When an earthquake hits, a part of the bottom plate of the flat-bottom cylindrical tank which has no anchor device, or anchor rigidity of which is week, will be lifted up from the foundation due to overturning moment. As a result, the axial compressive force of shell bottom course will increase and such a damage of shell plate as “Elephant Foot Bulge” will be caused.
In this report, an effective method is developed in order to calculate quantitatively the rate of increase in the axial compressive force of shell plate as the ratio “C_A” of the compressive force calculated in case of considering the uplift of opposite side bottom plate to that in neglecting the uplift. And the characteristics of main factors which have influence on “C_A” are examined in the calculation example for a fullscale tank.
Firstly, a static rocking analysis model for calculating “C_A” is shown, in which the rigidity in the vertical direction of anchor and foundation right below shell plate is replaced with the springs of elasticperfectly plastic type, and the uplift resistance force due to the liquid pressure on the uplifted part of bottom plate is considered to act on the lower edge of shell plate. The axial compressive force of shell bottom course in tilt side can be obtained with the equilibrium equations concerning the overturning moment and the vertical forces, such as anchor reaction force, foundation reaction force, uplift resistance force and tank self weight.
Secondly, from the comparison between this model calculation and the static tilt test of a thin bottom plate model tank which has 2, 034mm in diameter, it is shown that the calculation results are good agreement with the test results.
Last, the characteristics of main factors having influence on “C_A” are examined by parametric studies for a 75, 000m³ LNG storage tank. From these studies, it is clarified that; As the seismic loading becomes larger, the value of “C_A” increases. The less the rigidity of anchor becomes and/or the more that of foundation right below shell plate becomes, the higher the value of “C_A” grows. In the calculation example for the 75, 000m³ LNG storage tank which is designed with current seismic design code in Japan, the change rate of “C_A” is small within the range of the seismic loading usually applied with design code, and the absolute value of “C_A” nearly equals that of the case in which the uplift of bottom plate is disregarded.

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Floating roofs are used in large cylindrical storage tanks to prevent evaporation of oil. The single-deck floating roof considered herein consists of a thin circular plate, referred to as a ”deck”, attached to a buoyant ring with a hollow rectangular cross section referred to as a ”pontoon”. The deck plate is deformed to be created waves and is subjected to cyclic bending due to the wind load. Since this leads to the initiation of fatigue cracks at the welded joints, it is important to understand the wave characteristics in the deck plate. The authors reported a computational fluid dynamics (CFD) analysis and a sloshing response analysis of a cylindrical storage tank with the single-deck floating roof under a wind load in three another papers. In this paper, the vibration characteristics of the wave in the deck plates is described according to the previous three papers.

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Floating roofs are used in large cylindrical storage tanks to prevent evaporation of oil. The floating roof is said to vibrate in high winds like undulation of the sea surface. The wind induced, sea-surface-undulation-like vibration may initiate fatigue cracks at welded joints in the floating roof deck. In this two-part study, the authors attempted to simulate the vibration. At first, wind flow over an isolated cylindrical oil-storage tank was simulated without considering the motion of the roof. Computed unsteady pressure load data were transferred to structural analyses. Response analyses of the floating roof under the wind load are dealt with in another paper. The present paper describes the wind flow simulation. The computed pressure fluctuation over the roof exhibits broadband spectra and no remarkable dominant frequency. To gain some insights into characteristics of the roof pressure fluctuation and its association with global flow structures, the Snapshot Proper Orthogonal Decomposition (POD), the Dynamic Mode Decomposition (DMD), and the Complex POD were applied.

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It is very important in safety design of oil storage tanks to prevent their bottom plates from corrosion and to ensure them against earthquake damage. When a violent earthquake occurs, a part of the shell plate of unanchored cylindrical oil storage tanks will be lifted from their foundations due to overturning moment, and local strain of annular bottom plate near the shell to annular joint will increase. As the result, damage such as cracks of coating material on annular plate may be caused. This paper deals the uplift behavior of tanks due to earthquake.
In order to evaluate quantitatively the uplift displacement of shell lower edge of 110000m³ oil storage tanks by earthquakes, nonlinear time history analyses were carried out by using mechanical model of mass-spring system, where non-linearity associated with the partial uplift of shell plate is considered as rotational spring of a bilinear type. The analytical results show that EW direction wave of “Far off Sanriku earthquake (1994)” (with maximum acceleration 293gal) causes the maximum uplift about 5cm at shell lower edge. The critical value of shell uplift prescribed in evaluation of “existing horizontal load bearing capacity” of tanks by current Fire Service Law is regarded as about 21cm. Therefore the calculated uplift value of 5cm is lower than the critical value.

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The floating roofs are used in large cylindrical storage tanks to prevent evaporation of oil. The single-deck floating roof, considered herein, consists of a thin circular plate called “deck” attached to a buoyant ring of box-shaped cross section called “pontoon”. The deck plates are deformed to creat waves and they are subjected to cyclic bending due to wind load. This may lead to initiate fatigue cracks at the welded joints. It is important to know the characteristics of waves in the deck plate. The authors have reported the CFD analysis of a cylindrical storage tank due to uniform wind in another paper. This paper presents the axisymmetric finite element analysis for the sloshing response of the single-deck floating roofs in a cylindrical storage tank using the CFD results as the load condition. It is assumed that the liquid is incompressible and inviscid, and the roof is linear elastic while the sidewall and the bottom are rigid. The basic wave characteristics of the deck plate, such as frequency and amplitude, is investigated.

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The shell-to-bottom joint of unanchored oil storage tank will uplift due to overturning moment applied to the tank against strong horizontal seismic excitation, and excessive plastic strain cyclically occurs in this joint. Three large tanks spilled their contents over the port due to the failure caused by uplifting force applied to the tank shell in the 1978 Miyagiken-oki earthquake. This paper presents the systematic evaluation for structural integrity of a large-sized oil storage tank against strong earthquake. In the first method of this study, the nonlinear seismic response analysis taking the uplifting force applied to the tank shell into consideration is carried out, and useful information on the relation between the seismic character and the uplift displacement is derived. The second method is the elastic-plastic, large displcement finite element stress analysis of the shell-to-bottom joint under uplifting load. The relation between the peak strain at the toe of fillet weld of this joint and the seismic character is obtained from the 1st and 2nd method. Crack initiation and crack propagation behavior under cyclic bending load is investigated on the speciments with fillet weld joint by the experimental test for low cycle fatigue. The relation between the peak strain and the fatigue life at the toe of fillet weld of this joint is finally obtained. Consequently, the tank's integrity can be evaluated on the viewpoint of the seismic character, the uplift displacement of the shell-to-bottom joint, the peak strain and the fatigue life at the toe of weld of this joint.

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In order to examine the surface strain at crack initiation of coating material on annular plates of oil storage tank, the authers experimented with model specimens of coated steel plate. Five kinds of vinyl-ester resion system (C₁ to C₅) including glass flakes were tested as coating materials. The strain on steel plate surface corresponding to coating crack initiation strain of specimen C₃ was about 0.54%, and those of other specimens were more than 0.7%. Maximum peak strain on inner surface of annular plate calculated from the non-linear time history analysis results against the seismic wave of “Sanriku far offshore earthquake (1994)” was about 0.69%. These results show that cracks of coating material on annular plates may occur in case of C₃ by this level earthquake.

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The floating roofs are widely used to prevent evaporation of content in the large oil storage tanks. The 2003 Tokachi-Oki Earthquake caused severe damage to the floating roofs due to liquid sloshing. This accident becomes a cause and the structural integrity of the floating roofs for the sloshing has been actively studied. This paper presents the axisymmetric finite element analysis for the sloshing response of floating roofs in cylindrical storage tanks. The hydrodynamic coupling of fluid and floating roof under seismic excitation is taken into consideration in the analysis. It is assumed that the fluid is compressive and inviscid, and the roof is linear elastic while the sidewall and the bottom are rigid. The fluid behavior is formulated in terms of displacement as the Lagrangian approach. In order to remove the spurious modes, the free vibration analysis is carried out. The highly precise response solutions are given if the effective modes are only taken into consideration in the modal composition.

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Steel liner on inner surface of prestressed concrete (PC) cylindrical vessel may buckle by compressive deformation of the concrete which is caused at the construction stage as the steel liner is fitted on the concrete guard dike with anchors. The inside pressure on such a buckled plate will press it to PC vessel, and may make it into the unbuckled state under some condition.
In this report, the authors present the calculation method of the behavior of the buckled plate under pressure, and the results of numerical calculations for typical patterns.
As the result, the behavior of the buckled plate was clarified including the critical point when the whole plate touches entirely to the vessel in an unstable manner.

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