Interactive buckling and load carrying capacity of thin-walled beam–columns with intermediate stiffeners

The design of thin-walled beam–columns must take into account the overall instability and the instability of component plates in the form of local buckling. This investigation is concerned with interactive buckling of thin-walled beam–columns with central intermediate stiffeners under axial compression and a constant bending moment. The columns are assumed to be simply supported at their ends. The asymptotic expansion established by Byskov and Hutchinson (AIAA J. 15 (1977) 941) is employed in the numerical calculations performed by means of the transition matrix method and Godunov’s orthogonalisation. Instead of the finite strip method, the exact transition matrix method is used in this case. The most important advantage of this method is that it enables us to describe a complete range of behaviour of thin-walled structures from all global (flexural, flexural-torsional, lateral, distortional and their combinations) to local stability. In the presented method for lower bound estimation of the load carrying capacity of structures, it is postulated that the reduced local critical load should be determined taking into account the global pre-critical bending within the first order non-linear approximation to the theory of the interactive buckling of the structure. The paper’s aim is to expand the study of the equilibrium path in the post-buckling behaviour of imperfect structures with regard to the second order non-linear approximation. In the solution obtained, the transformation of buckling modes with an increase of the load up to the ultimate load, the effect of cross-sectional distortions and the shear lag phenomenon are included. The calculations are carried out for a few beam–columns. The results are compared to those obtained from the design code and to the data reported by other authors.The results discussed in the present study represent the most important results obtained by the authors in earlier investigations devoted to central intermediate stiffeners (Int. J. Solid Struct. 32 (1995) 1501; Eng. Trans. 43 (1995) 383; Int. J. Solid Struct. 37 (2000) 3323; Int. J. Solid Struct. 33 (1996) 315; Thin Wall. Struct. 39 (2001) 649; Arch. Mech. Eng. XLVIII (2001) 29).     

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.     

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。     

Tripping of thin-walled stiffeners in the axially compressed stiffened panel with lateral pressure

Tripping of stiffeners in stiffened panels under combined loads of axial force and lateral pressure is studied. Firstly, on the basis of the Vlasov's differential equation for torsional buckling of thin-walled bars, a generalized eigenvalue problem for tripping of stiffeners is derived by using the Galerkin's Method. Then the effect of the lateral pressure (dead load) to the critical axial stress (live load) upon tripping is investigated by solving the eigenvalue problem. The rotational restraint provided by the plate is taken into account. The effects of the compressive stress in the plate and the plate buckling mode are also discussed. Finally, an approximate equation to estimate the critical tripping stress with the effect of the lateral pressure is proposed. After some modifications, it can be applied in design rules for the purpose of checking the tripping strength of the stiffeners.     

Stub column tests of thin-walled complex section with intermediate stiffeners

A series of stub column tests on complex sections with intermediate stiffeners is presented in this paper. Initial geometric imperfections and material properties of the test specimens were measured. It is shown that the intermediate stiffeners could effectively enhance the local buckling stress of thin-walled sections. The test strengths are compared with the design strengths calculated using the direct strength method in the North American Specification and Australian/New Zealand Standard for cold-formed steel structures. It is shown that the direct strength method using finite strip method to obtain the buckling stresses is very conservative. Therefore, finite element method was used to predict the elastic buckling stresses. It is shown that the design strengths calculated using direct strength method based on the buckling stresses obtained from finite element analysis results generally agree with the test results well.     

不同截面形式高强冷弯薄壁槽钢构件受弯承载力试验研究

对36个屈服强度为550 MPa的高强冷弯薄壁槽钢受弯试件进行静力试验研究,考虑了加劲形式和卷边形式对试件受弯性能的影响,其中加劲形式分为无加劲、翼缘中间V形加劲和翼缘及腹板中间V形加劲3种,卷边形式分为直卷边、斜卷边和复杂卷边3种。试验结果表明：加劲形式和卷边形式是影响试件受弯承载力和屈曲模式的重要因素;与无加劲形式相比,采用板件中间V形加劲有效减小了板件宽厚比,试件受弯承载力提高了30%~70%;同种加劲形式下,短（直、斜）卷边试件受弯承载力提高幅度最大,复杂卷边试件提高幅度次之,长（直、斜）卷边试件提高幅度最小;试验过程中试件发生了局部屈曲、畸变屈曲与局部和畸变相关屈曲。对试验进行了有限元模拟,模拟结果与试验结果吻合较好。     

带加劲肋的复杂截面薄壁柱的试验研究

进行了带加劲肋的复杂截面管柱的一系列试验研究。测量了试件的初始几何缺陷和材料特性。加劲肋能有效增强薄壁构件的局部稳定性。将试验强度与采用北美、澳大利亚、新西兰规范中针对冷弯型钢结构的直接强度法计算的设计强度进行对比,结果表明,采用有线条法确定屈曲荷载的直接强度法非常保守。因此,采用有限元法确定弹性屈曲荷载,结果表明,采用此直接强度法计算的设计强度与试验结果吻合较好。     

Vibration correlation technique for the estimation of real boundary conditions and buckling load of unstiffened plates and cylindrical shells

Nondestructive experimental methods to calculate the buckling load of imperfection sensitive thin-walled structures are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. Vibration correlation technique (VCT) allows determining equivalent boundary conditions and buckling load for several types of structures without reaching the instability point. VCT is already widely used for beam structures, but the technique is still under development for thin-walled plates and shells. This paper intends to explain the capabilities and current limitations of this technique applied to two types of structures under buckling conditions: flat plates and cylindrical shells prone to buckling. Experimental results for a flat plate and a cylindrical shell are presented together with reliable finite element models for both cases. Preliminary results showed that the VCT can be used to determine the realistic boundary conditions of a given test setup, providing valuable data for the estimation of the buckling load by finite element models. Also numerical results herein presented show that VCT can be used as a nondestructive tool to estimate the buckling load of unstiffened cylindrical shells. Experimental tests are currently under development to further validate the approach proposed herein.     

Finite element buckling analysis of stiffened plates with filleted junctions

Modern aircraft wings are thin-walled structures composed of ribs, spars and stiffened panels, where the top skin is subject to compressive forces in flight that can cause buckling instability. If these panels are machined from a single billet of metal then the initial buckling performance can be significantly improved by increasing the fillet radius along the line junction between the stiffener webs and skin. Typically thin-walled structures are usually modelled with two dimensional elements. To model the stiffened panel with fillets three dimensional elements are required. For the stiffened panel selected for the analysis the paper shows that the three dimensional model shows a substantial increase in skin initiated buckling if the fillet is taken account of. A 5 mm radius leads to an increase of 34% increase in local buckling load performance for a skin portion of breath to thickness ratio of 100. The associated overall buckling load increases by 1.8%. The mass penalty for a 5 mm radius is 5.1%. To avoid local and overall buckling interaction an accurate measure of both buckling loads is very important and may have impact for designers. The three dimensional models with no fillets show very good agreement with the two dimensional models.     

Robust design of composite cylindrical shells under axial compression — Simulation and validation

Thin-walled shell structures like circular cylindrical shells are prone to buckling. Imperfections, which are defined as deviations from perfect shape and perfect loading distributions, can reduce the buckling load drastically compared to that of the perfect shell. Design criteria monographs like NASA-SP 8007 recommend that the buckling load of the perfect shell shall be reduced by using a knock-down factor. The existing knock-down factors are very conservative and do not account for the structural behaviour of composite shells. To determine an improved knock-down factor, several authors consider realistic shapes of shells in numerical simulations using probabilistic methods. Each manufacturing process causes a specific imperfection pattern; hence for this probabilistic approach a large number of test data is needed, which is often not available. Motivated by this lack of data, a new deterministic approach is presented for determining the lower bound of the buckling load of thin-walled cylindrical composite shells, which is derived from phenomenological test data. For the present test series, a single pre-buckle is induced by a radial perturbation load, before the axial displacement controlled loading starts. The deformations are measured using the prototype of a high-speed optical measurement system with a frequency up to 3680 Hz. The observed structural behaviour leads to a new reasonable lower bound of the buckling load. Based on test results, the numerical model is validated and the shell design is optimized by virtual testing. The results of test and numerical analysis indicate that this new approach has the potential to provide an improved and less conservative shell design in order to reduce weight and cost of thin-walled shell structures made from composite material.     

Behavior of thin-walled circular hollow section tubes subjected to bending

Thin-walled steel circular hollow sections (CHSs) are widely used in wind turbine towers. The tower tubes are mainly subjected to bending. There have been a few experimental studies on the bending behavior of thin-walled CHS steel tubes. This paper describes a series of bending tests to examine the influence of section slenderness on the inelastic and elastic bending properties of thin-walled CHS. In addition, the influence of stiffeners welded in the steel tube is considered. Sixteen bending tests were performed up to failure on different sizes of CHS with diameter-to-thickness ratio (D/t) varying from 75 to 300. The experimental results showed that the specimens with small diameter-to-thickness ratios failed by extensive plastification on the central part of the tube. With the increase of diameter-to-thickness ratio, the local buckling phenomena became more pronounced. The stiffeners in the steel tubes increased the load carrying capacity and improved the ductility of the specimens. The experimental results were compared with current design guidelines on thin-walled steel members in AISC-LRFD, AS4100 and European Specification. It was found that the test results agreed well with the results based on AS4100 design code.     

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.     

A study into optimization of stiffeners in plates subjected to shear loading

A great deal of attention has been focused on plates subjected to shear loading over the past decades. One main fact in design of such elements, which fall in the category of thin-walled structures, is their buckling behavior. Plate girders and recently shear walls are being widely used by structural engineers, as well as ship and aircraft designers. The role of stiffeners is proved to be vital in design of such structures to minimize their weight and cost.In this work, by using ANSYS finite element method of analysis, some 1200 plates are analyzed in order to study the role of stiffeners and to come up with some limits for an optimized design procedure. This eigenvalue method of analysis is first validated with the theoretical calculations and known cases for a wide range of typical panel geometries.The results show that the number of panels produced by intermediate transverse stiffeners should not be less than the value of plate's aspect ratio. In other words, the transverse stiffeners should divide the length of the plate to portions equal or less than its width.It is also shown that the optimum geometric properties of the stiffeners correspond to the point when the buckling shape of a plate changes from the overall mode to local mode. Furthermore, all stiffened plates, with a similar aspect ratio and number of stiffeners, have a specific value of EI_s/aD, for which the critical shear stress is optimal. In addition, some expressions to predict these properties are presented.     

The single perturbation load approach applied to imperfection sensitive conical composite structures

The importance of taking into account geometric imperfections for cylindrical and conical thin-walled structures prone to buckling had been already recognized by the first authors dealing with new formulations. Nowadays, the analysts still use empirically based lower-bound methods such as the NASA SP-8007 guideline to calculate the required knock-down factors (KDFs), which does include important mechanical properties of laminated composite materials, such as the stacking sequence. New design approaches that allow taking full advantage of composite materials are required.The single perturbation load approach (SPLA), a new deterministic approach first proposed by Hühne, will be investigated with unstiffened composite conical structures varying the geometry, lamina and layup. The SPLA׳s capability for predicting KDF is compared with the NASA approach. The SPLA was applied to the geometrically perfect structures and to the structure with geometric imperfections of two types, mid-surface imperfections and thickness imperfections. The study contributes to the European Union (EU) project DESICOS, whose aim is to develop less conservative design guidelines for imperfection sensitive thin-walled structures.     

Experimental investigation of thin-walled complex section concrete-filled steel stub columns

An innovative X section with intermediate stiffeners of thin-walled concrete-filled steel stub was proposed in this study. The X section was firstly brake-pressed from structural steel sheets to form three edges open section with intermediate stiffener in each edge, then a plate with intermediate stiffener was welded to the open section to form the closed section. The intermediate stiffener was designed to enhance the local buckling stress of the thin-walled specimens. Stub column tests of both hollow steel tubes and concrete-filled steel tubes were performed. Material properties of the self-compacting concrete and steel used in the test specimens were also measured. Design methods specified in current design standard and proposed by other researchers are used to predict the design strengths of test specimens. It is shown that the predicted design strengths are conservative.     

Analysis of thin-walled structures by finite strip and finite layer methods

The finite strip and finite layer methods are powerful tools for the analysis of thin-walled structures. In this paper, the finite strip method is applied to study the behavior of cold-formed steel beams including webs with longitudinal stiffeners. Comparisons are made with AISI specifications and published data. The finite layer method is used to investigate the buckling behavior of sandwich panels with thin facings and rigid foam cores. Effects of variable core stiffnesses (due to uneven curing, etc.) on the buckling strength are quantified and presented.     

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.     

G550高强冷弯薄壁槽钢受弯构件力学性能与设计方法

为了研究高强冷弯薄壁槽钢受弯构件的力学性能和设计方法,对3种板件加劲形式的G550高强冷弯薄壁型钢槽形截面受弯构件进行了试验研究和有限元参数分析。结果表明,板件加劲形式对高强冷弯薄壁槽钢受弯构件屈曲模式和受弯承载力有显著影响,翼缘V形加劲比腹板V形加劲能够更有效地提高构件抗弯承载力,构件抗弯承载力的变化规律与屈曲模式有关。根据有限元参数分析结果,在已有直接强度法基础上回归出适用于高强冷弯薄壁槽钢受弯构件的直接强度法修正公式。     

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。     

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。