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.     

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.     

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.     

Buckling analysis design of steel frames

Steel design codes do not provide sufficient information for the efficient design of steel structures against out-of-plane failure, and what is provided is often overly conservative. The method of design by buckling analysis (DBA) specified in one code corrects this situation for beams, but the extension of this method to columns is only referred to, while there is no guidance on how to apply this method to the design of beam-columns and frames.Beam DBA uses the design code formulation for the member nominal design strengths in terms of the section moment capacities and the maximum moments at elastic buckling, accurate predictions of which may be determined by computer programs. Column DBA is similar, in that it uses the design code formulation for the column nominal design strengths in terms of the section compression capacities and accurate predictions of the elastic buckling.However, design codes do not provide formulations for the direct buckling design of beam-columns, but instead use the separate results of beam design and column design in interaction equations. The further extension to frames is not directly possible, because frames are not designed as a whole (except through the rarely used methods of advanced analysis), but as a series of individual members. This paper shows how the method of DBA can be used to design beam-columns and frames as well as beams and columns. Two example frames are designed and very significant economies are demonstrated when the DBA method is used.     

Collapse design of large steel digester tanks

This paper deals with practical problems encountered in the design of seismically loaded liquid-filled vertical tanks. Global stability, buckling under combined action of axial compression and internal pressure and the effect of flexible boundaries on axial buckling are studied. The question of the mutual interaction of global and local failure modes is considered. Numerical studies on the basis of finite element-discretized-shell models are carried out which show the typical features of the different failure modes. Both the effect of internal pressure on axial buckling (elephant foot failure) as well as the flexibility of the base ring results in noteworthy reductions of the axial buckling resistance. Global stability effects turned out to play no major role in the present tank design.     

Overall stability considerations in the design of steel structures

Generally, the analyses used to determine the distribution of bending moments and internal forces in a structure are first-order analyses. Such analyses neglect the so-called P-Δ effects: (the effects produced by the vertical forces acting through the laterally deflected position of the structure). Thus, the stiffness and strength of the structure are overestimated.

The present design procedure recognizes this neglect: the structure is first classified as either sway prevented or sway permitted. For either case the forces and moments predicted by the first order analyses are translated into member sizes through the use of ‘interaction equations’. In the sway permitted condition, however, these equations are adjusted to require an increase in column size to attempt to account for the neglect of the P-Δ effects.

In the P-Δ method of design, the secondary forces, produced by the vertical loads acting through the laterally displaced shape of the structure, are included directly in the analysis. This approach removes the artificial distinction between a sway prevented and a sway permitted structure, which is implied by the present ‘K factor’ design approach to columns, and leads to a more rational technique for the design of columns and bracing systems.     

Response modification factor of elevated water tanks with reinforced concrete pedestal

A probabilistic method based on FEMA P695 is employed for validating the response modification factor of reinforced concrete pedestals in elevated water tanks. In the current codes and standards, the response modification factor of elevated water tanks is mainly based on engineering judgement. Ten models of elevated water tanks with different tank sizes and pedestal heights are selected for the investigation. Initially, the prototypes are designed based on the current codes and standards. Next, the finite element models of the prototypes are developed. By performing incremental dynamic analysis, the probability of collapse for each prototype is calculated under different seismic loading conditions and system uncertainties. The results of the study validate and confirm the current response modification factor values and show that the tank size has a significant effect on the nonlinear seismic response behaviour of elevated water tanks. In addition, it is revealed that heavy tank sizes that are designed in accordance with codes and guidelines are more vulnerable under seismic loading compared with light and medium tank sizes.     

Buckling of rings in column-supported bins and tanks

Theories for the out-of-plane buckling of rings under uniform circumferential compression are well established. However these theories are not applicable to rings in column-supported bins where the circumferential stress in the ring varies significantly over the cross-section and around the circumference.

This paper deals with the out-of-plane buckling of annular plate rings in column-supported bins and tanks. The stress distributions in such rings are first examined using a finite element shell analysis. A closed-form solution for the buckling of rings under non-uniform circumferential stresses is then derived. Numerical results from the closed-form solution are compared with those from a finite element shell buckling analysis, and close agreement is found. The significant effect of stress non-uniformity on the buckling predictions is demonstrated. Finally, simplified equations are given which are suitable for structural design purposes, and which closely model the predictions of the more rigorous solution.     

Application of evolutionary global optimization techniques in the design of RC water tanks

This paper presents evolutionary-based optimization procedures for designing conical reinforced concrete water tanks. The material cost of the tank that includes concrete, reinforcement, and formwork required for walls and floor was chosen as the objective function in the nonlinear optimization problem formulation. The wall thicknesses (at the bottom and at the top), base thickness, depth of water tank, and wall inclination were considered as design variables.Three advanced optimization techniques to solve the nonlinear constrained structural optimization problems were investigated. These methods are: (1) Shuffled Complex Evolution (SCE), (2) Simulated Annealing (SA) and Genetic Algorithm (GA). Several tests were performed to illustrate the robustness of these techniques and results were encouraging for SCE Method. The SCE method proved to be superior to the SA and GA methods in obtaining the best discovered solutions. The paper concludes that the robust search capability of SCE algorithm technique is well suited for solving the structural problem in hand.     

Seismic response of liquid-filled elevated tanks

The main focus of the current study is to evaluate the performance of elevated tanks under seismic loading. In this study, the finite element (FE) technique is used to investigate the seismic response of liquid-filled tanks. The fluid domain is modeled using displacement-based fluid elements. Both time history and modal analyses are performed on an elevated tank. Using the FE technique, impulsive and convective response components are obtained separately. Furthermore, the effect of tank wall flexibility and sloshing of the water free surface are accounted for in the FE analysis. In this study complexities associated with modeling of the conical shaped tanks are discussed. This study shows that the proposed finite element technique is capable of accounting for the fluid-structure interaction in liquid containing structures. Using this method, the study of liquid sloshing effects in tanks with complex geometries such as conical tanks is made possible. The results of this study show that the current practice predicts the response of elevated tanks with reasonable accuracy.     

Strength design criteria for steel members at elevated temperatures

Design equations for structural steel members at elevated (fire) temperatures are evaluated through comparisons with nonlinear finite element simulations. The study includes comparative analyses of the American Institute of Steel Construction (AISC) and European Committee for Standardization (CEN) design provisions for laterally unsupported I-shaped columns, beams, and beam-columns at temperatures between ambient to 800 ^°C. The Eurocode 3 provisions are shown to predict the simulated finite element results within about 10%-20%. On the other hand, the AISC specification predicts strengths that are up to twice as large (unconservative) as the simulated results. The discrepancies are largest for members of intermediate slenderness and temperatures above 300 ^°C. Modifications to the AISC equations are proposed that provide improved accuracy with calculated strengths typically within 20%-30% of the simulated results. Limitations of the member-based assessments and future research and development needs for structural fire engineering are discussed.     

A coupled finite element genetic algorithm technique for optimum design of steel conical tanks

Steel conical tanks having an upper cylindrical section and supported by a reinforced concrete shaft are widely used for water containment in elevated tanks. During the past few decades, a number of conical tanks have failed as a result of buckling of the steel vessel due to inadequate selection of the shell thickness. In the current study a powerful numerical tool that couples a non-linear finite element model and a genetic algorithm optimization technique is developed specifically for the analysis and design of steel conical tanks. The developed numerical tool is capable of selecting the set of design variables which satisfies the structure safety requirements while achieving a minimum structure weight and consequently minimum cost.     

Buckling of steel columns in fire conditions

A simple method for the design of steel columns in fire conditions is presented. The method adopts the European buckling curves for the design of axially loaded bare metal sections as the basic design curves for steel columns in fire conditions. The method has been compared with experimental results made recently in several European countries and the agreement is shown to be excellent and on the safe side.     

关于消防水箱设计的探讨

阐述了在自动喷水灭火临时高压给水系统中,如何确定消防水箱的设置高度,探讨了根据不同组合设置,如何合理可靠的设置消防水箱的补水与水位监视报警信号,以做好消防水箱的设计工作。     

A coupled finite element genetic algorithm for optimum design of stiffened liquid-filled steel conical tanks

In the current study an optimum design technique of stiffened liquid-filled steel conical tanks subjected to global and local buckling constraints is developed using a numerical tool that couples a non-linear finite element model developed in-house and a genetic algorithm optimization technique. This numerical tool is an extended version of an earlier one, adapted for the optimum design of unstiffened conical tanks. The design variables considered in the current study are the shell thicknesses, the geometry of the steel vessel as well as the dimensions and number of stiffeners. The developed numerical tool is capable of selecting the set of design variables that leads to optimum safe design. The analysis is conducted twice; first, case of stiffeners free at their bottom edge, which represents the case of retrofitting an existing tank. In the second case the stiffeners are assumed to be anchored to the bottom slab of the tank, which represents the situation of a newly designed tank. Finally, the optimum design of the stiffened tanks is compared to the optimum design of unstiffened tanks computed in a previous study.     

液化烃球罐水喷雾冷却系统的设计与计算

介绍了液化烃的性质及发生火灾的特点 ,对液化烃储罐火灾的危险性及水喷雾冷却、灭火机理进行了分析 ,列举了液化烃球罐水喷雾系统的设计计算实例 ,提出了设计中应注意的问题     

Buckling of compressed rectangular plates at non-uniformly elevated temperatures

A perturbation analysis of the influence of non-uniformly elevated temperatures upon the critical buckling loads of uniaxially compressed rectangular plates is presented. Within the framework of the uncoupled theory of thermal stresses a temperature dependence of the modulus of elasticity has been taken into consideration. In the special case of a simply supported square plate, the range of practical applicability of the resulting approximate formula has been checked by means of a variational finite-difference method.     

城市消防水池设计探讨

根据设计实践，探讨了城市消防水池的设计中应该注意的问题，并提出了建议。通过周密设计消防水池的选址、池型和池容，合理利用已有条件以减少池容、降低造价，以及发挥整体优势并合理设置消防水池等，能够实现消防水池的确保使用和经济设置。     

广州东圃桥高桩承台钢吊箱设计与施工

介绍了广州东圃特大桥高桩承台钢吊箱设计与施工，阐述了采用有底钢吊箱施工深水高桩承台的施工工艺，得出采用该技术实现了深水高桩承台的干作业施工，既保证了工程质量，又节省了时间和费用，有一定的经济、社会效益。