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RESEARCH PAPERS

Sloshing Effects on the Seismic Design of Horizontal-Cylindrical and Spherical Industrial Vessels

[+] Author and Article Information
Spyros A. Karamanos1

Department of Mechanical & Industrial Engineering, University of Thessaly, 38334 Volos, Greeceskara@mie.uth.gr

Lazaros A. Patkas, Manolis A. Platyrrachos

Department of Mechanical & Industrial Engineering, University of Thessaly, 38334 Volos, Greece

1

Corresponding author.

J. Pressure Vessel Technol 128(3), 328-340 (Sep 12, 2005) (13 pages) doi:10.1115/1.2217965 History: Received May 04, 2005; Revised September 12, 2005

The present paper investigates sloshing effects on the earthquake design of horizontal-cylindrical and spherical industrial vessels. Assuming small-amplitude free-surface elevation, a linearized sloshing problem is obtained, and its solution provides sloshing frequencies, modes, and masses. Based on an “impulsive-convective” decomposition of the container-fluid motion, an efficient methodology is proposed for the calculation of seismic force. The methodology gives rise to appropriate spring-mass mechanical models, which represent sloshing effects on the container-fluid system in an elegant and simple manner. Special issues, such as the deformability of horizontal-cylindrical containers or the flexibility of spherical vessel supports, are also taken into account. The proposed methodology can be used to calculate the seismic force, in the framework of liquid container earthquake design, and extends the current design practice for vertical cylindrical tanks stated in existing seismic design specifications (e.g., API Standard 650 and Eurocode 8). The methodology is illustrated in three design examples.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Industrial vessels (horizontal cylinder and sphere)

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Figure 2

Liquid container under external excitation

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Figure 3

Configuration of a horizontal-cylindrical liquid container

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Figure 4

Variation of the first four sloshing frequencies of a two-dimensional circular container with respect to liquid height (λn=ωn2R∕g), in a two-dimensional circular container

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Figure 5

Variation of sloshing and impulsive mass ratios mass ratios M1C∕ML, M2C∕ML, ΣMkC∕ML, MI∕ML with respect to liquid height in a two-dimensional circular container

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Figure 6

Mechanical model representing sloshing in liquid storage vessels

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Figure 7

Beam-type deformation of a long horizontal cylinder

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Figure 8

Mechanical model representing sloshing in a deformable horizontal cylindrical container

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Figure 9

Variation of the fundamental sloshing frequency ω1(1) in a horizontal cylinder [longitudinal excitation], with respect to the liquid depth; finite element results versus equivalent rectangle predictions

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Figure 10

Equivalent rectangular container concept to approximate the sloshing response of horizontal cylinders under longitudinal excitation

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Figure 11

Variation of the first three sloshing frequencies of a horizontal cylinder under longitudinal excitation, with respect to the liquid height

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Figure 12

Variation of the first three sloshing masses of a horizontal cylinder under longitudinal excitation, with respect to the liquid height

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Figure 13

Variation of the first sloshing mass of a horizontal cylinder under longitudinal excitation, with respect to the liquid height and the aspect ratio of the container

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Figure 14

Configuration of a spherical container

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Figure 15

Variation of the first four sloshing frequencies of a two-dimensional circular container with respect to liquid height (λn=ωn2R∕g), in a spherical container

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Figure 16

Variation of sloshing and impulsive mass ratios mass ratios M1C∕ML, M2C∕ML, ΣMkC∕ML, MI∕ML with respect to liquid height in a spherical container

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Figure 17

Deformation and equilibrium of support system in spherical containers

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Figure 18

Mechanical model representing sloshing in an elevated spherical container

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Figure 19

Elastic design spectrum (normalized), from Eurocode 8 for soil class B, importance factor equal to 1, and two different damping ration (0.5% and 2%)

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Figure 20

Configuration for half-full long cylindrical pressure vessel

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Figure 21

Spherical vessel of design example

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