• Structural Engineering and Mechanics
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• v.40 no.5
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• pp.665-688
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• 2011

This paper presents a theoretical analysis for the free vibration of rectangular tanks partially filled with an ideal liquid. Wet dynamic displacements of the tanks are approximated by combining the orthogonal polynomials satisfying the boundary conditions, since the rectangular tanks are composed of four rectangular plates. The classical boundary conditions of the tanks at the top and bottom ends are considered, such as clamped, simply supported, and clamped-free boundary conditions. As the facing rectangular plates are assumed to be geometrically and structurally identical, the vibration modes of the facing plates of the tanks can be divided into two categories: symmetric and antisymmetric modes with respect to the planes passing through the center of the tanks and perpendicular to the free liquid surface. The liquid displacement potentials satisfying the Laplace equation and liquid boundary conditions are derived, and the wet dynamic modal functions of a quarter of the tanks can be expanded by the finite Fourier transform for compatibility requirements along the contacting surfaces between the tanks and liquid. An eigenvalue problem is derived using the Rayleigh-Ritz method. Consequently, the wet natural frequencies of the rectangular tanks can be extracted. The proposed analytical method is verified by observing an excellent agreement with three-dimensional finite element analysis results. The effects of the liquid level and boundary condition at the top and bottom edges are investigated.

• Structural Engineering and Mechanics
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• v.13 no.5
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• pp.533-542
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• 2002

This paper considers the buckling and post-buckling behavior of empty metal storage tanks under wind load. The structures of such tanks may be idealized as cantilever cylindrical shells, and the structural response is investigated using a computational model. The modeling employs a doubly curved finite element based on a theory by Simo and coworkers, which is capable of handling large displacements and plasticity. Buckling results for tanks with four different geometric relations are presented to consider the influence of the ratios between the radius and the height of the shell (R/L), and between the radius and the thickness (R/t). The studies aim to clarify the differences in the shells regarding their imperfection-sensitivity. The results show that thin-walled short tanks, with R/L = 3, display high imperfection sensitivity, while tanks with R/L = 0.5 are almost insensitive to imperfections. Changes in the total potential energy of tanks that would buckle under the same high wind pressures are also considered.

• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.557-572
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• 2018

The academic research works about liquid storage tanks are reviewed for the purpose of providing valuable reference to the engineering practice on their aseismic design. A summary of the performance of tanks during past earthquakes is described in this paper. Next, the seismic response of tanks under unidirectional earthquake is reported, supplemented with the dynamic response under multidirectional motions. Then, researches on the influence of soil-structure interaction are brought out to help modify the seismic design approach of tanks in different areas with variable properties of soils. Afterwards, base isolation systems are reported to demonstrate their effectiveness for the earthquake-resistant design of liquid storage tanks. Further, researches about the liquid-structure interaction are reviewed with description of simplified models and numerical analytical methods, some of which consider the elastic effect of tank walls. Moreover, the liquid sloshing phenomenon on the hydrodynamic behaviors of tanks is presented by various algorithms including grid-based and meshfree method. And then the impact of baffles in changing the dynamic characteristics of the liquid-structure system is raised, which shows the energy dissipation by the vortex motion of liquid. In addition, uplifting effect is given to enhance the understanding on the capacity of unanchored tanks and some assessment of their development. At last, the concluding remarks and the aspects of extended research in the field of liquid storage tanks under seismic loads are provided, emphasizing the thermal stress analysis, the replaceable system for base isolation, the liquid-solid interaction and dynamic responses with stochastic excitations.

• Structural Engineering and Mechanics
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• v.9 no.6
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• pp.615-636
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• 2000

Some elevated water tanks have failed due to torsional vibrations in past earthquakes. The overall axisymmetric structural geometry and mass distribution of such structures may leave only a small accidental eccentricity between centre of stiffness and centre of mass. Such a small accidental eccentricity is not expected to cause a torsional failure. This paper studies the possibility of amplified torsional behaviour of elevated water tanks due to such small accidental eccentricity in the elastic as well as inelastic range; using two simple idealized systems with two coupled lateral-torsional degrees of freedom. The systems are capable of retaining the characteristics of two extreme categories of water tanks namely, a) tanks on staging with less number of columns and panels and b) tanks on staging with large number of columns and panels. The study shows that the presence of a small eccentricity may lead to large displacement of the staging edge in the elastic range, if the torsional-to-lateral time period ratio $({\tau})$ of the elevated tanks lies within a critical range of 0.7< ${\tau}$ <1.25. Inelastic behaviour study reveals that such excessive displacement in some of the reinforced concrete staging elements may cause unsymmetric yielding. This may lead to progressive strength deterioration through successive yielding in same elements under cyclic loading during earthquakes. Such localized strength drop progressively develop large strength eccentricity resulting in large localized inelastic displacement and ductility demand, leading to failure. So, elevated water tanks should have ${\tau}$ outside the said critical range to avoid amplified torsional response. The tanks supported on staging with less number of columns and panels are found to have greater torsional vulnerability. Tanks located near faults seem to have torsional vulnerability for large ${\tau}$.

• Earthquakes and Structures
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• v.2 no.4
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• pp.397-412
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• 2011

In this paper, the seismic response of elevated broad and slender liquid storage tanks isolated by elastomeric or sliding bearings was investigated. The accuracy of predictions of SAP2000 vs. 3D-BASIS-ME programs was examined. A comparative study of the performance of base isolated tanks when isolation bearings are placed at the top or at the bottom of the supporting tower structure was conducted. It was found that base isolation is quite effective in reducing the earthquake response of elevated liquid storage tanks in which high reductions of base shear and shaft displacement were achieved. Modeling the isolated tanks in SAP2000 was very successful in producing results that are nearly identical to those of program 3D-BASIS-ME. Placing the isolators at the top of the shaft in elevated tanks proved to be much better than placing them at the bottom.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.759-772
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• 2010

Seismic isolation is a well-known method to mitigate the earthquake effects on structures by increasing their fundamental natural periods at the expense of larger displacements in the structural system. In this paper, the seismic response of isolated and fixed base vertical, cylindrical, liquid storage tanks is investigated using a Finite Element Model (FEM), taking into account fluid-structure interaction effects. Three vertical, cylindrical tanks with different ratios of height to radius (H/R = 2.6, 1.0 and 0.3) are numerically analyzed and the results of response-history analysis, including base shear, overturning moment and free surface displacement are reported for isolated and non-isolated tanks. Isolated tanks equipped by lead rubber bearings isolators and the bearing are modeled by using a non-linear spring in FEM model. It is observed that the seismic isolation of liquid storage tanks is quite effective and the response of isolated tanks is significantly influenced by the system parameters such as their fundamental frequencies and the aspect ratio of the tanks. However, the base isolation does not significantly affect the surface wave height and even it can causes adverse effects on the free surface sloshing motion.

• Journal of Power System Engineering
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• v.14 no.6
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• pp.67-74
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• 2010

Many tanks are installed in ship and marine structures. They are often in contact with inner or outer fluid, like ballast, fuel and cargo tanks. Fatigue damages are sometimes observed in these tanks which seem to be caused by resonance with exciting force of engine and propeller. Vibration characteristics of these thin walled tanks in contact with fluid near engine and propeller are strongly affected by added mass of containing fluid. Therefore it is essentially important to estimate the added mass effect to predict vibration of the tanks. Many authors have studied vibration of cylindrical and rectangular tanks containing fluid. Few research on dynamic interaction among tank walls through fluid are reported in the vibration of rectangular tanks recently. In case of rectangular tanks, structural coupling between adjacent panels and effect of vibration modes of multiple panels on added mass have to be considered. In the previous report, A numerical tool of vibration analysis of a 3-dimensional tank is developed by using finite element method for plates and boundary element method for fluid region. In this paper, the coupling effect between panels of a tank on added mass of containing fluid, the effect of structural constraint between panels on each vibration mode for fluid region and mode characteristics in accordance with changing breadth of the plates are investigated numerically and discussed.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.2
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• pp.153-168
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• 2016

Sloshing phenomenon is a complicated free surface flow problem that increases the dynamic pressure on the sidewalls and the bottom of the storage tanks. When the storage tanks are partially filled, it is essential to be able to evaluate the fluid dynamic loads on the tank's perimeter. In this paper, a numerical code was developed to determine the pressure distribution on the rectangular and trapezoidal storage tanks' perimeters due to liquid sloshing phenomenon. Assuming the fluid to be inviscid, the Laplace equation and the nonlinear free surface boundary conditions were solved using coupled boundary element - finite element method. The code performance for sloshing modeling was validated using Nakayama and Washizu's results. Finally, this code was used for partially filled rectangular and trapezoidal storage tanks and free surface displacement, pressure distribution and horizontal and vertical forces exerted on the tanks' perimeters due to liquid sloshing phenomenon were estimated and discussed.

• Earthquakes and Structures
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• v.18 no.2
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• pp.171-184
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• 2020

The potential of using the roof water tanks as a mitigation measure to minimize the required separation gap and induced pounding forces due to collisions is investigated. The investigation is carried out using nonlinear dynamic analysis for two adjacent 3-story buildings with different dynamic characteristics under two real earthquake motions. For such analysis, nonlinear viscoelastic model is used to simulate forces due to impact. The sloshing force due to water movement is modelled in terms of width of the water tank and the instantaneous wave heights at the end wall. The effect of roof water tanks on the story's responses, separation gap, and magnitude and number of induced pounding forces are investigated. The influence of structural stiffness and storey mass are investigated as well. It is found that pounding causes instantaneous acceleration pulses in the colliding buildings, but the existence of roof water tanks eliminates such acceleration pulses. At the same time the water tanks effectively reduce the number of collisions as well as the magnitude of the induced impact forces. Moreover, buildings without constructed water tanks require wider separation gap to prevent pounding as compared to those with water tanks attached to top floor under seismic excitations.

• Environmental Engineering Research
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• v.22 no.1
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• pp.55-60
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• 2017

Provision of safe, accessible, and good water quality in the community is an important step towards reducing various waterborne illnesses. However, improving the quality of water should include spreading awareness to the public regarding the importance of cleaning their household water tanks. The aim of this study was to investigate the microbial quality of water of household water tanks in Dubai. The water samples from household water tanks were collected from forty houses, and a questionnaire was given to the residents to determine the history of the water tanks. The membrane filtration technique was used to quantify heterotrophic and total coliform bacteria on plate count agar and the violet red bile agar respectively. The overall results of this study have shown that 18 out of total 40 household water tanks contained different types of bacteria concentration level beyond local and widely accepted international standards. The overall results of this study indicated that there is a lack of awareness among residents regarding the importance of maintaining proper sanitation and hygiene of the household water tanks.