1. Friction Bearing Base Isolation
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

2. Topics Background Friction Bearing Mechanics and Modeling Parameters
Basic Behavior Examples
Plane Frame Example – Comparison of Rigid vs Isolated
Nonlinear Dynamic Analysis

3. Background Why Do Base Isolation? Conventional Rigid Foundation
Foundation with Base Isolation

4. Background Examples of Base Isolation Systems
Rubber Bearing (RB) System (oiles)

5. Background Examples of Base Isolation Systems
Lead Rubber Bearing (LRB) System (oiles)

6. Background Examples of Base Isolation Systems
Friction Pendulum System (FPS) (oiles)

7. Background
Examples of Base Isolation Systems

8. Background
Examples of Base Isolation Systems

9. R & D – Modeling of Friction Bearing Systems
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

10. Mechanics and Modeling Parameters
Equilibrium wrt one-dimensional,
horizontal motion:

11. Mechanics and Modeling Parameters
Equilibrium wrt horizontal, bi-axial motion – coupled plasticity: U 1 2 U1 U2

12. Mechanics and Modeling Parameters
The FE model – one-dimensional, horizontal motion: V UV E
KAX S H UY

13. 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,
ε = constant that controls the transition of μmax between very low and
very high bearing pressures,
α = 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.

14. Mechanics and Modeling Parameters
Variable Coefficient of Friction
μmin = 0.04
μmax0 = 0.12
μmaxp = 0.05
α = 0.6
ε = 0.012
μmax vs. Bearing Pressure
μ (f) vs. Slider Velocity

15. Mechanics and Modeling Parameters
The BASE ISOLATION ELEMENT Command:

16. Mechanics and Modeling Parameters
BASE ISOLATION Command Elements
Bridge Pier and Superstructure Separated by a Base Isolation Element

17. 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

18. Mechanics and Modeling Parameters
BASE ISOLATION Command Elements

19. Mechanics and Modeling Parameters
BASE ISOLATION Command Elements V RD UV E
KAX S H UY

20. Mechanics and Modeling Parameters
BASE ISOLATION Command Elements

21. Mechanics and Modeling Parameters
BASE ISOLATION Command Elements
At first onset of sliding:
Friction Force = vBFμFB, vBF > 1.0
vBF = 1.0 by default

22. Basic Behavior Examples
Flat sliding surface, constant bearing pressure,
constant friction μ = 0.05
variable friction, μmax = 0.05
Flat sliding surface, varying 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

23. Basic Behavior Examples
Flat Sliding Surface, Constant Bearing Pressure,
Constant Friction μ = 0.05
L = 1 in, μ = 0.05

24. Basic Behavior Examples
Flat Sliding Surface, Constant Bearing Pressure,
Constant Friction μ = 0.05
UNITS INCHES LBS
JOINT COORDINATES S S 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 KAX 1.E8 FRICTION CONSTANT FC 0.05
END
PRINT ELEMENT PROPERTIES
LOAD 1
JOINT LOADS
1 FORCE Y

25. 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 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

26. 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 KAX 1.E8 FRICTION CONSTANT FC 0.05
END
PRINT ELEMENT PROPERTIES
Friction Bearing Element Data
=============================
Element Start Jnt End Jnt
FB XZ ACS = E+00 RD = E+00 Kax = E+09 Uy = E-02
TH1 = E+00 TH2 = E+00 TH3 = E+00
Fc = E-01 Fmin = E+00 Fmax0 = E+00 Fmaxp = E+00
BF = Alpha = E+00 Epsilon = E+00

27. Basic Behavior Examples
Flat Sliding Surface, Constant Bearing Pressure,
Constant Friction μ = 0.05

28. Basic Behavior Examples
Flat Sliding Surface, Constant Bearing Pressure,
Constant Friction μ = 0.05

29. Basic Behavior Examples
2. Flat Sliding Surface, Constant Bearing Pressure,
Variable Friction μmax = 0.05
UNITS INCHES LBS
JOINT COORDINATES S S 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 KAX 1.E8 ACS
FRICTION VARIABLE ALPHA 0.6 EPS FMIN
FMAX FMAXP 0.05
END
LOAD 1
JOINT LOADS
1 FORCE Y

30. 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 KAX 1.E8 ACS
FRICTION VARIABLE ALPHA 0.6 EPS FMIN
FMAX FMAXP 0.05
END
μmax0 = 0.12, μmaxp = 0.05, μmin = 0.03
ε = 0.012
FB = lbs, ACS = 10.0 in2
μmax = 0.12 – (0.12 – 0.05)tanh(12.0) = 0.05

31. Basic Behavior Examples
2. Flat Sliding Surface, Constant Bearing Pressure,
Variable Friction μmax = 0.05
μmax = 0.05, μmin = 0.03
α = 0.6

32. Basic Behavior Examples
2. Flat Sliding Surface, Constant Bearing Pressure,
Variable Friction μmax = 0.05

33. Basic Behavior Examples
2. Flat Sliding Surface, Constant Bearing Pressure,
Variable Friction μmax = 0.05

34. Basic Behavior Examples
Flat Sliding Surface, Varying Bearing Pressure,
Constant Friction μ = 0.05
L = 1 in, μ = 0.05

35. 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 FREQ 8.0
INTEGRATE -
FROM 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

36. Basic Behavior Examples
Flat Sliding Surface, Varying Bearing Pressure,
Constant Friction μ = 0.05

37. Basic Behavior Examples
Flat Sliding Surface, Varying Bearing Pressure,
Constant Friction μ = 0.05

38. Basic Behavior Examples
Flat Sliding Surface, Varying Bearing Pressure,
Constant Friction μ = 0.05

39. Basic Behavior Examples
4. Flat Sliding Surface, Constant Bearing Pressure, Constant Friction μ = 0.05, BF = 1.5
UNITS INCHES LBS
JOINT COORDINATES S S 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 KAX 1.E8 FRICTION CONSTANT FC 0.05 BF 1.5
END
PRINT ELEMENT PROPERTIES
LOAD 1
JOINT LOADS
1 FORCE Y

40. Basic Behavior Examples
4. Flat Sliding Surface, Constant Bearing Pressure, Constant Friction μ = 0.05, BF = 1.5

41. Basic Behavior Examples
Flat Sliding Surface, Constant Bearing Pressure, Constant Friction μ = 0.05, BF = 1.5

42. Basic Behavior Examples
Flat Sliding Surface, Constant Bearing Pressure, Constant Friction μ = 0.05, BF = 1.5

43. Basic Behavior Examples
Flat Sliding Surface, Constant Bearing Pressure, Constant Friction μ = 0.05, BF = 1.5

44. Basic Behavior Examples
5. Convex Sliding Surface, RD = 50 Inches, Constant Bearing Pressure, Constant Friction μ = .05
UNITS INCHES LBS
JOINT COORDINATES S S 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 KAX 1.E8 FRICTION –
CONSTANT FC 0.05
END
PRINT ELEMENT PROPERTIES
LOAD 1
JOINT LOADS
1 FORCE Y

45. Basic Behavior Examples
5. Convex Sliding Surface, RD = 50 Inches,
Constant Bearing Pressure, Constant Friction μ = 0.05

46. Basic Behavior Examples
5. Convex Sliding Surface, RD = 50 Inches, Constant Bearing Pressure, Constant Friction μ = 0.05

47. Comparison of Rigid vs Isolated
Plane Frame Example
Comparison of Rigid vs Isolated
W18X35 (typ)
W14X53 (typ)
Concrete
B = 48”, H = 6”
Pinned
10’ (typ)

48. Comparison of Rigid vs Isolated
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 KAX 1.E8 FRICTION CONSTANT FC 0.05
END

49. Comparison of Rigid vs Isolated
Plane Frame Example
Comparison of Rigid vs Isolated
Nonlinear Static and Dynamic Analysis Operations
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
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

50. Rigid Frame: UXmax, T = 2.49 seconds; T1 = .131 seconds
Plane Frame Example
Comparison of Rigid vs Isolated
Rigid Frame: UXmax, T = 2.49 seconds; T1 = seconds

51. Isolated Frame: UXmax, T = 5.549 seconds; T1eff =
Plane Frame Example
Comparison of Rigid vs Isolated
X 2.767E+00
Y E-04
Z 0.0
X 2.757E+00
Y E-05
Z 0.0
Isolated Frame: UXmax, T = seconds; T1eff =
= secs

52. Comparison of Rigid vs Isolated
Plane Frame Example
Comparison of Rigid vs Isolated
Convensional Rigid Foundation
Foundation with Base Isolation

53. Comparison of Rigid vs Isolated
Plane Frame Example
Comparison of Rigid vs Isolated

54. Comparison of Rigid vs Isolated
Plane Frame Example
Comparison of Rigid vs Isolated

55. 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

56. Nonlinear Dynamic Analysis
Summary
Analysis Parameters and Operation
Transient Loading – Time Step Size

57. Nonlinear Dynamic Analysis
Summary: Analysis Parameters and Operation
vb (BETA) = 0.25 – constant average acceleration integration method
(unconditionally stable for linear analysis)

58. Nonlinear Dynamic Analysis
Summary: Analysis Parameters and Operation

59. Nonlinear Dynamic Analysis
Summary: Analysis Parameters and Operation

60. 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:
Δt ≤ Tmin/10.0 seconds
For f cutoff = 33 Hz, Tmin = seconds, Δt ≤ seconds