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Fluid-Structure Interaction

Contributions of Fluid to Rocking–Bulging Interaction of Rectangular Tanks Whose Walls Are Rigid and Bottom Plate Rectilinearly Uplifts

[+] Author and Article Information
Tomoyo Taniguchi

Department of Civil Engineering
Tottori University
4-101 Koyama-Minami Tottori
680-8552, Japan
e-mail: t_tomoyo@cv.tottori-u.ac.jp

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received April 28, 2011; final manuscript received June 8, 2012; published online December 4, 2012. Assoc. Editor: Spyros A. Karamanos.

J. Pressure Vessel Technol 135(1), 011304 (Dec 04, 2012) (7 pages) Paper No: PVT-11-1105; doi: 10.1115/1.4007286 History: Received April 28, 2011; Revised June 08, 2012

At the event of severe earthquakes, the tank rocking response appears subsequent to the tank bulging response. A spring-mass-rigid body combined model was proposed for analyzing the tank response and the required quantities for the model have been rigorously defined based on the mathematical solution of fluid pressure on the tank accompanying the tank response of interest. To date, the apparent density of fluid for the rocking and the bulging responses and the effective mass of those are available for this purpose. However, observations revealed that the interaction between the rocking response and the bulging response is stimulated by the effective mass of fluid for the rocking–bulging interaction that is understood as a part of the effective mass of fluid for the tank bulging response that is also under the action of the rotational inertia. Therefore, regarding a ratio of the apparent density of fluid for the tank rocking response to the original density of fluid as the intensity of a contribution of fluid to the tank rocking response, the apparent density of fluid for the rocking–bulging interaction is defined intuitively and conveniently. The effective mass of fluid for the rocking–bulging interaction is subsequently defined. The distribution of the apparent density of fluid for the rocking–bulging interaction inside the tank is drawn for a combination of the various aspects of tank and the ratios of the uplift width of the tank bottom. The ratios of the effective mass of fluid for the rocking–bulging interaction to the total mass of fluid of the tank as well as the ratios of the arm length to the centroid of the effective mass of that to the tank geometry are also depicted by the same manner.

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References

Figures

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Fig. 1

(a) Equilibrium of forces on the small volume, (b) boundary conditions for Laplace's equation, and (c) forces acting on the small volume

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Fig. 2

Ratios of the apparent density of fluid for the tank bulging response to the original fluid density

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Fig. 3

Boundary conditions for Laplace's equation

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Fig. 4

(a) Analytical model, (b) equilibrium of forces on the small volume, and (c) forces acting on the small volume

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Fig. 5

(a) Ratios of the apparent density of fluid for the tank rocking response to the original fluid density (uplift width = 1%), (b) ratios of the apparent density of fluid for the tank rocking response to the original fluid density (uplift width = 50%), and (c) ratios of the apparent density of fluid for the tank rocking response to the original fluid density (uplift width = 100%)

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Fig. 6

(a) Ratios of the apparent density of fluid for the rocking–bulging interaction to the original fluid density (uplift width = 1%), (b) ratios of the apparent density of fluid for the rocking–bulging interaction to the original fluid density (uplift width = 50%), and (c) ratios of the apparent density of fluid for the rocking–bulging interaction to the original fluid density (uplift width = 100%)

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Fig. 7

Ratios of effective mass of fluid for the rocking–bulging interaction to mass of tank content

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Fig. 8

(a) Ratios of the horizontal length of a moment arm to the width of the tank and (b) ratios of the vertical length of a moment arm to the height of the tank

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