Lower bound estimation of load-carrying capacity of thin-walled structures with intermediate stiffeners

The design of thin structures must take into account the overall instability and the instability of component plates in the form of local buckling. This investigation is concerned with the interactive buckling of thin-walled structures with central intermediate stiffeners under axial compression and/or a constant bending moment. The structures are assumed to be simply supported at the ends. The lower bound estimation of load-carrying capacity on the basis of the post-buckling behaviour of thin-walled structures with imperfections is studied when the distortional deformations are taken into account. The asymptotic expansion established by Byskov and Hutchinson (AIAA J. 15 (1977) 941) is employed in the numerical calculations performed using the transition matrix method. The present paper is a continuation of previous work by the authors (Int. J. Solids Struct. 32 (1995) 1501; 33 (1996) 315; 37 (2000) 3323), where the interactive buckling of thin-walled beam-columns with central intermediate stiffeners in the first- and the second-order approximation were considered. In the solution obtained, the transformation of buckling modes with an increase in the load up to the ultimate load, the effect of cross-sectional distortions and the shear lag phenomenon are included. The results obtained are compared with data reported by other authors.     

Distortional buckling formulae for cold-formed steel C and Z-section members: Part I—derivation

This paper presents the derivation of generalised beam theory (GBT)-based fully analytical formulae to provide distortional critical lengths and bifurcation stress resultant estimates in cold-formed steel C and Z-section members (i) subjected to uniform compression (columns), pure bending (beams) or a combination of both (beam–columns), (ii) with arbitrary sloping single-lip stiffeners and (iii) displaying four end support conditions. These formulae incorporate genuine folded-plate theory, a feature which is responsible for their generality and high accuracy. After a brief outline of the GBT fundamentals and linear stability analysis procedure, the main concepts and steps involved in the derivation of the distortional buckling formulae are described and discussed. Moreover, the paper also includes a few remarks concerning novel aspects related to the distortional buckling behaviour of Z-section beams and C-section beam–columns, which were unveiled by the GBT-based approach. Finally, note that, in a companion paper [Thin-Walled Struct., 2004 doi: 10.1016/j.tws.2004.05.002], the formulae derived here are validated and their application, accuracy and capabilities are illustrated. In particular, the GBT-based estimates are compared with exact results and, when possible, also with values yielded by the formulae developed by Lau and Hancock, Hancock, Schafer and Teng et al.     

Influence of load-non-uniformity and eccentricity on the stability and load carrying capacity of orthotropic tubular columns of regular hexagonal cross-section

The paper contains an analysis of the influence of non-uniformity and eccentricity of compressive loads on global and local buckling, on interactive buckling, and on the load-carrying capacity of thin-walled columns. Isotropic and orthotropic tubular columns of regular hexagonal cross-section have been examined. Equilibrium equations for the first and the second order non-linear approximation have been solved using the asymptotic Byskov–Hutchinson method. Numerical calculations have been performed for numerous different loading modes of isotropic columns and also for several loading modes of orthotropic columns. The results are presented in diagrams with some conclusions.     

Buckling and post buckling of thin-walled composite columns with intermediate-stiffened open cross-section under axial compression

The thin-walled composite columns with an open cross-section reinforced by intermediate stiffener under axial compression have been considered. The finite element method is employed to study the buckling behaviour of the thin-walled composite column. Eigenvalue analyses are carried out first to predict the buckling load and buckling mode shapes of the column, and then the geometric nonlinear analyses are performed to investigate the nonlinear buckling properties and post-buckling behaviour of the thin-walled structures. The type of angle ply symmetric laminate is used. The investigation is performed over several values of ply arrangement angle and various values of stiffener parameter. The numerical results show a significant effect of the intermediate stiffeners and composite ply angle on loading capacity and buckling behaviour of the thin-walled composite column. The research provides insight into the thin-walled structure and composite laminate, which is employed to enhance the loading capacity of thin-walled composite structures.     

Experimental behaviour of concrete-filled stiffened thin-walled steel tubular columns

An experimental study on the structural behaviour of concrete-filled stiffened thin-walled steel tubular columns is presented in this paper. The stiffening was achieved by welding longitudinal stiffeners on the inner surfaces of the steel tubes. Companion tests were also undertaken on 12 unstiffened concrete-filled steel tubular (CFST) columns, with or without steel fibres in the infill concrete. The test results showed that the local buckling of the tubes was effectively delayed by the stiffeners. The plate buckling initially occurred when the maximum load had almost reached for stiffened specimens, thus they had higher serviceability benefits compared to those of unstiffened ones. Some of the existing design codes were used to predict the load-carrying capacities of the tested composite columns.     

Experimental research on mechanical behavior of concrete-filled thin-walled stiffened square steel tubular short column under axial load

为研究带肋薄壁方钢管混凝土轴压短柱的受力性能,以钢管宽厚比、加劲肋宽度和加劲肋个数为参数,对26个薄壁方钢管混凝土短柱进行了试验研究。研究结果表明：对于无肋试件,在达到承载力以前管壁已经发生鼓曲,且试件宽厚比越大,鼓曲越早发生,鼓曲部位的钢管截面越早退出工作,没有发挥出钢管混凝土的优势。设置加劲肋后薄壁方钢管混凝土短柱的受力性能得到明显改善,钢管壁的局部鼓曲得以延缓,材料强度得到了充分利用,试件承载力提高。当试件宽厚比为60、80时,加劲肋宽度对试件承载力影响最明显,加劲肋宽度越大,承载力越高,增加加劲肋个数对试件承载力影响不大;而当试件宽厚比为100时,设置单个加劲肋已不能满足对管壁局部屈曲的抗弯刚度要求,必须增加加劲肋的个数以增加约束钢管变形的支撑点,减小管壁局部屈曲的波长,提高试件局部屈曲的临界荷载。同时利用ABAQUS有限元计算软件对薄壁带肋方钢管混凝土轴压短柱的受力全过程进行了模拟,并将试验结果与有限元模拟结果进行了对比,两者吻合良好,为下一步分析奠定基础。     

A semi-analytical model for local post-buckling analysis of stringer- and frame-stiffened cylindrical panels

A fast semi-analytical model for the post-buckling analysis of stiffened cylindrical panels is presented. The panel is comprised of a skin (shell) and stiffeners in both longitudinal (stringers) and circumferential direction (frames). Local buckling modes are considered where the skin may buckle within a bay and may induce rotation of the stiffeners. Stringers and frames are considered as structural elements and are thus not ‘smeared’ onto the skin. Large out-of-plane deflections and thus non-linear strain–displacement relations of skin and stiffeners are taken into account. The displacements of skin and stiffeners are approximated by trigonometric functions (Fourier series). First, a linear buckling eigenvalue analysis is carried out and some combination of buckling eigenmodes is chosen as imperfection. Then the load history is started and the Fourier coefficients are determined by minimizing the stiffened panel's energy at each load level. A curve-tracing algorithm, the Riks method, is used to solve the equations. The present model can be used to assess the post-buckling behavior of stiffened panels, for example, aircraft fuselage sections.     

带肋薄壁方钢管混凝土轴压短柱设计探讨

薄壁方钢管混凝土能取得较好的经济效果,适宜在结构中用作柱构件。但薄壁钢管在荷载较大时易发生局部屈曲,且降低对混凝土的约束。研究表明,在钢管纵向设置加劲肋可有效延缓管壁局部屈曲,改善构件工作性能。针对该新型方钢管混凝土轴压短柱,探讨子板件最大宽厚比及加劲肋的最小刚度确定方法。最后利用国内外常用的钢管混凝土设计规范对已有充分加劲的试验构件进行承载力计算,通过分析比较确定这些规范计算公式的适用性,供工程实践参考。     

加劲薄壁钢管混凝土柱的试验性能

对加劲薄壁钢管混凝土柱的结构性能进行试验研究。通过在钢管内表面焊接纵向加劲肋实现加强的作用。同时对12个不带加劲肋的钢管混凝土柱进行试验,部分柱的填充混凝土中加有钢纤维。试验结果表明,加劲肋可以有效延迟钢管局部屈曲现象的出现。当加劲构件达到最大承载量时钢板才出现屈曲,所以相比普通钢管混凝土,加劲钢管混凝土具有更高的适用性。     

Performance-based analysis of concrete-filled steel tubular beam–columns,Part II: Verification and applications

The theory and algorithms of a performance-based analysis (PBA) technique for the nonlinear analysis and performance-based design of thin-walled concrete-filled steel tubular (CFST) beam–columns with local buckling effects were presented in a companion paper. Initial local buckling and effective strength/width formulas for steel plates are incorporated in the PBA program to account for local buckling effects. Performance indices are used in the PBA program to quantify the section, axial ductility and curvature ductility performance of thin-walled CFST beam–columns. This paper presents the verification and applications of the PBA program developed. The axial load–strain curves, ultimate axial loads and moment–curvature curves for thin-walled CFST columns predicted by the PBA program are verified by experimental data. The PBA program is then utilized to investigate the effects of local buckling, depth-to-thickness ratio, concrete compressive strengths, steel yield strengths and axial load levels on the stiffness, strength and ductility performance of thin-walled CFST beam–columns under axial load and biaxial bending. The PBA technique developed is shown to be efficient and accurate and can be used directly in the performance-based design of thin-walled CFST beam–columns and implemented in advanced analysis programs for composite columns and frames.     

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。     

板件中间加劲的复杂卷边槽钢轴压构件弹性畸变屈曲应力的实用计算法

为了研究板件中间加劲的复杂卷边槽钢轴压构件畸变屈曲临界应力的简便计算方法,应用有限条分析软件CUFSM对冷弯薄壁板件中间加劲的复杂卷边槽钢以及腹板中间V型加劲的复杂卷边槽钢共90个轴压构件进行数值模拟,分析各参数对构件弹性畸变屈曲临界应力的影响。经拟合分析,得出针对板件中间加劲的复杂卷边槽钢、腹板中间V型加劲的复杂卷边槽钢轴压构件的弹性畸变屈曲临界应力的简化计算公式,并验证该公式的有效性。     

High strength thin-walled rectangular concrete-filled steel tubular slender beam-columns,Part I: Modeling

High strength thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-columns under eccentric loading may undergo local and overall buckling. The modeling of the interaction between local and overall buckling is highly complicated. There is relatively little numerical study on the interaction buckling of high strength thin-walled rectangular CFST slender beam-columns. This paper presents a new numerical model for simulating the nonlinear inelastic behavior of uniaxially loaded high strength thin-walled rectangular CFST slender beam-columns with local buckling effects. The cross-section strengths of CFST beam-columns are modeled using the fiber element method. The progressive local and post-local buckling of thin steel tube walls under stress gradients is simulated by gradually redistributing normal stresses within the steel tube walls. New efficient Müller's method algorithms are developed to iterate the neutral axis depth in the cross-sectional analysis and to adjust the curvature at the columns ends in the axial load–moment interaction strength analysis of a slender beam-column to satisfy equilibrium conditions. Analysis procedures for determining the load–deflection and axial load–moment interaction curves for high strength thin-walled rectangular CFST slender beam-columns incorporating progressive local bucking and initial geometric imperfections are presented. The new numerical model developed is shown to be efficient for predicting axial load–deflection and axial load–moment interaction curves for high strength thin-walled rectangular CFST slender beam-columns. The verification of the numerical model and parametric studies is given in a companion paper.     

高强冷弯薄壁型钢卷边槽形截面轴压构件试验研究及承载力分析

对63根屈服强度550MPa高强冷弯薄壁型钢卷边槽形截面轴压构件进行试验研究,分析了构件的屈曲模式和极限承载力,并将参考AISI规范、澳洲规范和北美规范及我国现行行业标准《低层冷弯薄壁型钢房屋建筑技术规程》（报批稿）计算的构件承载力与试验结果进行分析比较。在此基础上,对高强超薄壁型钢卷边槽形截面轴压构件的承载力合理计算模式进行研究。结果表明：高强超薄壁型钢卷边槽形截面轴压构件在宽厚比较大时会出现畸变屈曲模式;采用等效板件方法计算加劲板件有效宽度后,我国《低层冷弯薄壁型钢房屋建筑技术规程》（报批稿）适用于屈曲强度550MPa、厚度小于2.00mm的冷弯薄壁型钢卷边槽形截面构件承载力计算。     

Inelastic bifurcation of cold-formed singly symmetric columns

The paper describes a technique for determining the overall flexural and flexural–torsional bifurcation loads of locally buckled cold-formed channel columns. The method of analysis uses an inelastic geometric non-linear finite strip local buckling analysis to determine the flexural and torsional tangent rigidities of a locally buckled section. These tangent rigidities are substituted into the flexural and flexural–torsional bifurcation equations to calculate the inelastic overall buckling loads. The members are assumed to be geometrically perfect in the overall sense but can include geometric imperfections and yielding in the local mode. The bifurcation analysis is applied to cold-formed plain channel columns. The bifurcation loads and failure modes are compared with tests of fixed-ended columns and shown to be in good agreement with the tests. The effect of yielding is highlighted in the paper.     

冷弯薄壁槽钢轴压柱的卷边研究

采用有限元软件ABAQUS对两端固接的冷弯薄壁槽钢柱的屈曲性能进行研究分析,探讨卷边形式、卷边高度和壁厚对槽钢轴压柱的屈曲荷载和屈曲模式的影响,从而确定当构件截面面积不变时对抵抗屈由最有利的卷边形式.     

Finite element technique for design of stub columns

This paper presents a finite element analysis on the post-buckling behaviour of thin-walled cold-formed lipped channel and hat-section stub columns under axial compression. The specimens were modelled exactly as that used in the carefully controlled stub column tests conducted by Zaras and Rhodes. Numerical predictions on the load versus end-shortening characteristics and ultimate load capacity of the structures were obtained using a non-linear finite element analysis. The effect of the input parameters such as the degree of prescribed initial imperfection and the size of the element mesh, on the convergence of the solution is examined. The initial imperfection for post-buckling analysis is achieved by making use of the exact linear buckling wave form. Standard design procedures are developed for post-buckling analysis for thin-walled stub columns using finite element method. Results from the design procedure correlate well with experimental data and BS5950 predictions.     

Non-linear model for stability of thin-walled composite beams with shear deformation

A geometrically non-linear theory for thin-walled composite beams is developed for both open and closed cross-sections and taking into account shear flexibility (bending and warping shear). This non-linear formulation is used for analyzing the static stability of beams made of composite materials subjected to concentrated end moments, concentrated forces, or uniformly distributed loads. Composite is assumed to be made of symmetric balanced laminates or especially orthotropic laminates. In order to solve the non-linear differential system, Ritz's method is first applied. Then, the resulting algebraic equilibrium equations are solved by means of an incremental Newton–Rapshon method. This paper investigates numerically the flexural–torsional and lateral buckling and post-buckling behavior of simply supported beams, pointing out the influence of shear–deformation for different laminate stacking sequence and the pre-buckling deflections effect on buckling loads. The numerical results show that the classical predictions of lateral buckling are conservative when the pre-buckling displacements are not negligible, and a non-linear buckling analysis may be required for reliable solutions.     

Static and dynamic interactive buckling of isotropic thin-walled closed columns with variable thickness

The present paper deals with static and dynamic analysis of interactive buckling of thin-walled closed columns with variable thickness subjected to in-plane constant and/or pulse loading. This investigation is concerned with thin-walled structures with corners bevelled at the angle of 45° under axial compression. The plate model is adopted for the structures. The material, all plates are made of, is subject to Hooke's law. The structures are assumed to be simply supported at the ends. The differential equations of motion have been obtained from Hamilton's principle. In this paper the static solution has been obtained by Koiter's asymptotic method in the second-order approximation. The study is based on the numerical method of the transition matrix using Godunov's orthogonalization. The interaction of an overall mode with two local modes having the same wavelength has been considered (i.e. three-mode approach). The nonlinear equations of dynamic stability are solved with the Runge–Kutta method. The calculations are carried out for settled imperfections.     

Optimization — the basis of code-making and reliability verification

As early as 1971 Rosenblueth and Mendoza (Rosenblueth E, Mendoza E. Reliability optimization in isostatic structures. J Eng Mech Div, ASCE 1971;97(EM6):1625–42) published a paper on structural optimization the concepts of which have been refined later by Hasofer in 1974 (Hasofer AM. Design for infrequent overloads. Earthquake Eng and Struct Dynamics 1974;2(4):387–8) and Rosenblueth in 1976 (Rosenblueth E. Optimum design for infrequent disturbances. J Struct Div, ASCE 1976;102(ST9):1807–25) particularly in the context of earthquake resistant design. In essence, these authors proposed to distinguish between structures that can fail upon completion or never and structures which can fail under rare ‘disturbances’. Furthermore they distinguished between ‘single mission structures’ and structures which are systematically rebuilt after failure. The consequences of their findings for code making, especially for setting safety targets apparently have been overlooked since then. In fact, it is rather a yearly failure rate that has to be specified and verified and not a failure probability for an arbitrary reference time. The paper thoroughly reviews Rosenblueth's and Hasofer's developments and extends the concepts to failures including ultimate limit state failure under normal and extreme conditions, serviceability failure, fatigue and other deterioration and, finally, obsolescence. Some newly needed computational tools are addressed. Partial safety factors are derived for stationary failure processes and a new verification format for fatigue and other deterioration is proposed. Tools for optimization of structural components are presented.