GTStrudl

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GTStrudl Modeling and Analysis Of Friction
Bearing Base Isolation
Michael H. Swanger, Ph.D. Georgia Tech CASE
Center GTSUG 2007 June 18-21, 2007 Jupiter, FL
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Topics

1. Background
2. Friction Bearing Mechanics and Modeling
   Parameters
3. Basic Behavior Examples
4. Plane Frame Example Comparison of Rigid vs
   Isolated
5. Nonlinear Dynamic Analysis

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Background
Why Do Base Isolation?
Conventional Rigid Foundation
Foundation with Base Isolation
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Background
Examples of Base Isolation Systems
Rubber Bearing (RB) System (oiles)
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Background
Examples of Base Isolation Systems
Lead Rubber Bearing (LRB) System (oiles)
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Background
Examples of Base Isolation Systems
Friction Pendulum System (FPS) (oiles)
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Background
Examples of Base Isolation Systems
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Background
Examples of Base Isolation Systems
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Background
R D Modeling of Friction Bearing Systems

• Reinhorn, Constantinou, et. al., SUNY Buffalo
• Teflon bearing behavior
• 3D-BASIS Computer Program for Nonlinear
  Dynamic
• Analysis of Three-Dimensional Base Isolated
  Structures
• Whittaker, Fenves, SUNY Buffalo, University of
  California
• Berkeley
• Almazan, De la Llera, University of Chile

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Mechanics and Modeling Parameters
Equilibrium wrt one-dimensional, horizontal
motion
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Mechanics and Modeling Parameters
Equilibrium wrt horizontal, bi-axial motion
coupled plasticity
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Mechanics and Modeling Parameters
The FE model one-dimensional, horizontal motion
V
UV
E
KAX
S
H
UY
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Mechanics and Modeling Parameters
Variable Coefficient of Friction
With Respect to Velocity and Pressure
µmin coefficient of friction at very low
velocity, µmax0 coefficient of friction at zero
bearing pressure, µmaxp coefficient of friction
at very high bearing pressures, e constant that
controls the transition of µmax between very low
and very high bearing pressures, a constant
that controls the transition of µ between low and
high relative slider velocities, FB the
bearing force, ACS effective contact area of
the slider with the bearing surface.
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Mechanics and Modeling Parameters
Variable Coefficient of Friction
µmin 0.04 µmax0 0.12 µmaxp 0.05 a 0.6 e
0.012
µ (f) vs. Slider Velocity
µmax vs. Bearing Pressure
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Mechanics and Modeling Parameters
The BASE ISOLATION ELEMENT Command
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Mechanics and Modeling Parameters
BASE ISOLATION Command Elements
Bridge Pier and Superstructure Separated by a
Base Isolation Element
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Mechanics and Modeling Parameters
BASE ISOLATION Command Elements
Global PLANE OF MOTION Relevant Global Sliding Displacement Degrees of Freedom Bearing Displacement Degree of Freedom
XY UX, UY UZ
XZ UX, UZ UY
YZ UY, UZ UX
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Mechanics and Modeling Parameters
BASE ISOLATION Command Elements
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Mechanics and Modeling Parameters
BASE ISOLATION Command Elements
V
RD
UV
E
KAX
S
H
UY
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Mechanics and Modeling Parameters
BASE ISOLATION Command Elements
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Mechanics and Modeling Parameters
BASE ISOLATION Command Elements
At first onset of sliding Friction Force
vBFµFB, vBF gt 1.0 vBF 1.0 by default
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Basic Behavior Examples

• Flat sliding surface, constant bearing pressure,
• constant friction µ 0.05
• Flat sliding surface, constant bearing pressure,
• variable friction, µmax 0.05
• Flat sliding surface, varying bearing pressure,
• constant friction µ 0.05
• Flat sliding surface, constant bearing pressure,
• constant friction µ 0.05, BF 1.5
• 5. Convex sliding surface, RD 50 inches,
• constant bearing pressure, constant friction µ
  0.05
• 6. Plane frame rigid vs isolated comparison

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Basic Behavior Examples

• Flat Sliding Surface, Constant Bearing Pressure,
• Constant Friction µ 0.05

L 1 in, µ 0.05
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Basic Behavior Examples

• Flat Sliding Surface, Constant Bearing Pressure,
• Constant Friction µ 0.05

UNITS INCHES LBS JOINT COORDINATES 1 0.0 0.0
2 0.0 -1.0 S 3 1.0 0.0 S 4 0.0 0.0
1.0 S TYPE SPACE TRUSS MEMBER INCIDENCES 1 1
3 2 1 4 CONSTANTS E 1.E10 MEMBER PROPERTIES
1 2 AX 1.0 BASE ISOLATION ELEMENT DATA 'FB1'
INCIDENCES START 2 END 1 TYPE FRICTION BEARING -
PLANE XZ UY 0.005 KAX 1.E8 FRICTION CONSTANT
FC 0.05 END PRINT ELEMENT PROPERTIES LOAD
1 JOINT LOADS 1 FORCE Y -10000.0
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Basic Behavior Examples

• Flat Sliding Surface, Constant Bearing Pressure,
• Constant Friction µ 0.05

MAXIMUM NUMBER OF CYCLES 10 CONVERGENCE TOLERANCE
EQUIL 0.001 NONLINEAR ANALYSIS UNITS CYCLES
SECONDS TRANSIENT LOAD 'TL1' JOINT 1 FORCE X
FUNCT SINE AMPL 0.5E10 FREQ 2.0 INTEGRATE -
FROM 0.000000 TO 1.0 AT 0.001 END TRANSIENT
LOAD LOAD LIST 'TL1' DYNAMIC PARAMETERS STORE
VELOCITY ON STORE ACCELERATION ON STORE
ABSOLUTE ACCELERATION USE EXTERNAL FILE SOLVER
MAXIMUM NUMBER OF EQUILIBRIUM CYCLES 20
CONVERGENCE TOLERANCE ENERGY 0.001 INITIAL
STRESS LOAD '1' PRINT MAX END OF DYNAMIC
PARAMETERS INERTIA OF JOINTS WEIGHT EXISTING
TRANSL ALL 1.0 DAMPING PROPORTIONAL TO STIFFN
0.005 DYNAMIC ANALYSIS NONLINEAR BETA 0.250000
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Basic Behavior Examples

• Flat Sliding Surface, Constant Bearing Pressure,
• Constant Friction µ 0.05

BASE ISOLATION ELEMENT ELEMENT DATA 'FB1'
INCIDENCES START 2 END 1 TYPE FRICTION BEARING -
PLANE XZ UY 0.005 KAX 1.E8 FRICTION CONSTANT
FC 0.05 END PRINT ELEMENT PROPERTIES
Friction Bearing Element Data
Element
Start Jnt End Jnt ------- ---------
------- FB1 XZ 2 1
ACS 0.0000E00 RD 0.0000E00 Kax
0.1000E09 Uy 0.5000E-02
TH1 0.0000E00 TH2
0.0000E00 TH3 0.0000E00
Fc 0.5000E-01 Fmin
0.0000E00 Fmax0 0.0000E00 Fmaxp
0.0000E00
BF 1.000 Alpha 0.0000E00 Epsilon
0.0000E00
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Basic Behavior Examples

• Flat Sliding Surface, Constant Bearing Pressure,
• Constant Friction µ 0.05

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Basic Behavior Examples

• Flat Sliding Surface, Constant Bearing Pressure,
• Constant Friction µ 0.05

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Basic Behavior Examples
2. Flat Sliding Surface, Constant Bearing
Pressure, Variable Friction µmax 0.05
UNITS INCHES LBS JOINT COORDINATES 1 0.0 0.0
2 0.0 -1.0 S 3 1.0 0.0 S 4 0.0 0.0
1.0 S TYPE SPACE TRUSS MEMBER INCIDENCES 1 1
3 2 1 4 CONSTANTS E 1.E10 MEMBER PROPERTIES
1 2 AX 1.0 BASE ISOLATION ELEMENT ELEMENT DATA
'FB1' INCIDENCES START 2 END 1 TYPE FRICTION
BEARING - PLANE XZ UY 0.005 KAX 1.E8 ACS
10.0 - FRICTION VARIABLE ALPHA 0.6 EPS 0.012
FMIN 0.03 - FMAX0 0.12 FMAXP
0.05 END LOAD 1 JOINT LOADS 1 FORCE Y -10000.0
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Basic Behavior Examples
2. Flat Sliding Surface, Constant Bearing
Pressure, Variable Friction µmax 0.05
BASE ISOLATION ELEMENT DATA 'FB1' INCIDENCES
START 2 END 1 TYPE FRICTION BEARING - PLANE
XZ UY 0.005 KAX 1.E8 ACS 10.0 - FRICTION
VARIABLE ALPHA 0.6 EPS 0.012 FMIN 0.03 -
FMAX0 0.12 FMAXP 0.05 END
µmax0 0.12, µmaxp 0.05, µmin 0.03 e
0.012 FB 10000.0 lbs, ACS 10.0 in2 µmax
0.12 (0.12 0.05)tanh(12.0) 0.05
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Basic Behavior Examples
2. Flat Sliding Surface, Constant Bearing
Pressure, Variable Friction µmax 0.05
µmax 0.05, µmin 0.03 a 0.6
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Basic Behavior Examples
2. Flat Sliding Surface, Constant Bearing
Pressure, Variable Friction µmax 0.05
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Basic Behavior Examples
2. Flat Sliding Surface, Constant Bearing
Pressure, Variable Friction µmax 0.05
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Basic Behavior Examples

• Flat Sliding Surface, Varying Bearing Pressure,
• Constant Friction µ 0.05

L 1 in, µ 0.05
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Basic Behavior Examples

• Flat Sliding Surface, Varying Bearing Pressure,
• Constant Friction µ 0.05

MAXIMUM NUMBER OF CYCLES 10 CONVERGENCE TOLERANCE
EQUIL 0.001 NONLINEAR ANALYSIS UNITS CYCLES
SECONDS TRANSIENT LOAD 'TL1' JOINT 1 FORCE X
FUNCT SINE AMPL 0.5E10 FREQ 2.0 JOINT 1 FORCE Y
FUNCT SINE AMPL 2000.0 FREQ 8.0 INTEGRATE -
FROM 0.000000 TO 1.0 AT 0.001 END TRANSIENT
LOAD LOAD LIST 'TL1' DYNAMIC PARAMETERS STORE
VELOCITY ON STORE ACCELERATION ON STORE
ABSOLUTE ACCELERATION USE EXTERNAL FILE SOLVER
MAXIMUM NUMBER OF EQUILIBRIUM CYCLES 20
CONVERGENCE TOLERANCE ENERGY 0.001 INITIAL
STRESS LOAD '1' PRINT MAX END OF DYNAMIC
PARAMETERS INERTIA OF JOINTS WEIGHT EXISTING
TRANSL ALL 1.0 DAMPING PROPORTIONAL TO STIFFN
0.005 DYNAMIC ANALYSIS NONLINEAR BETA 0.250000
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Basic Behavior Examples

• Flat Sliding Surface, Varying Bearing Pressure,
• Constant Friction µ 0.05

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Basic Behavior Examples

• Flat Sliding Surface, Varying Bearing Pressure,
• Constant Friction µ 0.05

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Basic Behavior Examples

• Flat Sliding Surface, Varying Bearing Pressure,
• Constant Friction µ 0.05

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Basic Behavior Examples
4. Flat Sliding Surface, Constant Bearing
Pressure, Constant Friction µ 0.05, BF 1.5
UNITS INCHES LBS JOINT COORDINATES 1 0.0 0.0
2 0.0 -1.0 S 3 1.0 0.0 S 4 0.0 0.0
1.0 S TYPE SPACE TRUSS MEMBER INCIDENCES 1 1
3 2 1 4 CONSTANTS E 1.E10 MEMBER PROPERTIES
1 2 AX 1.0 BASE ISOLATION ELEMENT DATA 'FB1'
INCIDENCES START 2 END 1 TYPE FRICTION BEARING -
PLANE XZ UY 0.005 KAX 1.E8 FRICTION CONSTANT
FC 0.05 BF 1.5 END PRINT ELEMENT
PROPERTIES LOAD 1 JOINT LOADS 1 FORCE Y
-10000.0
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Basic Behavior Examples
4. Flat Sliding Surface, Constant Bearing
Pressure, Constant Friction µ 0.05, BF 1.5
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Basic Behavior Examples

1. Flat Sliding Surface, Constant Bearing Pressure,
   Constant Friction µ 0.05, BF 1.5

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Basic Behavior Examples

1. Flat Sliding Surface, Constant Bearing Pressure,
   Constant Friction µ 0.05, BF 1.5

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Basic Behavior Examples

1. Flat Sliding Surface, Constant Bearing Pressure,
   Constant Friction µ 0.05, BF 1.5

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Basic Behavior Examples
5. Convex Sliding Surface, RD 50 Inches,
Constant Bearing Pressure, Constant Friction µ
.05
UNITS INCHES LBS JOINT COORDINATES 1 0.0 0.0
2 0.0 -1.0 S 3 1.0 0.0 S 4 0.0 0.0
1.0 S TYPE SPACE TRUSS MEMBER INCIDENCES 1 1
3 2 1 4 CONSTANTS E 1.E10 MEMBER PROPERTIES
1 2 AX 1.0 BASE ISOLATION ELEMENT DATA 'FB1'
INCIDENCES START 2 END 1 TYPE FRICTION BEARING -
PLANE XZ RD 50.0 UY 0.005 KAX 1.E8 FRICTION
CONSTANT FC 0.05 END PRINT ELEMENT
PROPERTIES LOAD 1 JOINT LOADS 1 FORCE Y
-10000.0
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Basic Behavior Examples
5. Convex Sliding Surface, RD 50 Inches,
Constant Bearing Pressure, Constant Friction µ
0.05
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Basic Behavior Examples
5. Convex Sliding Surface, RD 50 Inches,
Constant Bearing Pressure, Constant Friction µ
0.05
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Plane Frame Example Comparison of Rigid vs
Isolated
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Plane Frame Example Comparison of Rigid vs
Isolated
Rigid
STATUS SUPPORT JOINTS 1 TO 6 JOINT RELEASES 1
TO 6 MOMENT Z
Isolated
STATUS SUPPORT JOINTS 1 TO 6 JOINT RELEASES 1
TO 6 FORCE X Y MOMENT Z UNITS INCHES LBS BASE
ISOLATION ELEMENT DATA 'FB1' TO 'FB6' ATTACH TO
1 TO 7 TYPE FRICTION BEARING - PLANE XZ RD
50.0 UY 0.005 KAX 1.E8 FRICTION CONSTANT FC
0.05 END
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Plane Frame Example Comparison of Rigid vs
Isolated
Nonlinear Static and Dynamic Analysis Operations
LOAD LIST 'EQ2' DYNAMIC PARAMETERS STORE
VELOCITY ON STORE ACCELERATION ON STORE
ABSOLUTE ACCELERATION USE EXTERNAL FILE SOLVER
MAXIMUM NUMBER OF EQUILIBRIUM CYCLES 20
CONVERGENCE TOLERANCE ENERGY 0.001 INITIAL
STRESS LOAD '1' PRINT MAX END OF DYNAMIC
PARAMETERS DYNAMIC ANALYSIS NONLINEAR BETA
0.25 COMPUTE TRANSIENT FORCES REACTIONS
UNITS INCHES KIPS DEAD LOAD 1 DIR -Y ALL
MEMBERS MAXIMUM NUMBER OF CYCLES 10 CONVERGENCE
TOLERANCE EQUILIBRIUM 0.001 LOAD LIST 1 NONLINEAR
ANALYSIS INERTIA OF JOINTS LUMPED DAMPING
PROPORTIONAL TO STIFFN 0.005 TRANSIENT LOADING
'EQ2' SUPPORT ACCELERATION TRANSLATION X FILE
'ELCENTRO' INTEGRATE FROM 0.0 TO 10.0 AT
0.001 END TRANSIENT LOAD
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Plane Frame Example Comparison of Rigid vs
Isolated
Rigid Frame UXmax, T 2.49 seconds T1
.131 seconds
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Plane Frame Example Comparison of Rigid vs
Isolated
X 2.767E00 Y -5.237E-04 Z 0.0
X 2.757E00 Y -3.376E-05 Z 0.0
Isolated Frame UXmax, T 5.549 seconds T1eff

2.26 secs
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Plane Frame Example Comparison of Rigid vs
Isolated
Convensional Rigid Foundation
Foundation with Base Isolation
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Plane Frame Example Comparison of Rigid vs
Isolated
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Plane Frame Example Comparison of Rigid vs
Isolated
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The Friction Bearing Isolation Element
Summary

• Nonlinear, requiring nonlinear static and dynamic
  analyses
• Three global DOFs Translation X, Y, and Z,
• coupled plasticity, bilateral interaction
• 3. Compression only
• 4. Equilibrium/force recovery assumes small
  displacements,
• nonlinear geometric effects neglected
• 5. Can be oriented wrt a local coordinate system
• 6. General bearing force, variable coefficient of
  friction

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Nonlinear Dynamic Analysis
Summary

• Analysis Parameters and Operation
• Transient Loading Time Step Size

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Nonlinear Dynamic Analysis
Summary Analysis Parameters and Operation
vb (BETA) 0.25 constant average acceleration
integration method (unconditionally stable for
linear analysis)
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Nonlinear Dynamic Analysis
Summary Analysis Parameters and Operation
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Nonlinear Dynamic Analysis
Summary Analysis Parameters and Operation
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Nonlinear Dynamic Analysis
Summary Transient Loading Time Step Size
TRANSIENT LOADING 'EQ2' SUPPORT ACCELERATION
TRANSLATION X FILE 'ELCENTRO' INTEGRATE FROM
0.0 TO 10.0 AT 0.001 END TRANSIENT LOAD

• Size of time step size must be sufficiently small
  to capture
• the time points corresponding to the loading
  extreme points
• Size of time step must be sufficiently small to
  capture
• response of structure
• ?t Tmin/10.0 seconds
• For f cutoff 33 Hz, Tmin 0.0303
  seconds, ?t 0.003 seconds