Buckling experiments on steel silo transition junctions: I: Experimental results

Large elevated steel silos for the storage of bulk solids generally consist of a cylindrical vessel above a conical discharge hopper supported on a cylindrical skirt. The cone–cylinder–skirt transition junction is subject to a large circumferential compressive force which is derived from the horizontal component of the meridional tension in the conical hopper, so either a ring is provided or the shell walls are locally thickened to strengthen the junction. Extensive theoretical studies have examined the buckling and collapse strengths of these junctions, leading to theoretically based design proposals. However, no previous experimental study on steel silo transition junctions has been reported due to the considerable difficulties associated with testing these thin-shell junctions at model scale. This paper presents the results of a series of tests on cone–cylinder–skirt–ring junctions in steel silos under simulated bulk solid loading. In addition to the presentation of test results including geometric imperfections and failure behavior, the determination of buckling modes and loads based on displacement measurements is examined in detail.     

Plastic buckling of complete toroidal shells of elliptical cross-section subjected to internal pressure

The plastic bifurcation buckling pressures of 60 internally-pressurised, perfect, complete toroidal shells of elliptical cross-section are given in the present paper, assuming elastic, perfectly plastic, material behaviour. The shell buckling programs employed in the computations were BOSOR 5 and INCA. Denoting the major-to-minor axis ratio by k, the numerical results show that the plastic buckling pressures are considerably lower than their elastic counterparts in the range 1.25≤k≤1.5 and are approximately equal to them for k=2.5. A limited study of the effects of non-axisymmetric initial geometric imperfections on the buckling pressures of the shells was also carried out using the INCA code. For the four cases studied the post-buckling behaviour was stable. This means that designers can use the buckling pressures given herein for perfect shells as a basis for their initial designs.     

Buckling experiments on steel silo transition junctions: II: Finite element modeling

This paper is concerned with the finite element modeling of the experiments on cone–cylinder–skirt–ring transition junctions in steel silos under simulated bulk solid loading presented in the companion paper. Before presenting the finite element results, the issue of modeling the interaction between the stored solid and the shell wall throughout the loading process is first examined. Results from nonlinear bifurcation analyses using the perfect shapes and nonlinear analyses using the measured imperfect shapes are then presented and compared with the experimental results. These comparisons show that despite the structural complexity of steel silo transition junctions, their behavior can be satisfactorily predicted by finite element analyses taking into account a number of important factors including geometric imperfections, effects of welding and the interaction between the junction and the stored solid. Next, the paper presents results of nonlinear analyses of these junctions with assumed eigenmode-affine imperfections. These results shed considerable light on the effect of ring buckling on the load-carrying capacity of transition junctions. Finally, the implications of the experimental and finite element results for the design of steel silo transition junctions are discussed.     

An equivalent stiffness approach for modelling the behaviour of compression members according to Eurocode 3

The development of design procedures based on inelastic advanced analysis is a key consideration for future steel design codes. In advanced analysis the effect of imperfections has to be modelled in such a way that the incremental analysis fully captures this effect in the process of moment redistribution. In modelling the influence of imperfections on the behaviour of individual members of real structures, different approaches have been used to globally represent this effect in the overall analysis of structural systems. They are referred to as the initial bow imperfection approach or as the equivalent transverse load approach. When using the abovementioned approaches in analysis of multiple member structural systems, the designer is required to arrange the directions of bow imperfections or equivalent transverse loads in such a way that the imperfection arrangement leads to the least constrained solution, i.e. the lowest ultimate load predicted from all possible sets of member initial imperfection arrangements. Since there is still ongoing research on the development of simple application rules ensuring that the designer obtains a unique solution when choosing a certain set of member initial imperfections, there is at the same time interest in the development of alternative approaches to modelling the influence of member imperfections on the behaviour of structural systems. This paper provides the necessary background information as well as describes the formulation and modelling techniques used in the development of a new approach to modelling the influence of imperfections on the stability behaviour of structural components and systems. This new approach, called hereafter an equivalent stiffness approach, has an advantage over the previously described approaches since an imperfect member is treated as a hypothetically straight element, flexural and axial stiffnesses of which at each load level are predicted in a continuous fashion dependent upon the actual force and deformation states. This type of modelling does not require any explicit modelling of equivalent geometric imperfections or equivalent forces and their directions in advanced analysis; therefore also it does not require any buckling mode assessment. Moreover, the effects of strain hardening and section class may conveniently be included in modelling. Finally, European buckling curves are used to estimate the values of parameters of the developed model that can be immediately used in advanced analysis conducted according to Eurocode 3.     

The collapse of steel model columns with unequal flanges. II. Imperfect

The collapse behaviour of pin-ended steel columns with unequal flanges is investigated using a modified version of the Shanley model. Particular attention is given to the effect of the geometrical imperfection size on the behaviour of columns having a range of flange area ratios and slenderness values. Columns which are initially straight are dealt with in a companion paper (The collapse of steel model columns with unequal flanges. I. Perfect. International Journal of Mechanical Sciences, in press, doi:10.1016/j.ijmecsci.2004.09.005). Compressive yield of the smaller flange is confirmed as an important source of failure for the column. However, tensile yield of this flange can also cause failure, particularly at relatively high slenderness and/or imperfection size. Failure caused by yielding of the smaller flange, whether compressive or tensile, is often characterised by violent load-shedding, and high imperfection-sensitivity, and this is most noticeable at intermediate slenderness. A graphical method is suggested for predicting the maximum load, and for showing the degree of imperfection sensitivity.     

Buckling strength verification of cantilevered cylindrical shells subjected to transverse load using Eurocode 3

At present, there are only a few studies concerning the application of different types of buckling strength verification according to Eurocode 3 at combined loading. Besides the stress design as classical hand calculation method of checking cylindrical steel shells against buckling failure, the new Eurocode 3 also offers two global numerical analyses at different modelling levels. The linear buckling analysis (LBA) combined with a materially nonlinear but geometrically linear analysis (MNA) is the simpler concept from the perspective of the modelling and calculation effort. The more sophisticated method is a geometrically and materially nonlinear analysis of the imperfect structure (GMNIA). This paper presents the application of both numerical concepts to the cantilevered shell subject to a transverse load at the free edge. The results are compared to those from stress design. There are specific features at both types of numerical analysis: As the determination of the plastic reference resistance and the buckling parameters is the main focus at MNA/LBA, the choice of proper equivalent geometric imperfections demands special diligence at GMNIA. The presented analyses show that the GMNIA concept in connection with consistent equivalent geometric imperfections may lead to a safe and economic design of cylinders subject to combined loading. At the particular load case the MNA/LBA concept currently suffers from the lack of proper regulations concerning the determination of the overall buckling reduction factor.     

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.     

对火灾中的铝结构进行局部屈曲分析:有限元模型

对温度升高时压力作用下的细长铝合金截面进行试验研究的结果已经表述在相关论文中。本文对这些试验进行了有限元模拟分析,为此构建了一个新的本构模型,用以计算火灾下的铝合金结构。从有限元模型中获得的临界温度与试验中得到的数据非常吻合(平均温差为1°C,标准偏差为7°C)。构建的有限元模型用于确定板的最大宽厚比,此时在板屈曲前已发生了完全的塑性变形。     

Finite element limit load analysis of thin-walled structures by ANSYS (implicit), LS-DYNA (explicit) and in combination

After discussing general properties of implicit FE analysis using ANSYS and explicit analysis using LS-DYNA it is shown when and how quasi-static limit load analyses can be performed by a transient analysis using explicit time integration. Then we focus on the remaining benefits of implicit analysis and how a proper combination of ANSYS and LS-DYNA can be used to prepare the transient analysis by common preprocessing and static analysis steps. Aspects of discretization, solution control, consideration of imperfections and methods of checking the results are outlined.     

Stability problems of steel structures in the presence of stochastic and fuzzy uncertainty

General ideas and problems of probability approach and its utilization in the verification of structural design procedures of EUROCODES are mentioned. The paper is aimed at the probability study of the ultimate limit state of a steel compressed member designed economically according to EUROCODE 3. The theoretical failure probability (reliability index) vs. ratio of permanent to variable load action is calculated by means of the Monte Carlo simulation method. The misalignment of the failure probability according to EN1990 is analysed. Initial imperfections are generally considered as random variables and random fields. The non-linear beam FEM is used. The influence of initial curvature shape and size variability of the member axis on the variability of load-carrying capacity is investigated. The probabilistic analysis is supplemented with the fuzzy analysis of the influence of uncertainties on the failure probability.