Bending of anisotropic inflated cylindrical beams

The bending behaviour of inflated beams has been studied for several decades. Several models have been developed to predict the load deflection behaviour of the beams. The various models treat the problem differently, particularly in the way the wrinkling moment and collapse moment are defined. This paper relates the wrinkling threshold to a stress criterion rather than a strain criterion. An important issue with respect to the collapse load is whether to regard the material as a true membrane or as a very thin shell. It will be shown that the three thin films used in this research PC, PPS, and PEI should be regarded as thin shells. A new model that predicts the collapse moment for these kind of materials has been developed, which incorporates orthotropic material properties. These material properties were obtained via biaxial testing by means of axial loading of a pressurised tube. Experiments were conducted to obtain the load deflection curves at five different pressure levels. The results were shown to correlate reasonably well, with the proposed theory.     

Elastic-Plastic Analysis of Rectangular Frames

For a ductile material such as steel, the stressstrain curve may be taken as linear up to the yield point and then indefinitely horizontal. Under this assumption, the first-named author has shown in 1963 that the response of a continuous beam or rigid frame under increasing loads may be traced from the beginning to collapse by a stepwise elastic analysis procedure. This procedure requires that the structure is subjected to concentrated loads only so that plastic hinges can form only at the ends of the elements which are themselves unloaded. In this paper, this restriction is removed by allowing uniform and concentrated loads to act on the elements. Consequently, a plastic hinge may form anywhere on an element, and the fixed-end moments and the stiffness coefficients of that element must then be modified for the next stage of elastic analysis. The advantage gained is enormous because previously a uniform load has to be replaced by a number of concentrated loads and a node placed at any point where there is a concentrated load.     

预压装配式预应力混凝土框架边柱拆除时抗连续倒塌性能试验研究与理论分析

对一榀二层二跨预压装配式预应力混凝土(PC)平面框架进行了静力拆除底层边柱的试验及理论分析,探究了裂缝发展、变形能力、破坏模式及连续倒塌机理。根据试验框架达到极限承载力时的状态,提出了边柱失效时简化的结构抗力分析模型,并推导出结构抗倒塌极限承载力的计算方法; 基于能量法建立近似的动力响应评估模型,根据试验框架静力加载荷载-位移曲线近似得到其在边柱瞬时失效时的动力响应曲线。结果表明:框架的受力过程可分为弹性、弹塑性、塑性铰以及倒塌4个阶段; 加载时试件的混凝土裂缝开展及破坏集中在失效边柱相邻区域框架梁两侧梁端结合部,除失效边柱外,其余框架柱以及失效柱远离区域框架梁端基本完好; 框架在小变形阶段按梁机制受力,存在压拱效应及空腹效应; 在大变形阶段不能按悬链线机制受力,由梁的受弯机制和空腹机制共同抵抗不平衡荷载; 边柱失效时预压装配式预应力混凝土框架最大抗力达到60.9 kN,最终倒塌位移为430 mm,梁端转角为10.0°～15.3°,具有较好的抗连续倒塌能力。     

Dynamic increase factor for pushdown analysis of seismically designed steel moment-resisting frames

The independent threat scenario of sudden column loss under localised damage is usually considered in progressive collapse assessment. The effect of the sudden removal of a column is like the sudden application of the gravity load on the structure when significant deformations occur. This conventional approach is based on the simplifying but realistic hypothesis that the peak dynamic response can be assessed with reasonable accuracy using the nonlinear static response. In this approach, amplified gravity loads are applied to the bays that are affected by the removed column to compensate for the dynamic effects corresponding to the real load redistribution. The paper investigates the dynamic increase factor to be considered in the nonlinear pushdown analysis of seismically designed steel moment-resisting frames. The influence of the fundamental parameters involved in progressive collapse analysis was highlighted. The effect of various design variables, such as the number of stories, the number of bays, the location of the removed column and the level of seismic design load was investigated. The dynamic increase factor was estimated in a way to generate the best match of the peak dynamic responses through the nonlinear static analysis. Finally, the values obtained were expressed as a function of the vertical displacement at the location of the removed column and then compared with the GSA formulation based on the ductility factor.     

Multi-cell carbon fibre composite box beams subjected to torsion with variable twist

The structural performance of multi-cell carbon fibre composite box beams when subjected to constrained torsional loading is examined in this paper. A simplified analytical procedure for determining the constrained torsional response of a specific class of multi-cell carbon fibre composite box beams is outlined in some detail. The constrained condition analysed is that of the cantilevered multi-cell beam with torque applied at the free end of the beam. Overall elastic couplings in the beams between bending, torsion and axial effects are eliminated from the analysis process through the use of constituent laminates for the thin walls of the cross-sections which are symmetrically layed-up about their own mid-planes and in such a manner that they possess in-plane orthotropy. The analysis procedure employed makes use, essentially, of the existing theories of torsion developed for isotropic construction and these are then suitably modified to account for the non-isotropic nature of the typical carbon fibre composite material. The resulting approach is shown to be able to predict the structural response of the multi-cell composite beams with a considerable degree of accuracy and comparisons between the theory and the results from finite element numerical modelling are shown to give close agreement. The torsional and warping rigidities of the composite multi-cell beams are calculated in a procedure which makes use of the appropriate membrane engineering elastic constants of the individual thin composite walls and the constituent thin walls can have different lay-up configurations provided the stiffness distribution around the sections is of a symmetrically disposed nature in order to preclude the influence of overall elastic couplings.     

Geometrically nonlinear numerical procedure for Saint-Venant's problem for a symmetrical elastic shell with a closed contour and circular axis

An original numerical procedure of treating Saint-Venant's problem for toroidal-like shells under pressure and bending moment is suggested. Its peculiarity consists in that the loading and displacement parameters are separated into two groups: the first one describes the ring-like transverse deformation of the shell cross section, while the second the beam-like axial deformation of the latter. One of them is considered separately in the sequential iteration procedure while the other is reckoned to be known. After each step of calculation, the parameters considered to be known are made more exact.A lot of the well-known problems widely presented in the literature are considered. Among them are: (1) Karman's problem, which explains the ovalization of the cross section and the enlarged flexibility of a pipe bend as compared to a straight pipe under bending; (2) the so-called pressure reduction effect when the internal pressure prevents ovalization, which is a demonstration of the influence of the geometrical nonlinearity even at small displacements; (3) Brazier's effect, which deals with nonlinearly enlarged ovalization of an initially straight elastic pipe with an increase in the bending moment.The main advantage of the method is that it allows analyzing a toroidal shell of arbitrary cross section with a variable wall thickness. As an example, a toroidal shell with two long symmetrical axial cracks is considered, where cracks are modeled as the jumps of the contour angular displacement whose values are related to the crack depth.     

膜结构的荷载分析

本文采用非线性曲面膜单元和曲线索单元编制了膜结构内力计算程序,对实际制作的模型在风荷载和雪荷载作用下应力、位移的变化规律及皱折处理的方法作了研究,得到了结论对实际工程设计很有帮助。     

Analytical modelling of plastic collapse in compressed elliptical hollow sections

The plastic collapse response of structural steel elliptical hollow section (EHS) profiles in compression is examined in this paper. As an initial step, a parametric study to identify the factors that determine which plastic mechanisms would arise has been carried out using finite element (FE) results from the current work and experimental data from the literature. All investigated EHS had a cross-sectional aspect ratio of two. The parametric study revealed four plastic collapse mechanisms and showed that the “split flip disc” plastic collapse mechanism is the most likely to appear in compressed EHS. Thus, the present work is focussed on this failure mechanism, for which an analytical model to describe the relationship between load and deformation is developed. Coupled with the consideration of the elastic, yielding and strain hardening characteristics of steel, the derived analytical model enables construction of the full load-deformation behaviour of compressed EHS to be established. The parameters controlling the shape and size of the plastic hinges have been investigated and found to be of key importance; hence, special care has been taken in their definition. Finally, the developed load-displacement curves have been compared with both finite element results and experimental data. The comparisons have revealed good agreement, confirming the ability of the analytical model to predict the collapse response of elliptical tubes.     

索加强张拉膜结构的荷载分析方法

本从几何非线性有限元分析原理出发，推导了适合于索加强张拉膜结构荷载分析的非线性有限元公式，提出了一种解决膜单元皱折问题的简单、有效方法，编制了计算饥程序，从而完成了索加强张拉膜结构的荷载分析问题．最后以日本冲绳第75届博览会入口膜结构作为计算实例，得到了令人满意的结果。     

矩形薄膜褶皱影响因素试验研究

薄膜广泛应用于土木工程和航空航天工程领域。薄膜因荷载引起的褶皱变形会随多种因素的影响而呈现不同的变化特征,但目前相关研究较少。为此,通过矩形薄膜受剪试验,研究薄膜结构的褶皱影响因素及其对褶皱特征参数的影响规律。为减小边界条件的误差扰动,研发高精度的试验装置。借助千分尺施加预张位移和剪切位移,采用激光位移传感器对褶皱变形进行非接触测量。根据褶皱幅值、角度、半波长和数量等特征参数的变化情况,研究剪切位移、预张位移、薄膜厚度等因素对褶皱变形的影响。结果表明：随着剪切位移的增加,褶皱幅值增大,褶皱数量增多而褶皱半波长减小,而褶皱角度未见明显变化;预张位移的增加能够显著减小褶皱幅值和半波长,但使褶皱角度增大、褶皱数量增多;增加薄膜厚度能够有效减小褶皱数量,但使褶皱幅值和半波长增大,而对褶皱角度的影响却很小。     

受扭圆环薄膜褶皱变形的试验研究

通过对圆环薄膜进行受扭试验,研究薄膜的褶皱变形机理及其随影响因素的变化规律。为减小边界条件的误差扰动,研发高精度试验装置。通过砝码和同步装置对圆环膜施加预张力,借助旋转平台施加扭矩,采用激光位移传感器对褶皱变形进行非接触测量,主要研究边界条件、预张力以及膜厚等因素对薄膜褶皱变形及其特征参数的影响规律。结果表明：随着扭转角的增加,褶皱幅值逐渐增大,由于没有二次屈曲发生,褶皱数量和褶皱半波长没有明显变化;增大预张力能够有效提高薄膜刚度,从而褶皱幅值和褶皱半波长减小,但使褶皱数量增多;膜厚增加能够提高薄膜的抗弯刚度,在相同扭转角和预张力的情况下,褶皱数量减少,但使得褶皱幅值和褶皱半波长增大。研究成果揭示褶皱因素对褶皱变形的影响规律,有助于通过其影响特性对薄膜褶皱变形进行有效控制,保证薄膜结构的形面精度。     

结构抗连续倒塌设计分析方法探讨

结构发生连续倒塌将会导致严重的生命和财产损失,造成重大的社会影响,因而日益受到工程设计人员的关注。欧美等国已相继制定了连续倒塌相关的设计规范并提出了相应的设计分析方法,但还不够完善。对现有的结构连续倒塌相关的规范设计及分析方法进行总结和归纳,并指出其中存在的一些问题。提出了在进行多重荷载路径法分析时应通过结构自重的施工模拟来考虑结构初始态的重大影响,以及运用结构动力学理论推导出结构在不同构件失效时间下的动力响应,建议在进行多重荷载动力分析时应考虑不同构件失效时间的影响。最后对动力弹塑性时程分析方法在结构抗连续倒塌设计分析中的应用进行了初步的探讨,阐述了动力弹塑性时程分析的基本方法及其优点和缺点。     

Static liquefaction of fibre reinforced sand under monotonic loading

This paper explores the possibility of improving the monotonic undrained response of a loose clean sand which normally appears susceptible to the phenomenon of static liquefaction by mixing the sand with discrete flexible fibres. It is shown that the reinforcement inclusions reduce the potential for the occurrence of liquefaction in both compression and extension triaxial loadings and convert a strain softening response (typical for a loose unreinforced sand) into a strain hardening response. Fibre orientation distribution and the apparent sand matrix densification due to the presence of fibres in the voids appear important for the fibre reinforced soil behaviour. Normalisation of the effective stress paths with the mean effective stress at the end of consolidation shows a common path once the characteristic state is reached irrespective of the fibre concentration. The mobilised angles of friction coming from the slopes of the stress paths at large strains are very different for compression and extension and this is a consequence of the anisotropic nature of the distribution of fibre orientations. When full liquefaction of reinforced specimens is induced by strain reversal, the lateral spreading of soil seems to be prevented. Analytical developments including the key aspect of fibre orientation distribution, have shown that once the tensile contribution of fibres has been taken out of the composite stresses, the experimental data in the stress plane for all the tests at large shear strains nicely collapse onto a unique line corresponding very closely to the mobilised steady state or critical state angle of friction of the tested sand.     

Progressive collapse analysis of steel frames: Simplified procedure and explicit expression for dynamic increase factor

Progressive collapse refers to a phenomenon in which local damage in a primary structural element leads to total or partial structural system failure. When investigating the progressive collapse of structures, nonlinear dynamic procedures lead to more accurate results than static procedures. However, nonlinear dynamic procedures are very complicated and the evaluation or validation of the results can become very time consuming. Therefore, it is better to use simpler methods. For static analyses, the gravity force applied to the removed column bay should be multiplied by a constant factor of two. However, using a constant dynamic increase factor (DIF) is only appropriate for elastic systems. According to the optimal design of structures, the assumption of elastic behavior after column removal is conservative. Thus, it is necessary to establish an expression for DIF that considers inelastic responses. In this paper, a simplified analysis procedure for the progressive collapse analysis of steel structures is presented using the load displacement and capacity curve of a fixed end steel beam. The results of the proposed method are in good agreement with nonlinear dynamic analysis results. Also, the capacity curve, obtained by dividing the accumulated area under the nonlinear static load displacement curve by the corresponding displacement of the column removed point, is used to predict the progressive collapse resistance of the column removed structure. Finally, an explicit expression for the DIF is established for elastic-perfectly plastic and elastic plastic with catenary action behavior.     

Non-linear analysis of perforated steel plates subjected to localised symmetrical load

Although the literature contains a number of studies which have been developed to describe the non-linear behaviour of ordinary plates, few works are available on perforated plates, and studies on non-linear behaviour of perforated plates under localised symmetrical load are not studied in depth. The aim of this paper is to provide some insights into the elasto-plastic behaviour of plate girder web panels with circular holes under localised symmetrical load.Numerical analyses of square and rectangular perforated plates with centred and eccentric holes were developed. Results provide new insights into post-critical mechanisms in perforated plates subjected to localised loads when the length of the symmetrical compressive load, hole diameter and steel yield limit vary. An increase in the critical slenderness of the plate (a value at which transition from elastic to plastic collapse occurs) and a corresponding reduction in the elastic critical load occur when the dimensions of the hole increase. A further increase in the critical slenderness occurs when the length of the localised load is reduced. High-performance steel may be subject to buckling with a lower possibility of post-critical mechanisms: a reduction in critical slenderness occurs when the steel grade increases. Lastly, numerical analyses of slender and thick perforated plates were developed and their results compared.     

On buckling collapse and failure analysis of thin-walled composite lipped-channel columns subjected to uniaxial compression

The paper deals with buckling of short thin-walled lipped-channel columns, simply supported on both ends and subjected to uniformly distributed compressive load. The main objective of the study was to investigate the structure׳s work in far post-buckling state and at collapse corresponding to the moment of the column׳s stiffness loss. The following measuring devices and methods were applied: electrical strain gauges for strain measurements, a laser sensor to measure the displacements, and the Acoustic Emission method. Along with running the experimental tests, the non-linear stability of compressed composite columns was analyzed with the Finite Element Method. The numerical and experimental results showed good agreement.     

结构周期延长对倒塌分析中地震动强度指标选择的影响

当结构在强震作用下接近倒塌状态时,其刚度和承载力的退化会导致结构周期延长,为此,研究了周期延长对地震动强度指标选择的影响,将不同周期调整系数β对应的谱加速度(Sa(βT1),T1为弹性基本周期）作为地震动强度指标时,研究其倒塌分析结果的离散性。基于等效单自由度结构周期（Teq）,提出了等效周期谱加速度（Sa(Teq)）。研究结果表明：当周期调整系数β增大时,结构抗倒塌能力分析结果的离散性呈现先减小后增大的趋势。与传统地震动强度指标Sa(T1)相比,所提出的Sa(Teq)可以考虑结构非线性变形引起的周期延长,能有效降低倒塌分析结果的离散性达30%以上。     

Design by analysis of ductile failure and buckling in torispherical pressure vessel heads

Thin shell torispherical pressure vessel heads are known to exhibit complex elastic–plastic deformation and buckling behaviour under static pressure. In pressure vessel Design by Analysis, the designer is required to assess both of these behaviour modes when specifying the allowable static load. The EN and ASME boiler and pressure vessel codes permit the use of inelastic analysis in design by analysis, known as the direct route in the EN Code. In this paper, plastic collapse or gross plastic deformation loads are evaluated for two sample torispherical heads by 2D and 3D FEA based on an elastic-perfectly plastic material model. Small and large deformation effects are considered in the 2D analyses and the effect of geometry and load perturbation are considered in the 3D analysis. The plastic load is determined by applying the ASME twice elastic slope criterion of plastic collapse and an alternative plastic criterion, the Plastic Work Curvature criterion. The formation of the gross plastic deformation mechanism in the models is considered in relation to the elastic–plastic buckling response of the vessels. It is concluded that in both cases, design is limited by formation of an axisymmetric gross plastic deformation in the knuckle of the vessels prior to formation of non-axisymmetric buckling modes.     

Elasto-plastic buckling of compression members as a coupled instability

In the paper the author shows that plastic deformations can be considered as a bifurcational instability of the atomic lattice. Thus, the plastic buckling of a compression bar is examined like a coupled instability between the general buckling by flexural and the local buckling by plastic deformations. The modified Hunt-Burgan model is studied and an interaction relationship between the elastic buckling load and the plastic collapse load is determined. Although this relationship is obtained in an elastic field, the form corresponds to the Ayrton-Perry relationship for plastic buckling, used by Maquoi and Rondal for the analytical expressions of the ECCS buckling curves. However, one can see that the general imperfections corresponding to Eulerian buckling and local imperfection due to residual stresses have different effects, in opposition to Maquoi-Randal relationships. A new relationship for the simple plastic buckling and coupled plastic buckling are proposed.     

Elastic-plastic collapse of non-uniform cylindrical shells subjected to uniform external pressure

The objective of this paper is to derive analytical solutions for the elastic buckling and plastic collapse pressures of a cylindrical shell with reduced thickness over part of its circumference. The section of reduced thickness is used to represent a corroded region in a pipe. The proposed solutions are extensions of Timoshenko's solutions for the elastic-plastic collapse of a linear elastic, perfectly plastic cylindrical shell subjected to uniform external pressure. A modified interaction formula for the fully plastic membrane forces and bending moments in the non-uniform cylinder has been proposed for plastic collapse. A parametric study shows that the elastic buckling pressure decreases smoothly with corrosion angle when the corrosion depth is less than 0.5t. When the corrosion depth is greater than 0.5t, the elastic buckling strength first decreases very rapidly with corrosion angle. Furthermore, the elastic buckling pressure decreases uniformly with corrosion depth when the corrosion angles are greater than 30°, while the elastic buckling strength decreases more rapidly at higher corrosion depths when corrosion angles are less than 30°. Another parametric study on a steel pipe shows that the initial and fully plastic yield pressures both decrease monotonically with corrosion depth for a given corrosion angle and imperfection.