Discrete Models for Seismic Analysis of Liquid Storage Tanks of Arbitrary Shape and Fill Height (original) (raw)
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SEISMIC ANALYSIS OF LIQUID STORAGE TANK
2011
Liquid storage tanks are commonly used for storing chemicals in various Industrial plants. They also find application in various power plants for storing oil, water for various requirements. Experience shows that the under seismic loads storage tanks undergo damage which will lead to leaking of the tank’s contents. This analysis aims at studying the deformation behavior of a typical liquid storage tank under seismic loads by accounting fluid structure interaction effects. Modal analysis is performed to arrive at the fundamental frequency of sloshing and combined frequencies of liquid and steel tank. This paper aims to developing a complete three dimensional modeling of liquid tank including fluid structure interaction. A 3-dimensional finite element model is built using fluid and shell elements. Bottom of the steel tank is fixed at bolt positions. Liquid element nodes are allowed to move freely in vertical direction where as nodes on the periphery are attached to steel tank so that relative radial movement is constrained. Modal analysis is done on complete three dimensional models and Sloshing frequency is found. The comparison shows that analytical estimation sloshing frequency matches with the 3-d analysis. A full time history analysis is performed to find deformation behavior of the tank. Time response of forces and moments at critical locations is reported. Deformation behavior of the tank is obtained successfully.
Simple Procedure for Seismic Analysis of Liquid-Storage Tanks
Structural Engineering International, 2000
This paper provides the theoretical background of a simplified seismic design procedure for cylindrical ground-supported tanks. The procedure takes into account impulsive and convective (sloshing) actions of the liquid in flexible steel or concrete tanks fixed to rigid foundations. Seismic responses-base shear, overturning moment, and sloshing wave height-are calculated by using the site response spectra and performing a few simple calculations. An example is presented to illustrate the procedure, and a comparison is made with the detailed modal analysis procedure. The simplified procedure has been adopted in Eurocode 8. Fig. 1: Elephant-foot buckling of a tank wall (courtesy
Seismic analysis of cylindrical liquid storage tanks
Computers & Structures, 1989
This paper summarizes the results of a comprehensive analytical investigation concerning the seismic analysis of ground supported, circular cylindrical liquid storage tanks subject to a horizontal component of earthquake ground motion. A procedure to evahrate the dynamic seismic response of a wide range of cylindrical liquid storage tanks is developed. The procedure, which is applicable to tanks both completely full and partially full with liquid, has been incorporated into a BASIC computer program. Several numerical examples are presented which illustrate application of the procedure and verify its NOTATION frequency constant (5252 ft/sec) diameter of a cylindrical tank Young's modulus Young's modulus for steel (34000 ksi) height of a cylindrical tank equivalent stiffness of flexible shell and stationary fluid mass spring stiffness of liquid mass participating in first sloshing mode shell membrane stress resultants convective hydrodynamic base shear impulsive hydropic base shear maximum pseudo spectral acceleration spectral acceleration of fundamental sloshing fluid mass maximum spectral displacement spectra1 displa~ent of fund~en~l s~o~in3 fluid mass radius of cylindrical shell rn~irn~ water surface displa~ment natural frequency, cycles/set nondimensional frequency function acceleration of gravity shell wall thickness height of liquid in tank height to stationary fluid mass, q,, measured from the base of the tank height to fundamental sloshing fluid mass, m,, measured from the base of the tank distance measured from the free surface of the liquid to the location of the stationary fluid mass, m, distance measured from the free surface of the liquid to the location of the sloshing fluid mass ~~ci~ting in the first mode of vibration, m, axial wave number total mass of fluid in tank stationary liquid mass mass of liquid participating in the first sloshing
Free Surface Sloshing Effect on Dynamic Response of Rectangular Storage Tanks
2012
Dynamic analysis of liquid storage tanks is one of interesting subjects in the earthquake engineering. In the present paper, the staggered displacement method is utilized for analysing concrete storage tanks. In the proposed method, surface sloshing of the liquid do main is considered in addition to the effect of impulsive component of the liquid on the structure response. Also, different damp ing coefficients are applied on the various co mponents of the liquid. Foundation is assumed to be rig id and an artificial dynamic load as well as a real ground mot ion record are used to analyse the tank-liquid coupled system in t ime domain. The resulted response is co mpared with those obtained from the co mmercial software. It is found that the convective term affects responses extensively and must be considered in seismic safety analysis of storage tanks.
Analysis of Seismic Sloshing Displacements in Rectangular Liquid Storage Tanks with SPH Method
Afyon Kocatepe University Journal of Sciences and Engineering, 2018
Bu çalışmada, yatay yönde yer sarsıntısına maruz kalan prizmatik bir tankta gerçekleşen çalkalanma modellemesi düzgünleştirilmiş parçacık hidrodinamiği yöntemiyle (SPH) gerçekleştirilmiştir. SPH yöntemi sonuçları bir deney ve ANSYS Fluent modeli sonuçlarıyla doğrulanmıştır. Deneyden ve Fluent modeliyle elde edilen çalkalanma profilleri burada ele alınan SPH yöntemi sonucuyla müthiş bir uyumluluk göstermektedir. Bu çalışma irdelenen SPH yöntemi, süreksizlikleri yakalama ve hareketli sınırları ele almada oldukça etkilidir.
Seismic Sloshing in a Horizontal Liquid Storage Tank
Structural Engineering International, 2014
A horizontal water storage tank was analyzed for seismic shaking at the ITER Tokamak Complex in France. The objectives were to (a) estimate the seismic forces in the tank; (b) calculate the sloshing response of the tank; (c) determine if baffles are needed to control sloshing; and (d) evaluate the possibility of using a single fixed support in the longitudinal direction to allow free thermal expansion of the tank. An approximate conservative analysis predicted very high sloshing waves and seismic forces in the tank. The fluid-structure interaction in the tank showed that only about 28% of the liquid moves with the tank wall and generates seismic forces in the longitudinal direction. The remaining 72% of the liquid sloshes near the free surface and does not generate significant seismic forces. The sloshing wave is not high enough in the longitudinal direction as the fundamental sloshing mode is not excited because of its very low natural frequency. Hence, baffles are not needed to control sloshing. The seismic force is low enough for a single fixed support to resist the entire seismic force in the longitudinal direction.
Effect of Earthquake Frequency Content on 3D Sloshing in Rectangular Tanks
2019
Available online at: www.jseeonline.com Earthquake frequency content has a significant effect on sloshing wave amplitude and height in liquid storage tanks. In this paper, the finite element method had been used to obtain the three dimensional fluid-structure interaction response of the rectangular tanks to access the sloshing interference effects at the tank corners under various seismic input motions with different frequency contents. The flexibility of the tank wall as well as the structural and fluid damping have been taken into account to obtain more reliable and realistic results. It has also been shown that the 3D sloshing interference may increase the total wave height significantly at the corners of the tanks compared to the values presented in the design codes, which shows the maximum sloshing wave with much lower values and at a different location. It has been finally shown that the 3D sloshing effects relates to the ratio of the width and the length of the tank. Effect o...
On the seismic behaviour and design of liquid storage tanks
2011
The paper examines some special issues on the structural behaviour of uprightcylindrical liquid storage tanks, which are widely used in industrial facilities and for water storage. Two main design standards are considered: EN 1998-4, a relatively new standard, and Appendix E of API 650, which has been through substantial amendments and revisions in its new version (11 th edition, 2007). There are significant differences between the two specifications, which are due to the fact that there exist several controversial issues on this subject, open to further research. These issues are (a) the number of modes necessary to estimate accurately the convective seismic force due to the hydrodynamic behaviour of the liquid containment; (b) the appropriate combination of the impulsive and the convective component of seismic force; (c) the uplifting behaviour of unanchored tanks, with emphasis on the base plate behaviour and the increase of meridional compression; (d) the choice of an appropriat...
Acta Physica Polonica A, 2019
Accurate prediction of the vibration characteristics of the sloshing motion is essential for the analysis and design of liquid storage tanks subjected to base motion. The virtual mass method is a computationally efficient approach to determine the hydrodynamic forces generated by incompressible and inviscid fluids in accelerated containers since the virtual mass method involves meshing of the fluid boundaries rather than the entire fluid domain. Hydrodynamic actions of the sloshing liquid are taken into consideration by coupling a virtual fluid mass matrix to the structural points on the wetted regions of the tank wall. Analysis of the free surface displacements of the contained liquid can be carried out using the virtual mass method and this paper focuses on the application of the virtual mass method for the analysis of the vibration frequencies and mode shapes of the sloshing modes in rectangular and cylindrical liquid storage tanks. Firstly, the theoretical background for the analytical solution of the mode shapes and modal frequencies is presented for rectangular and cylindrical liquid tanks. This is followed by the description of the procedure used to apply the virtual mass method to obtain the sloshing modes and mode shapes of the contained liquid. The effects of various surface mesh topologies on the predicted vibration characteristics are compared with the analytical solutions as well as the results of an experimental study conducted on scaled rectangular and cylindrical containers mounted on a shake table.
Evaluation of Code Provisions for Seismic Performance of Unachored Liquid Storage Tanks
Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2015)
Seismic performance of two unanchored liquid-storage tanks with tank diameter of 24.5 m and 36 m and operating liquid height of 12.2 m and 20.0 m, respectively were investigated using Coupled Eulerian-Lagrangian (CEL) and mechanical spring-mass analogy nonlinear finite element computational methods. The CEL approach includes the effects of higher modes of liquid vibration (sloshing), liquid breaking effects, and liquid-structure interaction during seismic loading. The modern seismic design provisions for liquid-storage tanks, on the other hand, are based on a mechanical spring-mass analogy. This approach neglects the higher vibration modes for the sloshing water, liquid-structure interaction, and effects of tank base uplift on seismic performance. For the tanks, base uplift histories were computed with both modeling approaches through nonlinear time history analysis performed using five recorded earthquake acceleration data. The uplift histories were compared to evaluate the adequacy of code seismic design provisions for unanchored tanks, and to determine whether the mechanical spring-mass analogy can be used to predict seismic performance of unanchored tanks. Analysis results show that the traditional mechanical spring-mass analogy, which is the basis for the current seismic design provisions, does not capture tank uplift history and its effects on dynamic loads. This approach underpredicts the total numbers of tank uplifts during seismic loading. The maximum tank base uplift computed using mechanical spring-mass analogy had an average error between 22% and 58 % for each tank. The results show that there is a need to developed a modify version of the traditional mechanical spring-mass analogy to be used for predicting seismic performance of unanchored liquid-storage tanks.