Short-term behaviour of shallow thin-walled concrete dome under uniform external pressure

Thin-walled spherical concrete shells or domes find widespread use in many applications, including in many iconic engineering structures of historical and religious significance. Despite this, very few experimental investigations have been reported in the open literature of shallow spherical concrete domes which allow for the effects of geometric and material non-linearities and of imperfections to be identified. This information is essential, however, in order to validate sophisticated numerical treatments, as well as to calibrate practical design and construction guidelines and is therefore much-needed. This paper reports an experimental study of a shallow thin-walled concrete dome under short-term loading, without the use of reinforcement in the concrete. The dome is 30 mm thick and has a base diameter of 3 m, being supported on a steel ring beam. The testing of the dome to failure under a uniform external pressure is described in the paper, and it is shown that it failed in a non-axisymmetric buckling mode well before the concrete reached its compressive strength. The failure pressure is compared with the ‘theoretical’ buckling results and the analytical results based on finite element analyses. In particular, this paper presents a comprehensive set of experimental data for the load–displacement and load–strain relationships and their distributions across the spherical dome throughout the loading regime.     

Flexural-torsional buckling of shallow arches with open thin-walled section under uniform radial loads

An arch with an open thin-walled section that is subjected to a radial load uniformly distributed around the arch axis may suddenly buckle out of its plane of loading and fail in a flexural-torsional buckling mode. The classical flexural-torsional buckling load for an arch with an open thin-walled section under a uniform radial load has been obtained by a number of researchers, based on the consideration that the uniform radial load produces a uniform axial compressive force without in-plane bending prior to the occurrence of flexural-torsional buckling. This assumption is correct for deep arches. However, the uniform radial load may produce substantial bending actions in shallow arches prior to flexural-torsional buckling, and so the classical buckling analysis based on the assumption of uniform axial compression may produce incorrect flexural-torsional buckling loads for shallow arches. This paper investigates the flexural-torsional buckling of shallow arches with an open thin-walled section that are subjected to a radial load uniformly distributed around the arch axis. It is found that shallow arches under a uniform radial load are subjected to combined in-plane compressive and bending actions prior to flexural-torsional buckling, and that using the classical buckling solution for circular arches under uniform compression produces incorrect buckling loads for shallow arches. A rational finite element model is developed for the flexural-torsional buckling and postbuckling analysis of shallow arches with an open thin-walled section, which allows the buckling loads to be obtained correctly.     

Time-dependent and thermal behaviour of spherical shallow concrete domes

This paper investigates the long-term and thermal behaviour of spherical shallow, thin walled concrete domes. Although these structures are vulnerable to creep, shrinkage and thermal effects, a thorough understanding of their time-dependent behaviour has hitherto not been fully established. The paper aims to provide outcomes and insight to enhance the effective design and safe use of shallow concrete domes, and a theoretical model, which accounts for the membrane and bending behaviour, as well as for creep, shrinkage and thermal effects, is developed for this purpose. The analytical model uses variational principles, equilibrium requirements, and the time-dependent constitutive relations of the concrete material. The equilibrium equations derived from this boundary value problem are solved via the so-called multiple shooting numerical method, which enables the incorporation of the variable thickness of the shell, its different boundary conditions, and various types of axisymmetric loadings in the solution. A numerical example and a parametric study, which highlight the capabilities of the proposed theoretical model and which provide some insight into the long-term and thermal behaviour of shallow concrete domes, are presented. The results show that long-term and thermal effects play important roles in the behaviour and structural safety of shallow, thin-walled concrete domes, and so these effects need to be fully understood and quantifiable.     

Performance-based analysis of concrete-filled steel tubular beam-columns, Part I: Theory and algorithms

This paper presents a performance-based analysis (PBA) technique based on fiber element formulations for the nonlinear analysis and performance-based design of thin-walled concrete-filled steel tubular (CFST) beam-columns with local buckling effects. Geometric imperfections, residual stresses and strain hardening of steel tubes and confined concrete models are considered in the PBA technique. Initial local buckling and effective strength/width formulas are incorporated in the PBA program to account for local buckling effects. The progressive local buckling of a thin-walled steel tube filled with concrete is simulated by gradually redistributing normal stresses within the steel tube walls. Performance indices are proposed to quantify the section, axial ductility and curvature ductility performance of thin-walled CFST beam-columns under axial load and biaxial bending. Efficient secant algorithms are developed to iterate the depth and orientation of the neutral axis in a thin-walled CFST beam-column section to satisfy equilibrium conditions. The analysis algorithms for thin-walled CFST beam-columns under axial load and uni- and biaxial bending are presented. The PBA program can efficiently generate axial load-strain curves, moment-curvature curves and axial load-moment strength interaction diagrams for thin-walled CFST beam-columns under biaxial loads. The proposed PBA technique allows the designer to analyze and design thin-walled CFST beam-columns made of compact or non-compact steel tubes with any strength grades and normal and high-strength concrete. The verification and applications of the PBA program are given in a companion paper.     

Strength and ductility of high strength concrete-filled steel tubular beam-columns

The ultimate strength and ductility of high strength thin-walled concrete-filled steel tubular (CFST) beam-columns with local buckling effects, are investigated in this paper, using a performance-based analysis (PBA) technique. The PBA technique accounts for the effects of geometric imperfections, residual stresses, strain hardening, local buckling and concrete confinement on the behavior of high strength thin-walled CFST beam-columns. The accuracy of the PBA technique is further examined by comparisons with experimental results. The PBA program is employed to study the effects of depth-to-thickness ratio, concrete compressive strengths, steel yield strengths and axial load levels on the stiffness, strength and ductility of high strength thin-walled CFST beam-columns under combined axial load and biaxial bending. The results obtained indicate that increasing the depth-to-thickness ratio and axial load levels significantly reduces the stiffness, strength and ductility of CFST beam-columns. Increasing concrete compressive strengths increases the stiffness and strength, but reduces the axial ductility and section performance of CFST beam-columns. Moreover, the steel yield strength has a significant effect on the section and strength performance of CFST beam-columns but does not have a significant effect on their axial and curvature ductility.     

大矢跨比球面网壳局部双层形式及稳定性分析

首先比较了适宜大矢跨比球面网壳的基本三角形网格划分形式,指出最优网格划分法得到的三类型数量(杆长、三角形、节点)最少、最经济。提出了构造球面网壳局部双层形式的方法,基于最优网格划分短程线型与三向格子形网壳,构造五种具有工程应用价值的局部双层形式。采用几何非线性有限元理论和屈曲路径跟踪技术,对几种网壳形式进行了深入的稳定分析。研究了稳定承载力随杆件尺寸变化规律,按梁单元与杆单元分析不同的稳定特性,大矢跨比局部双层与单层网壳稳定特性比较,以及小矢跨比网壳的屈曲特性。     

Reliable and accurate prediction of the experimental buckling of thin-walled cylindrical shell under an axial load

Reliable and accurate method of the experimental buckling prediction of thin-walled cylindrical shell under an eccentric load is presented. The experimental arrangement and specimens are discussed in detail, including the measurement of the geometric imperfections of the specimen's surface using a coordinate measuring machine. Different FE models, in terms of complexity, are used to simulate the experiment arrangement in an attempt to get a good agreement with the experimental buckling loads and study the effect of measured initial geometric imperfections, load eccentricity, load eccentricity position along the shell's circumferential direction and different experimental arrangement that influence the boundary conditions. It has been demonstrated that FE models with simplified rigid support conditions overestimate the prediction of the experimental buckling load even though these models included the effects of the measured initial geometric imperfections and load eccentricity. By contrast, FE models with realistically modeled support conditions achieved the best result. The average deviation −1.59% from the experimental buckling loads was achieved using the FE model simulating the mounting devices as elastic bodies and with surface-to-surface contact interaction behavior on the support. The presented work also demonstrated the strong influence of the eccentric load position along the imperfect shell's circumferential direction on the buckling of the thin-walled shell.     

A theoretical analysis of the local buckling in thin-walled bars with open cross-section subjected to warping torsion

Results of a theoretical analysis of the local buckling in thin-walled bars with open cross-section subjected to warping torsion are presented. The local critical bimoment, which generates local buckling of a thin-walled bar and constitutes the limit of the applicability of the classical Vlasov theory, is defined. A method of determining local critical bimoment on the basis of critical warping stress is developed. It is shown that there are two different local critical bimoments with regard to absolute value for bars with an unsymmetrical cross-section depending on the sense of torsion load (sign of bimoment). However, for bars with bisymmetrical and monosymmetrical sections, the determined absolute values of local critical bimoments are equal to each other, irrespective of the sense of torsional load. Critical warping stresses, local critical bimoments and local buckling modes for selected cases of thin-walled bars with open cross-section are determined.     

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.     

Strength of slender concrete filled high strength steel box columns

The use of thin walled steel sections coupled with concrete infill has been used on various building projects with great advantage. The currently available international standards for composite structures are limited to the design of concrete filled steel columns with compact sections. However, there is limited research work in the literature available which is concerned with slender concrete filled thin-walled steel columns. This paper presents a comprehensive experimental study of thin walled steel sections utilising high strength steel of a thin walled nature and filled with normal strength concrete. A numerical model is developed herein in order to study the behaviour of slender concrete filled high strength steel columns incorporating material and geometric non-linearities. For this analysis, the equilibrium of the member is investigated in the deformed state, using the idealised stress–strain relationships for both the steel and concrete materials, considering the elastic and plastic ranges. This paper presents both an experimental and theoretical treatment of coupled local and global buckling of concrete filled high strength steel columns sometimes termed interaction buckling. The experimental results of columns with high strength steel casings conducted herein by the authors are used for comparison. The effect of the confined concrete core is also addressed and the method shows good agreement with the experimental results of concrete filled steel columns with compact sections. The behaviour of concrete filled steel slender columns affected by elastic or inelastic local buckling is also investigated and compared with relevant experimental results. The paper then concludes with a design recommendation for the strength evaluation of slender composite columns using high strength steel plates with thin-walled steel sections, paying particular attention to existing codes of practice so as not to deviate from current design methodologies.     

Effects of imperfections of the buckling response of composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling response and failure of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have six different shell-wall laminates two different shell-radius-to-thickness ratios. The shell-wall laminates include four different orthotropic laminates and two different quasi-isotropic laminates. The shell-radius-to-thickness ratios includes shell-radius-to-thickness ratios equal to 100 and 200. The numerical results include the effects of traditional and nontraditional initial imperfections and selected shell parameter uncertainties. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The nontraditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. The cylinder parameter uncertainties considered include uncertainties in geometric imperfection measurements, lamina fiber volume fraction, fiber and matrix properties, boundary conditions, and applied end load distribution. Results that include the effects of these traditional and nontraditional imperfections and uncertainties on the nonlinear response characteristics, buckling loads and failure of the shells are presented. The analysis procedure includes a nonlinear static analysis that predicts the stable response characteristics of the shells, and a nonlinear transient analysis that predicts the unstable response characteristics. In addition, a common failure analysis is used to predict material failures in the shells.     

轴压下薄壁圆柱形壳屈曲试验承载力的准确可靠预测方法

论述了一种能可靠并准确预测偏心荷载下薄壁圆柱形壳屈曲试验的方法。详细描述了试验装置和试件,包括用配套的设备测量试件表面的几何缺陷。为了精确地预测屈曲试验的荷载,根据不同的复杂度建立了不同的有限元模型模拟试验装置,并研究了初始几何缺陷、荷载偏心、沿柱圆周方向的荷载偏心位置和影响边界条件的不同试验装置对屈曲承载力的影响。解释了具有简单刚性支座的有限元模型会过高估计屈曲试验承载力的原因。尽管这些模型均考虑了初始几何缺陷和荷载偏心的影响。作为对比,计算了考虑实际支座条件有限元模型的结果。在有限元模型中,用弹性实体单元模拟固定装置,用面—面接触单元模拟试件与支座间的接触面,计算出的屈曲承载力与试验有着平均约-1.59%的偏离。沿有缺陷薄壁圆柱形柱圆周方向的荷载偏心位置对屈曲承载力有显著影响。     

冷弯薄壁卷边槽钢轴压构件畸变与局部相关屈曲试验研究

对卷边尺寸不同的两类腹板中间设置加劲卷边槽形截面,共18个冷弯薄壁型钢固支轴压试件进行畸变屈曲与局部屈曲相关作用的静力试验研究。得到试件的屈曲模式、相关屈曲行为、破坏模式以及极限荷载。试验结果表明：畸变屈曲与局部屈曲的耦合相关对试件的变形和极限荷载有不利作用;畸变屈曲与局部屈曲的耦合相关作用存有较大的屈曲后承载力;畸变屈曲与局部屈曲的耦合相关顺序,即畸变屈曲 局部屈曲耦合相关、局部屈曲 畸变屈曲耦合相关,对试件的变形、非线性平衡路径、破坏模式以及极限荷载的影响有所不同。采用ABAQUS有限元软件对试件进行模拟分析,计算结果与试验结果吻合良好。     

Finite strip elastic buckling solutions for thin-walled metal columns with perforation patterns

Approximate finite strip eigen-buckling solutions are introduced for local, distortional, flexural, and flexural-torsional elastic buckling of a thin-walled metal column with perforation patterns. These methods are developed to support a calculation-based strength prediction approach for steel pallet rack columns employing the American Iron and Steel Institute׳s Direct Strength Method, however they are generally posed and could also be useful in structural studies of thin-walled thermal or acoustical members made of steel, aluminum, or other metals. The critical elastic global buckling load including perforations is calculated by reducing the finite strip buckling load of the cross-section without perforations using the weighted average of the net and gross cross-sectional moment of inertia along the length of the member for flexural (Euler) buckling, and for flexural-torsional buckling, using the weighted average of both the torsional warping and St. Venant torsional constants. For local buckling, a Rayleigh–Ritz energy solution leads to a reduced thickness stiffened element equation that simulates the influence of decreased longitudinal and transverse plate bending stiffness caused by perforation patterns. The cross-section with these reduced thicknesses is input into a finite strip analysis program to calculate the critical elastic local buckling load. Local buckling at a perforation is also treated with a net section finite strip analysis. For distortional buckling, a reduced thickness equation is derived for the web of an open cross-section to simulate the reduction in its transverse bending stiffness caused by perforation patterns. The approximate elastic buckling methods are validated with a database of 1282 thin shell finite element eigen-buckling models considering five common pallet rack cross-sections featuring web perforations that include 36 perforation dimension combinations and twelve perforation spacing combinations.     

薄板混凝土组合截面部分外包组合柱(弱轴)滞回性能足尺试验研究

为了研究薄板混凝土组合截面部分外包组合柱（弱轴）的滞回性能,对3个薄板混凝土组合截面部分外包组合柱（弱轴）足尺试件在恒定轴压下进行了水平低周反复荷载试验,观察了加载过程中薄壁板件翼缘局部屈曲和混凝土裂缝开展与压溃现象,得到了试件的荷载 位移滞回曲线。根据试验结果分析了试件的承载力、抗侧刚度、延性与耗能、破坏模式等力学性能。结果表明：试件具有较好的变形能力和耗能能力;试件的破坏模式为柱脚部位混凝土压溃和拉结筋屈服甚至拉断,随之薄壁板件翼缘发生局部屈曲。研究进一步丰富了薄板混凝土组合截面部分外包组合柱研究成果,为该类柱设计规范的制订和工程应用提供了理论依据和技术储备。     

考虑杆件失稳的单层球面网壳稳定性分析与试验研究

为研究杆件初始缺陷和杆件失稳对网壳结构稳定性的影响,采用ANSYS有限元分析软件,引入杆件的初始缺陷,考虑杆件自身的屈曲破坏,确定其最不利整体缺陷模态和杆件缺陷模态。采用传统梁单元模型和精细化壳单元模型分别对采用圆钢管、矩形钢管、工字钢三种不同截面形式杆件的网壳结构进行稳定性分析,结果表明,考虑杆件缺陷的网壳结构稳定承载力大幅度降低。进行杆件轴力跟踪分析和杆件失稳传导分析发现,单层网壳的整体稳定破坏源于单根杆件的率先屈曲,杆件失稳瞬间迅速向相邻杆件传导,导致结构整体破坏。进行了K6（2）工字钢截面网壳的加载破坏试验,验证了预设缺陷的单根杆件失稳并传递诱发了整体破坏,且承载力受工字钢弱轴缺陷的影响很大。     

Strength of cold-formed lipped channel beams under interaction of local,distortional and lateral torsional buckling

Cold-formed thin-walled lipped channel steel beams may undergo buckling modes such as short half-wavelength local buckling, intermediate half-wavelength distortional buckling and long half-wavelength lateral-torsional buckling or a combination of these before failure. ABAQUS software based on finite element analysis is used to analyse the interaction behaviour of these buckling modes in this study. The finite element model, after calibration with experimental results available in the literature, is used to perform parametric studies, to evaluate the behaviour and strength of such beams under different types of interactions due to variation of material and member properties. The large volume of synthetic data thus generated over a range of failure modes along with the available test results are used to evaluate different equations for calculating the strength of such cold-formed lipped channel beams. Based on the comparison, a method for the design of lipped channel beams failing under the interaction of local, distortional and overall lateral torsional buckling is recommended.     

基于广义梁理论的薄壁构件屈曲模态有限元分析

提出基于广义梁理论(GBT)的新方法,将各向同性薄壁构件通过壳体有限元分析方法(FEA)获得的弹性屈曲模态分解成整体、畸变和局部屈曲模态。其创新之处在于仅使用GBT截面变形模态,而非构件变形模态。该方法能够单独计算各屈曲模态,更好地了解各构件的后屈曲特性和强度曲线。根据GBT的经典假设,忽略剪切应变和横向张力。通过有限元方法得到的各模态与经典GBT计算结果一致。     

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

Experimental and numerical research on full-scale high strength thin-walled rectangular steel slender tubes filled with high strength concrete has not been reported in the literature. In a companion paper, a new numerical model was presented that simulates the nonlinear inelastic behavior of uniaxially loaded high strength thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-columns with local buckling effects. The progressive local and post-local buckling of thin steel tube walls under stress gradients was incorporated in the numerical model. This paper presents the verification of the numerical model developed and its applications to the investigation into the fundamental behavior of high strength thin-walled CFST slender beam-columns. Experimental ultimate strengths and load-deflection responses of CFST slender beam-columns tested by independent researchers are used to verify the accuracy of the numerical model. The verified numerical model is then utilized to investigate the effects of local buckling, column slenderness ratio, depth-to-thickness ratio, loading eccentricity ratio, concrete compressive strengths and steel yield strengths on the behavior of high strength thin-walled CFST slender beam-columns. It is demonstrated that the numerical model is accurate and efficient for determining the behavior of high strength thin-walled CFST slender beam-columns with local buckling effects. Numerical results presented in this study are useful for the development of composite design codes for high strength thin-walled rectangular CFST slender beam-columns.