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.

Generalized SDOF system for dynamic analysis of concrete rectangular liquid storage tanks: effect of tank parameters on response

2010 ◽  
Vol 37 (2) ◽  
pp. 262-272 ◽  
Author(s):  
J. Z. Chen ◽  
M. R. Kianoush
Keyword(s):  
Dynamic Response ◽  
Natural Frequencies ◽  
Hydrodynamic Pressure ◽  
Characteristic Parameter ◽  
Added Mass ◽  
Tank Wall ◽  
Storage Tanks ◽  
Effective Height ◽  
Sdof System ◽  
Liquid Storage

This paper presents the results of parametric studies on the seismic response of concrete rectangular liquid storage tanks using the generalized single-degree-of-freedom (SDOF) system. The effects of height of liquid and width of tank on the dynamic response of liquid storage tanks are investigated. The liquid level varies from the empty condition to a full tank. Also, instead of the commonly used ratio of width of tank to liquid height, Lx/HL, the ratio of width of tank to full height of the tank wall, Lx/Hw, is used as a characteristic parameter of tanks to study the effect of tank size on the dynamic response. The trends of added mass of liquid, effective height, and natural frequencies for different sizes of tanks are established. The values of the added mass of liquid due to impulsive hydrodynamic pressure and the effective height in the relationship with the ratios Lx/Hw and HL/Hw are determined and can be used in the seismic design of liquid storage tanks. Since the natural frequencies of liquid-containing structures are within a band of frequencies between that of a full tank and that of an empty tank, the recommended frequency to be used in the design of the tank wall is the frequency that causes the maximum dynamic response .

Effects of Base Uplifting on the Seismic Response of Unanchored Liquid Storage Tanks

2012 ◽  
Author(s):  
Maria Vathi ◽  
Spyros A. Karamanos
Keyword(s):  
Seismic Response ◽  
Pushover Analysis ◽  
Hydrodynamic Pressure ◽  
Base Plate ◽  
Seismic Loading ◽  
Storage Tanks ◽  
Liquid Storage ◽  
Detailed Simulation ◽  
Steel Tank ◽  
Static Pushover Analysis

Unanchored liquid storage tanks under strong earthquake loading tend to uplift. In the present study, the effects of base uplifting on the seismic response of unanchored tanks are presented with emphasis on elephant’s foot buckling, base plate strength and shell-to-base connection capacity. Towards this purpose, base uplifting mechanics is analyzed through a detailed simulation of the tank using non-linear finite elements, and a static pushover analysis is conducted that considers the hydrodynamic pressure distribution due to seismic loading on the tank wall and the base plate. The uplifting provisions from EN 1998-4 and API 650 Appendix E standards are briefly described. Numerical results for a typical 27.8-meter-diameter steel tank are compared with the above design provisions.

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.

scholarly journals Dynamic Responses of Liquid Storage Tanks Caused by Wind and Earthquake in Special Environment

2019 ◽  
Vol 9 (11) ◽  
pp. 2376 ◽  
Author(s):  
Wei Jing ◽  
Huan Feng ◽  
Xuansheng Cheng
Keyword(s):  
Wind Speed ◽  
Interference Effect ◽  
Storage Tank ◽  
Great Influence ◽  
Dynamic Responses ◽  
Tank Wall ◽  
Storage Tanks ◽  
Earthquake Interaction ◽  
Liquid Storage ◽  
Liquid Storage Tank

Based on potential flow theory and arbitrary Lagrangian–Eulerian method, shell–liquid and shell–wind interactions are solved respectively. Considering the nonlinearity of tank material and liquid sloshing, a refined 3-D wind–shell–liquid interaction calculation model for liquid storage tanks is established. A comparative study of dynamic responses of liquid storage tanks under wind, earthquake, and wind and earthquake is carried out, and the influences of wind speed and wind interference effect on dynamic responses of liquid storage tank are discussed. The results show that when the wind is strong, the dynamic responses of the liquid storage tank under wind load alone are likely to be larger than that under earthquake, and the dynamic responses under wind–earthquake interaction are obviously larger than that under wind and earthquake alone. The maximum responses of the tank wall under wind and earthquake are located in the unfilled area at the upper part of the tank and the filled area at the lower part of the tank respectively, while the location of maximum responses of the tank wall under wind–earthquake interaction is related to the relative magnitude of the wind and earthquake. Wind speed has a great influence on the responses of liquid storage tanks, when the wind speed increases to a certain extent, the storage tank is prone to damage. Wind interference effect has a significant effect on liquid storage tanks and wind fields. For liquid storage tanks in special environments, wind and earthquake effects should be considered reasonably, and wind interference effects cannot be ignored.

The Formulations of Shear Force and Overturning Moment of the Large-Upright-Unanchored Industrial Liquid Storage Tanks Subjected to Horizontal Ground Excitations

2005 ◽  
Author(s):  
Mutlu Ozer
Keyword(s):  
Shear Force ◽  
Excitation Frequency ◽  
Response Analysis ◽  
Tank Wall ◽  
Storage Tanks ◽  
Base Shear ◽  
Ground Acceleration ◽  
Dynamic Coefficients ◽  
Liquid Storage ◽  
Overturning Moment

The dynamic response analysis is performed for the formulations of shear force and overturning moment of the large-upright-unanchored industrial liquid storage tanks subjected to horizontal ground acceleration. As the tank is accelerated in the horizontal direction, it tends to uplift from its foundation, and hydrodynamic pressures on the tank wall vary with height in non-linear fashion. In this study, the distribution of hydrodynamic pressures and its center are directly correlated to formulate shear force and overturning moment. Initially, the equations of shear force and overturning moment derived by assuming hydrodynamic pressures exerted on tank wall vary in parabolic trend. Then derived equations are multiplied by dynamic coefficients, which are basically the function of peak ground acceleration, excitation frequency and the ratio of liquid’s height to radius of tanks. Dynamic coefficients are formulated through the shake table experiment of the model tanks excited by computer generated ground motion. The equations proposed in this paper for base shear and overturning moment are only the function of total weight of tank, the ratio of liquid’s height to radius, specific weight of liquid and dynamic coefficients for shear force and overturning moment. Therefore, proposed equations are very simple, efficient and easy to perform in calculating of shear forces and overturning moments of the large-upright industrial liquid storage tanks subjected to lateral earthquake loads. The results are verified with different codes (e.g. Eurocode8, API and AWWA-100...).

scholarly journals Generalized SDOF system for dynamic analysis of concrete rectangular liquid storage tanks

2021 ◽  
Author(s):  
Jun Zheng Chen
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Seismic Analysis ◽  
Design Procedure ◽  
Hydrodynamic Pressure ◽  
Added Mass ◽  
Tank Wall ◽  
Storage Tanks ◽  
Sdof System ◽  
Liquid Storage

Liquid storage tanks are essential facilities in lifeline and industrial systems. To ensure liquid tightness, serviceability is the prime design concern for these structures. While there have been major studies on the behavior of steel tanks, little attention has been paid to the behavior of rectangular concrete tanks. In this study, the dynamic response of concrete rectangular liquid storage tanks is investigated. In the current design practice, the response of liquid and tank structure is determined based on rigid tank wall and the lumped mass approach. However, the results of analysis show that the flexibility of tank wall increases the hydrodynamic pressures as compared to the rigid wall assumption. Also, recent studies show that the lumped added mass method leads to overly conservative results in terms of base shear and base moment. In addition, in spite of advanced analysis techniques available for dynamic analysis of liquid storage tanks such as finite element method and sequential coupling analysis procedure, there is a need to develop a simplified analysis method for practical applications. In this thesis, a simplified method using the generalized single degree of freedom (SDOF) system is proposed for seismic analysis of concrete rectangular liquid containing structures (LCS). Only the impulsive hydrodynamic pressure is considered. In the proposed method, the consistent mass approach and the effect of flexibility of tank wall on hydrodynamic pressures are considered. Different analytical methods are used to verify the proposed model in this study. The comparison of results based on the current design practice, the analytical-finite element models and full finite element model using ANSYS® shows that the proposed method is fairly accurate which can be used in the structural design of liquid containing structures. Parametric studies on seismic analysis of concrete rectangular LCS using the generalized SDOF system are carried out. Five prescribed vibration shape functions representing the first mode shape of fluid structure interaction system are used to study the effect of flexibility of tank wall and boundary conditions. The effect of flexibility of tank wall, the amplitude of hydrodynamic pressure, the added mass of liquid due to hydrodynamic pressure, the effective heights for liquid containing system and the effect of higher modes on dynamic response of LCS are investigated. In addition, the effect of variable size of tanks and liquid depth are studied. The contribution of higher modes to the dynamic response of LCS is included in the proposed model. A design procedure based on the structural model using the generalized SDOF system is proposed in this study. Design charts and tables for the added mass of liquid due to impulsive hydrodynamic pressure and the corresponding effective heights are presented. The proposed design procedure can be used for engineering design applications.

scholarly journals Generalized SDOF system for dynamic analysis of concrete rectangular liquid storage tanks

2021 ◽  
Author(s):  
Jun Zheng Chen
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Seismic Analysis ◽  
Design Procedure ◽  
Hydrodynamic Pressure ◽  
Added Mass ◽  
Tank Wall ◽  
Storage Tanks ◽  
Sdof System ◽  
Liquid Storage

Liquid storage tanks are essential facilities in lifeline and industrial systems. To ensure liquid tightness, serviceability is the prime design concern for these structures. While there have been major studies on the behavior of steel tanks, little attention has been paid to the behavior of rectangular concrete tanks. In this study, the dynamic response of concrete rectangular liquid storage tanks is investigated. In the current design practice, the response of liquid and tank structure is determined based on rigid tank wall and the lumped mass approach. However, the results of analysis show that the flexibility of tank wall increases the hydrodynamic pressures as compared to the rigid wall assumption. Also, recent studies show that the lumped added mass method leads to overly conservative results in terms of base shear and base moment. In addition, in spite of advanced analysis techniques available for dynamic analysis of liquid storage tanks such as finite element method and sequential coupling analysis procedure, there is a need to develop a simplified analysis method for practical applications. In this thesis, a simplified method using the generalized single degree of freedom (SDOF) system is proposed for seismic analysis of concrete rectangular liquid containing structures (LCS). Only the impulsive hydrodynamic pressure is considered. In the proposed method, the consistent mass approach and the effect of flexibility of tank wall on hydrodynamic pressures are considered. Different analytical methods are used to verify the proposed model in this study. The comparison of results based on the current design practice, the analytical-finite element models and full finite element model using ANSYS® shows that the proposed method is fairly accurate which can be used in the structural design of liquid containing structures. Parametric studies on seismic analysis of concrete rectangular LCS using the generalized SDOF system are carried out. Five prescribed vibration shape functions representing the first mode shape of fluid structure interaction system are used to study the effect of flexibility of tank wall and boundary conditions. The effect of flexibility of tank wall, the amplitude of hydrodynamic pressure, the added mass of liquid due to hydrodynamic pressure, the effective heights for liquid containing system and the effect of higher modes on dynamic response of LCS are investigated. In addition, the effect of variable size of tanks and liquid depth are studied. The contribution of higher modes to the dynamic response of LCS is included in the proposed model. A design procedure based on the structural model using the generalized SDOF system is proposed in this study. Design charts and tables for the added mass of liquid due to impulsive hydrodynamic pressure and the corresponding effective heights are presented. The proposed design procedure can be used for engineering design applications.

Sloshing Loads in Liquid-Storage Tanks with Insufficient Freeboard

2005 ◽  
Vol 21 (4) ◽  
pp. 1185-1192 ◽  
Author(s):  
Praveen K. Malhotra
Keyword(s):  
Storage Capacity ◽  
Ground Motions ◽  
Tank Wall ◽  
Storage Tanks ◽  
Simple Method ◽  
Long Period ◽  
Liquid Storage

Seismic ground motions excite long-period sloshing response in liquid-storage tanks. A minimum freeboard is needed to prevent the sloshing waves from impacting the roof of tanks. Since freeboard results in unused storage capacity, many tanks are not provided with the sufficient freeboard. As a result, sloshing waves impact the roof, generating additional forces on the roof and tank wall. This article presents a simple method of estimating these forces.

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