The shape of circumferential weld-induced imperfections in thin-walled steel silos and tanks

The strength of thin-walled cylindrical shell structures is highly dependent on the nature and magnitude of imperfections. Most importantly, circumferential imperfections have been reported to have an especially detrimental effect on the buckling resistance of these shells under axial load. Due to the manufacturing techniques commonly used during the erection of steel silos and tanks, specific types of imperfections are introduced into these structures, among them circumferential weld-induced imperfections between strakes of steel plates. The shape of such a localised circumferential imperfection has been shown to have a great influence on the degree of strength loss of thin-walled cylindrical shell structures. The results of a survey of imperfections in an existing silo at a location in Port Kembla, Australia in combination with linear elastic shell bending theory was used to develop and calibrate a shape function which accurately describes the geometric features of circumferential weld imperfections. The proposed shape function is the first function to combine shell theory with actual field imperfection measurements. It is a continuous function and incorporates all the necessary features to represent the geometry of a circumferential weld-induced imperfection. It was found that after filtering out the effects of overall imperfections three parameters governed the shape of the surveyed imperfections: the depth, the wavelength and the roundness.     

Static buckling analysis of thin cylindrical shell with centrally located dent under uniform lateral pressure

One of the common failure modes of thin cylindrical shell subjected to external pressure is buckling. The buckling pressure of these shell structures are dominantly affected by the geometrical imperfections present in the cylindrical shell which are very difficult to alleviate during manufacturing process. Dent is one of the common geometrical imperfections present in thin shell structures which may be formed due to mechanical damage caused by accidental loading or impact. In this work, influence of various dent parameters (dent length, dent width, dent depth and angle of orientation of the dent) on the critical buckling pressure of thin cylindrical shells with a centrally located dent is studied using non-linear static finite-element analysis of ANSYS under external pressure with simply supported boundary conditions at the top and bottom edges of the thin cylindrical shell.     

Mode interaction in thin-walled equal-leg angle columns

This paper presents and discusses numerical results, obtained through Ansys shell finite element analyses, dealing with the post-buckling behaviour (mostly elastic, but also elastic–plastic), ultimate strength and failure mode nature of fixed-ended and pin-ended thin-walled equal-leg angle steel columns with coincident critical flexural-torsional and minor-axis flexural buckling loads (i.e., experiencing very strong coupling effects between these two global instability phenomena) – for comparative purposes, columns that are buckling in pure flexural-torsional and flexural modes are also analysed. Since the main aim of the work is to investigate the column imperfection-sensitivity, the analyses concern otherwise identical columns containing initial geometrical imperfections with different shapes and amplitudes, combining the competing critical buckling modes – particular attention is paid to the sign of the minor-axis flexural component. The results reported consist of column (i) elastic equilibrium paths and the corresponding peak loads and deformed configurations and (ii) elastic–plastic collapse loads and mechanisms, making it possible to assess how they are influenced by the initial geometrical imperfections.     

A numerical investigation into the effect of pressure on holes and cracks in water supply pipes

The effect of water pressure in a pipe on the rate of leakage from leak openings in the pipe is one of the main factors influencing leakage that is still not understood sufficiently. In this study, the behaviours of different types of leak openings (round holes and longitudinal and circumferential cracks) on pressurized pipes were investigated for different pipe materials (uPVC, steel, cast iron and asbestos cement) using finite element analysis. Linear elastic behaviour was assumed. The study found that (1) pipe stresses are significantly affected by a leak opening, and can easily exceed the material's yield strength in the vicinity of the opening; (2) round holes show the smallest expansion with pressure, followed by circumferential cracks and then longitudinal cracks; (3) the areas of all leak openings increase linearly with pressure; (4) longitudinal pipe stresses affect the behaviours of round holes and circumferential cracks, but not that of longitudinal cracks; and (5) the effect of pressure on a leak opening increases exponentially with increasing hole diameter or crack length. An equation is proposed for modelling the effect of pressure on individual leaks.     

Ultimate strength of stiffened plates with a square opening under axial and out-of-plane loads

The high strength to weight ratio and high stiffness to weight ratio of stiffened plates find wide application in aircraft structures, ship structures, offshore oil platforms and lock gates. The strength and stability of stiffened plates is highly influenced by openings and initial imperfections. The main objective is to study the behaviour of stiffened steel plates with openings up to collapse and to trace the post-peak behaviour under axial and out-of-plane loads. Four stiffened steel plates with a square opening were fabricated for testing. Angle sections were used as stiffeners. Imperfections in the plate, stiffener and overall imperfection of the whole panel were measured. All fabricated panels were tested to failure. A finite element (FE) model was developed for the analysis of stiffened plates with initial imperfections and validated with the test results. Parametric studies were conducted using the developed FE model, and interaction curves and equations were developed for the design of stiffened plates with initial imperfections and openings. The interactive effect for stiffened panels with a square opening was found to be linear, with proportional reduction of the ultimate axial load carrying capacity due to the constant out-of-plane load.     

对称双圆弧柱壳的非线性屈曲

对于潜艇艇体耐压壳结构,屈曲特性在设计中被广泛关注。针对一种新型潜艇耐压艇体结构-对称双圆弧环肋柱壳,推导了相应的弹塑性失稳系数。采用非线性大挠度理论,给出了静水压力作用下含初始缺陷的对称双圆弧环肋柱壳大挠度弹塑性屈曲临界压力计算式。讨论了开口角、周向相当波数和初始几何缺陷对临界压力的影响。计算结果表明,开口角对结构弹塑性屈曲的临界压力影响很小,而周向相当波数是影响临界压力的主要因素。     

板片结构稳定性分析的改进随机缺陷法

初始几何缺陷对板片结构体系稳定性的影响是板片结构计算和设计中的一个关键问题。提出一种考虑初始几何缺陷的改进随机缺陷法 ,它弥补了一般随机缺陷法人工计算量大的缺点 ,也回答了设计临界荷载和一致缺陷法得到的临界荷载的可靠性问题。实例为一试验模型 ,通过理想模型、一致缺陷法、改进随机缺陷法以及试验结果的对比 ,得出一些对板片结构体系设计和研究有益的结论。     

Theoretical elastoplastic buckling of stringer stiffened cylindrical shells

A linear analysis method is offered to predict the theoretical elastoplastic buckling of stringer stiffened cylindrical shells subjected to longitudinal loading. Welding residual stresses are taken into account in the calculation, but effects of geometrical imperfections and pre-buckling displacements are ignored.The examples analysed show a good correlation between the analytical results and those obtained experimentally with stocky models of moderate geometrical imperfections.     

Effect of size and orientation of a centrally located dent on the ultimate strength of a thin square steel plate under axial compression

Thin steel plates are widely used in many structural applications because of its high load carrying capacity with less weight. The load carrying capacity of thin plates mainly depends on the imperfections present in them. Dent is one of the common geometrical imperfections present in thin shell structures which may be formed due to mechanical damage caused by accidental loading or impact. In this work, influence of various dent parameters (dent length, dent width, dent depth and angle of orientation of the dent) on the ultimate strength of a thin square plate with a centrally located dent is studied using nonlinear static finite-element analysis, under uni-axial compressive loading with simply supported boundary conditions.     

Buckling behaviour of a liquid storage tank

The buckling behaviour of a liquid storage tank built up of circular cylindrical shell-sections with different thicknesses is investigated. In any partially filled state the critical vacuum for bifurcation is determined taking into account the weight of the structure. For a storage tank with small geometrical imperfections the behaviour is analysed asymptotically using Koiter's general post-buckling theory. The initial post-buckling analysis based on the assumption of linear pre-buckling behaviour indicates that the storage tank is imperfection-sensitive in any partially filled state. Finally, bifurcation analyses accounting for nonlinear pre-buckling show that the assumption of linear pre-buckling is a good approximation even at high liquid levels.     

The structural performance of polymeric linings for nominally cylindrical gravity pipes

This paper considers both the linear elastic and creep buckling of polymeric pipe linings used for the rehabilitation of gravity pipes, for which external groundwater pressure has been identified as the prime source of loading. Theoretically perfect and imperfect conditions are considered, with the imperfections taken to be in the form of a concentric or eccentric annulus between the rigid host pipe (cylindrical constraint) and polymeric lining. Under these conditions two recently obtained mathematical procedures for the prediction of linearly and non-linearly elastic buckling are compared with the results of complementary laboratory testing. Linear elastic conditions are shown to be well approximated by undertaking short-term (≈30 min) testing under increasing pressure to failure. Controlled imperfections are introduced into the laboratory tests and excellent correlation with the theoretical predictions is obtained. In particular, the dominant geometrical imperfections are shown to be major influences on the obtained buckling pressure. The mathematical models are then adapted to simulate the creep buckling process under long-term constant pressure. The results obtained are again compared with those provided by complementary physical testing, and appropriate conclusions are made.     

考虑T应力下受压岩体水力压裂特性分析

自然状态下岩体多处于受压状态,分析受压岩体水力压裂性质对于完善和发展水力压裂技术有着重要意义。基于线弹性断裂力学的基本理论,对受压岩体水力压裂性质开展研究,通过最大周向应变准则,考虑裂隙尖端非奇异项即T应力的影响,推导出闭合和非闭合状态下临界水压和临界起裂角计算式。将该计算式用于某岩石水力压裂工程实例计算,所得计算值与实际值较为吻合。最后分析了闭合和非闭合情形下泊松比和侧压力系数对临界水压和临界起裂角的影响。该文研究可为实际水力压裂技术提供一定的理论参考。     

集中荷载作用下钢筋砼简支梁的孔洞合理形状和合理位置的有限元分析

本文主要通过平面有限元计算分析 ,研究集中荷载作用下的开孔简支梁在弹性阶段孔边应力分布 ,从而确定孔洞的合理形状和合理位置。     

Structural sensitivity of circular sewer liners to geometrical imperfections

The impact of geometrical defects of liners on their structural performance has been examined in this article. The major common imperfections, such as gap, ovality and wavy imperfections, have been taken into consideration. In the first step, the influence of separate imperfections is presented. Then, the combination of coinciding defects is examined. The formula for weighted influence of individual defects has been found, based on a wide range of FEM calculations and statistical interpretation. All the examinations performed led to improving the general formula for critical groundwater pressure.     

单层网壳结构稳定性分析的改进随机缺陷法

初始几何缺陷对网壳结构稳定性的影响是结构设计中的一个关键问题.对一致缺陷模态法和随机缺陷法的优缺点进行理论分析,提出了改进随机缺陷法,它弥补了随机缺陷法人工计算量大的缺点,也回答了设计临界荷载和一致缺陷模态法得到的临界荷载的可靠性问题.     

Parametric study on buckling behaviour of dented short carbon steel cylindrical shell subjected to uniform axial compression

Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings, etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells, but in this paper only effect of a dent on strength of a short (Lc/Rc∼1, Rc/t=117, 175, 280) cylindrical shell is considered for analysis. The dent is modeled on the FE surface of perfect cylindrical shell for different angles of inclination and sizes at half the height of cylindrical shell. The cylindrical shells with a dent are analyzed using non-linear static buckling analysis. From the results it is found that in case of shorter dents, size and angle of inclination of dents do not have much effect on static buckling strength of thin cylindrical shells, whereas in the case of long dents, size and angle of inclination of dents have significant effect. But both short and long dents reduce the static buckling strength drastically. It is also found that the reduction in buckling strength of thin cylindrical shell with a dent of same size and orientation increases with increase in shell thickness.     

K6型单层球面网壳的弹塑性稳定

本文有计划地对1200余例实际尺寸的K6型单层球面网壳进行了双重非线性全过程分析,求得了它们的极限承载力,系统地考察了初始缺陷和荷载不对称分布等因素对网壳性能的影响,并重点讨论了材料非线性对网壳极限承载力的影响.通过这种大规模参数分析研究,较全面了解了K6型单层球面网壳弹塑性稳定性能的规律,在此基础上对以往仅考虑几何非线性的网壳极限稳定承载力实用公式进行了修正.     

Buckling behaviour of prestressed steel stayed columns with imperfections and stress limitation

A steel column that is reinforced by prestressed stays, generally has an increased strength in axial compression. In the past, greater emphasis was placed on obtaining a higher critical buckling load. However, detailed knowledge of the post-buckling behaviour is important to ensure the safety and efficiency of the structure. The current work examines the buckling behaviour of a stayed column with geometrical imperfections, and stress limitation relating to possible material failure. A geometrically nonlinear model accounting for imperfect buckling behaviour of a stayed column was formulated using the Rayleigh–Ritz method, and then validated, using the finite element method. It is shown from these studies that the system tends to be most sensitive to imperfections at a prestress level that yields the highest critical load, and that the real maximum load capacity seems to increase as the prestress increases with a given configuration. The findings suggest that the optimal prestress should be greater than that found from using the previous convention that was based on linear analysis.     

腹板开矩形孔复杂卷边冷弯槽钢梁局部屈曲性能及直接强度法研究

为了研究腹板开孔复杂卷边冷弯槽钢梁的局部屈曲性能，以及探究北美冷弯型钢结构设计规范(AISI S100-2016)中腹板开孔冷弯槽钢梁局部屈曲直接强度法计算公式的可靠性，对孔高比(孔洞高度与腹板高度的比值)分别为0、0.2、0.4、0.6和0.8的10个腹板开矩形孔复杂卷边冷弯槽钢梁纯弯试件进行了静力试验研究。试验结果表明，开孔和不开孔试件均发生以局部屈曲为主的屈曲破坏模式，与不开孔试件相比，开孔试件的受弯承载力下降，且下降幅度随孔高比的增大而增大。利用ANSYS有限元程序对试验进行了模拟分析，分析结果与试验结果吻合良好；在此基础上，采用经试验验证的有限元模型，通过变换腹板高度、板厚和孔高比开展了有限元参数分析，并根据有限元参数分析结果对已有腹板开孔冷弯槽钢梁的弹性局部屈曲临界应力近似计算公式进行了修正。基于试验结果、有限元参数分析结果以及修正的弹性局部屈曲临界应力近似计算公式，对AISI S100-2016中开孔冷弯槽钢梁发生以局部屈曲为主破坏时的直接强度法计算公式进行了修正。     

Sensitivity analysis of stability problems of steel plane frames

The objective of the paper is to analyse the influence of initial imperfections on the load-carrying capacity of a single storey steel plane frame comprised of two columns loaded in compression. The influence of the variance of initial imperfections on the variance of the load-carrying capacity was calculated by means of Sobol’ sensitivity analysis. Monte Carlo based procedures were used for computing full sets of first order and second order sensitivity indices of the model. The geometrical nonlinear finite element solution, which provides numerical results per run, was employed. The mutual dependence of sensitivity indices and column non-dimensional slenderness is analysed. The derivation of the statistical characteristics of system imperfections of the initial inclination of columns is described in the introduction of the present work. Material and geometrical characteristics of hot-rolled IPE members were considered to be random quantities with histograms obtained from experiments. The Sobol sensitivity analysis is used to identify the crucial input random imperfections and their higher order interaction effects.