Wind buckling of metal tanks during their construction

Shell structures are usually designed by considering their final shape and configuration, so that it is assumed that stability during the construction will be satisfied without further thought. However, evidence from recent collapses of metal tanks under moderate winds shows that this is a matter that requires special attention. This paper reports analytical studies of tanks for the oil industry that failed during their construction in the Argentinean Patagonia under moderate winds. The cylindrical part of the tanks was set up in place with point welding, but the roof was not yet in place at the time of collapse. To understand the mechanism of failure, static, geometrically nonlinear finite element modeling of the tanks was carried out, in which the shell was represented as close as possible to the actual conditions during the construction stage at which it failed. The results show that for the wind velocities prevalent at the time of collapse, an explanation of the failure mechanism can only be achieved by taking into account several special features of the structure under construction, i.e. the localized nature of welding and the influence of the incomplete junction with the bottom plate.     

Wind buckling of tanks with conical roof considering shielding by another tank

Oil storage tanks are usually arranged in groups in tank farms, and this configuration may affect their buckling and postbuckling strength under wind loads. The assessment of wind action on tank structures is performed in this work by means of wind tunnel experiments to evaluate the pattern of pressure distribution for a tank which is shielded by another tank under various configurations and separation between them. The experimental results show significant changes in pressures due to shielding effects. In a second stage the structural response under the pressures previously evaluated is performed by finite element analysis using both linear bifurcation and geometrically nonlinear analysis. Results of two-tank interaction are compared with those of an isolated tank. Based on the results, it is concluded that the changes in wind pressures due to group effects induce changes in buckling loads and in the associated deflected patterns.     

Wind pressures and buckling of cylindrical steel tanks with a dome roof

An experimental/computational strategy is used in this paper to evaluate the buckling behavior of steel tanks with a dome roof under exposure to wind. First, wind tunnel experiments using small scale rigid models were carried out, from which pressure distributions due to wind on the cylindrical part and on the roof were obtained. Second, a computational model of the structure (using the pressures obtained in the experiments) was used to evaluate buckling loads and modes and to study the imperfection sensitivity of the tanks. The computational tools used were bifurcation buckling analysis (eigenvalue analysis) and geometrical nonlinear analysis (step-by-step incremental analysis). Geometric imperfections and changes in the buckling results due to reductions in the thickness were also included in the study to investigate reductions in the buckling strength of the shell. For the geometries considered, the results show low imperfection sensitivity of the tanks and buckling loads associated with wind speeds 45% higher than those specified by the ASCE 7-02 standard.     

Wind pressures and buckling of cylindrical steel tanks with a conical roof

Tanks with a conical roof are studied in this paper under wind load, for a roof which is supported by rafters and columns. Buckling occurs in the form of deflections in the cylindrical shell and the buckling mode is localized in the windward region. Both bifurcation analysis and geometrically nonlinear analysis have been performed using finite element discretizations of the structure. The wind pressures have been obtained from wind tunnel experiments performed as part of the research, and have been obtained for tank geometries for which information was not previously available. The results show high imperfection sensitivity of tanks with a conical roof, and buckling loads for wind velocities in the same order as those expected to occur in the Caribbean region.     

Buckling of cylindrical open-topped steel tanks under wind load

Vertical cylindrical welded steel tanks are typical thin-walled structures which are very susceptible to buckling under wind load. This paper investigates the buckling behavior of open-topped steel tanks under wind load by finite element simulation. The analyses cover six common practical tanks with volumes of 2×10³ m³ to 100×10³ m³ and height-to-diameter ratios H/D<1. The linear elastic bifurcation analyses are first carried out to examine the general buckling behavior of tanks under wind load, together with comparison to that of tanks under uniform pressure and windward positive pressure (only loaded by positive wind pressure in the windward region). The results show that for larger tanks in practical engineering, the stability carrying capacity of wind load is relatively lower. It is also indicated that the buckling behavior of tanks under wind load is governed by the windward positive pressure while wind pressure in other region of tank essentially has no influence on the buckling performance. The geometrically nonlinear analyses are then conducted to investigate the more realistic buckling behavior of tanks under wind load. It is found that the buckling behaviors of perfect tanks and imperfect tanks are much different. The weld induced imperfection only has little influence on the wind buckling behavior while the classical buckling mode imperfection has significant influence, leading to a considerable reduction of wind buckling resistance. The influences of thickness reduction of cylindrical wall, liquid stored in the tank and wind girder on the buckling behavior are also examined. It shows that the thickness reduction of cylindrical wall considerably reduces the wind buckling resistance while sufficient liquid stored in the tank and wind girder significantly increase the wind buckling resistance.     

Localized support settlements of thin-walled storage tanks

This paper investigates the influence of support settlements on the out-of-plane displacements of thin-walled cylindrical tanks with a fixed top roof. The shell considered is representative of many steel tanks constructed in Puerto Rico and in the United States, and has a ratio between the diameter and the height of the order of 2.5, with slenderness ratio (radius to thickness) of the order of 1,700. The behavior of the tank is investigated using the finite element computer package ABAQUS by means of a geometrically non-linear algorithm for the analysis and linear elastic material behavior. Results are presented for geometrically linear analysis, geometrically nonlinear analysis and bifurcation buckling analysis. It is shown that the equilibrium path is highly non linear and that the shell displays a plateau for a settlement of the order of half the thickness of the shell. Linear results provide a poor indication of the real displacements in the shell, so that geometric nonlinearity should be included in the analysis for working loads.     

Flexural-torsional buckling of shallow arches with open thin-walled section under uniform radial loads

An arch with an open thin-walled section that is subjected to a radial load uniformly distributed around the arch axis may suddenly buckle out of its plane of loading and fail in a flexural-torsional buckling mode. The classical flexural-torsional buckling load for an arch with an open thin-walled section under a uniform radial load has been obtained by a number of researchers, based on the consideration that the uniform radial load produces a uniform axial compressive force without in-plane bending prior to the occurrence of flexural-torsional buckling. This assumption is correct for deep arches. However, the uniform radial load may produce substantial bending actions in shallow arches prior to flexural-torsional buckling, and so the classical buckling analysis based on the assumption of uniform axial compression may produce incorrect flexural-torsional buckling loads for shallow arches. This paper investigates the flexural-torsional buckling of shallow arches with an open thin-walled section that are subjected to a radial load uniformly distributed around the arch axis. It is found that shallow arches under a uniform radial load are subjected to combined in-plane compressive and bending actions prior to flexural-torsional buckling, and that using the classical buckling solution for circular arches under uniform compression produces incorrect buckling loads for shallow arches. A rational finite element model is developed for the flexural-torsional buckling and postbuckling analysis of shallow arches with an open thin-walled section, which allows the buckling loads to be obtained correctly.     

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.     

Reduced stiffness buckling of sandwich cylindrical shells under uniform external pressure

A reduced stiffness lower bound method for the buckling of laterally pressure loaded sandwich cylindrical shell is proposed. Also, an attempt is made to assess the validity of the proposed reduced stiffness lower bound with FEM numerical examples. In addition, the proposed method is compared with classical and Plantema's approaches of the buckling of the laterally pressure loaded sandwich cylindrical shell. Comparison of the proposed reduced stiffness lower bound with that obtained from non-linear FEM analysis verifies that it indeed provides a safe lower bound to the buckling of laterally pressure loaded sandwich cylindrical shells. The attractive feature of the proposed reduced stiffness method is that it can be readily used in designing laterally pressure loaded sandwich cylindrical shells without being concerned about geometrical imperfections.     

The UWO contribution to the NIST aerodynamic database for wind loads on low buildings: Part 3. Internal pressures

Wind tunnel tests of generic low buildings have been conducted at the University of Western Ontario for contribution to the National Institute on Standards and Technology (NIST) aerodynamic database. Part 1 provided the archiving format and basic aerodynamic data. In Part 2, the data of external pressures were compared with existing wind load provisions for low buildings. This paper, Part 3, deals with an investigation of wind-induced internal pressures of low-rise buildings with realistic dominant opening and leakage scenarios. Data from one building model with four different opening sizes were compared with numerical simulations. The existing theory, using the unsteady orifice discharge equation, works well for the building models used in this study, given the external pressures near the openings, irrespective of shifts of wind direction and upstream terrain. Numerical simulations can capture the temporal variations of the internal pressure fluctuations, as well as mean values.The internal pressure fluctuations for the building with leakage (nominally sealed building) are attenuated as they pass through the openings, while mean values are consistent with spatially averaged external pressures. Internal pressure resonance occurs for the dominant opening (3.3% open ratio) with building leakage. Effects of oblique wind angles on internal pressure dynamics are not significant, at least for the openings in the centre of wall, as is the case herein. Peak internal pressures occur for a wind direction normal to the wall with a dominant opening. Measured internal pressure coefficients are compared with current wind load provisions. Some peak values were found to exceed the recommended design values for the dominant windward wall opening cases.     

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.     

Vibration, buckling and collapse of ovaloid toroidal tanks

A shell-theory finite element analysis is carried out for toroidal tanks with ovaloid cross-section. The analysis serves to determine the natural frequencies, and the buckling and collapse pressures. A variety of support conditions are considered, including lines of support at the inner and outer equator of the tank. For validation, comparison is made with previously published results for stress, vibration, and buckling of elliptical toroidal shells. Finally, a parametric study is carried out to determine the influence on the natural frequency, and buckling and collapse pressures, of shell size, shell thickness, material properties, and support conditions.     

风荷载下均匀厚度的锚固柱状壳体的屈曲

与承受均匀外部压力作用下的柱状壳体相比,承受不均匀风压的柱状壳体表现出不同的屈曲性能。不同的长宽比下,会出现相当复杂多样的屈曲模式;线性和非线性屈曲分析的结果也会有很大的不同。相比之下,除了较短的柱体或边界条件发生变化外,在均匀外压力作用下,柱体常出现环向失稳,且受几何变化的影响很小。对风压力下厚度均匀的锚固短柱壳和长度适中的柱壳进行了广泛的研究,旨在获得筒仓和锚固贮水池设计的有用信息,以防止其在风载作用下发生屈曲。线性和非线性有限元分析结果表明,短圆筒中出现环向受压失稳模式。对长度适中的柱,截面出现呈椭圆状的前屈曲对屈曲强度有重要的影响。参考均匀外压下的传统临界值,得到风荷载下线性和非线性临界滞止压力的经验公式。简要探讨了屈服和缺陷敏感性的影响。     

Modification of -equation in the SSRC Guide for buckling of monosymmetric I-beams under transverse loads

Finite element buckling analyses of monosymmetric I-beams subjected to transverse loading applied at different heights with respect to the mid-height of the cross-section were conducted. Transverse loads consisting of a mid-span point load and a uniformly distributed load were considered in the investigation. Four types of end restraint also were considered. The method suggested in SSRC Guide was compared with the finite element method (FEM) results. In order for C-equation in the SSRC Guide to be applicable for monosymmetric I-beams, it must be modified to contain three variables; A_m, B_m, and D_m. The first two variables A_m and B_m are modified variables A and B in the SSRC Guide whereas the third variable, D_m, developed herein, is the new modification factor for monosymmetric I-beams. The applicability of this new design rule is limited to monosymmetric I-beams in which the degree of monosymmetry, ρ, is within the range from 0.1 to 0.9.     

Experimental and numerical study of wind pressures on irregular-plan shapes

This paper presents the results of a program of wind tunnel model tests on pressure distributions for irregular-plan shapes (L- and U-shaped models). The experiments were carried out in a closed-circuit wind tunnel and a multi-channel pressure measurement system was used to measure mean values of loads on 1:100 scale models. The same tests were carried out on a cube-shaped model as an experimental validation. The effectiveness of the model shape in changing the surface pressure distributions is assessed over an extended range of wind directions. The experimental data for the L- and U-shaped models showed different wall pressure distributions from those expected for single rectangular blocks. Furthermore, a Computational Fluid Dynamics (CFD) code was used to illustrate some particular cases and to provide a better understanding of the flow patterns around these irregular-plan models and of the pressure distributions induced on their faces. Computed pressure coefficients have also been compared with wind tunnel results for normal and oblique wind incidence. A general good agreement has been found for normal wind incidence whereas some differences have occurred for other directions.     

Mechanism for buckling of shield tunnel linings under hydrostatic pressure

In this paper, the effects of segmental joints, dimensions of segments, and ground conditions on buckling of the shield tunnel linings under hydrostatic pressure are studied by analytical and numerical analysis. The results show that radial joints have significant impacts on the buckling behavior: the shield tunnel linings with flexible joints buckles in a single wave mode in the vicinity of K joint, while those with rigid joints buckles in a multi-wave mode around the linings. Hydrostatic buckling strength is found to increase with the flexural rigidity of the radial joint and the thickness of segment increasing. This study shows that ground support increases the buckling strength dramatically, while earth pressure reduces the capacity to resist hydrostatic buckling. The tunnel linings during construction are found to be easier to buckle than that during operation. Meanwhile, the buckling of tunnel linings is studied by theoretical analysis of buried tube buckling.     

A study on buckling of thin conical frusta under axial loads

Experiments were performed wherein conical frusta of aluminium of thicknesses between 0.7 and 1.62 mm and semi-apical angles range of 16–29° were axially compressed in a universal testing machine. The load–deformation curves and deformed shapes of specimens were recorded. These deformed in axisymmetric concertina mode and non-symmetric diamond modes.A three dimensional numerical simulation was carried out for all samples tested under quasi-static loading using ANSYS^®. Various stages of collapse of the shell, including non-symmetrical lobe formation were simulated for the first time, and material, geometric and contact non-linearities were incorporated. The plastic region of the material curve was assumed to be piecewise linear. Tensile tests were performed on standard samples to obtain stress–strain curves. Results thus obtained compared well with the experiments.Based on the formation of rolling and stationary plastic hinges an analysis was also carried out to study the behaviour of shells under axial compression and results were compared with experimental and numerical results.     

A generalized analytical approach to the buckling of simply-supported rectangular plates under arbitrary loads

An analytical approach for the elastic stability of simply-supported rectangular plates under arbitrary external loads is presented which, for the first time, may be described as ‘exact’. This is achieved through the use of exact solutions for the in-plane stresses and the adoption of double Fourier series for the buckled profiles which, together, ensure that accurate results are obtained in the Ritz energy technique. Several cases of plate buckling under direct, shear and bending loads (or their combinations) are studied to show the generality of the proposed approach, with the ensuing results compared with existing data (if available) and with numerical FE results.     

Inelastic stability of conical tanks

The aim of this investigation is to study the effect of different imperfection shapes on the inelastic stability of liquid-filled conical tanks and to determine the critical imperfection shape that would lead to the minimum inelastic limit load. The study is carried out numerically using a self-developed shell element used to simulate a number of conical tanks having an imperfection shape in the form of Fourier series of equal coefficients. The Fourier analysis of the buckling modes indicates that the existence of axisymmetric imperfection will lead to the critical inelastic limit load for conical tanks.     

Hydrostatic, wind and non-uniform lateral pressure solutions for containment vessels

The governing Flügge stability equations in coupled form are used for cylinders subjected to external pressure that varies circumferentially. Three cases are considered: fluid (hydrostatic) pressure, wind pressure and partial (patch) circumferential pressure. The wind load follows the Australian Standard AS 1170.2 (1989). Longitudinal variation of the load is not considered. The numerical process gives the stagnation buckling pressure for different shell geometry and simple support conditions at each end. The Galerkin method is employed to orthogonalize the error made with the introduction of the finite series into the governing equations. The solutions are compared with a few published solutions in the literature.