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

1988 ◽  
Vol 55 (3) ◽  
pp. 648-653 ◽  
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.

Development of a New Method of Baseline Correction on Earthquake Strong Motions and Its Application to Long Period Sloshing Responses of Liquid Storage Tanks During Strong Earthquakes

2003 ◽  
Author(s):  
Chikahiro Minowa
Keyword(s):  
Ground Motion ◽  
Low Frequency ◽  
Strong Motion ◽  
Correction Method ◽  
New Method ◽  
Baseline Correction ◽  
Storage Tanks ◽  
Low Frequencies ◽  
Long Period ◽  
Liquid Storage

In this paper, a new method of baseline correction on strong motion acceleration records is presented and the fundamental concept for baseline corrections on the earthquake strong motions is described. Considering the filtering effect, the earthquakes ground motion displacements of 1995 JMA KOBE, 1999 Kocaeli YPT and 1999 Chi-Chi TCU068 are discussed. Also, the linear sloshing responses of large liquid tanks subjected to these motions were discussed. Since liquid storage tanks show the low frequency (long period) sloshing characteristics and the strong motion characteristics of 1999 Kocaeli and Chi-Chi earthquakes are also low frequencies and large permanent displacements, the sloshing responses in large liquid tanks, especially in long natural periods, were significantly affected by the low frequency motions (large permanent displacements) of these devastating earthquakes. It is very important to use suitable ground motion characterized low frequency content for earthquake resistant design of liquid storage tanks. The baseline correction method presented in the paper may be adequately used to correct strong motion records for large liquid storage design.

scholarly journals Dynamic response of concrete rectangular liquid storage tanks

2021 ◽  
Author(s):  
Jun Zheng Chen
Keyword(s):  
Dynamic Response ◽  
Ground Motion ◽  
Added Mass ◽  
Tank Wall ◽  
Storage Tanks ◽  
Lumped Mass ◽  
Sequential Method ◽  
Mode Superposition Method ◽  
Liquid Storage ◽  
Vertical Ground

In this thesis, the dynamic response of concrete rectangular liquid storage tanks is investigated. In previous studies, the tank wall has been assumed as rigid in the calculation of hydrodynamic pressures. The effect of flexibility of tank wall is considered in this study. The analytical solutions for both impulsive pressure and convective pressure induced by both horizontal and vertical ground motions are presented. A 2-D coupled analysis model of tank wall is proposed. The hydrodynamic pressures are considered as external forces applied on the tank wall. Through a technique called the sequential method, the two fields of fluid and structure are coupled. The time-history analysis using the mode superposition method and the direct step-by-step integration method are carried out. Two rectangular tanks are analyzed. From the comparison of the results obtained from the proposed model with those proposed by other researchers, such as added mass model based on the rigid wall boundary condition, it shows that the lumped mass approach overestimates the base shear and wall displacement. The effect of wall flexibility on displacements, base shears and base moments are also discussed. A combination of the added mass method and the sequential method is used to study liquid storage tanks subjected to the vertical ground motion. It is found that the effect of the vertical acceleration should be considered in dynamic analysis of rectangular tanks. It is concluded that the total response of the structures should be based on the sum of the response under both horizontal and vertical components of ground motion.

scholarly journals Dynamic response of concrete rectangular liquid storage tanks

2021 ◽  
Author(s):  
Jun Zheng Chen
Keyword(s):  
Dynamic Response ◽  
Ground Motion ◽  
Added Mass ◽  
Tank Wall ◽  
Storage Tanks ◽  
Lumped Mass ◽  
Sequential Method ◽  
Mode Superposition Method ◽  
Liquid Storage ◽  
Vertical Ground

In this thesis, the dynamic response of concrete rectangular liquid storage tanks is investigated. In previous studies, the tank wall has been assumed as rigid in the calculation of hydrodynamic pressures. The effect of flexibility of tank wall is considered in this study. The analytical solutions for both impulsive pressure and convective pressure induced by both horizontal and vertical ground motions are presented. A 2-D coupled analysis model of tank wall is proposed. The hydrodynamic pressures are considered as external forces applied on the tank wall. Through a technique called the sequential method, the two fields of fluid and structure are coupled. The time-history analysis using the mode superposition method and the direct step-by-step integration method are carried out. Two rectangular tanks are analyzed. From the comparison of the results obtained from the proposed model with those proposed by other researchers, such as added mass model based on the rigid wall boundary condition, it shows that the lumped mass approach overestimates the base shear and wall displacement. The effect of wall flexibility on displacements, base shears and base moments are also discussed. A combination of the added mass method and the sequential method is used to study liquid storage tanks subjected to the vertical ground motion. It is found that the effect of the vertical acceleration should be considered in dynamic analysis of rectangular tanks. It is concluded that the total response of the structures should be based on the sum of the response under both horizontal and vertical components of ground motion.

Simplified Model for the Seismic Performance of Unanchored Liquid Storage Tanks

2015 ◽  
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.

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

1995 ◽  
Vol 22 (1) ◽  
pp. 180-189 ◽  
Author(s):  
David T. Lau ◽  
Xianguang Zeng
Keyword(s):  
Bottom Plate ◽  
Response Analysis ◽  
Beam Model ◽  
Nonlinear Behaviour ◽  
Storage Tanks ◽  
One Dimensional ◽  
Nonlinear Springs ◽  
Liquid Storage ◽  
Cylindrical Tanks ◽  
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.

Buckling at the Top of a Fluid-Filled Tank During Base Excitation

1987 ◽  
Vol 109 (4) ◽  
pp. 374-380 ◽  
Author(s):  
S. Natsiavas ◽  
C. D. Babcock
Keyword(s):  
Computer Code ◽  
Base Excitation ◽  
Storage Tanks ◽  
Linear Combinations ◽  
Ground Acceleration ◽  
A Value ◽  
Liquid Storage ◽  
System Equations ◽  
Set Up ◽  
General Dynamic

An explanation is provided for the earthquake-induced damage observed at the top of liquid storage tanks. An analysis is developed and the results are compared with experimental work. The basic steps of the analysis, which is developed for the general dynamic response of fluid-filled tanks under horizontal ground excitation, are first presented. In this analysis, the structural displacements are expanded in appropriate series forms which involve both rigid body and flexible components. The latter components are expressed as linear combinations of terms, each of which is a product of a function with assumed spatial dependence and an unknown time-dependent function. These time functions are then determined from the solution of the fluid/structure system equations, which are set up by employing Hamilton’s principle. In the present work, results are obtained and compared with model tests carried out at Caltech, during which buckling was observed at the top of the tank under a known base excitation history. Computing analytically the corresponding pressure distribution and using the BOSOR computer code for the buckling computations, a value for the amplitude of the ground acceleration which results in buckling at the top of the tank is calculated. Good correlation with the test work is obtained.

Energy Method for Base Uplifting Analysis of Liquid-Storage Tanks

1996 ◽  
Vol 118 (3) ◽  
pp. 332-335 ◽  
Author(s):  
P. K. Malhotra ◽  
A. S. Veletsos
Keyword(s):  
Energy Method ◽  
Close Agreement ◽  
Base Plate ◽  
Large Displacements ◽  
Rigid Foundation ◽  
Tank Wall ◽  
Storage Tanks ◽  
Infinite Beam ◽  
Exact Analysis ◽  
Liquid Storage

A solution, based on Ritz energy method, is presented for the uplifting analysis of a uniformly loaded semi-infinite beam supported on a rigid foundation. Motivated by a need to understand the effects of earthquake-induced base uplifting in unanchored liquid-storage tanks, the solution accounts for the nonlinearities associated with large displacements and material yielding in the base plate, and considers the constraining action of the tank wall. The results are in close agreement with those from the “exact” analysis.

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