seismic response of above ground storage tanks

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E05SR33-1

11th ICSGE

17-19 May 2005

Cairo - Egypt

Ain Shams University

Faculty of Engineering

Department of Structural Engineering

Eleventh International Colloquium on Structural and Geotechnical Engineering

SEISMIC RESPONSE OF LIQUID STORAGE TANKS

RESTING ON THE GROUND

A.M. ELHOSINY1 M. K. ZIDAN

2H. H. ORFY

3

ABSTRACT

Large capacity, ground supported, cylindrical liquid-storage steel tanks are designed to be

either fully anchored or unanchored at their base. Different models for liquid storage tanks

resting on the ground subjected to seismic load have been developed using ( Ansys) program.

The models considered the contact condition between the base plate and the ground and the

sloshing mode inside the tank. The models developed were compared to study the effect of

the tank base condition on the different response parameters. The models were used to obtain

the time history of the different response parameters of the tank elements. When fully

anchored tanks are subjected to strong ground shaking, large base shear is induced, imposing

high demands on the base anchorage system and foundation. Tanks unanchored at their baseexperience partial base uplifting when subjected to strong shaking. Increased flexibility

associated with base uplifting reduces the base shear. However, due to reduction of contact

area between the base and the ground, the axial compressive stress in walls increases.

Parametric variations are carried out to study the effects of various geometry parameters on

the response of the tank.

Keywords: circular; ground tanks; sloshing; base shear; uplift; contact; hoop stresses; fluid

elements.

1 INTRODUCTION

Liquid storage tanks are important components of lifeline and industrial facilities. Behaviorof large tanks during seismic events has implications far beyond the mere economic value of

the tanks and their contents. Similarly, failure of tanks storing combustible materials, can

lead to extensive uncontrolled fires.

Steel ground-based tanks consist essentially of a steel wall that resists outward liquid

pressure, a thin flat bottom plate that prevents liquid from leaking out, and a thin roof plate

that protects contents from the atmosphere. It is common to classify such tanks in two

categories depending on support conditions: anchored and unanchored tanks. Anchored tanks

must be connected to large foundations to prevent the uplift in the event of earthquake

1

Associate Prof., Struct. Dep.Ain Shams Univ.Cairo- Egypt2 Professor., Struct. Dep.Ain Shams Univ.Cairo- Egypt

3 Graduate Student Ain Shams Univ.Cairo- Egypt



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occurrence. However, improperly detailed anchors may damage the shell under seismic

loading resulting in a ripped tank bottom. Hence, it is common, particularly for large size

tanks, to support the shell on a ring wall foundation without anchor bolts and to support the

bottom plate on a compacted soil though, sometimes, ring walls are omitted. Anchored tanks

are either horizontal or vertical. Circular vertical tanks made of carbon steel are more

numerous than any other type because they are efficient in resisting liquid hydrostatic pressure mostly by membrane stresses, simple in design, and easy in construction.

Problems associated with the seismic behavior of liquid storage tanks involve the analysis of

three systems: the tank, the soil and the liquid, as well as the interaction between them along

their boundaries. The up-to-date technology in the non-linear finite element analysis of plates

and shells is utilized to model the tank wall and base plate. The Eulerian finite element

method is used to model the liquid inside the liquid domain while the Lagrangian-Eulerian

finite element method is used to model the liquid boundaries.

Analysis of the seismic behavior of unanchored tanks also includes the effect of large

amplitude base uplifting. It has been observed in past earthquakes that the bottom plate can

be lifted by as much as one foot or more, and therefore, its behavior affects the response of

the overall system. The uplifting problem is a special type of the non-linear contact problem between two bodies. Thus, the evolution of contact analysis as well as large deflection and

rotation analysis of plates and shells are strongly related to the area of the seismic behavior of

unanchored tanks. It also involves the seismic behavior of the soil and the dynamic soil-

structure interaction.

Performance of ground–based tanks during past earthquakes showed the following structural

typical damage:

• Buckling near the base of the shell due to excessive axial compressive stresses. Shell

buckling is typically characterized by “elephant foot bulges”, which appear a short

distance above the base. Sometimes, buckling may also occur at the top part of the shell.

• Damage to roof caused by sloshing of the liquid and insufficient freeboard.• Differential settlement of the foundation.

Many researchers have investigated the dynamic behavior of liquid storage tanks both

theoretically and experimentally to enable the design of such tanks to resist earthquakes.

Some researchers have been employing the finite element method to investigate contact

problems, soil plasticity and large amplitude liquid sloshing as well as both fluid-structure and

soil-structure interactions.

Large capacity, ground supported, cylindrical liquid-storage steel tanks are designed to be

either fully anchored or unanchored at their base (API 1993; AWWA 1996). When subjected

to strong ground shaking, fully anchored tanks develop large base shear and overturning

moment, due to the fluid hydrodynamic action, and impose high demands on their base

anchorage system and foundation. High stresses in vicinity of poorly detailed anchors cantear the tank wall, and large base shear can overcome friction, causing the tank to slide. In

regions of strong shaking, it is practically impossible to design tanks to withstand forces

obtained through elastic analysis. Elastic forces are reduced by factors of three or more to

obtain the design forces.

Tanks unanchored at their base experience partial base uplifting when subjected to strong

shaking. However, due to reduced contact of the wall with the foundation, the walls axial

compressive stress increases, sometimes leading to buckling of the wall. They me be

subjected to foundation penetration, plastic rotation at plate boundary, radial separation

between the plate and foundation. Large uplifts can cause uneven and permanent settlement

of the wall due to nonlinear soil response. Several cycles of large plastic rotation can rupture

the plate-shell junction. Different methods of base isolation have been proposed to improvethe seismic performance of tanks (Malhotra 1997a, b).



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Early developments of the seismic response of liquid storage tanks considered the

hydrodynamic effect of the liquid to be divided into two components; an impulsive pressure

caused by the portion of the liquid accelerating with the tank, and a convective pressure

caused by the portion of the liquid sloshing in the tank ( Housner [12]). A different approach

to the analysis of flexible containers was developed by Veletsos [17]. The tank was assumed

to behave as a single degree of freedom system, to vibrate in a prescribed mode and to remaincircular during vibrations. Later, Veletsos and Yang [15, 16] estimated maximum base shear

by modifying Housner's model to consider the first cantilever mode of the tank.

In 1980 and 81, Haroun and Housner [4, 5, 7, 8, 9, 10, 11], used a boundary integral theory to

derive the fluid added mass matrix, thus reducing considerably the number of unknowns in

the problem of deformable cylindrical tanks. The model was applied to predict the maximum

seismic response by means of a response spectrum. Later, Haroun included more

complicating effects in his analyses, such as the effect of soil-structure-fluid interaction on the

dynamic response of flexible tanks [3].

The objective of this research is to develop a mathematical model to be used for predicting the

response of large capacity cylindrical liquid-storage steel tanks either fully anchored or

unanchored at their base when they are subjected to horizontal ground shaking. The proposedmodels take into consideration the sloshing effect, the uplift of base, and the flexibility of the

tank.

2 ASSUMPTIONS AND MODELS

In this research, three different mathematical models were used to analyze the problem of

ground-based tanks. The models are described as follows:

• Model 1: The simple mechanical Model is used to analyze anchored tanks, Figure (1).

• Model 2: A Finite Element Model was built using the (ANSYS) structural analysis

program to analyze anchored tanks with fixed-base boundary conditions, Figure (2).

• Model 3: Another Finite Element Model was built using the (ANSYS) program toanalyze the un-anchored tanks but with including surface-to-surface contact boundary

conditions, Figure (3).

The properties of each model are described as follows.

3 SIMPLE MECHANICAL MODEL

Housner mechanical model, shown in Figure (1), was formulated as an idealization for

estimating liquid response in seismically excited rigid rectangular and circular tanks. The

model proposed values for equivalent masses to represent the impulsive and convective

components of the fluid mass. Properties of model parameters are computed from the tank

geometry and the characteristics of the contained fluid. Further refinements of the model

were included by Haroun (1980) and Veletsos (1977) to add other mass and stiffness toaccount for shell flexibility. The model is currently adopted by the American Petroleum

Institute [2]. The procedure considers two response modes of the tank and its contents: the

response of the tank shell and roof together with a portion of the contents which moves in

union with the shell, and the fundamental sloshing mode of the contents, Figure (1).

Rigid Ground Tanks

The structure consists of the circular tank full of fluid. The fluid in the tank is replaced with

the rigid and sprung masses represented by mass m1 and mass m2, that is attached to the tank

wall by a linear spring of stiffness k c, as shown in Figure (1.a). The impulsive and convective

masses are located at distances X 1 and X 2 respectively from the bottom of the tank. The

storage tank is assumed to be rigid cylindrical shell with head range H (maximum water



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depth) and diameter (D). The parameters describing the model of a rigid cylindrical tank are

given below. According to the (API) code formulas[2]:

For D/H> 4/3

H

D

H

D

W

W

T 866.0

866.0tanh1 =

(1)

Where

W 1 is the weight of the effective mass of the tank contents for determining impulsive

lateral earthquake forces.

W T is the total weight of the fluid

For D/H<4/3, the liquid content in the lower part of the tank (below depth equal to 3/4 of the

diameter) is considered to respond as a rigid body as far as impulsive forces are concerned.

The effective weight of the upper portion of the content is determined from Equation (1)

using D/H =4/3. The total effective weight is determined by adding the full weight of thelower portion of the contents to the effective weight of the upper portion. Thus, the effective

weight W 1 is determined from:

H

D

W

W

T

218.00.11 −=

(2)

The formula used to determine the convective forces, 2W , is:

=

H D H

D

W

W

T

67.3tanh230.02 (3)

Where

W 2 is the weight (pounds) of the effective mass of the

tank contents for determining convictive lateral

earthquake forces.

The height of the centroid of the lateral seismic forces applied due to the impulsive mass, X 1 ,

from the bottom of the tank shell may be determined according to the Diameter/Height ratio.

For D/H > 4/3, the formula used to determine the height of the centroid of the impulsive force

is

375.01=

H X

(4)

The formula for height of the centroid of the convective force X2, is

−

−=

H D H D

H D

H

X

67.3sinh

67.3

167.3

cosh

0.12 (5)

The above equations were derived based on the assumption that the tank is infinitely rigid. In

reality, storage tanks have typically natural periods in the range of 0.10 to 0.25 seconds. Toaccount for this flexibility approximately, the maximum ground motion used in the analysis is



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3-D Shell element It is a 4 node quadrilateral element having both bending and membrane capabilities. Both in-

plane and normal loads are permitted. The element has six degrees of freedom at each node:

translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z-axes.

The element is assumed to be isotropic with constant thickness.

3-D Contained Fluid element

It is a modification of the 3-D structural solid element. The fluid element is used to model

fluids contained within vessels having no net flow rate. The fluid element is particularly well

suited for calculating hydrostatic pressures and fluid/solid interactions. Acceleration effects,

such as in sloshing problems, may be included. The fluid element is defined by eight nodes

having three degrees of freedom at each node: translation in the nodal x, y, and z directions.

The geometry, node locations, and coordinate system for this element are shown in Figure (4).

The element has isotropic material properties. Young’s modulus, which is interpreted as the

“fluid elastic modulus”, should be the bulk modulus of the fluid. The density property is used

to compute a weight of the fluid. The shape functions of the contained fluid element and the

derivation of its Element matrices are described in the manual of the structural analysis program ( ANSYS )

Free Surface Effects:

The free surface is handled with an additional special spring effect. This is implicitly done by

the program by adding springs from each node to ground, with the spring constants being

positive on the top of the element, and negative on the bottom. For an interior node, positive

and negative effects cancel out and, at the bottom where the boundary must be fixed to keep

the fluid from leaking out; the negative spring has no effect. Positive springs are added only

to faces. The surface springs tend to retard the hydrostatic motions of the element from their

correct values. The element is permitted to “bend” without the bulk modulus resistance being

mobilized, as shown in Figure (5). While this motion is permitted, other motions in a static

problem often result, which can be thought of as energy-free eddy currents. For this reason,

small shear and rotational resistances are built in.

3-D Contact element

It is used to represent contact and sliding between 3-D "target" surfaces and a deformable

surface, defined by this element, Figure (6). The element has three degrees of freedom at

each node: translations in the nodal x, y, and z directions and is located on the surfaces of 3-D

shell elements without mid-side nodes.

3-D Target segment element It is a single element with a 4 node quadrilateral shape, Figure (6). This element has three

degrees of freedom at each node: translations in the nodal x, y, and z directions. It is a

geometric entity in space that senses and responds when one or more contact elements move

into a target segment element.

Surface-to-Surface Contact element

The contact element has the same geometric characteristics as the shell element face with

which it is connected. Contact occurs when the element surface penetrates one of the target

segment elements on a specified target surface. Coulomb and shear stress friction is allowed.

For shell elements, the same nodal ordering between shell and contact elements defines upper

surface contact; otherwise, it represents bottom surface contact. The target surfaces mustalways be on its outward normal direction. The 3-D contact surface elements are associated



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with the 3-D target segment elements via a shared real constant set. In studying the contact

between two bodies, the surface of one body is conventionally taken as a contact surface and

the surface of the other body as a target surface. For rigid-flexible contact, the contact surface

is associated with the deformable body; and the target surface must be the rigid surface. The

contact and target surfaces constitute a “Contact Pair”. The contact detection points (i.e. the

integration points) are located either at nodal points or Gauss points Figure (7). The contactelement is constrained against penetration into target surface at its integration points.

However, the target surface can, in principle, penetrate through into the contact surface. The

penetration distance is measured along the normal direction of contact surface located at

integration points to the target surface Figure (8). The formulae and derivation of the element

matrices are found in the manual of the analysis program.

The Constraints For The Contained Fluid Elements

The contained fluid elements at boundaries are constrained such that the coincident nodes of

both the fluid and shell elements at the wall boundary should have the same displacements

(are coupled) in the direction normal to the interface only, while the relative movements in the

tangential and vertical directions are allowed to occur. At the base, fluid element nodes areallowed to move on the surface of the tank bottom plate and are coupled only in the vertical

direction.

5 NONLINEAR STRUCTURAL ANALYSIS

ANSYS employs the "Newton-Raphson" approach to solve nonlinear problems. It uses

automatic time stepping based on number of equilibrium iterations used in the last time step

(more iterations cause the time step size to be reduced). The program continues to do

equilibrium iterations until the convergence criteria are satisfied or until the maximum

number of equilibrium iterations is reached. The ANSYS program provides three different

vector norms to use for convergence checking:

• The infinite norm repeats the single-DOF check at each DOF in the model.

• The L1 norm compares the convergence criterion against the sum of the absolute

values of force (and moment) imbalance for all DOFs.

• The L2 norm (which is used in this problem) performs the convergence check using

the square root sum of the squares of the force (and moment) imbalances for all DOFs.

6 NUMERICAL RESULTS

Numerical study was carried out to study and evaluate the performance and accuracy of the

developed finite element model, which uses the fluid element and the interface bottom

element, in detecting the sloshing effect and the uplift of the base, and also to compare the

results obtained by the finite element model with those obtained by the simple model. A steelground tank, whose properties are summarized in table (1), was analyzed using three models:

• Model-1: represents a discrete two degrees-of-freedom system, Figure (1.b) and

includes the impulsive and convective components of fluid mass. The

simple Model, whose properties are described in table (2), is used to analyze

anchored tanks.

• Model-2: A Finite Element Model was built using the (ANSYS) structural analysis

program to analyze anchored tanks with fixed-base boundary conditions. It

contains shell and contained fluid elements, Figure (2).

• Model-3: A Finite Element Model was built similar to Model 2 except that it contains

surface-to-surface contact boundary conditions, Figure (3). It can simulate

the uplift of base plate from foundation and was used to analyze the un-anchored tanks.



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A time history analysis was carried out for the three models using (as input) a part of the

scaled north-south component of the 1940 Elcentro earthquake, which has a peak ground

acceleration of 0.31882 g , Figure (9). The results obtained by using all models were

compared.

Table (1). Properties Of Circular Steel Ground Tank Geometric

PropertiesValue Material Properties Value

Height of the tank,

( m )11.00

Fluid density,

(3

/ m N )1000

Diameter of the tank,

( m )

12.00 Fluid bulk

modulus,(2/ m )

2.0685E+9

Height of water,

( m )

11.00 Steel modulus of

elasticity, (2/ m N )

2E+11

Steel Poisson’s ratio 0.3

Steel density,

(3/ m N )

7833.4

Table (2) Model-1 Properties

Geometric Properties ValueMaterial

PropertiesValue

Stiffness of the

impulsive mass sk ,

( m N / )

1.944 Impulsive weight

1W , N 95634

Stiffness of the

convective mass ck ,

( m N / )

0.9525E-4 Convective weight

2W ,

31878

The height of the

centroid of the

impulsive force 1 X ,

( m )

4.4

The height of thecentroid of the

convective force 2 X ,

( m )

8.15

Figure (10) shows the time history for some of the Response parameters for anchored tank

obtained by using Model-1

Figure (11) shows the time history for some of the Response parameters for anchored tank

obtained by using Model 2

Figure (12) shows the time history for some of the Response parameters for un-anchored tankobtained by using Model-3



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The study shows reasonable agreement between the simple model and the finite element

model with regards to the base shear for anchored tanks. As for un-anchored tanks, it was

observed that the base shear induced in an un-anchored tank is (10%) smaller than that

resulting on a similar anchored tank. This is due to the rigid body motion of the structure,

which absorbs the earthquake energy through the rocking motion. However, the stresses in

walls at the bottom of an un-anchored tank are going to be larger than those of a similaranchored tank subjected to the same ground motion.

Parametric Study

Later, a parametric study was carried out, using the Finite Element Models to investigate the

effect of varying the tank slenderness ratio (height-to-radius ratio) on the tank response, for

both anchored and un-anchored tanks and to verify the stability of the model over a range of

geometry parameters. Different structures with different height-to-width ratios had been

analyzed. Both the tank height and diameter were changed but keeping the tank capacity as

constant for all cases.

Figure 13: shows the variation of Response Parameters versus the tank height-to-radius ratio

(H/R) for Anchored TanksFigure 14: shows the variation of Response Parameters versus the tank height-to-radius ratio

(H/R) for Un-Anchored Tanks

For the cases studied of anchored and unanchored tanks, it was found that the base shear and

the wall stresses, both increase as the slenderness ratio H/R increases.

7 CONCLUSIONS

In this research, the behavior of liquid tanks resting directly on the ground was investigated.

Different finite element models were built up and utilized to analyze tanks of various

boundary conditions. The models include different 3-D element types, such as 3-D contained

fluid element, 3-D contact element, and 3-D target element. The models can accurately

simulate the base partial uplift and the re-contact condition during the uplift motion. The

models are also capable to consider the fluid-structure interaction accurately. An extensive

parametric study was carried out concerning the effect of some factors of the tank geometry

on its response. Using of the proposed 3-D finite element model with the fluid element gives

detailed comprehensive results for wall axial and hoop stresses and for the fluid sloshing,

which cannot be obtained by using the simple mechanical model. The cases studied for un-

anchored tanks showed the effect of uplift motion in reducing the base shear relative to

anchored tanks. However, the accompanying increase in wall stresses should be observed.

The study also showed the effect of tank slenderness ratio on the tank base shear and wall

stresses.

REFERRENCES

[1] American Water Works Association, AWWA Standard for Welded Steel Tanks for

Water Storage, American Welding Society, New England Water Works Association,

AWWA D100-84, Denver, Colorado, March 1985.

[2] American Petroleum Institute, Welded Steel Tanks for Oil Storage, API Standard 650,

7th Edition, Washington, D.C., 1980.

[3] Haroun, M.A., and Abdel-Hafiz, E.A., A Simplified Seismic Analysis of Rigid Base

Liquid Storage Tanks Under Vertical Excitations with Soil-Structure Interaction,

International Journal of Soil Dynamics and Earthquake Engineering, Vol. 5, No. 4, October

1986, pp. 217-225.



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[4] Haroun, M.A., Stress Analysis of Rectangular Walls Under Seismically Induced

Hydrodynamic Loads, Bulletin of the Seismological Society of America, Vol. 74, No. 3,

June 1984, pp. 1031-1041.

[5] Haroun, M.A., and Warren, W.L., TANK - A Computer Program for Seismic Analysis

of Tanks, Proceedings of the Third Conference on Computing in Civil Engineering, ASCE,

California, April 1984, pp. 665-674.[6] Haroun, M.A., Behavior of Unanchored Oil Storage Tanks: Imperial Valley

Earthquake, Journal of Technical Topics in Civil Engineering, Vol. 109, April 1983, pp. 23-

40.

[7] Haroun, M.A., and Housner, G.W., Complications in Free Vibration Analysis of

Tanks, Journal of Engineering mechanics, ASCE, Vol. 108, 1982, pp. 801-818.

[8] Haroun, M.A., and Housner, G.W., Dynamic Characteristics of Liquid Storage Tanks,

Journal of Engineering mechanics, ASCE, Vol. 108, 1982, pp. 783-800.

[9] Haroun, M.A., Earthquake Response of Deformable Liquid Storage Tanks, Journal of

Applied Mechanics, ASME, Vol. 48, No. 2, June 1981, pp. 411-418.

[10] Haroun, M.A., and Housner, G.W., Seismic Design of Liquid Storage Tanks, Journal

of Technical Councils, ASCE, Vol. 107, April 1981, pp. 191-207.[11] Haroun, M.A., Dynamic Analyses of Liquid Storage Tanks, Earthquake Engineering

Research Laboratory, Report No. EERL 80-4, California Institute of Technology, February

1980.

[12] Housner, G., Dynamic Pressure on Accelerated Fluid Containers, Bulletin of the

Seismological Society of America, Vol. 47, 1957, pp. 15-35.

[13] Malhotra, P. K. (1997a). “Method for seismic base isolation of liquid-storage tanks.”

J. Struct. Engrg., ASCE, 123(1), 113-116.

[14] Malhotra, P. K. (1997b). “New method for seismic isolation of liquid-storage tanks.”

J. Earthquake Eng. Struct. Dyn., 26(8), 839-847.

[15] Veletsos, A.S., and Yang, J.Y., Earthquake Response of Liquid Storage Tanks,

Proceedings of the EMD Specialty Conference, ASCE, Raleigh, N.C., 1977, pp. 1-24.

[16] Veletsos, A.S., and Yang, J.Y., Dynamics of Fixed Base Liquid Storage Tanks,

Proceedings of U.S.-Japan Seminar on Earthquake Engineering Research with Emphasis on

Lifeline Systems, Japan Society for Promotion of Earthquake Engineering, Tokyo, Japan,

November 1976, pp. 317-341.

[17] Veletsos, A.S., Seismic Effects in Flexible Liquid Storage Tanks, Proceedings of the

5th World Conference on Earthquake Engineering, Rome, Italy, Vol. 1, 1974, pp. 630-639.



E05SR33-11

X1

X2H1 mo

m1K/2K/2

x ( t )

G(t)

Rigid Wall

Ho Ks

Kc

Xs

Xc

W1

W2

G(t)

Fig.1.a: Rigid Tank. Fig.1.b: Flexible Tank.

Fig. 1: Housner’s Mechanical Model.

Fig.2: Model II (the finite element model

for anchored tank)

Fig.3: Model 3 (the finite element model for un-

anchored tank).

m1

m2

X1

X2



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Fig.4 3-D Contained Fluid Element Fig.5: Bending without resistance

Fig.6 3-D Surface-to-Surface Contact Elements

Fig.7: Contact Detection Point Locations at Gauss Point

F Fig.8 Penetration Distance



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-4

-3

-2

-1

0

1

2

3

4

1 3 5 7 9 11 13 15 17 19 21 23

time (sec)

a c c e l e r a t i o n

( m / s e c 2 )

Fig.9 Scaled north-south component of the 1940 Elcentro earthquake time history.

Fig.10.a: the total base shear ( x F )

Fig. 10.b: displacements in the X direction ( xu ) for 2W (convective mass)

Fig.10: Response time history for anchored tank Model 1



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Fig.11.a: the total base shear ( x F ) Fig.11.b: stress for lower right steel wall element

Fig.11.c: hoop-stress for lower right steel wall

element Fig.11.d: displacements in the Z-direction ( z u )

for right upper point of water

Fig.11: Response time history for anchored tank Model 2



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Fig. 12.a: the total base shear ( x F ) Fig.12.b: stress for lower right steel wall

element

Fig. 12.c: hoop-stress for lower right steel wall

element

Fig. 12.d: displacements in the Z-direction

( z u ) for right upper point of

water

Fig. 12.e gap in the Z-direction ( z u ) for left

point of steel base

Fig. 12.f gap in the Z direction ( z u ) for

right point of steel base

Fig. 12: Response time history for un-anchored tank Model 3



E05SR33-16

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 1.5 1.83 2.64 3.17

H/R

F x / F z

0.00E+00

5.00E+07

1.00E+08

1.50E+08

2.00E+08

2.50E+08

1 1.5 1.83 2.64 3.17

H/R

S T R E S S

Fig. 13.a: the total base shear and the total

weight of the tank

Fig. 13.b: the maximum absolute stress for

lower right steel element

Sloshing

0.3

0.35

0.4

0.45

0.5

0.55

1 1.5 1.83 2.64 3.17

H/R

V e r

t i c a l D i s p l a c e m e n t ( m )

Fig. 13.c: the maximum absolute sloshing

displacements ( z u ) for upper

right point of water surface

Fig. 13: Variation of Response Parameters versus the tank height-to-radius ratio (H/R) for

Anchored Tank.



E05SR33 17

0

0.2

0.4

0.6

0.8

1 1.83 2.64

H/R ratio

R e a c t i

o n F a c t o r

ress

5.00E+05

5.05E+07

1.01E+08

1.51E+08

2.01E+08

2.51E+08

3.01E+08

3.51E+08

1 1.83 2.64

H/R ratio

S t r e s s ( N / m 2 )

Fig. 14.a: the total base shear and the total

weight of the tank

Fig. 14.b: the maximum absolute stress for

lower right steel element

5.00E+05

5.05E+07

1.01E+08

1.51E+08

2.01E+08

2.51E+08

1 1.83 2.64

H/R ratio

S t r e s s ( N / m 2 )

0.2

0.204

0.208

0.212

0.216

0.22

1 2 3 4

H/R ratio

S l o s h i n g ( m )

Fig. 14.c: the maximum absolute hoop-

stress for lower right steel

element of wall

Fig. 14.d: the maximum absolute sloshing

displacements ( z u ) for upper right

point of water surface

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

8.00E-02

1 1.83 2.64

H/R ratio

G a p D i s t a n c e ( m )

Fig. 14.e: the maximum absolute gap distance

( z u ) for right point of base plate

Fig. 14: Variation of Response Parameters versus the tank height-to-radius ratio (H/R) for

Un-Anchored Tank.

seismic response of above ground storage tanks

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