Dynamic Behavior and Response Analysis
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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.

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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

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


Dynamic behavior and response analysis of fluid tank systems

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.


Dynamic behavior and response analysis of fluid tank systems

Courtesy U.C. Berkley


Dynamic behavior and response analysis of fluid tank systems

Courtesy U.C. Berkley


Dynamic behavior and response analysis of fluid tank systems

Courtesy U.C. Berkley


Dynamic behavior and response analysis of fluid tank systems

Courtesy U.C. Berkley


Dynamic behavior and response analysis of fluid tank systems

  • 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.


The approximate cantilever beam approach

The Approximate“Cantilever-Beam” Approach

  • 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


Purposes of this study

Purposes of This Study

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.


Dynamic behavior and response analysis of fluid tank systems

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


Modeling approach i tank

Modeling Approach I -Tank

  • 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


Modeling approach ii 3 d contained fluid elements

Modeling Approach II - 3-D Contained Fluid Elements

  • 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


Modeling approach iii meshing fea models

Modeling Approach III - Meshing FEA Models

  • 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


Dynamic behavior and response analysis of fluid tank systems

  • partially filled with a near incompressible water

  • water-contained fluid elements

  • tank--shell and beam elements

  • interaction between water and tank wall is included


Dynamic behavior and response analysis of fluid tank systems

How to verify the numerical solution fromANSYS FEA models?


Dynamic behavior and response analysis of fluid tank systems

ANSYS

Rigid Tanks

Theory

Rigid Tanks

Yes

ANSYS

Flexible Tanks

Approximate

Flexible Tanks

Comparison

&

Conclusion

AWWA

Simplified “Rigid”

Tank Method

ANSYS

Unanchored


Dynamic behavior and response analysis of fluid tank systems

1st Natural Mode Shape – Water Sloshing

One-Cosine Type Sloshing Mode


Dynamic behavior and response analysis of fluid tank systems

2nd Natural Mode Shape – Water Sloshing

Two-Cosine Type Sloshing Mode


Dynamic behavior and response analysis of fluid tank systems

3rd Natural Mode Shape – Water Sloshing

Three-Cosine Type Sloshing Mode


Dynamic behavior and response analysis of fluid tank systems

4th Natural Mode Shape – Water Sloshing

Four-Cosine Type Sloshing Mode


Dynamic behavior and response analysis of fluid tank systems

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.


Dynamic behavior and response analysis of fluid tank systems

For RigidTanks

ANSYSResults

Modeling approach is acceptable

TheoreticalResults

FlexibleTank Analysis


Modal analysis for flexible tanks

Modal Analysis for Flexible Tanks

  • 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)


Dynamic behavior and response analysis of fluid tank systems

1st Natural Mode Shape – Full Tank


Dynamic behavior and response analysis of fluid tank systems

2nd Natural Mode Shape – Full Tank


Dynamic behavior and response analysis of fluid tank systems

3rd Natural Mode Shape – Full Tank


Dynamic behavior and response analysis of fluid tank systems

1st Natural Mode Shape - Partially Full Tank


Dynamic behavior and response analysis of fluid tank systems

2nd Natural Mode Shape – Partially Full Tank


Dynamic behavior and response analysis of fluid tank systems

3rd Natural Mode Shape – Partially Full Tank


Dynamic behavior and response analysis of fluid tank systems

1st Natural Mode Shape – Tall-Full Tank


Dynamic behavior and response analysis of fluid tank systems

1st Natural Mode Shape – Short-Full Tank


Dynamic behavior and response analysis of fluid tank systems

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


Dynamic behavior and response analysis of fluid tank systems

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


Modal frequency comparison

Modal Frequency Comparison


Dynamic behavior and response analysis of fluid tank systems

Modal Frequency Comparison


Modal frequency comparison1

Modal Frequency Comparison


Dynamic behavior and response analysis of fluid tank systems

Modal Frequency Comparison


Dynamic behavior and response analysis of fluid tank systems

Modal Frequency Comparison


Dynamic behavior and response analysis of fluid tank systems

Modal Frequency Comparison


Dynamic behavior and response analysis of fluid tank systems

For FlexibleTanks

Approximate“Cantilever-Beam”Results

Acceptable

ANSYSResults


Dynamic behavior and response analysis of fluid tank systems

Earthquake Response

Analyses

(ANSYS Results)


Earthquake ground input el centro n s adjusted 0 4g

Earthquake Ground Input: El Centro N-S Adjusted 0.4g

  • Acceleration

  • Velocity

  • Displacement


Pressure time history 3 ft from base

Pressure Time History (3 ft. from Base)


Dynamic behavior and response analysis of fluid tank systems

Pressure distribution along wall

at  = 0o and

T=3.21 Sec.


Dynamic behavior and response analysis of fluid tank systems

Compare with RigidTanksolutions:

Pressure distribution along wall

at  = 0o


Dynamic behavior and response analysis of fluid tank systems

Courtesy U.C. Berkley


Stress time history results

Stress Time History Results

  • Hoop and Axial Stress Z=-21 ft

    at  = 0o

  • Hoop and Axial Stress Z=-21 ft

    at  = 180o


Dynamic behavior and response analysis of fluid tank systems

Water Surface Displacement Time History

 =180o

 =0o


Dynamic behavior and response analysis of fluid tank systems

Water Surface Profile at Time=5.09sec.

(Maximum Water Surface Displacement = 33 inches)


Von mises stress distribution at t 4 63 sec

von Mises Stress Distribution at T=4.63 sec.


Dynamic behavior and response analysis of fluid tank systems

Courtesy U.C. Berkley


Dynamic behavior and response analysis of fluid tank systems

Base Shear Time History Results


Dynamic behavior and response analysis of fluid tank systems

Overturning Moment Time History


Comparison of ansys results with that from awwa d100

Method

Base Shear

(kips)

Comparison

(%)

FEA

ANSYS

620

100

Approximate

Approach

591

95.3

Simplified

in AWWA

487

78.6

Comparison of ANSYS Results with that from AWWAD100


Spectrum analysis comparison

Spectrum Analysis Comparison


Conclusions

Conclusions

  • 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.


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