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.     

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.     

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.     

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.     

Y形柱稳定性分析研究

Y形柱是机场航站楼屋盖支承体系中常采用的一种构件形式,作为主要承重构件,其稳定性决定了屋盖结构的整体承载能力。利用荷载-位移全过程跟踪技术,考虑几何非线性、材料非线性和初始几何缺陷,研究了在竖向和水平风、地震作用下薄壁Y形柱的稳定性。研究表明:竖向荷载作用下Y形柱以分叉段平面外屈曲为主要失稳模式;Y形柱对初始几何缺陷不敏感;水平风荷载对Y形柱稳定性不起控制作用;竖向和水平荷载作用下,发生面外失稳前柱子分叉处已经进入塑性变形,柱子强度问题先于整体失稳。     

Wind loads on large cylindrical open-topped tanks in group

Vertical cylindrical tanks for fluid and bulk storage are generally with very thin wall so they are very susceptible to buckling under wind loads. One of the main challenges for designers is the scarcity of reliable wind loads on tanks. A particular case of wind loads on tanks may occur when a tank is situated at the corner of a group in tank farm or distribution station, since it is expected to be loaded by different wind pressures compared with those of an isolated tank. In this paper, a large number of wind tunnel tests are conducted to investigate the wind loads on vertical cylindrical open-topped tanks in group, with main focus on the grouping effect of large cylindrical tanks with a very low aspect ratio. Three types of tank groups are covered in this study: two adjacent tanks including tandem, parallel and staggered configurations, three adjacent tanks in triangular array and four adjacent tanks in square array. The effects of spacing between tanks and wind attack angle on wind pressure distributions of both external and internal wall are investigated, and the difference of wind loads on tanks in a group compared with those on an isolated tank is discussed.     

Challenges in the computation of lower-bound buckling loads for tanks under wind pressures

This paper reports on the implementation of a lower-bound approach for the buckling of imperfection-sensitive shells using general purpose finite element codes. The stability of cylindrical steel tanks under wind pressure is evaluated for two tank configurations: conical roof tanks and open top tanks. For both tank configurations, several geometric relations are considered in order to find the variation of the knock-down factor as the geometry changes. The reduced energy method is implemented to compute a lower-bound for critical wind pressures and the results are compared with the static non-linear analysis carried out on the same models. An alternative way to implement the reduced energy method is presented to improve the results obtained with the proposed methodology.     

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。     

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.     

Performance evaluation of a transmission tower by substructure test

In this paper, a half-scaled substructure test was performed to evaluate the failure mode of an existing transmission tower subjected to wind load. A loading scheme was devised to reproduce the dead and wind loads acting on the prototype transmission tower. The load was enforced on the model structure using two actuators and a triangular jig mounted on the reduced model. Preliminary numerical analysis was carried out to evaluate the stability and member force of the specimen for the design load. When the substructured transmission tower was loaded by 270% of its maximum allowable buckling load, local buckling occurred in joints of leg members with weak constraints. From the experimental results, such as load-displacement curves, displacements, and strains of members, it was concluded that the local buckling was due to the additional eccentric force caused by unbalanced deformation of the specimen.     

Buckling analysis of a cooling tower shell with measured and theoretically-modelled imperfections

Geometrical imperfections were measured using photogrammetric techniques on an existing reinforced concrete cooling tower shell. The imperfections, related to the radii of such a real shell, were used as input data to create a real shape of the cooling tower. Numerical analysis was carried out for three models: (P) perfect shell of revolution, (M) shell with measured imperfections, (T) shell with a theoretical imperfection corresponding to the primary buckling mode under dead load. The buckling analysis was related to the linearized eigenvalue problem of elastic shells. The shell midsurface was approximated by eight-node quadrilateral isoparametric finite elements. Computations were carried out using the ANKA computer code. Critical values of the load parameter enable confirmation of a partial correlation between existing imperfections and buckling modes under dead load. The most disadvantageous direction of the wind load application on the real shell was found, in order to evaluate the decrease in the load-carrying capacity of the cooling tower shell against buckling. Theoretically modelled imperfections give rather unrealistic values of buckling loads of the real shell.     

Buckling behavior of cold-formed zed-purlins partially restrained by steel sheeting

This paper presents a study on the buckling behaviour of purlin-sheeting systems under wind uplift loading. The restraint provided by the sheeting to the purlin is modeled by using two springs representing the translational and rotational restraints. The analysis is performed using finite strip methods in which the pre-buckling stress is calculated based on the same model used for the buckling analysis rather than taken as the ‘pure bending’ stress. The results obtained from this study show that, for both local and distortional buckling, the restraints have significant influence on the critical loads through their influence on the pre-buckling stress rather than directly on the buckling modes. While for lateral-torsional buckling, the influence of the restraints on the critical loads is mainly due to their influence on the buckling modes rather than the pre-buckling stress.     

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.     

非对称荷载对大跨度非规则单层网壳结构性能的影响

以某大跨度非规则单层网壳为研究背景,应用ANSYS通用有限元分析软件对网壳结构进行了建模并重点模拟了风荷载、雪荷载、温度效应等多种非对称荷载作用,进行了静力分析、特征值屈曲分析以及非线性稳定分析。得到了网壳结构在15种典型荷载组合下的内力、位移结果,分析了非对称荷载对网壳结构静力性能的影响;考虑了几何非线性、材料非线性、初始缺陷,得到了网壳结构在非对称荷载作用下的稳定系数,分析了非对称荷载对网壳结构稳定性能的影响。强调指出非对称荷载作用在大跨度单层网壳结构设计中的重要性,为大跨度非规则单层网壳设计提供参考。     

Effect of building length on wind loads on low-rise buildings with a steep roof pitch

A wind tunnel model study was carried out on long, low-rise buildings with a steep roof pitch to determine the effect of the length-to-span aspect ratio on the external wind pressure distributions. The study showed a significant increase in the magnitude of the negative pressure coefficients on the leeward roof and wall, with an increase in aspect ratio, for oblique approach winds. These large suction pressures also generate large design wind load effects on the frames near the gable-end. The 1989 edition of the Australian standard for wind loads, AS 1170.2-1989 was found to underestimate the wind loads on steep pitch gable-roof buildings of aspect ratio greater than 3, on areas near the windward gable-end, and hence the critical bending moments in the supporting structural frames. The current Australian/New Zealand wind load standard, AS/NZS 1170.2-2002 specifies increased negative pressure coefficients on the leeward half of high pitch roof buildings, and critical bending moments in the supporting frames calculated from these distributions agree quite well with values obtained from the wind tunnel study. However, other major standards severely underestimate the critical bending moments, and the effective pressure coefficients producing those bending moments, especially on the leeward roof slope.     

Wind loads on curved roofs

Curved roofed buildings are increasingly used in the modern built environment because they offer aerodynamically efficient shapes and provide architects and designers with an alternative to regular rectangular building forms. However, there is little information available on the wind loads on these roof forms. The Eurocode for wind actions (EN1991-1-4) includes pressure coefficients for a limited range of aspect ratio cylindrical roofs from measurements in low-turbulence conditions but only for wind blowing normal to the eaves. There is some concern regarding the reliability of these data, consequently EN1991-1-4 allows National Choice (National Determined Parameter) for wind loads on these roofs. This paper describes a series of parametric wind tunnel studies undertaken at BRE to measure wind pressures on a wide range of curved roof models in a properly scaled atmospheric boundary layer simulation and gives an alternative to the EN1991-1-4 recommended procedure.     

Low-rise gable roof wind loads: Characterization and stochastic simulation

Mitigation of the damage caused by windstorms to low-rise buildings is a high priority in the wind engineering community. The development of cost-effective methods to withstand the effects of extreme winds can be advanced through improved modeling of wind loads acting on low-rise roof structures. This study explores the effects of the spatial and probabilistic characteristics of pressure fields on the aggregate uplift acting on roof panels of low-rise gable roof buildings representative of typical homes. Pressure time histories obtained at roof locations for buildings of varying roof slope at several angles of incidence in the boundary layer wind tunnel at Clemson University are used to characterize the correlation statistics between tap locations and model the marginal probability density function at individual tap locations. This information is incorporated into a multi-variate non-Gaussian simulation algorithm to study the effects of various levels of correlation on the aggregate uplift on sheathing panels. Comparisons are made between the simulated aggregate uplift and ASCE 7-98 provisions [Minimum Design Loads for Buildings and Other Structures, ASCE 7-98 Standard, American Society of Civil Engineers, New York [1]] as well as laboratory generated failure capacities for sheathing panels.     

Design rules for out-of-plane stability of roller bent steel arches with FEM

This paper describes a numerical investigation into the out-of-plane buckling behavior of freestanding roller bent steel arches. As roller bent arches have structural imperfections which differ considerably from those of hot-rolled or welded sections, specific attention is paid to their inclusion in the numerical model. Sensitivity analyses are performed to assess the influence of the imperfections due to roller bending on the out-of-plane buckling response. The accuracy of the finite element model is checked by comparing the results with earlier performed experiments as presented in a related paper. The finite element model is able to replicate the structural behavior displayed by the experiments with good accuracy. A database is created with elastic–plastic buckling loads for a large number of freestanding roller bent arches. The numerical data is analyzed and presented in a so-called imperfection parameter diagram from which imperfection parameter curves are derived. The imperfection parameter curves are substituted into the European column curve formulation, leaving the original column curve formulation unaffected but extending its applicability to the out-of-plane buckling response of roller bent arches. The column curve with proposed imperfection parameter expressions can be used to check the out-of-plane buckling response of a roller bent steel arch with known non-dimensional slenderness.     

Stability of combined imperfect conical tanks under hydrostatic loading

Steel conical vessels with upper cylindrical caps are widely used as liquid containments in elevated water tanks. This type of structure for containing water is referred to as “combined conical tank”. A number of catastrophic failures of combined conical tanks occurred during the past decades in various locations around the globe. Previous studies available in the literature focused on pure conical tanks, where the vessels have no upper cylindrical caps. The current study focuses on characterizing the buckling behaviour of combined conical tanks under the effect of hydrostatic pressure. The study is conducted numerically using a three-dimensional finite element model developed in-house. The effects of geometric imperfection and residual stresses as well as the variation of the geometric and material parameters on the buckling capacity of combined conical tanks are investigated. Finally, a comparison between the buckling capacities of combined and equivalent pure conical tanks is conducted.     

A method to assess peak storm wind speeds using detailed damage surveys

A detailed damage survey of a single, wood-framed, structure, which had a complete roof failure during the passage of a gust front in southern Ontario, was performed. Radar data was used to estimate upper level wind speeds associated with the gust front. Details pertaining to the structural failure, including the debris field, were obtained. Wind tunnel pressure time histories, in a simulated atmospheric boundary layer, were used to establish the roof height, gust wind speed at failure. This speed was smaller than the upper level speed found from the analysis of the radar. The flight of the roof was also examined, and confirmed the wind speeds obtained from the structural analysis of the failure. The study illustrates that detailed damage surveys, which incorporate the use of wind tunnel test data and debris flight in the analysis, can shed considerable light on the details of the wind speeds at failure, reducing the uncertainty caused by the many assumptions in such analyses.