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.     

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.     

谐波沉降下开顶罐的屈曲分析

研究有关谐波沉降下开顶罐的屈曲性能。首先,研究各种谐波数下开顶罐的极限谐波沉降和屈曲性能。结果显示受小波数影响的上壳体发生屈曲,而受大波数影响时则在壳体的其他地方发生屈曲。随着谐波数的增加,在壳体底部也出现越来越多的屈曲点。此外,对开顶罐来说,受小波数影响时其极限谐波沉降大大降低,而受大波数影响时其极限谐波沉降降低极少。对开顶罐的屈曲性能进行数值研究,考察高径比(h/r)和径厚比(r/t)的影响。可知:在某种特定的谐波数下,极限谐波沉降与高径比(h/r)为单调递减的关系。同样的,随着谐波数的增加,极限谐波沉降的降低变化越来越小。而在某种特定的谐波数下,极限谐波沉降与径厚比(r/t)也为单调递减的关系。此外,随着谐波数的增加,极限谐波沉降的降低变化也越来越小。最后,将开顶罐和锥形顶罐的屈曲结果进行比较。结果显示,受小波数影响的开顶罐比不受锥形顶约束的锥形顶罐更能承受大的谐波沉降。然而,受大波数影响时,开顶罐与锥形顶罐的沉降持续能力有所不同。     

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 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.     

Numerical and experimental investigations of the response of aluminum cylinders with a cutout subject to axial compression

Understanding how a cutout influences the load bearing capacity and buckling behavior of a cylindrical shell is critical in the design of structural components used in automobiles, aircrafts, and marine applications. Numerical simulation and analysis of moderately thick and thin unstiffened aluminum cylindrical shells (D/t=45, 450 and L/D=2, 5, 10), having a square cutout, subjected to axial compression were systematically carried out in this paper. The investigation examined the influence of the cutout size, cutout location, and the shell aspect ratio (L/D) on the prebuckling, buckling, and postbuckling responses of the cylindrical shells.An experimental investigation on the moderately thick-walled shells was also carried out. A good correlation was observed between the results obtained from the finite element simulation and the experiments. Furthermore, empirical equations, in the form of a ‘buckling load reduction factor’ were developed using the least square regression method. These simple equations could be used to predict the buckling capacities of several specific types of cylindrical shells with a cutout.     

The dispersion of fugitive emissions from storage tanks

This paper presents laboratory experiments of the dispersion and flow field downwind of cylindrical buildings such as petrochemical storage tanks. We consider buildings of height to diameter aspect ratio A=H_b/D, in the range from 1 to 0.5, submerged within deep, aerodynamically rough, neutral and stable boundary layers. Emissions are neutrally buoyant with no significant vertical momentum, releases being made from point sources at heights H_s in the range of H_b⩽H_s⩽1.5H_b, except in studies with floating roof tanks where the release was from an annulus between the roof and the internal tank wall. Various configurations are examined which include buildings in isolation, in conjunction with bunds (low surrounding walls) and in small groups. Characteristics of the mean velocity and dispersion fields are discussed and compared with results for releases in the absence of buildings and for releases in the presence of cuboid buildings. Dispersion characteristics of the cylindrical buildings are found to be aspect ratio dependent. Further, the presence of bunds results in a significant impact on the velocity and concentration fields leading to considerable reductions in ground-level concentrations.     

Buckling strength of the cylindrical shell and tank subjected to axially compressive loads

This paper aims to develop practical design equations and charts estimating the buckling strength of the cylindrical shell and tank subjected to axially compressive loads. Both geometrically perfect and imperfect shells and tanks are studied. Numerical analysis is used to evaluate buckling strength. The modeling method, appropriate element type and necessary number of elements to use in numerical analysis are recommended. According to the results of the parametric study of the perfect shell, the buckling strength decreases significantly as the diameter-to-thickness ratio increases, while it decreases slightly as the height-to-diameter ratio increases. These results are different from those in the case of columns. The buckling strength of the perfect tank placed on an extremely soft foundation and a stiff foundation increases by up to 1.6% and 5.6%, respectively, compared with that of the perfect shell. The buckling strength of the shell and tank decreases significantly as the amplitude of initial geometric imperfection increases. Convenient and sufficiently accurate design equations and charts used for estimating buckling strength are provided.     

Parametric study on buckling behaviour of dented short carbon steel cylindrical shell subjected to uniform axial compression

Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings, etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells, but in this paper only effect of a dent on strength of a short (Lc/Rc∼1, Rc/t=117, 175, 280) cylindrical shell is considered for analysis. The dent is modeled on the FE surface of perfect cylindrical shell for different angles of inclination and sizes at half the height of cylindrical shell. The cylindrical shells with a dent are analyzed using non-linear static buckling analysis. From the results it is found that in case of shorter dents, size and angle of inclination of dents do not have much effect on static buckling strength of thin cylindrical shells, whereas in the case of long dents, size and angle of inclination of dents have significant effect. But both short and long dents reduce the static buckling strength drastically. It is also found that the reduction in buckling strength of thin cylindrical shell with a dent of same size and orientation increases with increase in shell thickness.     

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.     

Static buckling analysis of thin cylindrical shell with centrally located dent under uniform lateral pressure

One of the common failure modes of thin cylindrical shell subjected to external pressure is buckling. The buckling pressure of these shell structures are dominantly affected by the geometrical imperfections present in the cylindrical shell which are very difficult to alleviate during manufacturing process. Dent is one of the common geometrical imperfections present in thin shell structures which may be formed due to mechanical damage caused by accidental loading or impact. In this work, influence of various dent parameters (dent length, dent width, dent depth and angle of orientation of the dent) on the critical buckling pressure of thin cylindrical shells with a centrally located dent is studied using non-linear static finite-element analysis of ANSYS under external pressure with simply supported boundary conditions at the top and bottom edges of the thin cylindrical shell.     

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.     

Experiments on dented cylindrical shells under peripheral pressure

In spite of numerous papers in the literature on the buckling behavior of cylindrical shell structures, the effect of local large imperfections caused by physical contacts has not been exhaustively examined yet. To this end, this paper reports on an experimental program on the buckling and post-buckling response of thin cylindrical shells with local dent imperfections under uniform external pressure. The results of this study can be used in practical structures with similar geometric features, i.e. D/t ratio.     

Elastic buckling of horizontal barrelled shells filled with liquid—Numerical analysis

In the paper an alternative for horizontal cylindrical tank is presented. The proposed solution has the form of a barrelled tank in which the classical cylindrical shell is replaced by the barrelled one. The geometry of this shape is described. The buckling behaviour of the horizontal barrelled shell filled with liquid is analysed. The liquid level and the negative internal pressure which appear during emptying of the tank are also taken into consideration. On the basis of numerical analyses number of plots as well as analytical formulae are elaborated as a tool for design of barrelled tank with respect of stability criterion. Analyses are made on three families of barrelled shells of different capacities. In each family the capacity and length are constant. Advantages of barrelled tanks in comparison with cylindrical one are discussed.     

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%.     

Critical sizes of ground and underground horizontal cylindrical tanks

The paper deals with ground and underground horizontal cylindrical tanks supported at both ends. The ground tanks are loaded with internal hydrostatic pressure and small negative pressure. On the other hand, the underground tanks are located in water containing soil and loaded with external hydrostatic pressure. Critical states of both structures are determined based on solving the equation of stability of cylindrical shell. The problem so defined has been converted to calculation of critical thicknesses of walls for the family of circular cylindrical tanks of different capacities. Critical sizes of the structures have been determined as functions of dimensionless critical thickness and dimensionless tank length.     

无粘结预应力技术在大直径圆柱壳中的应用和问题探讨

利用轴对称圆柱壳有矩理论进行水池设计,并进行了现场测试。设计中预应力钢筋的摩擦损失取自现场试验数据,为张拉控制应力的1 9%。工程实例表明,无粘结预应力混凝土技术应用于大直径圆柱壳可有效地控制裂缝产生,获得可观的经济和社会效益。在使用阶段,建议对0 4倍池壁高度以下截面应按偏心受拉构件计算,以上截面仍按轴心受拉构件计算。底板下的锚桩除了有效抗浮之外,还能大大降低底板的厚度。施工时应保证钢绞线与锚固壁柱上的锚垫板垂直,并选用适当的夹片式锚具,使其表面硬度与钢绞线的表面硬度差≥HRc1 0 (HRc为洛氏硬度)。     

Buckling of circular cylindrical shells partially subjected to external liquid pressure

Theoretical analyses are presented for the buckling of circular cylindrical shells partially subjected to external liquid pressure. The shells are assumed to stand vertically with the lower end clamped, and the upper end clamped or free. In the analyses, the Donnell equations are used for the basic equation, and prebuckling deformation as well as the membrane state of stress of the shell are taken into account. The Galerkin method is used, and the critical pressures at various liquid heights as well as the wave numbers, are obtained for a wide range of the geometrical parameters of the shell Z. A convenient chart which indicates the buckling liquid height for a given shell and liquid are presented. Experimental studies are also conducted by using test cylinders made of polyester film, and water. The theoretical and experimental results for the buckling liquid height, are in excellent agreement.     

Stability of circular cylindrical steel shells under combined loading

Circular cylindrical shells made of steel are used in a large variety of civil engineering structures, e.g. in off-shore platforms, chimneys, silos, tanks, pipelines, bridge arches or wind turbine towers. They are often subjected to combined loading inducing membrane compressive and/or shear stress states which endanger the local structural stability (shell buckling). A comprehensive experimental and numerical investigation of cylindrical shells under combined loading has been performed which yielded a deeper insight into the real buckling behaviour under combined loading . Beyond that, it provided rules how to simulate numerically the realistic buckling behaviour by means of substitute geometric imperfections. A comparison with existing design codes for interactive shell buckling reveals significant shortcomings. A proposal for improved design rules is put forward.