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

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

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

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

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

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

Background Examples of Base Isolation Systems

Background Examples of Base Isolation Systems

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

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

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

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

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.

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

Mechanics and Modeling Parameters The BASE ISOLATION ELEMENT Command:

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

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

Mechanics and Modeling Parameters BASE ISOLATION Command Elements

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

Mechanics and Modeling Parameters BASE ISOLATION Command Elements

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

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

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

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

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

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 = 0.0000E+00 RD = 0.0000E+00 Kax = 0.1000E+09 Uy = 0.5000E-02 TH1 = 0.0000E+00 TH2 = 0.0000E+00 TH3 = 0.0000E+00 Fc = 0.5000E-01 Fmin = 0.0000E+00 Fmax0 = 0.0000E+00 Fmaxp = 0.0000E+00 BF = 1.000 Alpha = 0.0000E+00 Epsilon = 0.0000E+00

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

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

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

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 ε = 0.012 FB = 10000.0 lbs, ACS = 10.0 in2 μmax = 0.12 – (0.12 – 0.05)tanh(12.0) = 0.05

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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 0.005 KAX 1.E8 FRICTION CONSTANT FC 0.05 END

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

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 = .131 seconds

Isolated Frame: UXmax, T = 5.549 seconds; T1eff = Plane Frame Example Comparison of Rigid vs Isolated X 2.767E+00 Y -5.237E-04 Z 0.0 X 2.757E+00 Y -3.376E-05 Z 0.0 Isolated Frame: UXmax, T = 5.549 seconds; T1eff = = 2.26 secs

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

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

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

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

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

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

Nonlinear Dynamic Analysis Summary: Analysis Parameters and Operation

Nonlinear Dynamic Analysis Summary: Analysis Parameters and Operation

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 = 0.0303 seconds, Δt ≤ 0.003 seconds