Buckling of Cylindrical Tunnel Liners

Buckling of thin cylindrical shell liners used for the stabilization of soft ground tunnels is treated as the buckling of an elastic ring restrained radially and tangentially by an infinite surrounding elastic medium. Stiffness components for the elastic medium are derived and used to provide various levels of approximation for the elastic critical loads and associated modes of the liner when subject to overburden pressure loading. For most practical tunnel liners, elastic buckling is found to occur in modes having relatively short circumferential wavelengths. In these circumstances an approximation introduced into the critical pressure analysis allows both the lowest critical pressure and its associated mode shape to be represented explicitly in terms of a single “soft ground tunnel buckling parameter”; this single composite parameter encapsulates all the relevant ground and liner geometric and material properties. It is this closed-form analytical representation of elastic critical buckling that provides a particularly convenient basis for predicting elastic-plastic failure. When imperfections are introduced, liner collapse and the various forms of ground failure can be modeled by methods analogous to the Ayrton-Perry expression for columns. Two generalized imperfection parameters emerge: one for liner collapse and the other for each of three possible, soft ground, failure modes. It is suggested that the analytical simplicity of the approach should make it an attractive alternative basis for at least the initial, rational, design of soft ground tunnel liners.     

Buckling Analysis of Nonuniform and Axially Graded Columns with Varying Flexural Rigidity

In this paper, we present a novel analytic approach to solve the buckling instability of Euler-Bernoulli columns with arbitrarily axial nonhomogeneity and/or varying cross section. For various columns including pinned-pinned columns, clamped columns, and cantilevered columns, the governing differential equation for buckling of columns with varying flexural rigidity is reduced to a Fredholm integral equation. Critical buckling load can be exactly determined by requiring that the resulting integral equation has a nontrivial solution. The effectiveness of the method is confirmed by comparing our results with existing closed-form solutions and numerical results. Flexural rigidity may take a majority of functions including polynomials, trigonometric and exponential functions, etc. Examples are given to illustrate the enhancement of the load-carrying capacity of tapered columns for admissible shape profiles with constant volume or weight, and the proposed method is of benefit to optimum design of columns against buckling in engineering applications. This method can be further extended to treat free vibration of nonuniform beams with axially variable material properties.     

侧向冲击荷载下钢筋混凝土墩柱的性能

采用数值仿真技术建立了足尺钢筋混凝土墩柱精细有限元模型, 分析了侧向冲击荷载下墩柱的动态响应和抗冲击性能, 提出了一种基于截面损伤因子的损伤评估方法, 讨论了不同碰撞参数对钢筋混凝土墩柱破坏模式和损伤机理的影响.结果表明: 冲击荷载下钢筋混凝土墩柱的耗能主要分为接触区域局部耗能和构件整体耗能; 当冲击体的初始动能恒定时, 冲击质量和冲击速度的不同组合会导致钢筋混凝土墩柱损伤破坏机理的显著差异; 基于截面损伤因子的损伤评估方法可以比较准确地描述墩柱的破坏状态.轴压力对墩柱抗撞能力的有利贡献比较有限, 且墩柱随着轴力的增大更易发生剪切破坏; 冲头刚度对碰撞力和墩柱动态响应的影响十分显著.      

Problems and feasibilities of testing the cyclic behaviour of thin sheet steels

This report deals with the testing problems of thin sheet steels subjected to cyclic load and introduces at the same time the appropriate techniques to procure the reliable and significant testing results. Practically, a proper judgement of cyclic fatigue behaviours of such conventional deep drawing steels is only possible, if the specimens were to be tested either under strain control mode in elastic-plastic range with sufficient plastic deformations or load controlled in elastic range by using the notched specimens with adequate local strain concentration. Besides the study of specific material properties, as absolutely determined by using the unnotched specimens, the influence of notch geometry can also be investigated by means of the notched specimens. For a promising performance of elastic-plastic cyclic tests on thin sheets the use of a particular specimen shape with uncritical length of high buckling resistance is most essential. Moreover, a special grip with great precision is necessary to ensure an axial and rigid alignment of specimens. In the course of a development an optimal specimen shape and its gripping device has been designed. The cyclic properties of some thin sheet steels, obtained in this way, are also illustrated.     

Compression Tests on Cylinders with Circumferential Weld Depressions

The behavior of thin cylindrical shells under axial compression is very sensitive to imperfections in the initial geometry. Local axisymmetric imperfections are among the most detrimental and have been shown to be a regular feature of circumferentially welded joints in civil engineering shell structures such as steel silos and tanks. Many of the experiments on which current design rules are based were performed on elastic Mylar, copper, or aluminum specimens, which have some very different characteristics to those of steel shells. Furthermore, very few laboratory tests have ever examined the consequences of fabrication processes on shell buckling strength, although these strongly influence the amplitudes and forms of geometric imperfections. This paper presents the findings of a careful experimental program on large steel cylinders fabricated with a fully welded circumferential joint. Thorough measurements were made of the initial imperfections and their transformation into a buckling mode. The results are compared with elastic-plastic finite-element predictions and the most recent design standard.     

Shear-Flexural Buckling of Cantilever Columns under Uniformly Distributed Load

Approximate buckling formulas for shear–flexural buckling of cantilever columns subjected to a uniformly distributed load are derived, based on Timoshenko’s energy method. In this method the deflection curve at buckling is approximated by a trial function. Instead of trying to describe all possible buckling modes with one trial function, two trial functions are used: one to describe shear dominated localized buckling, another to describe bending dominated global buckling. It is investigated whether the bending dominated global buckling modes can best be described using polynomial functions, trigonometric functions, or a function defined by the lateral (flexural and shear) deflection of the cantilever column under uniformly distributed lateral load. The results of the derived formulas are compared to the exact solution and other approximate buckling formulas found in the literature. Attention is drawn to the fact that the shear–flexural buckling load cannot exceed the shear buckling load.     

Complementary Energy Based Formulation for Torsional Buckling of Columns

A unique formulation for the elastic torsional buckling analysis of columns is developed in this paper based on the principle of stationary complementary energy. It is well known that in displacement based numerical formulations, discretization errors lead to stiffer behavior; hence convergence from above. On the other hand, discretization errors in complementary energy based numerical formulations lead to softer behavior in linear elasticity problems, which is a desired feature from the engineering view point. However, complementary energy based formulations can only overpredict the buckling loads for the flexural buckling problems of columns unless the physical conditions are compromised. In this study a formulation based on the principle of stationary complementary energy is considered for the elastic torsional buckling analysis of columns. The complementary energy expression is obtained from the well known total potential energy functional by using Frederichs’ transformation. In contrast to flexural buckling analysis of columns, it is shown that when the principle of stationary complementary energy is used, the torsional buckling loads can be underpredicted. A mathematical proof is provided to elucidate this property. The convergence behavior of the approximate solutions is illustrated through numerical examples for several columns with different boundary conditions.     

Buckling of Vertical Cylindrical Shells Under Combined End Pressure and Body Force

This paper is concerned with the elastic buckling of vertical cylindrical shells under combined end pressure and body force. Such buckling problems are encountered when cylindrical shells are used in a high-g environment such as the launching of rockets and missiles under high-propulsive power. The vertical shells may have any combination of free, simply supported, and clamped ends. Based on the Goldenveizer-Novozhilov thin shell theory, the total potential energy functional is presented and the buckling problem is solved using the Ritz method. Highlight in the formulation is the importance of the correct potential energy functional which includes the shell shortening due to the circumferential displacement. The omission of this contributing term leads to erroneous buckling solutions when the cylindrical shell is not of moderate length (length-to-radius ratio smaller than 0.7 or larger than 3). New solutions for body-force buckling parameters are presented for stubby cylindrical shells to long tube-like shells that approach the behavior of columns. The effects of the shell thickness and length on buckling parameter are also investigated.     

连续退火机组带钢瓢曲临界张力的研究

 根据金属塑性理论建立了带钢稳定通板的理论模型,并对模型进行求解,求解分为张力加载与辊子转动两步进行。系统地研究了瓢曲的形成与发展,以及辊形与带钢尺寸对带钢瓢曲临界张力的影响等。结果表明：引起带钢瓢曲的横向压缩应力由不均匀拉伸诱发的横向压缩应力和由摩擦产生的附加横向压缩应力两部分构成,瓢曲在带钢传输过程中逐步形成;对比发现有限元模拟的瓢曲发生与长大过程与大生产的情况基本一致,瓢曲的宽度约为2～4mm。并且带钢瓢曲的临界张力随着辊子凸度的增大、辊子平台区长度的减小、辊面粗糙度的减小、带钢厚度的减小而逐渐减小。     

Stability Criteria for Euler Columns with Intermediate and End Axial Loads

Presented herein are exact stability criteria for Euler columns under intermediate and end concentrated axial loads. The stability criteria cover all combinations of classical boundary conditions, arbitrary location of the intermediate concentrated load, and ratios of the magnitude of the intermediate load to the end load. Also included is the buckling problem of a new class of Euler columns where one segment is in tension while the other segment in compression.     

Dynamic Thermal Buckling of Functionally Graded Spherical Caps

In the present work, dynamic buckling behavior of clamped functionally graded spherical caps suddenly exposed to a thermal field is studied using the finite-element procedure. The material properties are graded in the thickness direction. The temperature load corresponding to a sudden jump in the maximum average displacement in the time history of the shell structure is taken as the dynamic buckling temperature. Numerical study is carried out to highlight the influences of shell geometries and material gradient index on the critical buckling temperature.     

Static Stability of Beam-Columns under Combined Conservative and Nonconservative End Forces: Effects of Semirigid Connections

Stability criteria that evaluate the effects of combined conservative and nonconservative end axial forces on the elastic divergence buckling load of prismatic beam-columns with semirigid connections is presented using the classic static equilibrium method. The proposed method and stability equations follow the same format and classification of ideal beam-columns under gravity loads presented previously by Aristizabal-Ochoa in 1996 and 1997. Criterion is also given to determine the minimum lateral bracing required by beam-columns with semirigid connections to achieve “braced” buckling (i.e., with sidesway inhibited). Analytical results obtained from three cases of cantilever columns presented in this paper indicate that: (1) the proposed method captures the limit on the range of applicability of the Euler’s method in the stability analysis of beam-columns subjected to simultaneous combinations of conservative and nonconservative loads. The static method as proposed herein can give the correct solution to the stability of beam-columns within a wide range of combinations of conservative and nonconservative axial loads without the need to investigate their small oscillation behavior about the equilibrium position; and (2) dynamic instability or flutter starts to take place when the static critical loads corresponding to the first and second mode of buckling of the column become identical to each other. “Flutter” in these examples is caused by the presence of nonconservative axial forces (tension or compression) and the softening of both the flexural restraints and the lateral bracing. In addition, the “transition” from static instability (with sidesway and critical zero frequency) to dynamic instability (with no sidesway or purely imaginary sidesway frequencies) was determined using static equilibrium. It was found also that the static critical load under braced conditions (i.e., with sidesway inhibited) is the upper bound of the dynamic buckling load of a cantilever column under nonconservative compressive forces. Analytical studies indicate the buckling load of a beam-column is not only a function of the degrees of fixity (ρa and ρb), but also of the types and relative intensities of the applied end forces (Pci and Pfj), their application parameters (ci, ηj, and ξj), and the lateral bracing provided by other members (SΔ).     

Static Stability Formulas of a Weakened Timoshenko Column: Effects of Shear Deformations

The static stability analysis of two-dimensional Timoshenko columns weakened at an arbitrary section is derived in a classic manner. The effects of shear deformations along the column, influenced by the additional shear force induced by the applied axial load as the member deforms according to the modified shear equation proposed by Haringx, are presented and studied in detail. The proposed model also captures: (1) the influence on the buckling load capacity of the column when an arbitrary weakened section is formed at any location; (2) the tension buckling phenomenon due to the low shear stiffness of columns made of composite materials or elastomeric rubbers; and (3) the beneficial effects of an additional lateral bracing located at the weakened section to alleviate the buckling load reduction of the column. Seven classical and nonclassical cases of columns mostly used in civil and mechanical engineering are summarized in condensed formulas which allow the straightforward determination of buckling loads and shapes.     

Theory of Combined Sway and Nonsway Frames Buckling

Conventional design procedures for rigid jointed frames encourage a situation in which more than one buckling mode could occur simultaneously. Even though this practice is known to often give rise to increased sensitivity of buckling loads to small initial imperfections, current design practice is usually lacking in explicit design guidance. This paper seeks to explore the extent to which buckling loads in framed structures are reduced by the effects of modal interactions arising when designs are optimized. It takes, as a specific example, the situation where the buckling and bending planes for a rigid-jointed frame coincide and for which sway and nonsway buckling modes occur at similar load levels. It explores the extent to which elastic-plastic buckling loads may be affected by interactions of sway and nonsway modes and compares predictions with results from a recently conducted test program. It is suggested that the theoretical approach described has the potential to provide an extended and improved alternative to existing design practice.     

Thermal Postbuckling of Uniform Columns on Elastic Foundation—Intuitive Solution

Finite element and Rayleigh-Ritz methods have been effectively used to evaluate the thermal postbuckling behavior of columns with immovable ends in the axial direction. However, these methods do suffer from problems like large computational effort or complex algebra because of the nonlinear nature of the problem. A simple, intuitive method is proposed herein to predict the postbuckling load carrying capacity of uniform columns on elastic foundation. The present method requires the knowledge of only the linear thermal buckling load parameter and the tension developed in the column. The present method, when applied to simply supported and clamped columns gives exactly the same results as those obtained by the Rayleigh-Ritz method.     

基于岩爆碎屑研究的高楼山隧道岩爆机理分析与类型判定

在建高楼山隧道是通达陇南市及四川省九寨沟的控制性工程,项目具有“三高一大”的特点,是复杂地质条件下深埋特长公路隧道的典型代表.以现场两种岩爆类型为研究对象,通过冲击岩爆实验系统并设定不同应力路径,首先进行了岩爆实验全过程分析,而后对比研究了板裂屈曲型岩爆实验碎屑(岩爆碎屑1)、爆破冲击型岩爆实验碎屑(岩爆碎屑2)和现场收集的不知类型的岩爆碎屑(岩爆碎屑3)的质量、尺度分布及形状分形维数特征.在此基础上,结合岩爆实验图像变化过程,深化了对不同类型岩爆碎屑成因及岩爆机理的认识.结果表明：(1)板裂屈曲型岩爆和爆破冲击型岩爆区别在于破坏主导机制不同,一种为张拉破坏主导,另一种为张剪破坏主导.(2)岩爆碎屑1以中粒、条板状碎屑为主,在长度方向上更容易破碎,且质量远大于岩爆碎屑2,这与竖向应力集中形成板裂化结构的板裂屈曲型岩爆孕育机制密不可分.(3)动载的介入使得岩爆碎屑2受剪切作用明显,因而在厚度方向的破碎更容易且破碎程度更高,形成以粗粒、片状碎屑为主的碎屑,该类型碎屑在现场岩爆中由于质量较大、体积较大、弹射距离较远,因此危害性可能更大.(4)通过上述比对分析,可基本判定岩爆碎屑3对应的岩爆类...     

Textile-Reinforced Mortar versus FRP Jacketing in Seismic Retrofitting of RC Columns with Continuous or Lap-Spliced Deformed Bars

The effectiveness of a new structural material, namely, textile-reinforced mortar (TRM), was investigated experimentally in this study as a means of confining oldtype reinforced concrete (RC) columns with limited capacity due to bar buckling or due to bond failure at lap splice regions. Comparisons with equal stiffness and strength fiber-reinforced polymer (FRP) jackets allow for the evaluation of the effectiveness of TRM versus FRP. Tests were carried out on nearly full scale nonseismically detailed RC columns subjected to cyclic uniaxial flexure under constant axial load. Ten cantilevertype specimens with either continuous or lap-spliced deformed longitudinal reinforcement at the floor level were constructed and tested. Experimental results indicated that TRM jacketing is quite effective as a means of increasing the cyclic deformation capacity of oldtype RC columns with poor detailing, by delaying bar buckling and by preventing splitting bond failures in columns with lap-spliced bars. Compared with their FRP counterparts, the TRM jackets used in this study were found to be equally effective in terms of increasing both the strength and deformation capacity of the retrofitted columns. From the response of specimens tested in this study, it can be concluded that TRM jacketing is an extremely promising solution for the confinement of reinforced concrete columns, including poorly detailed ones with or without lap splices in seismic regions.     

Quasi-Static Indentation Behavior of Honeycomb Sandwich Materials and Its Application in Impact Simulations

Both the crushing and indentation behaviors of sandwich materials are important aspects in failure analysis and energy absorption. In this paper, the core crushing strength of honeycomb materials from the experiment is briefly introduced, and the indentation of sandwich structures is studied in detail. Using the beam on elastic-plastic foundation models, theoretical formulations for predicting indentation behavior of sandwich materials are proposed, from which the mechanical response of elastic-plastic sandwich beams are obtained. Three stages of failure are clearly depicted by the global stiffness changes in the load versus displacement curve of elastic-plastic beams. The models are compared with the available experimental data and numerical simulation, and relatively close agreements are achieved. The compliance and compliance gradient derived form the indentation models are then incorporated with the equation of motion of the projectile to study impact response of elastic-plastic beams, and the impact energy dissipation due to the plasticity of elastic-plastic sandwich beam is uniquely recovered from the derived damping ratio. The beam on elastic-plastic foundation models proposed can be used to predict the indentation behavior of honeycomb sandwich materials, and the unique incorporation of the compliance and compliance gradient of the elastic-plastic sandwich beams in the standard mass-spring model can be utilized to characterize the effect of core compression and plasticity in the impact process.     

Seismic Behavior of Hollow Stiffened Steel Bridge Columns

Rectangular columns constructed from steel plates are widely used to support highway bridges in Japan. Columns of this type, designed without special consideration for ductility, sustained damage during the 1995 Hyogo-ken Nanbu earthquake. This paper describes tests of 24 large-scale models of hollow and concrete-filled stiffened rectangular columns in order to investigate their seismic performance. Testing under constant axial loading and cyclic bending as well as on the shaking table was carried out. It was found that columns partially filled with concrete had a larger strength than did hollow columns, but their displacement capacity was sometimes smaller. Bridge column models tested on the shaking table tended to sustain increasing displacements in only one direction, and columns tested by reverse cyclic loading possessed member displacement ductility capacities between 2.6 and 6.1, even though the columns had not been designed specifically for ductility. A rational and simple empirical method for estimating the deformation capacity of hollow columns subjected to reverse cyclic loading that considers the different modes of buckling is proposed and a design example is provided.