A Review of the Shell Buckling and Stiffener Ring Design for Cylindrical Steel Storage Tanks

2016 ◽  
Author(s):  
Eyas Azzuni ◽  
Sukru Guzey
Keyword(s):  
Circumferential Stress ◽  
Local Buckling ◽  
Design Procedure ◽  
Wind Load ◽  
External Pressure ◽  
Storage Tanks ◽  
Design Standards ◽  
Buckling Mode ◽  
Load Pressure ◽  
Cylindrical Steel

Cylindrical steel storage tanks are shells designed to store different types of products such as liquids or grain. The thickness of the shell is calculated to withstand the circumferential stress resulting from the hydrostatic pressure due to the stored product. A unique situation when there is no stored product leads to the vulnerability of the shell to buckle when there is wind load due to external pressure. There are two major types of buckling modes: local and general. The local buckling mode is studied analytically in various studies and is easy to mitigate. The general buckling mode can be more damaging to the tank and more costly to mitigate. The prevention of general buckling due to wind load pressure is achieved through the addition of stiffener rings. However, the stiffener rings design procedure used by various design standards has little known background. This paper reviews the current design approach’s origin and explains a semi-analytical justification for it. The unfolding of the design expressions can lead to more freedom in design variables selection leading to more economical designs.

Design of Cylindrical Steel Storage Tanks: A Linear Elastic Analysis Approach

2016 ◽  
Author(s):  
Eyas Azzuni ◽  
Sukru Guzey
Keyword(s):  
Hydrostatic Pressure ◽  
Circumferential Stress ◽  
Liquid Product ◽  
Analysis Approach ◽  
Storage Tanks ◽  
Bottom Edge ◽  
Linear Elastic ◽  
Cylindrical Steel ◽  
The One ◽  
Thin Shell Theory

A cylindrical steel storage tank is a cylindrical shell subjected to internal hydrostatic pressure due to the stored liquid product. The hydrostatic pressure causes the shell to experience circumferential stress. This circumferential stress can lead to the yielding of the shell if its thickness is not designed properly. The design of step-walled steel storage tanks requires the calculation of the required thickness of each shell course. A conservative way of calculating each course’s thickness is using the one-foot method (1FM). This method calculates the required thickness to withstand the hydrostatic pressure one foot above the bottom edge of the shell course under consideration. Another method, which is more refined than the 1FM, is the variable-design-point method (VDM), which finds the point in the course where the maximum circumferential stress is. VDM calculates the required shell thickness to withstand that maximum circumferential stress. However, VDM does not capture the circumferential stress resulting from the bottom edge yielding moment accurately for some thank geometries. A new linear analysis approach using thin-shell theory is presented in this paper. The approach captures the plastic yielding moment of the bottom edge accurately, and may produce more economical and safe designs than 1FM and VDM.

Design of cylindrical steel liquid tanks with stepped walls using One-foot method

2021 ◽  
Vol 7 (4) ◽  
pp. 162
Author(s):  
Özer Zeybek
Keyword(s):  
Wall Thickness ◽  
Calculation Method ◽  
External Pressure ◽  
Thin Wall ◽  
Buckling Mode ◽  
Equivalent Thickness ◽  
Steel Tanks ◽  
Uniform Wall ◽  
Hand Calculation ◽  
Cylindrical Steel

Cylindrical steel tanks are used in most countries to store bulk volumes of both solid and liquid products such as water, oil, gasoline and grain. Such steel tanks are prone to buckling when subjected to external pressure either due to vacuum or due to wind. These types of shell structures are generally controlled by elastic buckling failure because of the thin wall thickness. Cylindrical shells are commonly constructed with stepwise variable wall thickness due to economic reasons. The thickness of the tank shell wall is designed to increase from top to bottom because the stress resultants on the tank wall gradually increase towards the base of the tank. For open-top tanks, a primary stiffening ring is required at or near the top to maintain roundness under all loads. Stress resultants in a primary stiffening ring were previously identified by the Author for uniform wall thick tanks. In this new study, the applicability of this hand calculation method in stepped wall tanks has been investigated. Pursuant to this goal, a specified tank shell was designed considering One-foot method. Then, the stepped wall tank was transformed into an equivalent 1-course tank for hand calculation. Using the previously developed hand calculation method by Author, a test for the in-plane bending moment in the ring was conducted to achieve an acceptable value for stepped wall tanks. The analysis results show that the previously proposed method for uniform wall thick tanks may also be used for stepped wall tanks considering an equivalent thickness. On the other hand, using Linear Buckling Analysis (LBA), the buckling mode was obtained for two different stepped wall tanks in the study.

ELASTIC BUCKLING OF THIN-WALLED CIRCULAR TUBES CONTAINING AN ELASTIC INFILL

2006 ◽  
Vol 06 (04) ◽  
pp. 457-474 ◽  
Author(s):  
M. A. BRADFORD ◽  
A. ROUFEGARINEJAD ◽  
Z. VRCELJ
Keyword(s):  
Axial Compression ◽  
A Priori ◽  
Local Buckling ◽  
Steel Tube ◽  
Transcendental Equation ◽  
Buckling Mode ◽  
Buckling Stress ◽  
Elastic Tubes ◽  
Thin Walled ◽  
Energy Formulation

Circular thin-walled elastic tubes under concentric axial loading usually fail by shell buckling, and in practical design procedures the buckling load can be determined by modifying the local buckling stress to account empirically for the imperfection sensitive response that is typical in Donnell shell theory. While the local buckling stress of a hollow thin-walled tube under concentric axial compression has a solution in closed form, that of a thin-walled circular tube with an elastic infill, which restrains the local buckling mode, has received far less attention. This paper addresses the local buckling of a tubular member subjected to axial compression, and formulates an energy-based technique for determining the local buckling stress as a function of the stiffness of the elastic infill by recourse to a transcendental equation. This simple energy formulation, with one degree of buckling freedom, shows that the elastic local buckling stress increases from 1 to [Formula: see text] times that of a hollow tube as the stiffness of the elastic infill increases from zero to infinity; the latter case being typical of that of a concrete-filled steel tube. The energy formulation is then recast into a multi-degree of freedom matrix stiffness format, in which the function for the buckling mode is a Fourier representation satisfying, a priori, the necessary kinematic condition that the buckling deformation vanishes at the point where it enters the elastic medium. The solution is shown to converge rapidly, and demonstrates that the simple transcendental formulation provides a sufficiently accurate representation of the buckling problem.

scholarly journals Rational Modeling of Ultimate Pipe Strength Under Bending and External Pressure

2000 ◽  
Author(s):  
André C. Nogueira ◽  
Glenn A. Lanan
Keyword(s):  
Deep Water ◽  
Limit State ◽  
Local Buckling ◽  
External Pressure ◽  
Pressure Effects ◽  
Combined Loading ◽  
Empirical Prediction ◽  
Limit State Design ◽  
Controlled Conditions ◽  
Offshore Pipeline

The capacity of pipelines to resist collapse or local buckling under a combination of external pressure and bending moment is a major aspect of offshore pipeline design. The importance of this loading combination increases as oil and gas projects in ultra deep-water, beyond 2,000-m water depths, are becoming reality. The industry is now accepting, and codes are explicitly incorporating, limit state design concepts such as the distinction between load controlled and displacement controlled conditions. Thus, deep-water pipeline installation and limit state design procedures are increasing the need to understand fundamental principles of offshore pipeline performance. Design codes, such as API 1111 (1999) or DNV (1996, 2000), present equations that quantify pipeline capacities under combined loading in offshore pipelines. However, these equations are based on empirical data fitting, with or without reliability considerations. Palmer (1994) pointed out that “it is surprising to discover that theoretical prediction [of tubular members under combined loading] has lagged behind empirical prediction, and that many of the formula have no real theoretical backup beyond dimensional analysis.” This paper addresses the ultimate strength of pipelines under combined bending and external pressure, especially for diameter-to-thickness ratios, D/t, less than 40, which are typically used for deep water applications. The model is original and has a rational basis. It includes considerations of ovalization, anisotropy (such as those caused by the UOE pipe fabrication process), load controlled, and displaced controlled conditions. First, plastic analysis is reviewed, then pipe local buckling under pure bending is analyzed and used to develop the strength model. Load controlled and displacement controlled conditions are a natural consequence of the formulation, as well as cross section ovalization. Secondly, external pressure effects are addressed. Model predictions compare very favorably to experimental collapse test results.

Elastic analysis of exponential FGM disks subjected to internal and external pressure

2013 ◽  
Vol 3 (3) ◽  
Author(s):  
Mohammad Nejad ◽  
Majid Abedi ◽  
Mohammad Lotfian ◽  
Mehdi Ghannad
Keyword(s):  
Radial Direction ◽  
Circumferential Stress ◽  
External Pressure ◽  
Functionally Graded ◽  
Elastic Analysis ◽  
The Finite Element Method ◽  
Graded Materials ◽  
Material Inhomogeneity ◽  
Closed Form Analytical Solution ◽  
Stress Profiles

AbstractAssuming exponential varying properties in the radial direction and constant Poisson’s ratio, a closed-form analytical solution based on the elasticity theory is obtained to elastic analysis of disks made of functionally graded materials (FGMs) subjected to internal and external pressure. Following this, radial displacement, radial stress, and circumferential stress profiles are plotted for different values of material inhomogeneity constant, as a function of radial direction. The displacements and stresses distributions are compared with the solutions of the finite element method (FEM) and comparison with the corresponding numerical solution indicates that the proposed solution has excellent convergence and accuracy.

Buckling of Thin-Walled Long Steel Cylinders Subjected to Bending

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Sotiria Houliara ◽  
Spyros A. Karamanos
Keyword(s):  
Structural Response ◽  
Cylinder Wall ◽  
Imperfection Sensitivity ◽  
Bifurcation Instability ◽  
Buckling Mode ◽  
Cross Sectional ◽  
Moment Capacity ◽  
Thin Walled ◽  
Cylindrical Steel ◽  
Element Technique

The present paper investigates structural response and buckling of long unstiffened thin-walled cylindrical steel shells, subjected to bending moments, with particular emphasis on stability design. The cylinder response is characterized by cross-sectional ovalization, followed by buckling (bifurcation instability), which occurs on the compression side of the cylinder wall. Using a nonlinear finite element technique, the bifurcation moment is calculated, the post-buckling response is determined, and the imperfection sensitivity with respect to the governing buckling mode is examined. The results show that the buckling moment capacity is affected by cross-sectional ovalization. It is also shown that buckling of bent elastic long cylinders can be described quite accurately through a simple analytical model that considers the ovalized prebuckling configuration and results in very useful closed-form expressions. Using this analytical solution, the incorporation of the ovalization effects in the design of thin-walled cylinders under bending is thoroughly examined and discussed, considering the framework of the provisions of the new European Standard EN1993-1-6.

Ruga mechanics of soft-orifice closure under external pressure

2021 ◽  
Vol 477 (2249) ◽  
Author(s):  
Hanxun Jin ◽  
Alexander K. Landauer ◽  
Kyung-Suk Kim
Keyword(s):  
Surface Layer ◽  
Limit Load ◽  
Phase Evolution ◽  
External Pressure ◽  
Soft Material ◽  
Buckling Mode ◽  
Cross Sectional ◽  
Threefold Symmetry ◽  
Instability Modes ◽  
Symmetry Mode

Here, we report the closure resistance of a soft-material bilayer orifice increases against external pressure, along with ruga-phase evolution, in contrast to the conventional predictions of the matrix-free cylindrical-shell buckling pressure. Experiments demonstrate that the generic soft-material orifice creases in a threefold symmetry at a limit-load pressure of p / μ  ≈ 1.20, where μ is the shear modulus. Once the creasing initiates, the triple crease wings gradually grow as the pressure increases until the orifice completely closes at p / μ  ≈ 3.0. By contrast, a stiff-surface bilayer orifice initially wrinkles with a multifold symmetry mode and subsequently develops ruga-phase evolution, progressively reducing the orifice cross-sectional area as pressure increases. The buckling-initiation mode is determined by the layer's thickness and stiffness, and the pressure by two types of the layer's instability modes—the surface-layer-wrinkling mode for a compliant and the ring-buckling mode for a stiff layer. The ring-buckling mode tends to set the twofold symmetry for the entire post-buckling closure process, while the high-frequency surface-layer-wrinkling mode evolves with successive symmetry breaking to a final closure configuration of two- or threefold symmetry. Finally, we found that the threefold symmetry mode for the entire closure process provides the orifice's strongest closure resistance, and human saphenous veins remarkably follow this threefold symmetry ruga evolution pathway.

Evaluating Large Aboveground Storage Tanks Subject to Seismic Loading: Part I — Closed-Form Solutions and Equivalent Static Analysis

2018 ◽  
Author(s):  
Phillip E. Prueter ◽  
Seetha Ramudu Kummari
Keyword(s):  
Closed Form ◽  
Static Analysis ◽  
Storage Tank ◽  
Fluid Structure Interaction ◽  
Seismic Loading ◽  
Storage Tanks ◽  
Design Standards ◽  
Closed Form Solutions ◽  
Structure Interaction ◽  
Explicit Dynamic

Evaluating the dynamic response of large, aboveground storage tanks exposed to seismic loading is multifaceted. There are foundation-structure and fluid-structure interaction effects that can influence the overall tank behavior and likely failure modes. Additionally, local stresses at anchor bolt support chair attachments and the shell-to-floor junction can be difficult to quantify without detailed finite element analysis (FEA). Often times, performing explicit dynamic analysis with liquid sloshing effects can be time consuming, expensive, and even impractical. The intent of this paper is to summarize simplified analysis techniques that can be leveraged to evaluate aboveground storage tanks subject to seismic loading. Closed-form calculations to establish a recommended design for a tank, including seismic considerations, are available in storage tank design standards, including API 650 [1] (Appendix E). Seismic design standards have evolved significantly in recent years. Furthermore, for many vintage, in-service storage tanks, explicit seismic considerations were not incorporated into the original design. In Part I of this study, these design equations and other closed-form solutions are used to evaluate the structural integrity of a large, in-service, mechanically-anchored storage tank. The design equations in API 650 [1] are used to form the basis of simplified, equivalent static analysis, where seismic loads are applied to a three-dimensional FEA model via equivalent lateral body forces. These practical results are then compared to explicit dynamic seismic behavior of the same tank with fluid-structure interaction effects considered (in Part II of this study [2]). These comparisons offer insight into the appropriateness of using simplified hand-calculations and equivalent static analysis (and their relative conservatism) in lieu of more rigorous explicit dynamic and fluid sloshing simulations.

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