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 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 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.     

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。     

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 strength of cylindrical steel tanks under harmonic settlement

Large vertical cylindrical steel tanks for bulk and fluid storage are usually constructed in soft foundations, so it is not surprising that tank foundations are susceptible to various types of settlement beneath the tank wall, which is usually decomposed as a Fourier series in harmonics. In this paper, buckling strength of cylindrical fixed-roof steel storage tanks under harmonic settlement is investigated through great deal of numerical analyses by the FE computer package ANSYS. Three types of buckling analyses are carried out which are the LBA, GNA, GNIA proposed also by Eurocode 3. The results show that the equilibrium path from both GNA and GNIA is highly nonlinear, and it seems ungrounded to establish design criterion on the principle of superposition based on the linear elastic theory. The influences of the harmonic wave number n, the radius-to-thickness ratio r/t, the height-to-radius ratio h/r, and the geometric imperfection δ₀/t on the buckling strength of the storage tanks are mainly investigated. The ultimate harmonic settlements for various tank geometries are addressed and plotted in each analysis together with the buckling modes. The buckling modes from GNA and GNIA agree well with the lowest linear bifurcation buckling modes from LBA, and take mainly two types of deformations: shearing buckling extending throughout the entire height for the lower wave number n=2–4 and the elephant's foot failure occurring at the upward settlement zone caused by the meridional compression for the higher wave number n>4. It is also indicated from the results that both the ultimate harmonic settlement and the buckling mode of the tank are closely correlative with the geometric parameters: the wave number n, the radius-to-thickness ratio r/t, the height-to-radius ratio h/r, and the initial geometric imperfection δ₀/t.     

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.     

The effects of long term uniform corrosion on the buckling of ground based steel tanks under seismic loading

Material degradation due to corrosion significantly alters the seismic response of ground-based cylindrical steel storage tanks. A numerical study is conducted to investigate the effects of internal shell corrosion on the dynamic buckling of three cone roof ground-based, steel cylindrical tanks with height to diameter ratios (H/D) of 0.40, 0.63 and 0.95, subjected to horizontal seismic base excitations. Internal corrosion is considered as a time dependent uniform thinning of the wall at the upper and the lower parts of the tank being in contact with, respectively, atmospheric oxygen and acid gases and residual water. Detailed numerical models of the tank–liquid systems at different stages of corrosion degradation are subjected to two representing accelerograms and for each model the critical peak ground acceleration (PGA) for dynamic buckling of the shell and its associated mode of failure are evaluated. It is found that in all three tanks, the critical PGA is markedly reduced with thinning of the shell, irrespective of the type of ground input. The buckling mode of failure of the tanks also changed from an elastic diamond-shaped failure at the top of the shell to an elasto-plastic elephant foot type failure near the base, after 10 years for the shorter tanks (H/D=0.4 and 0.63) and after 15 years for the tallest tank. The effects of uniform corrosion degradation on the critical buckling load of the tanks were found to be such that after 20 years of thinning due to corrosion, the static loading alone was responsible for the elephant foot buckling of the shell.     

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.     

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.     

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.     

Experiments on the deflection and buckling behavior of ring-stiffened cylindrical shells under wind pressure

Buckling behavior of thin circular cylindrical shells stiffened by one or two rings has been studied in a wind tunnel. Both the prebuckling deflection and the buckling load were measured with a variety of a specimens in a smooth flow, and the effects of the stiffeners on them were examined. For comparison purposes, the buckling load of each specimen under hydrostatic pressure was also measured.The results indicate that the prebuckling deflection and ovalling oscillation can be significantly suppressed by relatively light stiffeners. As the flexural rigidity, E_sI_s, of the ring increases, the axial buckling mode changes from a symmetric one accompanied by ring deflection to another one with the rings acting as nodes, at a critical value of E_sI_s. This critical value was found to be nearly equal to that for the hydrostatic pressure. On the other hand, contrary to the hydrostatic pressure case, the buckling load gradually increases with an increase in E_sI_s, even for values of E_sI_s greater than the critical value.     

Instability of cracked CFRP composite cylindrical shells under combined loading

Numerical analysis of cracked composite cylindrical shells under combined loading is carried out to study the effect of crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, torsion, internal pressure and external pressure are obtained, using the finite element method. In general, the internal pressure increases the critical buckling load of the CFRP cylindrical shells while torsion and external pressure decrease it. Numerical analyses show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell while for cylindrical shells under combined external pressure and axial load, the global buckling shape is insensitive to the crack length and crack orientation.     

Dynamic buckling of anchored steel tanks subjected to horizontal earthquake excitation

We investigate dynamic buckling of aboveground steel tanks with conical roofs and anchored to the foundation, subjected to horizontal components of real earthquake records. The study attempts to estimate the critical horizontal peak ground acceleration (Critical PGA), which induces elastic buckling at the top of the cylindrical shell, for the impulsive hydrodynamic response of the tank-liquid system. Finite elements models of three cone roof tanks with height to diameter ratios (H/D) of 0.40, 0.63 and 0.95 and with a liquid level of 90% of the height of the cylinder were used in this study. The tank models were subjected to accelerograms recorded during the 1986 El Salvador and 1966 Parkfield earthquakes, and dynamic buckling computations (including material and geometric non-linearity) were carried out using the finite element package ABAQUS. For the El Salvador accelerogram, the critical PGA for buckling at the top of the cylindrical shell decreased with the H/D ratio of the tank, while similar critical PGAs regardless of the H/D ratio were obtained for the tanks subjected to the Parkfield accelerogram. The elastic buckling at the top occurred as a critical state for the medium height and tallest models regardless of the accelerogram considered, because plasticity was reached for a PGA larger than the critical PGA. For the shortest model (H/D=0.40), depending on the accelerogram considered, plasticity was reached at the shell before buckling at the top of the shell.     

Interference effects on wind loading of a row of closely spaced tall buildings

Interference effects on a row of square-plan tall buildings arranged in close proximity are investigated with wind tunnel experiments. Wind forces and moments on each building in the row are measured with the base balance under different wind incidence angles and different separation distances between buildings. As a result of sheltering, inner buildings inside the row are found to experience much reduced wind load components acting along direction of the row (x) at most wind angles, as compared to the isolated building situation. However, these load components may exhibit phenomena of upwind-acting force and even negative drag force. Increase in x-direction wind loads is observed on the upwind edge building when wind blows at an oblique angle to the row. Other interference effects on y-direction wind loads and torsion are described. Pressure measurements on building walls and numerical computation of wind flow are carried out at some flow cases to explore the interference mechanisms. At wind angle around 30° to the row, wind is visualized to flow through the narrow building gaps at high speeds, resulting in highly negative pressure on associated building walls. This negative pressure and the single-wake behavior of flow over the row of buildings provide explanations for the observed interference effects. Interference on fluctuating wind loads is also investigated. Across-wind load fluctuations are much smaller than the isolated building case with the disappearance of vortex shedding peak in the load spectra. Buildings in a row thus do not exhibit resonant across-wind response at reduced velocities around 10 as an isolated square-plan tall building.     

Buckling of fixed-roof aboveground oil storage tanks under heat induced by an external fire

This paper presents computational modeling and results of steel storage tanks under heat induced by an adjacent fire. In this research, modeling is restricted to the structural behavior of the tank, with emphasis on thermal buckling of the shell. Two tanks that buckled under a huge fire in Bayamón, Puerto Rico in 2009, are investigated in detail: a small tank with a self-supported conical roof, and a large tank in which the conical roof is supported by a set of rafters and columns. For a tank that is empty, the results show that a relatively low temperature is enough to produce static buckling of the shell. In pre-buckling states, the cylindrical shell has thermal expansion; at the critical state the displacements reverse and inwards displacements are observed at advanced post-buckling states. Parametric studies are performed to understand the influence of the shell thickness, the level of fluid stored in the tank, the area affected by fire in the circumferential direction, and the temperature gradient through the thickness. The buckling modes are compared with real deflection of tanks that were affected by fire.     

Buckling of cylindrical shells with longitudinal joints under external pressure

In this article, the bucking of cylindrical shells with longitudinal joint has been investigated through the experimental and numerical analysis. It was clarified that the buckling behavior of cylindrical shells with longitudinal joints under lateral external pressure is not only related to its dimension, but also longitudinal joint and an imperfection. The buckling of cylindrical shells with rigid joint buckles only once and in multi-lobe buckling, whereas one with flexible joints buckles twice and firstly in single-lobe buckling in the vicinity of the joint, secondly in multi-lobe buckling in remaining un-deformed area. And the more flexible the longitudinal joint, the lower the critical pressure, with respect to the same dimension of jointed cylindrical shells and imperfection condition. Moreover the numerical analysis approaches were also presented and verified, by which the imperfection can greatly enlarge the effect of joint on buckling has been demonstrated.     

Modelluntersuchungen zur Windeinwirkung auf stählerne Doppelmantelbehälter

The model tests of wind action on the steel double‐shell tanks. The paper shows the results of the wind tunnel tests on the double shell cylindrical vertical tank models with fixed and floating roofs. During tests the pressure distribution onto both shells and onto the roofs was measured. The influence of the following parameters on the wind load value and distribution was analysed: – Distance between tank shells (3 distances) – Type of roof (floating or fixed) – Position of floating roof (4 positions). The measurement results have been presented as graphs of the pressure coefficients (C_p).     

Tragverhalten und Bemessung windbelasteter Kreiszylinderschalen mit diskreter Verankerung

Structural behaviour and design of wind‐loaded cylindrical shells with discrete anchorage. Stubby cylindrical shells are often used as storage tanks. Because of their large diameters, in general they are not anchored continuously, but discretely. Nevertheless, the previous investigations of the stress and strain state of the shell were done almost exclusively by assuming a continuous anchorage. In the contribution, it is analyzed for the critical load case wind on the emptied tank, how the internal forces and the buckling strength verification are changed, if the discrete anchorage is realistically taken into consideration at the tensile zone of the base cross section. The differences are quantified. From it, it can be concluded, that a continuously anchorage may be used in the mechanical model, if the interaction buckling strength verification of the stress design is only exploited up to 90%.