Nonlinear behaviour of bottom plate in cylindrical liquid storage tanks for seismic applications

The paper presents a simplified pseudostatic approach to model the nonlinear behaviour of the bottom plate in unanchored cylindrical liquid storage tanks for seismic applications. In this paper, the problem of axisymmetric uplift of the bottom plate is studied for tanks supported on both rigid and elastic Winkler foundations. In the analysis, the bottom plate is modelled by one-dimensional beam and two-dimensional plate models. By comparing the results, it is found that the one-dimensional beam model gives accurate results acceptable for all practical design purposes, in view of the many other uncertainties in the tank uplift problem. The analysis results also show that the support foundation flexibility may have significant effects on the uplift behaviour of the tanks. Based on the axisymmetric uplift results, the paper then presents a simple approach to model the seismic partial uplift problem of unanchored tanks by means of nonlinear springs. Modelling parameters for the nonlinear springs are generated for dynamic uplift response analysis. Sensitivities of the uplift behaviour and the nonlinear spring modelling parameters to the tank height-to-radius ratio and the soil stiffness are also studied. Key words: axisymmetric uplift, cylindrical tanks, earthquakes, pressure vessel, shell, soil effect.

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Simplified Model for the Seismic Performance of Unanchored Liquid Storage Tanks

Volume 5: High-Pressure Technology; Rudy Scavuzzo Student Paper Competition and 23rd Annual Student Paper Competition; ASME NDE Division ◽

10.1115/pvp2015-45695 ◽

2015 ◽

Cited By ~ 4

Author(s):

Maria Vathi ◽

Spyros A. Karamanos

Keyword(s):

Bottom Plate ◽

Storage Tanks ◽

Mass System ◽

Aspect Ratios ◽

Liquid Storage ◽

Stress And Deformation ◽

Cylindrical Tanks ◽

Welded Connection ◽

Simplified Modeling ◽

Different Levels

Ground-supported unanchored liquid-storage cylindrical tanks, when subjected to strong seismic loading may exhibit uplifting of their bottom plate, which has significant effects on their dynamic behavior and strength. Those effects mainly concern: (a) the increase of axial (meridional) compression at the tank base, resulting in premature buckling in the form of elephant’s foot and (b) the significant plastic deformation at the vicinity of the welded connection between the tank shell and the bottom plate that may cause failure of the welded connection due to fracture and fatigue. The present study focuses on base uplifting mechanics and tank performance with respect to the shell/plate welded connection through a numerical two-step methodology: (1) a detailed finite element shell model of the tank for incremental static analysis, capable of describing the state of stress and deformation at different levels of loading and (2) a simplified modeling of the tank as a spring-mass system for dynamic analysis, enhanced by a nonlinear spring at its base to account for the effects of uplifting. Two cylindrical liquid storage tanks of different aspect ratios are modeled and analyzed in terms of local performance of the welded connection. The results are aimed at better understanding of tank uplifting mechanics and motivating possible amendments in existing seismic design provisions.

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Experimental and Numerical Investigations on Nozzle Reinforcements

Volume 8: Seismic Engineering ◽

10.1115/pvp2013-97430 ◽

2013 ◽

Cited By ~ 4

Author(s):

Matthias Wieschollek ◽

Benno Hoffmeister ◽

Markus Feldmann

Keyword(s):

Failure Modes ◽

Low Cycle Fatigue ◽

Experimental Tests ◽

Transverse Load ◽

Bottom Plate ◽

Storage Tanks ◽

Seismic Behaviour ◽

Numerical Investigations ◽

Liquid Storage ◽

Full Scale Tests

Pipes and nozzles attached to large liquid storage tanks can be susceptible to earthquake induced damages. Adequate design and detailing of shell nozzle reinforcements significantly improves their seismic performance. Damages to nozzles, often combined with elephant-foot-buckling, belong to the most frequent failure modes of large liquid storage tanks caused by earthquakes. The failure consequences depend very much on the liquid contents which may be hazardous; prevention of leakage is a crucial design and verification criteria. European and American standards provide detailed recommendations for structural dimensioning and detailing of shell nozzle reinforcements, however no reliable statements can be made to their seismic behaviour. This paper describes the results of six experimental tests on three typical types of shell nozzle reinforcements. These full scale tests were carried out in the range of ultra-low cycle fatigue for longitudinal and transverse load directions as they can be expected under seismic actions. Based on the evaluation of the test results appropriate FE-models were derived by which parametrical numerical investigations were conducted. Through these studies the influence of different parameters (e.g. thickness of shell plate, reinforcing plate, bottom plate etc.) on the seismic behaviour has been investigated. Finally recommendations for the dimensioning of nozzles reinforcements with particular attention to seismic resistance were developed.

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An Analytical Model for Unanchored Fluid-Filled Tanks Under Base Excitation

Journal of Applied Mechanics ◽

10.1115/1.3125843 ◽

1988 ◽

Vol 55 (3) ◽

pp. 648-653 ◽

Cited By ~ 25

Author(s):

S. Natsiavas

Keyword(s):

Ground Motion ◽

Bottom Plate ◽

Rigid Foundation ◽

Base Excitation ◽

Storage Tanks ◽

Cylindrical Tank ◽

Hydrodynamic Problem ◽

Liquid Storage ◽

Ground System ◽

Lift Off

A set of equations is derived describing the dynamic response of cylindrical liquid storage tanks under horizontal ground excitation. The structure consists of a flexible cylindrical tank with a roof and a bottom plate and rests on a flexible ground through a rigid foundation. Portion of the base of the tank may separate from and lift off the foundation during ground motion. The solution of the hydrodynamic problem is first found in closed form. Then, Hamilton’s principle is applied and the equations governing the behavior of the coupled fluid/structure/ground system are derived. During this procedure, the base uplifting is modeled by an appropriate rotational nonlinear spring placed between the base of the tank and the foundation.

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Seismic Response of Unanchored Liquid Storage Tanks

Volume 8: Seismic Engineering ◽

10.1115/pvp2013-97700 ◽

2013 ◽

Cited By ~ 2

Author(s):

Maria Vathi ◽

Patricia Pappa ◽

Spyros A. Karamanos

Keyword(s):

Structural Integrity ◽

Bottom Plate ◽

Storage Tanks ◽

Mass System ◽

Aspect Ratios ◽

Liquid Storage ◽

State Of Stress ◽

Stress And Deformation ◽

Simplified Modeling ◽

Different Levels

Unanchored liquid storage tanks under strong seismic loading may exhibit uplifting of their bottom plate, with significant effects on the dynamic behavior and the structural integrity of the tank. In the present paper, base uplifting mechanics is examined numerically through a two-step methodology: (a) a detailed finite element shell model of the tank for incremental static analysis, capable of describing the state of stress and deformation at different levels of loading and (b) a simplified modeling of the tank as a spring-mass system for dynamic analysis, enhanced by a nonlinear spring at its base to account for the effects of uplifting. Three cylindrical liquid storage tanks of different aspect ratios are modeled and examined both as anchored and unanchored. The results are aimed at possible revisions in the relevant seismic design provisions of EN 1998-4 and API 650.

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