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Dynamic Behavior and Response Analysis of Fluid/Tank Systems

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Dynamic Behavior and Response Analysis

of Fluid/Tank Systems

He Liu, Ph.D., P.E.

University Alaska Anchorage

Daniel H. Schubert, P.E.

Dept. of Environmental

Health & Engineering

ANTHC

Tanks Rupture: A water tank was lifted off a gravel base six to ten inches during an earthquake. After the earthquake, the tank was resting on the gravel base about 12 inches lower (due to buckle) and shifted about an inch to the west.

Courtesy U.C. Berkley

Courtesy U.C. Berkley

Courtesy U.C. Berkley

Courtesy U.C. Berkley

- Tank seismic Design Code is mainly
based onsimplifiedRigid Tank

assumption, and NO fluid/structure

interactionincluded

- Theoretical solutions are available
only for rigidtanks and no interaction

- Anapproximate “Cantilever Beam”
approach needs numerical proof.

- For approximate frequencies can be calculated
by equation

- f’0is the natural frequency of the fluid tank
system with roof mass

- fo is the natural frequency without the roof
- fFB and fSB is the natural frequency of an
empty tank with the mass of the roof

Use the Finite Element Analysis(FEA)

- To evaluate the performance of steel water tanks due to earthquake excitation
- To compare results with Design Code of AWWA’s simplified formula’s
- To verify the approximate “Cantilever-Beam”approach.

z

x

y

r

x

R

Tank Geometry

water level

Ht

H

tb

Radius =16 feet

Height = 26 feet

Water Depth = 24 feet

Wall Thickness =0.315in

=0o

ts

- Tank wall/roof/base
- - shell and beam elements

- Fluid
- - Fluid 3-D Contained FluidElement

- Material Properties
- Steel E = 29,000 ksi

- Steel density = 7.34x104 lb-sec2/in4

- Fluid density = 0.9345x104 lb-sec2/in4

- Fluid bulk modulus = 30x104 lb/in2

- 8 nodes - 3 DOF
- Free surface - added spring
- Bulk modulus = 30 x 104 lb/in2
- Fluid elements do not attached at tank
wall and base

- Coincident nodes coupled normal to
the interface to allow fluid relative

movement in tangential and vertical

directions

- Free horizontal movement at base

- Because of the system symmetry, one half
of the tank is modeled.

- Fluid elements are rectangular-brick
shaped whenever possible

- Number of Fluid Elements in ANSYS
Model:

- 640, 1280, 2112, 3072

- Based on accuracy and efficiency, 1280

fluid elements was chosen

- partially filled with a near incompressible water
- water-contained fluid elements
- tank--shell and beam elements
- interaction between water and tank wall is included

How to verify the numerical solution fromANSYS FEA models?

ANSYS

Rigid Tanks

Theory

Rigid Tanks

Yes

ANSYS

Flexible Tanks

Approximate

Flexible Tanks

Comparison

&

Conclusion

AWWA

Simplified “Rigid”

Tank Method

ANSYS

Unanchored

1st Natural Mode Shape – Water Sloshing

One-Cosine Type Sloshing Mode

2nd Natural Mode Shape – Water Sloshing

Two-Cosine Type Sloshing Mode

3rd Natural Mode Shape – Water Sloshing

Three-Cosine Type Sloshing Mode

4th Natural Mode Shape – Water Sloshing

Four-Cosine Type Sloshing Mode

Modal Analysis Results:

Comparison of Convective Frequencies

No. of Fluid Elements in ANSYSModel

Theory

(Units: Hz)

640

1280

2112

3072

1st mode

0.299

0.298

0.298

0.298

0.305

2nd mode

0.477

0.476

0.475

0.474

0.521

3rd mode

0.562

0.555

0.552

0.551

0.660

Note: Compared with results of linear theory, the first mode differs by 1.7%. Differences may be related to limitations on the linear theory, with nonlinear theory closer to FEA values.

For RigidTanks

ANSYSResults

Modeling approach is acceptable

TheoreticalResults

FlexibleTank Analysis

- A total of 54 geometric variations, with and without roofs, were analyzed.
- Tank/fluid variables were represented by three basic parameters:

- Tank geometric aspect ratios, as represented
by the tank height to radius (H/R)

- Tank shell wall thickness ratio represented
by the wall thickness to tank radius (ts/R)

- Liquid depth ratio(h/R)

1st Natural Mode Shape – Full Tank

2nd Natural Mode Shape – Full Tank

3rd Natural Mode Shape – Full Tank

1st Natural Mode Shape - Partially Full Tank

2nd Natural Mode Shape – Partially Full Tank

3rd Natural Mode Shape – Partially Full Tank

1st Natural Mode Shape – Tall-Full Tank

1st Natural Mode Shape – Short-Full Tank

1st Natural Mode Shape – Tall-Partial-Full Tank

2nd Natural Mode Shape – Tall-Partial-Full Tank

Modal Frequency Comparison

Modal Frequency Comparison

Modal Frequency Comparison

Modal Frequency Comparison

For FlexibleTanks

Approximate“Cantilever-Beam”Results

Acceptable

ANSYSResults

Earthquake Response

Analyses

(ANSYS Results)

- Acceleration
- Velocity
- Displacement

Pressure distribution along wall

at = 0o and

T=3.21 Sec.

Compare with RigidTanksolutions:

Pressure distribution along wall

at = 0o

Courtesy U.C. Berkley

- Hoop and Axial Stress Z=-21 ft
at = 0o

- Hoop and Axial Stress Z=-21 ft
at = 180o

Water Surface Displacement Time History

=180o

=0o

Water Surface Profile at Time=5.09sec.

(Maximum Water Surface Displacement = 33 inches)

Courtesy U.C. Berkley

Base Shear Time History Results

Overturning Moment Time History

Method

Base Shear

(kips)

Comparison

(%)

FEA

ANSYS

620

100

Approximate

Approach

591

95.3

Simplified

in AWWA

487

78.6

- FEA method allows for a more complete
evaluation of seismic loading conditions

on fluid/tank systems.

- Rigid tank assumptions provide
un-conservative solutions.

- “Cantilever-beam” approach provide
very good approximations for design

purpose.

- Further refinements in standard design
procedures should permit performance

based designs.