Form of circumferential weld-induced imperfections for tapered-wall cylindrical shell structures

Initial geometric imperfections have a great effect on the buckling strength of thin-walled cylindrical shells under axial compression, and the circumferential weld-induced imperfection is usually the most deleterious imperfection form. Two axisymmetric imperfection forms proposed by Rotter and Teng have widely been employed in the buckling analysis of cylindrical shells. However, the applicability of the two forms for tapered-wall cylinders needs further study, since they are derived from the elastic bending theory for long thin-walled cylinders with a constant wall thickness. This paper presents a modified form of circumferential imperfection for tapered-wall cylinders. Finite element analyses are carried out by employing the trapezoidal strain field approach to model the welding process, and the obtained circumferential depression shapes are used to evaluate the availability of the modified imperfection form. It is shown that the modified imperfection form is reasonable for any wall thickness ratio between two adjacent strakes, and the most suitable shape function, which is very close to the FE results, can be obtained by giving suitable values of the roundness in the modified form.     

The effect of geometric imperfections on the vibrations of anisotropic cylindrical shells

Analytical–numerical models to analyse the flexural vibration behaviour of anisotropic cylindrical shells are presented. The two models (denoted as Level-1 and Level-2 Analysis) have different levels of complexity and can be used to study the influence of important parameters, such as geometric imperfections, static loading, and boundary conditions. A specific anisotropic shell is used in the calculations in this paper. The influence of the imperfection shape and amplitude on the natural frequency is investigated for this shell via both the Level-1 and the Level-2 Analysis. Imperfections with the shape of the “lowest vibration mode” give a decrease of the natural frequency with increasing imperfection amplitude. The results of the Level-2 Analysis for the effect of imperfections on the natural frequency are in reasonable agreement with Finite Element calculations.     

Measurement and assessment of geometric imperfections in thin-walled panels

Thin-walled members may be subject to performance limitations arising through local or distortional buckling of slender elements comprising the cross-section of the member, or overall buckling of the member. The effects of structural instability may be aggravated by the presence of geometric imperfections in these elements. An investigation is presented into methods of measuring and assessing geometric imperfections in cold-rolled thin-walled steel panels. These methods can be used to characterise the geometry of prismatic thin-walled members that exhibit performance sensitivity due to geometric imperfections. The measurement procedures investigated include close-range photogrammetry, precise optical levelling, and the use of a co-ordinate measurement machine. The assessment procedure comprises a least-squares spectral decomposition of the measurements to characterise the imperfections existent in the panels under investigation, and estimates of the precision of the derived Fourier coefficients are used to inter-compare the three measurement procedures. The investigation has demonstrated that statistically significant imperfections may exist in thin-walled members at short and medium wavelengths, leading to a reduction in the load carrying capacity. Both optical levelling and the co-ordinate measurement machine technique can yield desirable results, but for high precision work, use of the co-ordinate measurement machine is recommended.     

Stresses and pressures in thin-walled structures with damage and imperfections

This paper is a sequel to a recent book of the author, in which stress concentrations and redistributions due to structural imperfections in thin-walled structures were reviewed. Here the emphasis is on other complementary aspects. Only shape damage and imperfections are considered in the paper, while intrinsic imperfections are out of the scope discussed. The mechanics of generation of damage is studied for several cases, including a relative in-plane displacement that induces an out-of-plane distortion; impact of an object on the structure; impact of the structure on a rigid surface; damage due to local buckling; and removal of part of the structure. Possible mechanisms that lead to the generation of imperfections include errors in construction; influence of misfits and misalignments; welding; and design-imperfections. Practical cases in which imperfections are measured and data banks of such information is also briefly reviewed. The field of mechanics of stress redistributions, and the modeling of distortional damage using numerical tools, are discussed with reference to previous publications by the author. New problems of changes in the pressures due to modifications in the shape are highlighted, with reference to the discharge of silos. Finally, several areas are identified in which future developments are expected for the next five to ten years.     

The effects of patch loads on thin-walled steel silos

This paper reports on the results of a detailed parametric study into the effects of patch loads on the stresses in thin-walled circular steel silos. Firstly, an analysis of the effects of a typical patch load on the stresses in a silo wall is presented. The results show that the stresses set up are complex and that they could potentially lead to failure of the silo by either elastic buckling or plastic collapse. A parametric study is then conducted which examines the effects of varying the circumferential width of the patch load, the vertical extent of the load, the point of application of the load and the pressure distribution within the load. The results show that the circumferential width of the applied load and the pressure distribution both strongly affect the form and magnitude of the stresses produced in the silo wall. The magnitudes of stresses in the silo wall were found to vary almost linearly with the vertical extent of the patch load.     

Dynamic FE simulations of buckling process in thin-walled cylindrical metal silos

The buckling of cylindrical steel silos is caused by the wall friction force due to shearing between the silo fill and silo wall. The aim of this paper is to investigate the stability process in a silo composed of thin-walled isotropic plain rolled sheets using a static and dynamic finite element analysis by taking both the geometric and material non-linearity into account during eccentric discharge. Silo shells were subjected to axisymmetric and non-axisymmetric loads imposed by a bulk solid following Eurocode 1. The differences between the results of static and dynamic analyses were comprehensively discussed. The advantages of a dynamic approach were outlined.     

On the incorporation of equivalent member imperfections in the in-plane design of steel frames

This work deals with the incorporation of equivalent member imperfections in the global analysis of steel frames and, in particular, is intended to clarify the Eurocode 3 (EC3) provisions involved in such procedure. In fact, these provisions stem from the well-known “European column buckling curves”, which means that they are based on the behaviour of simply supported isolated members under uniform compression (columns). First, one addresses the geometrically non-linear behaviour of isolated columns displaying arbitrary support conditions and different initial geometrical configurations. Then, the results obtained are used to propose a systematic and rational method to evaluate the appropriate “equivalent initial imperfections” that need to be incorporated in the second-order global elastic analysis of a frame or isolated compressed member. This method (i) is fully consistent with the EC3 column buckling curves and (ii) adopts critical buckling mode shape initial imperfections with amplitudes determined by means of closed-form analytical expressions. In order to enable a better grasp of the concepts involved and also to illustrate the capabilities of the proposed methodology, several numerical examples are presented and discussed throughout the paper.     

Numerical evaluation on shell buckling of empty thin-walled steel tanks under wind load according to current American and European design codes

Liquid storage steel tanks are vertical above-ground cylindrical shells and as typical thin-walled structures, they are very sensitive to buckling under wind loads, especially when they are empty or at low liquid level. Previous studies revealed discrepancies in buckling resistance of empty tanks between the design method proposed by the American Standard API 650 and the analytical formulas recommended by the European Standard EN1993-1-6 and EN1993-4-2. This study presents a comparison between the provisions of current design codes by performing all types of numerical buckling analyses recommended by Eurocodes (i.e. LBA-linear elastic bifurcation analysis, GNA-geometrically nonlinear elastic analysis of the perfect tank and GNIA-geometrically nonlinear elastic analysis of the imperfect tank). Such analyses are performed in order to evaluate the buckling resistance of two existing thin-walled steel tanks, with large diameters and variable wall thickness. In addition, a discussion is unfolded about the differences between computational and analytical methods and the conservatism that the latter method imposes. An influence study on the geometric imperfections and the boundary conditions is also conducted. Investigation on the boundary conditions at the foot of the tank highlights the sensitivity to the fixation of the vertical translational degree of freedom. Further, it is indicated that the imperfection magnitude recommended by the EN1993-1-6 is extremely unfavorable when applied to large diameter tanks. Comments and conclusions achieved could be helpful in order to evaluate the safety of the current design codes and shed more light towards the most accurate one.     

The measurement of imperfections in cylindrical thin-walled members

The structural behaviour of thin-walled circular cylindrical members has been shown to be imperfection sensitive. However, only little information of the exact nature of imperfections in such members is available. In this paper a method of measuring imperfections in circular cylindrical members is described, the method is simple to implement in a laboratory environment while providing accurate measurements. Numerical methods to process the measurements into three-dimensional imperfection maps are also presented along with an algorithm to distinguish between significant imperfection patterns and measurement ‘noise’. Results from a recent research project where this method has been used illustrate the derivations in this paper.     

初始几何缺陷对大跨度钢桁架吊装稳定性影响

利用大型通用有限元软件ANSYS对大跨度钢桁架吊装过程建立了有限元模型,研究了初始几何缺陷对大跨度钢桁架吊装的稳定性影响。结果表明,在两吊点方案中容易发生屈曲的位置为跨中上弦杆部分,而四吊点方案在吊装过程中跨中下弦杆部分较易发生平面外失稳。     

The influence of the fabrication process on the buckling of thin-walled steel box sections

Steel box sections are usually fabricated from flat plates which are welded at the corners. The welding process can introduce residual stresses and geometric imperfections into the sections which can influence their strength. For some thin-walled sections, large periodic geometric imperfections have been observed in manufactured sections. Subsequent investigations have indicated that the imperfections are in fact buckling deformations i.e. the box section has buckled due to welding residual stresses prior to any application of external load. The welding procedure and the behaviour of the box sections under load has been modelled using a finite element analysis that accounts for both geometric and material non-linearities. Tests have been carried out on box sections with a range of width to thickness ratios for the plate elements. Modelling has been shown to give good correlation with the test results. The conditions for buckling to take place as a result of the welding process have been established. A design method has been proposed.     

The conception of quasi-collapse-affine imperfections: A new approach to unfavourable imperfections of thin-walled shell structures

Despite of the intensive research effort of the last decades there are considerable gaps of knowledge concerning the imperfection sensitivity of steel shell structures, even with regard to the basic buckling cases. It is explained in the presented paper why the most unfavourable imperfection pattern does not exist for shell structures but only different unfavourable patterns depending on the imperfection amplitude. This amplitude-depending pattern cannot be determined with certainty because of the substantial influence of the material non-linearity and because of the numerous post-buckling paths which cross each other. However, the method of quasi-collapse-affine imperfections allows a reasonable approximation to the most unfavourable imperfection pattern. The basic thoughts of this concept are presented. The application of the concept to slender wind-loaded shells illustrates its capability.     

A coupled finite element genetic algorithm technique for optimum design of steel conical tanks

Steel conical tanks having an upper cylindrical section and supported by a reinforced concrete shaft are widely used for water containment in elevated tanks. During the past few decades, a number of conical tanks have failed as a result of buckling of the steel vessel due to inadequate selection of the shell thickness. In the current study a powerful numerical tool that couples a non-linear finite element model and a genetic algorithm optimization technique is developed specifically for the analysis and design of steel conical tanks. The developed numerical tool is capable of selecting the set of design variables which satisfies the structure safety requirements while achieving a minimum structure weight and consequently minimum cost.     

Global buckling and the interaction of initial imperfections of columns subjected to conservative loading

This paper deals with the problem of global instability of slender systems with imperfections. The inaccuracies in the systems are modelled assuming an initial curvature and the introduction of the eccentricity of an external load. Systems loaded by Euler’s load or by a force directed towards the positive pole are considered. The problem is formulated on the basis of an energetic method. Analysis of the global imperfections is carried out. The results of analytical, numerical and experimental research concerning the mutual relations between the introduced imperfections and their influence on the system behaviour are presented.     

Investigation of geometric imperfections and joint stiffness of support scaffold systems

This paper describes the findings from various site measurements of geometric imperfections of support scaffold systems, also known as falsework in industry. The measurements consist of out-of-straightness of the standards (uprights), out-of-plumb of the frame and loading eccentricity between the timber bearer and the U-head screw jack. The measurements were taken from different support scaffold construction sites before the pouring of concrete, representing actual initial geometric imperfections and loading eccentricity encountered in practice. The paper also reports the results of support scaffold joint tests. The tests were performed on randomly chosen used components to investigate the joint stiffness for rotations about vertical and horizontal axes. Tests were performed for various joint configurations (two-way, three-way, and four-way connections), bending axes, and loading directions. The statistical analysis of the data is presented in the paper for practical application in modelling and probabilistic assessment of support scaffold systems.     

Buckling of thin-walled torispherical heads in water heater tanks

The buckling strength of a thin-walled torispherical head in a residential electric water heater tank was investigated by both experimental and finite element analyses. Three water heater tanks pressurized with water were tested, and the strains on the heads and the pressure variations were measured and recorded. Finite element analysis was used to predict the buckling of the torispherical head. The effect of the imperfection induced by the contact nonuniformity between the torispherical head and the shell on the buckling of the structure is included. Good agreement between the test and finite element results shows that finite element models used in this paper are viable to predict the buckling pressure of a thin-walled torispherical head in a water heater tank. The results also show that the contact between the bottom head and the shell has a reinforcing effect on the buckling strength of the head. The contact imperfection will produce a dent adjacent to the knuckle region when the head buckles. The buckling pressure of the head perfectly contacting with the shell is 6.88% higher than that without contacting with the shell. The obtained results provide reference for the design and manufacture of water heater tanks.     

具有缺陷和应力限值的预应力钢支撑柱屈曲性能

通过预应力支撑加固的钢柱,一般增加了轴向抗压强度。过去,十分强调获得更高的临界屈曲荷载,然而,后屈曲性能是结构安全性和功能的重要保证。对具有几何缺陷和与可能的材料失效相关的应力极限的支撑柱的屈曲性能进行检验。考虑有几何缺陷支撑柱的屈曲性能,采用Rayleigh-Ritz方法对几何非线性模型公式化,并通过有限元方法进行验证。研究显示：对于承受最高临界荷载的预应力状态,系统对有几何缺陷的柱更为敏感。对某一给定形状结构,实际的最大荷载似乎随着预应力的增加而增加。研究建议：最佳的预应力取值应该大于基于传统方法的线性分析的结果。     

Seismic response of steel braced frames with shape memory alloy braces

In this paper, the seismic performance of steel frames equipped with superelastic SMA braces was investigated. To do so, buildings with various stories and different bracing configurations including diagonal, split X, chevron (V and inverted V) bracings were considered. Nonlinear time history analyses of steel braced frames equipped with SMA subjected to three ground motion records have been performed using OpenSees software. To evaluate the possibility of adopting this innovative bracing system and its efficiency, the dynamic responses of frames with SMA braces were compared to the ones with buckling restrained braces. After comparing the results, one can conclude that using an SMA element is an effective way to improve the dynamic response of structures subjected to earthquake excitations. Implementing the SMA braces can lead to a reduction in residual roof displacement and peak inter-story drift compare to the buckling restrained braced frames.     

关于圆柱壳几何缺陷分析中傅立叶级数选取的探讨

圆柱壳屈曲一般对壳壁上微小几何缺陷的型式和幅值均十分敏感.为了能将缺陷的不同分量和圆柱壳的结构特征联系起来以及研究缺陷各分量对壳屈曲强度的影响,缺陷通常采用傅立叶级数分解.然而,大多数先前的研究选取不适当的傅立叶级数得到不正确的结果.本文首先考察傅立叶级数的数学描述基础,进而讨论不同傅立叶级数在描述不同型式几何缺陷的表现,从而得出如何选取适当的傅立叶级数用来描述圆柱壳几何缺陷的结论.采用这些适当的傅立叶级数,能更好地了解圆柱壳几何缺陷的特征分量以及这些分量对壳体屈曲强度的影响.