal studs) are widely used in external wall panels in cold regions to reduce the cold bridging effect. However, no design method appears to be available for this type of structure. A possible method is to convert the perforated web of a thermal stud into a solid one with a reduced thickness (which is referred to as the equivalent thickness) and then adopt an existing design method for solid sections (e.g. EN 1993-1-3). This paper presents the development of a method to calculate the equivalent web thickness. The equivalent thickness calculation equation is based on regression analysis of a large number of finite element simulation results of elastic local buckling strength of perforated plates under compression, considering the effects of a number of different design variables such as plate depth, thickness, perforation patterns and dimensions of the plate. The FE simulations were carried out using a general FE software. This study suggests that the equivalent thickness is mainly related to the plate width to thickness ratio, the total width of perforation at the critical section and the width of the perforation zone (total plate width between the first and last perforation). A regression equation has been proposed to relate the equivalent thickness to these parameters. To demonstrate the validity of the proposed equivalent thickness method, the compression strengths of a large range of perforated columns have been simulated by using either the original perforated sections or the equivalent solid section; and a comparison of the simulation results shows good agreement between the two sets of results.     

高强冷弯薄壁型钢卷边槽形截面构件设计可靠度分析

基于已有的承载力试验研究结果,对屈服强度550MPa高强冷弯薄壁型钢中常用的卷边槽形截面轴压构件和偏压构件的计算模式不定性进行了分析,并统计分析了高强冷弯薄壁型钢强度不定性、几何特性不定性。在此基础上,采用改进一次二阶矩方法,按现有规范的抗力分项系数要求,计算了高强冷弯薄壁型钢卷边槽形截面轴压构件和偏压构件不同可能荷载组合下的可靠指标。结果表明：对于宽厚比符合规范要求的屈服强度550MPa高强冷弯薄壁型钢卷边槽形截面轴压构件和偏压构件,按现有规范的抗力分项系数计算得到的可靠指标均能满足目标可靠指标的要求,证明了所采用的承载力计算方法的适用性;但对于宽厚比超出规范要求的轴压和偏压构件,计算得到的可靠指标不能满足目标可靠指标的要求。     

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.     

Influence of autoclaving process parameters on the buckling and postbuckling behaviour of thin-walled channel section beams

The postbuckling behaviour and load carrying capacity of thin-walled composite channel sections subjected to uniform compression are presented. An analysis of the influence of parameters of the composite manufacturing process on strength properties and load carrying capacity of the thin-walled structure made of this composite has been conducted. The microstructure characteristics of composites is presented and discussed. The postbuckling behaviour and load carrying capacity of thin-walled channel section columns subjected to compression have been determined with the finite element method. The ANSYS software has been employed.     

Distortional theory of thin-walled beams

The classic thin-walled beam theory for open and closed cross-sections is generalized to include one distortional mode of deformation. Distortional cross-section parameters are introduced and the new orthogonality conditions for uncoupling of the axial displacement modes are given. A normalization technique for the distortional modes leads to unique distortional cross-section properties. The theoretical formulations for torsion and distortion are nearly similar and result in nearly identical equilibrium equations. However, for closed single- or multi-cell cross-sections the torsional and distortional shear flows may couple. A study of the order of magnitude of the governing torsional and distortional parameters shows the difference between open and closed cross-sections and the related solution types. The difference in the order of magnitude of the governing cross-section parameters also leads to approximate solution techniques. In the examples, section three cross-sections are used to illustrate variations of the theoretical parameters.     

Hysteretic behaviour of tubular joints under cyclic loading

This paper examines the cyclic performance of CHS joints used in steel tubular structures. Quasi-static experimental study into the response of eight T-joint specimens is described. Four of them are subjected to cyclic axial load, and the other four are subjected to cyclic in-plane bending. The general test arrangement, specimen details, and most relevant results (failure modes and load-relative deformation hysteretical curves) are presented. Some indexes to assess the seismic performance of tubular joints, including strength, ductility and energy dissipation, are synthetically analyzed and compared. Test results show that failure modes of axially loaded joints mainly contain weld cracking in tension and chord plastification in compression. But for joints under cyclic in-plane bending, both punching shear and chord plastification become regular failure modes accompanied by ductile fracture of the welds. Hysteretic curves take on a plump form in general. Ultimate strengths of joints are also compared with equation values for monotonic loading from various design codes. Results indicate the strength at a certain deformation limit can be regarded as the ultimate strength of a T-joint under cyclic loading and existing codes can be used to check it. It is also found that there is a significant distinction in the energy dissipation mechanism for tubular joints under different loading conditions. Finite element analyses are performed by taking into account weld geometry to facilitate the interpretation of the test results. It is identified that high tensile stress triaxiality can be one primary cause of weld cracking which happened under low cyclic load level.     

带肋冷弯薄壁方钢管混凝土柱滞回性能研究

对3根带肋冷弯薄壁方钢管混凝土柱进行滞回试验,主要参数为轴压比。试验结果表明：纵向加劲肋有效延缓了钢管壁局部屈曲的发生;其滞回曲线饱满,具有良好的耗能能力;随着轴压比的增大,柱承载力略有增大,而延性、耗能能力则明显减小;当横向位移大于6倍的屈服位移时,大轴压比的刚度退化速度最快。建立了该类试件的有限元模型,对比可得有限元模拟结果与试验结果吻合较好。基于有限元模型对该类构件开展机理分析和参数分析。结果表明：在带肋冷弯薄壁方钢管的约束下,核心混凝土的强度得到了较大提高;钢管局部屈曲发生在峰值荷载后,局部屈曲只发生在纵向加劲肋和钢管角部间;材料强度、轴压比、钢管宽厚比和长细比等参数对该类构件的承载力有较大影响;混凝土强度、轴压比和长细比对荷载-位移骨架曲线形状有较大影响。基于参数分析建议了该类构件的简化滞回模型,简化计算结果和有限元计算结果吻合较好。     

Application of surfaces of ultimate strength for thin-walled beams

This paper deals with the problem of ultimate load-carrying capacity of thin-walled sections subject to combined load. That has direct implementation in sizing and design of thin-walled structures. It is solved using the ultimate strength method based on the theory of plastic analysis of structures. It is assumed that the elastic strains are negligible in comparison to the plastic strains and that justifies the application of a fully plastic model. The following problems have to be analyzed before the sizing and design is completed:

• Load vectors and load components

• Locations of the plastic neutral axes

• The surface of ultimate strength

The most important achievement presented in this paper is an improvement for the location of the plastic neutral axis. Until now, the position of the plastic neutral axis has been localized by iterations, starting with the position from the elastic model. That led, in some cases, to a statically inadmissible model and lack of equilibrium in case of asymmetric sections or asymmetric loads.A successful solution to the problem consists in covering the whole section with a mesh of plastic neutral axes and a cluster of corresponding points on the surface of ultimate strength.One of the points on the surface has load components in proportion with the load vector. The corresponding location of the plastic neutral axis is precisely the one we are seeking.The load vector may be extended to pierce one of the triangles that the surface is made of. The coordinates of the point where the load vector is piercing the triangle is a weighted-average of the coordinates of three vertices of the triangle. The same weight is used to localize the plastic neutral axis corresponding to the piercing point of the surface.     

高强冷弯薄壁型钢卷边槽形截面偏压构件试验研究及承载力分析

进行了48根屈服强度550MPa高强冷弯薄壁型钢卷边槽形截面偏心受压构件试验,考虑了不同截面形式、厚度、长细比和荷载偏心方式的影响,研究了这类偏心受压构件的破坏模式、承载力影响因素以及构件承载力计算方法。结果表明：高强冷弯薄壁型钢偏压构件由于材料强度高,截面宽厚比较大,局部屈曲和畸变屈曲的影响较大,我国规范仅考虑了局部屈曲的影响而没有全面考虑畸变屈曲的影响,这使得部分发生畸变屈曲的试件计算结果偏于不安全,但又对不发生畸变屈曲的长细比较大的构件偏于保守。最后,在试验和现有规范方法比较分析的基础上,提出了一种适用于高强冷弯薄壁型钢偏压构件极限承载力的建议计算方法。该建议方法计算所得结果与试验结果吻合较好,且安全可靠,可供设计参考。