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Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 10 – Seismic Isolation Systems
Chapter 9 Seismic Isolation Systems
1
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
CONTENT 1. Introduction 2. Laminated Rubber Bearings 3. Lead-rubber Bearings 4. Friction Pendulum System 5. Other Seismic Isolation Systems 6. Example of adequacy assessment of a lead-rubber
bearing under Maximum Credible Earthquake (MCE) 2
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
Major References • Chapter 10
– Sections 10.1 to 10.5
http://mceer.buffalo.edu/publications/catalog/reports/LRFD-Based-Analysis-and-Design-Procedures-for-Bridge-Bearings-and-Seismic-Isolators-MCEER-11-0004.html
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Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
1. Introduction
• Overview of various isolator components developed, successfully tested and implemented.
• Emphasizes two main types of systems: – Laminated rubber bearing systems – Friction Pendulum System
• Overview of other systems and recent developments in isolation hardware also presented.
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Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
2. Laminated Rubber Bearings
• Laminated rubber bearings (elastomeric bearings) used extensively for bridge superstructures to accommodate temperature-induced movements deformations.
• In last 20 years, use extended to seismic isolation of buildings and other structures.
• Lead-rubber (lead-plug) bearing: – Elastomeric bearing with central lead plug designed to
yield under lateral deformation and to dissipate supplemental energy.
– Discussed in next section.
5
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
2. Laminated Rubber Bearings
Photo: Courtesy of M. Constantinou
6
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
2. Laminated Rubber Bearings
Image T. Saito
7
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
2. Laminated Rubber Bearings
• Elastomeric Bearings for Sakhalin I Orlan Platform. • Tested at University at Buffalo.
Photos: Courtesy of M. Constantinou
8
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
2. Laminated Rubber Bearings • Force-Displacement relationship for
various types of elastomeric bearings • Shear strain defined as lateral
displacement/total height of rubber
(From Thompson et al. 2000)
High Damping Rubber
Lead Rubber
Low Damping
Scragging
9
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
2. Laminated Rubber Bearings • Full-Scale Isolated Bridge Testing
Video
10
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
2. Laminated Rubber Bearings • Full-Scale Isolated Bridge Testing
-1.5 -1 -0.5 0 0.5 1 1.5-4
-3
-2
-1
0
1
2
3
4
Uy (in)
F (k
ip)
Force-Displacement Hysteresis - Side A
LC6 vs D5
-5 -4 -3 -2 -1 0 1 2 3 4 5-4
-3
-2
-1
0
1
2
3
4
Uy (in)
F (k
ip)
Force-Displacement Hysteresis-Side B
LC2 vs D9
11
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
2. Laminated Rubber Bearings • Disadvantage of Laminated Rubber Bearings:
– Relatively low damping provided by the rubber. • High damping rubbers:
– Developed for laminated rubber bearings. – Used mainly in Japan (Pan et al. 2004). – Significant more energy dissipation than low damping rubbers. – 20% damping at shear strains of 300%. – More susceptible to heat related property changes during cyclic loading and to
aging effects. – Increases complexity to predict short and long term properties for bounding
analysis. • Isolator damping external components:
– Lead plug inserted in center of the bearing (lead-rubber bearings). – External supplemental damping by hysteretic or viscous dampers.
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Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
2. Laminated Rubber Bearings • Key Parameters in Design of Laminated Rubber
Bearings: – Gravity load carrying capacity.
• Bearings must not be overloaded under gravity loads and vertical loads induced by lateral response.
– Rotational effects between the top and bottom of bearings.
– Maximum achievable relative displacement between top and base of bearing.
• Limited by allowable rubber strain or bearing stability – Minimum thickness of steel shims.
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Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
2. Laminated Rubber Bearings
• Gravity Load Carrying Capacity of Laminated-Rubber Bearings.
14
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 15
Gravity Load Carrying Capacity Overlapping Area Circular Bearings:
Ar
∆
2
( sin )4r
DA δ δ= −
12cos ( )D
δ − ∆=
2. Laminated Rubber Bearings
15
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 16
Gravity Load Carrying Capacity Overlapping Area Rectangular bearings:
Ar
∆( )rA B L= − ∆
2. Laminated Rubber Bearings
B
L
∆
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Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 17
Gravity Load Carrying Capacity Overlapping Area Cylindrical hollow bearings:
Ar
∆
( sin )rAA
δ δπ
−≈
12cos ( )D
δ − ∆=
o
2. Laminated Rubber Bearings
17
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 18
Gravity Load Carrying Capacity For a given compression load, P, the maximum shear strain, γc, in the rubber is given
by:
A is the rubber area bonded to the shim plates (the area must be reduced to Ar to take into
account the lateral displacement). G is the shear modulus of the rubber (0.5 to 1.0 MPa). S is the shape factor of each rubber layer. f1 is a numerical factor that depends on the shape of the bearing, the compressibility of the
rubber and the locations of the maximum shear strain (1.0 ≤ f1 ≤ 3.4).
1cP f
AGSγ = ⋅
2. Laminated Rubber Bearings
18
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 19
Gravity Load Carrying Capacity Shape factor, S:
Note: the shape factor, S, must be calculated for each rubber layer of thickness t and not for the total rubber thickness.
1cP f
AGSγ = ⋅
2. Laminated Rubber Bearings
circular
19
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 20
Gravity Load Carrying Capacity Shape factor, S:
Note: the shape factor, S, must be calculated for each rubber layer of thickness t and not for the total rubber thickness.
1cP f
AGSγ = ⋅
2. Laminated Rubber Bearings
The shape factor for a circular hollow bearing of outside diameter Do and inside diameter Di and made of rubber layers of thickness t is given by:
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Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 21
Gravity Load Carrying Capacity Coefficient f1 for circular bearings:
K is the bulk modulus of rubber( ≈ 2000 MPa).
1cP f
AGSγ = ⋅
f1
S K/G 2000 4000 6000 ∞
5 1.02 1.01 1.01 1.00 7.5 1.05 1.03 1.02 1.00 10 1.10 1.05 1.03 1.00
12.5 1.15 1.08 1.05 1.00 15 1.20 1.11 1.07 1.00
17.5 1.27 1.14 1.10 1.00 20 1.34 1.18 1.13 1.00
22.5 1.41 1.23 1.16 1.00 25 1.49 1.27 1.19 1.00
27.5 1.57 1.32 1.23 1.00 30 1.66 1.37 1.26 1.00
Location of maximum shear strain caused by a compression load.
2. Laminated Rubber Bearings
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Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 22
Gravity Load Carrying Capacity Coefficient f1 for rectangular bearings:
K is the bulk modulus of rubber ( ≈ 2000 MPa).
1cP f
AGSγ = ⋅
Location of maximum shear strain caused by a compression load.
K/G = 2000 L/B 0 0.2 0.4 0.6 0.8 1
S 5 1.53 1.44 1.39 1.33 1.27 1.22
7.5 1.55 1.45 1.41 1.35 1.30 1.25 10 1.57 1.48 1.43 1.38 1.33 1.29
12.5 1.60 1.51 1.46 1.41 1.37 1.34 15 1.64 1.54 1.50 1.46 1.42 1.39
17.5 1.69 1.59 1.54 1.51 1.48 1.45 20 1.74 1.64 1.60 1.56 1.54 1.52
22.5 1.79 1.70 1.65 1.63 1.61 1.59 25 1.85 1.76 1.72 1.69 1.68 1.66
27.5 1.92 1.83 1.79 1.77 1.75 1.74 30 1.98 1.90 1.86 1.84 1.83 1.82
2. Laminated Rubber Bearings
22
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 23
Gravity Load Carrying Capacity Coefficient f1 for rectangular bearings:
K is the bulk modulus of rubber( ≈ 2000 MPa).
1cP f
AGSγ = ⋅
Location of maximum shear strain caused by a compression load.
K/G = 4000 L/B 0 0.2 0.4 0.6 0.8 1
S 5 1.52 1.43 1.39 1.33 1.26 1.21
7.5 1.53 1.44 1.40 1.34 1.27 1.22 10 1.54 1.45 1.41 1.35 1.29 1.24
12.5 1.56 1.47 1.42 1.37 1.31 1.27 15 1.58 1.48 1.44 1.39 1.34 1.30
17.5 1.60 1.50 1.46 1.41 1.37 1.33 20 1.63 1.53 1.48 1.44 1.40 1.37
22.5 1.66 1.56 1.51 1.48 1.44 1.41 25 1.69 1.59 1.55 1.51 1.48 1.46
27.5 1.72 1.63 1.58 1.55 1.52 1.50 30 1.76 1.67 1.62 1.59 1.57 1.55
2. Laminated Rubber Bearings
23
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 24
Gravity Load Carrying Capacity Coefficient f1 for rectangular bearings:
K is the bulk modulus of rubber ( ≈ 2000 MPa).
1cP f
AGSγ = ⋅
Location of maximum shear strain caused by a compression load.
K/G = 6000 L/B 0 0.2 0.4 0.6 0.8 1
S 5 1.52 1.43 1.39 1.32 1.26 1.21
7.5 1.52 1.44 1.39 1.33 1.27 1.22 10 1.53 1.44 1.40 1.34 1.28 1.23
12.5 1.54 1.45 1.41 1.35 1.29 1.25 15 1.56 1.46 1.42 1.36 1.31 1.27
17.5 1.57 1.48 1.43 1.38 1.33 1.29 20 1.59 1.49 1.45 1.40 1.35 1.32
22.5 1.61 1.51 1.47 1.42 1.38 1.35 25 1.63 1.53 1.49 1.45 1.41 1.38
27.5 1.66 1.56 1.51 1.47 1.44 1.41 30 1.68 1.59 1.54 1.50 1.47 1.45
2. Laminated Rubber Bearings
24
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 25
Gravity Load Carrying Capacity Coefficient f1 for rectangular bearings:
K is the bulk modulus of rubber( ≈ 2000 MPa).
1cP f
AGSγ = ⋅
Location of maximum shear strain caused by a compression load.
K/G = ∞ L/B 0 0.2 0.4 0.6 0.8 1
S 5 1.51 1.43 1.38 1.32 1.25 1.20
7.5 1.51 1.43 1.38 1.32 1.25 1.20 10 1.51 1.43 1.38 1.32 1.25 1.20
12.5 1.51 1.43 1.38 1.32 1.25 1.20 15 1.51 1.43 1.38 1.32 1.25 1.20
17.5 1.51 1.43 1.38 1.32 1.25 1.20 20 1.51 1.43 1.38 1.32 1.25 1.20
22.5 1.51 1.43 1.38 1.32 1.25 1.20 25 1.51 1.43 1.38 1.32 1.25 1.20
27.5 1.51 1.43 1.38 1.32 1.25 1.20 30 1.51 1.43 1.38 1.32 1.25 1.20
2. Laminated Rubber Bearings
25
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 26
Gravity Load Carrying Capacity Coefficient f1 for cylindrical hollow bearings:
K is the bulk modulus of rubber( ≈ 2000 MPa).
1cP f
AGSγ = ⋅
Location of maximum shear strain caused by a compression load.
Do/Di = 10 Do/Di = 5
S K/G K/G 2000 4000 6000 ∞ 2000 4000 6000 ∞
5 3.18 3.18 3.18 3.18 2.34 2.33 2.33 2.33 7.5 3.19 3.18 3.18 3.18 2.35 2.34 2.34 2.33 10 3.19 3.18 3.18 3.18 2.36 2.35 2.34 2.33
12.5 3.20 3.19 3.18 3.18 2.38 2.35 2.35 2.33 15 3.21 3.19 3.19 3.18 2.41 2.37 2.35 2.33
17.5 3.22 3.20 3.19 3.18 2.44 2.38 2.36 2.33 20 3.25 3.20 3.19 3.18 2.47 2.40 2.37 2.33
22.5 3.27 3.21 3.20 3.18 2.51 2.42 2.39 2.33 25 3.30 3.23 3.21 3.18 2.55 2.44 2.40 2.33
27.5 3.34 3.24 3.21 3.18 2.60 2.46 2.42 2.33 30 3.38 3.26 3.22 3.18 2.66 2.49 2.43 2.33
2. Laminated Rubber Bearings
26
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 27
Gravity Load Carrying Capacity Critical buckling load in compression
A is the rubber area attached to the shim plates (the area must be reduced to Ar to take into account
the lateral displacement). G is the shear modulus of the rubber (0.5 à 1.0 MPa). S is the shape factor of each rubber layer. r is the radius of gyration of the bonded rubber (r2 = I / A, where I is the moment of inertia around the
weak axis of the bearing). Tr is the total rubber thickness. λ is a numerical factor that depends on the rotational stiffness of the rubber (λ=2.25 for circular or
rectangular bearings). Valid only for bolted bearings.
crr
GSArPT
π λ=
2. Laminated Rubber Bearings
27
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 28
Gravity Load Carrying Capacity Critical buckling load in compression
Circular bearings:
Square bearings:
Cylindrical hollow bearings:
t is the thickness of each rubber layer. Also valid for lead-rubber bearings since lead does not contribute to the
stability of the rubber.
4
0.218crr
GDPtT
=
4
0.340crr
GLPtT
=B = L
( ) 2
2
2
2
4 1 1
10.218
i i
o o
i
o
ocr
r
D DD D
DD
GDPtT
− −
+
=
2. Laminated Rubber Bearings
28
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 29
Gravity Load Carrying Capacity Critical displacement for simply supported bearings Instability by overturning occurs when the overturning
moment is larger than the stabilizing moment.
2. Laminated Rubber Bearings
29
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 30
Gravity Load Carrying Capacity Critical displacement for simply supported bearings Critical displacement, Dcr, causing overturning:
If Dcr ≤ D1:
If Dcr > D1:
2. Laminated Rubber Bearings
30
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 31
Gravity Load Carrying Capacity Critical displacement for simply supported bearings Critical displacement, Dcr, causing overturning :
If the behavior is represented by the effective stiffness, Keff :
2. Laminated Rubber Bearings
31
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 32
Gravity Load Carrying Capacity Tension force causing cavitation for bolted bearings. Delamination of the rubber and steel shims. Cavitation force for each bolt: PCAV = 3GeffAr
PCAV
2. Laminated Rubber Bearings
32
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 33
Rotations between the top and bottom of bearings For a rotation θ relative to the bottom part, the maximum shear strain, γr. Is given by:
L is the dimension perpendicular to the rotational plan (L for rectangular or square bearings, D
for circular bearings and Do for cylindrical hollow bearings). t is the thickness of each rubber layer. Tr is the total rubber thickness. f2 is a numerical factor that depends on the shape of the bearing, the compressibility of the
rubber and the location of the maximum shear strain (1.0 ≤ f2 ≤4.0)
2
2rr
L ftT
θγ = ⋅
2. Laminated Rubber Bearings
33
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 34
Rotations between the top and bottom of bearings Coefficient f2 for circular bearings:
K is the bulk modulus of rubber ( ≈ 2000 MPa).
S K/G 2000 4000 6000 ∞
5 0.37 0.37 0.37 0.37 7.5 0.36 0.36 0.37 0.37 10 0.34 0.36 0.36 0.37
12.5 0.33 0.35 0.36 0.37 15 0.31 0.34 0.35 0.37
17.5 0.30 0.33 0.34 0.37 20 0.28 0.32 0.33 0.37
22.5 0.27 0.31 0.32 0.37 25 0.25 0.29 0.32 0.37
27.5 0.24 0.28 0.31 0.37 30 0.23 0.27 0.30 0.37
Location of maximum shear strain caused by a rotation between the top and bottom of bearings.
2. Laminated Rubber Bearings
34
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 35
Rotations between the top and bottom of bearings Coefficient f2 rectangular bearings:
K is the bulk modulus of rubber ( ≈ 2000 MPa).
Location of maximum shear strain caused by a rotation between the top and bottom of bearings.
K/G = 2000 L/B 0 0.2 0.4 0.6 0.8 1
S 5 0.49 0.49 0.49 0.48 0.47 0.46
7.5 0.49 0.48 0.48 0.47 0.46 0.44 10 0.48 0.47 0.46 0.45 0.44 0.42
12.5 0.47 0.46 0.45 0.43 0.41 0.39 15 0.46 0.44 0.43 0.41 0.39 0.37
17.5 0.45 0.43 0.41 0.39 0.37 0.35 20 0.43 0.41 0.39 0.37 0.35 0.32
22.5 0.42 0.39 0.37 0.35 0.32 0.30 25 0.41 0.38 0.35 0.33 0.31 0.28
27.5 0.39 0.36 0.34 0.31 0.29 0.27 30 0.38 0.35 0.32 0.29 0.27 0.25
2. Laminated Rubber Bearings
35
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 36
Rotations between the top and bottom of bearings Coefficient f2 for rectangular bearings:
K is the bulk modulus of rubber ( ≈ 2000 MPa).
Location of maximum shear strain caused by a rotation between the top and bottom of bearings. .
K/G = 4000 L/B 0 0.2 0.4 0.6 0.8 1
S 5 0.50 0.49 0.49 0.49 0.48 0.46
7.5 0.49 0.49 0.49 0.48 0.47 0.45 10 0.49 0.48 0.48 0.47 0.46 0.44
12.5 0.48 0.48 0.47 0.46 0.45 0.43 15 0.48 0.47 0.46 0.45 0.43 0.41
17.5 0.47 0.46 0.45 0.43 0.42 0.40 20 0.46 0.45 0.43 0.42 0.40 0.38
22.5 0.45 0.44 0.42 0.40 0.38 0.36 25 0.45 0.43 0.41 0.39 0.37 0.35
27.5 0.44 0.42 0.39 0.37 0.35 0.33 30 0.43 0.40 0.38 0.36 0.34 0.31
2. Laminated Rubber Bearings
36
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 37
Rotations between the top and bottom of bearings Coefficient f2 for rectangular bearings:
K is the bulk modulus of rubber ( ≈ 2000 MPa).
Location of maximum shear strain caused by a rotation between the top and bottom of bearings.
K/G = 6000 L/B 0 0.2 0.4 0.6 0.8 1
S 5 0.50 0.50 0.50 0.49 0.48 0.47
7.5 0.49 0.49 0.49 0.49 0.48 0.46 10 0.49 0.49 0.49 0.48 0.47 0.45
12.5 0.49 0.48 0.48 0.47 0.46 0.44 15 0.48 0.48 0.47 0.46 0.45 0.43
17.5 0.48 0.47 0.46 0.45 0.44 0.42 20 0.47 0.46 0.45 0.44 0.42 0.40
22.5 0.47 0.46 0.44 0.43 0.41 0.39 25 0.46 0.45 0.43 0.42 0.40 0.38
27.5 0.45 0.44 0.42 0.40 0.38 0.36 30 0.45 0.43 0.41 0.39 0.37 0.35
2. Laminated Rubber Bearings
37
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 38
Rotations between the top and bottom of bearings Coefficient f2 for rectangular bearings:
K is the bulk modulus of rubber ( ≈ 2000 MPa).
Location of maximum shear strain caused by a rotation between the top and bottom of bearings. .
K/G = ∞ L/B 0 0.2 0.4 0.6 0.8 1
S 5 0.50 0.50 0.50 0.50 0.49 0.47
7.5 0.50 0.50 0.50 0.50 0.49 0.47 10 0.50 0.50 0.50 0.50 0.49 0.47
12.5 0.50 0.50 0.50 0.50 0.49 0.47 15 0.50 0.50 0.50 0.50 0.49 0.47
17.5 0.50 0.50 0.50 0.49 0.49 0.47 20 0.50 0.50 0.50 0.49 0.49 0.47
22.5 0.50 0.50 0.50 0.49 0.49 0.47 25 0.50 0.50 0.50 0.49 0.49 0.47
27.5 0.50 0.50 0.50 0.49 0.49 0.47 30 0.50 0.50 0.50 0.49 0.49 0.47
2. Laminated Rubber Bearings
38
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 39
Rotations between the top and bottom of bearings Coefficient f2 for cylindrical hollow bearings:
K is the bulk modulus of rubber( ≈ 2000 MPa).
Location of maximum shear strain caused by a rotation between the top and bottom of bearings
Exterior Surface
S Do/Di = 10 Do/Di = 5
K/G K/G 2000 4000 6000 ∞ 2000 4000 6000 ∞
5 0.37 0.38 0.38 0.38 0.36 0.36 0.37 0.37 20 0.27 0.31 0.33 0.38 0.25 0.29 0.31 0.37 30 0.22 0.27 0.29 0.38 0.20 0.25 0.27 0.37
Interior Surface
S Do/Di = 10 Do/Di = 5
K/G K/G 2000 4000 6000 ∞ 2000 4000 6000 ∞
5 0.30 0.31 0.31 0.32 0.31 0.31 0.32 0.33 20 0.18 0.23 0.26 0.33 0.18 0.23 0.25 0.33 30 0.12 0.19 0.23 0.33 0.12 0.18 0.22 0.33
2. Laminated Rubber Bearings
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Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 40
Maximum allowable lateral relative displacement For a lateral displacement, Δ, of the top part of the
bearing relative to the bottom part of the bearing, the maximum shear strain, γs ,is given by:
Tr is the total rubber thickness.
srT
γ ∆=
2. Laminated Rubber Bearings
40
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 41
Minimum thickness of steel shims Stress state in steel shims of circular bearings: Radial and circumferential (hoop stress) tension caused by
the shear stresses at the steel-rubber interface; Compression caused by the vertical pressure.
2. Laminated Rubber Bearings
41
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 42
Minimum thickness of steel shims Solution for elastic stress distribution developed by
Roeder et al. (1987). Axial pressure is maximum at the center of the shim:
2zPA
σ = −
3 1.652r
s s
t P t Pt A t Aθ
νσ σ + = = =
• ν is Poisson’s ratio of steel (0.3). • Minus sign indicates compression.
2. Laminated Rubber Bearings
42
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems 43
Minimum thickness of steel shims For design, Tresca’s yield criterion is used to limit the maximum shear
stress: The maximum shear stress , τmax, caused by the factored load is limited
to:
Therefore, the thickness of the steel shims is selected such that:
Pu is the factored compression load. The 1.65 factor applies for shims without holes. When holes are present, this
factor should be increased to 3.0.
max 1.65 22 2
r z
s
P tA t
σ στ −
= = +
max (0.6 ) 0.54y yF Fτ φ= =
1.65
1.08 2s
yu
tt AFP
≥−
2. Laminated Rubber Bearings
43
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
2. Laminated Rubber Bearings
• Lateral Stiffness of Laminated Rubber Bearings
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2. Laminated Rubber Bearings
• Natural Period of Vibration of Laminated-Rubber Bearings Supporting a Rigid Structure
45
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2. Laminated Rubber Bearings
• Damping Provided by Laminated Rubber Bearings – Experiments showed energy dissipation through
shear deformations in rubber layers of laminated-rubber bearings proportional to velocity.
– Damping modeled by equivalent viscous damping. – Natural rubber bearings: 5% to 10% damping. – High damping rubber bearing: up to 25% damping.
46
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
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2. Laminated Rubber Bearings
• Vertical Stiffness of Laminated Rubber Bearings – Vertical stiffness much larger than lateral stiffness. – Often assumed rigid in vertical direction. – In some applications, vertical deflection of
laminated rubber bearings may be important and vertical stiffness must be known.
47
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2. Laminated Rubber Bearings
• Vertical Stiffness of Laminated Rubber Bearings
48
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Adequacy assessment of bearings
http://mceer.buffalo.edu/publications/catalog/reports/LRFD-Based-Analysis-and-Design-Procedures-for-Bridge-Bearings-and-Seismic-Isolators-MCEER-11-0004.html
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Three evaluation criteria:
1. Verification for service loads; 2. Verification for the Design Earthquake (DE); and 3. Verification for Maximum Considered Earthquake (MCE)
Generally: MCE = 1.5 x DE
The analyses are conducted for the upper and lower bounds of the mechanical properties of the isolation system (see Chapter 11).
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for service loads
Shear strain caused by compression load: Pu = Factored axial load from applicable code with the cyclic component of the live
load multiplied by 1.75.
PD is the dead load; PLst is the static component of the live load and Plcy is
the cyclic component of the live load. γD et γL are load factors for the dead and live loads.
Ar = Overlapped area for a lateral displacement , ∆, equal to:
Non-seismic lateral displacement : ∆Sst (static), ∆Scy (cyclic).
1u uCs
r
P fA GS
γ = ⋅
Sst Scy∆ = ∆ + ∆
1.75u D D L Lst L LcyP P P Pγ γ γ= + +
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for service loads Shear strain due to lateral displacement:
Shear strain due to rotation:
Non-seismic rotation : θSst (static), θScy (cyclic)
1.75S
Sst ScyuS
rTγ
∆ + ∆=
2
2
( 1.75 )s
Sst Scyur
r
Lf
tTθ θ
γ+
= ⋅
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for service loads Buckling load at the lateral displacement caused by the
service loads:
Sst Scy∆ = ∆ + ∆
's
rcr cr
AP PA
=
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for service loads
A bearing design is considered adequate if: The amplification factor of 1.75 on the cyclic component of the live loads
applies only for the calculation of the rubber deformation but does not apply for the evaluation of the compression capacity and in the verification of the stability.
1 3.5D D L Lst
r
P P fA GS
γ γ+⋅ ≤
6.0s s s
u u uC S rγ γ γ+ + ≤
'
2.0( )
scr
D D L Lst Lcy
PP P Pγ γ
≥+ +
Compression capacity
Maximum shear strain
Stability of bearings
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for service loads Furthermore, the thickness of the steel shims, ts, must be at least
equal to:
The amplification factor of 1.75 on the cyclic component of the live
loads applies only for the calculation of the rubber deformation but does not apply for the evaluation of the steel shims.
α = 1.65 for shims without holes otherwise a value of 3.0 must be used.
The minimum thickness required for the steel shims correspond to a gage 14 sheet.
1.9 mm (0.075inch)1.08 2
( )
sr
yD D L Lst Lcy
tt AFP P P
α
γ γ
≥ ≥−
+ +
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for the Design Earthquake (DE)
Shear strain due to compression: Pu = Factored axial load; This load is determined according to the extreme load Combination I
of the AASHTO LRFD Bridge Design Code (AASHTO, 2007, 2010). PD is the dead load; PSLDE is the part of the live load, PL, assumed present during the
design earthquake (recommended to use ) and PEDE is the axial load caused by the design earthquake.
γD is the dead load factor applicable for a seismic load combination. Ar = Overlapping area at a displacement, ∆, equal to:
Non-seismic lateral displacement: ∆Sst (static), ∆Scy (cyclic) Displacement caused by the design earthquake: ∆EDE γ = 0.5
DE DEu D D SL EP P P Pγ= + +
0.5DESL LP P=
( )DEcyst ESS ΔΔΔγΔ ++=
1DE
u uC
r
P fA GS
γ = ⋅
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for the Design Earthquake (DE) Shear strain due to lateral displacement:
with:
DE
DE
S EuS
rTγ
γ∆ + ∆
=
( )S Sst Scyγ γ∆ = ∆ + ∆
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for the Design Earthquake (DE) A bearing design is considered adequate if:
is the shear strain due to the rotation caused by the service loads
as calculated earlier. No stability verification is required for the design
earthquake. A stability verification will be considered for the MCE.
Total shear strain 0.5 7.0C SDE DE
u u ursγ γ γ+ + ≤
s
urγ
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for the Design Earthquake (DE) Furthermore, the thickness of the steel shims, ts, must be at
least equal to:
The minimum thickness required for the steel shims correspond to a
gage 14 sheet.
1.65 1.9 mm (0.075inch)1.08 2
sr
yu
tt AFP
≥ ≥−
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for the Maximum Considered Earthquake (MCE)
Shear strain due to compression: Pu Factored axial load; This load is determined according to the extreme load
Combination I of the AASHTO LRFD Bridge Design Code (AASHTO, 2007, 2010). PD is the dead load; PSLMCE is the part of the live load, PL, assumed to be
present during the MCE (recommended to use ) et γD is the dead load factor applicable to the seismic load combination.
Ar = Overlapped area for a displacement, ∆, equal to:
Non-seismic displacement: ∆Sst (static), ∆Ssy (cyclic) Displacement caused by the MCE: ∆EMCE γ = 0.5
1MCE
u uC
r
P fA GS
γ = ⋅
MCE MCEu D D SL EP P P Pγ= + +
0.5MCE DESL SLP P= 1.5
MCE DEE EP P=
( )MCEcyst ESS ΔΔΔγΔ ++=
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for the Maximum Considered Earthquake
(MCE) Shear strain due to lateral displacement:
with:
0.5MCE
MCE
S EuS
rTγ
γ∆ + ∆
=
0.5 0.5 ( )S Sst Scyγ γ∆ = ∆ + ∆ 0.25( )Sst Scy= ∆ + ∆
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for the Maximum Considered Earthquake
(MCE) Critical buckling load at the MCE lateral displacement:
' 0.15MCE
rcr cr cr
AP P PA
= ≥
MCEEs ΔγΔ.Δ += 50
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for the Maximum Considered Earthquake (MCE)
A bearing design is considered adequate if: is the shear strain caused by the service loads rotation as calculated earlier.
The amplification factor of 1.75 on the cyclic component of the live loads applies
only for the calculation of the rubber deformation but does not apply for the evaluation of the compression capacity and in the verification of the stability.
Total shear strain
Bearing stability
0.25 9.0C SMCE MCE
u u ursγ γ γ+ + ≤
s
urγ
'
1.1MCEcr
u
PP
≥
2. Laminated Rubber Bearings
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Adequacy assessment of bearings Verification for the Maximum Considered Earthquake
(MCE) Furthermore, the thickness of the steel shims, ts, must be at
least equal to:
Fye is the probable yield strength of the steel shims = RyFy with Ry =
1.3 for ASTM A36 steel and 1.1 for ASTM A573 Grade 50 steel. The minimum thickness required for the steel shims correspond to a
gage 14 sheet.
1.65 1.9 mm (0.075inch)1.08 2
sr
yeu
tt AFP
≥ ≥−
2. Laminated Rubber Bearings
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2. Laminated Rubber Bearings • Seismic Isolation of Pallet-Type Steel Storage
Racks with Laminated Rubber Bearings – Very difficult for conventional steel storage rack to
meet seismic performance objectives of FEMA-460. – Evaluation of a novel base isolation system for
storage racks. • Patented by Ridg-U-Rak Inc., Erie, PA.
– Uni-axial and tri-axial shake table tests performed on directly bolted and base isolated storage racks loaded with simulated and real merchandise. 65
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2. Laminated Rubber Bearings • Seismic Isolation of Pallet-Type Steel Storage
Racks with Laminated Rubber Bearings – Lateral load-resisting systems of steel storage racks
• Moment-resisting frames in the down-aisle (longitudinal) direction.
• Braced frames in cross-aisle (transverse) direction.
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2. Laminated Rubber Bearings
• Seismic Isolation of Pallet-Type Steel Storage Racks with Laminated Rubber Bearings – Requirements of Base Isolation System for Storage
Racks • Provide base isolation in the cross-aisle direction only.
– Reduce horizontal accelerations in cross-aisle direction to reduce content spillage and structural damage.
– Range of down-aisle natural periods of typical rack structures already similar to typical base isolated structures ( ≥ 1.5 sec).
– Horizontal accelerations in down-aisle direction do not contribute substantially to content spillage.
• No interference with normal material handling operations. 67
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2. Laminated Rubber Bearings • Seismic Isolation of Pallet-Type Steel Storage
Racks with Laminated Rubber Bearings
Horizontal Support
Rubber Mount
Cross-AisleDow
n-Aisl
e
Upright
Low Friction Bearing Material
Box
WeldedStud
108
31
31
31
64
All Dimensions in mm
108
31
31
31
64
All Dimensions in mm
Courtesy of Ridg-U-Rak Inc.
68
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2. Laminated Rubber Bearings
• Seismic Isolation of Pallet-Type Steel Storage Racks with Laminated Rubber Bearings
108
31
31
31
64
All Dimensions in mm
108
31
31
31
64
All Dimensions in mm
Steel Plate
Rubber Layers
Rubber Durometer Horizontal Stiffness (kN/m) Equivalent Viscous Damping Ratio
40 47 0.20 60 93 0.22
69
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2. Laminated Rubber Bearings
• Seismic Isolation of Pallet-Type Steel Storage Racks with Laminated Rubber Bearings
Courtesy of Ridg-U-Rak Inc
70
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2. Laminated Rubber Bearings • Seismic Isolation of Pallet-Type Steel Storage
Racks with Laminated Rubber Bearings
Courtesy of Ridg-U-Rak Inc
Isolated Rack Conventional Rack Video 71
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3. Lead-rubber Bearings • Lead-rubber bearing composed of a laminated-rubber bearing
with a cylindrical lead plug inserted in it center. • Lead plug introduced to increase damping by hysteretic shear
deformations of the lead.
Photo: Courtesy of M. Constantinou
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3. Lead-rubber Bearings
• Reasons to use lead for central plug: – At room temperature, lead behaves as elastic-plastic solid. – Yields in shear at low stress of about 10 MPa. – Lead is hot-worked at room temperature.
• Properties continuously restored when cycled in inelastic range. • Very good fatigue resistance properties.
– Lead commonly available since used in batteries at purity level of more than 99.9%
73
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3. Lead-rubber Bearings • Properties of Lead-Rubber Bearings
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3. Lead-rubber Bearings • SRMD Testing Machine, UC-San Diego
DIS LR Bearing, Vertical Load = 558 kips, Displacement = 22 in, velocity = 60 in/s 75
Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems
CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems
3. Lead-rubber Bearings • SRMD Testing Machine, UC-San Diego
DIS LR Bearing, 400% strain
76
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3. Lead-rubber Bearings • Failure Test, NIED, Tsukuba, Japan
77
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3. Lead-rubber Bearings
• Modeling of Lead-Rubber Bearings
k1
k2 Fy
78
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3. Lead-rubber Bearings
• Modeling of Lead-Rubber Bearings
k1
k2 Fy
79
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3. Lead-rubber Bearings
• Modeling of Lead-Rubber Bearings
k1
k2 Fy
80
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3. Lead-rubber Bearings
• Modeling of Lead-Rubber Bearings
81
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4. Friction Pendulum System • General Description
– FPS manufactured by Earthquake Protection Systems (EPS), Richmond, California.
– Friction-type sliding bearing using gravity as restoring force.
82
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4. Friction Pendulum System
• General Description – Articulated friction slider traveling on spherical
concave lining surface.
83
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4. Friction Pendulum System • General Description
Photo: Courtesy of M. Constantinou
84
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4. Friction Pendulum System • General Description
• Sliders on smooth flat surface that dissipates energy by friction with parallel linear springs to provide re-centering capabilities
• Typically PTFE on polished stainless steel surface • Slider on concave surface to provide re-centering capabilities through
gravity – Friction Pendulum bearing shown below
85
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4. Friction Pendulum System
– Salkhalin II offshore gas platform bearings.
– Largest seismic isolators. – 700mm displacement. – 87,400kN vertical load.
– Full-scale testing – Reduced scale dynamic testing
(load of up to 13,000kN, velocity of 1m/sec).
Photo: Courtesy of M. Constantinou
86
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FPS Isolator, Vertical Load = 3490 kips, Displacement = 29 in, velocity = 53 in/s
87
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4. Friction Pendulum System
New International Terminal San Francisco International Airport
88
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4. Friction Pendulum System
HAYWARD CITY HALL, CALIFORNIA NEXT TO HAYWARD FAULT
53 FP BEARINGS AND 15 NONLINEAR VISCOUS DAMPING DEVICES
600 mm DISPLACEMENT CAPACITY
Courtesy of M. Constantinou
89
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4. Friction Pendulum System
KODIAK, ALASKA COLD TEMPERATURE APPLICATION -40 DEG TEMPERATURE, STRONG WIND
Courtesy of M. Constantinou
90
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• Properties of Frictionless Pendulum System
91
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• Properties of Frictionless Pendulum System
92
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Partial list of standard dimensions for concave surfaces of friction pendulums Radius of Curvature, mm (inch) Diameter of concave surface, mm (inch)
1555 (61)
356 (14) 457 (18) 559 (22) 787 (31) 914 (36)
2235 (88)
686 (27) 787 (31) 914 (36) 991 (39)
1041 (41) 1118 (44) 1168 (46) 1295 (51) 1422 (56)
3048 (120) 686 (27)
1422 (56)
3962 (156)
1600 (63) 1778 (70)
2692 (106) 3150 (124)
6045 (238)
1981 (78) 2388 (94)
2692 (106) 3327 (131) 3632 (143)
4. Friction Pendulum System
93
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• Properties of Pendulum System including Friction 4. Friction Pendulum System
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4. Friction Pendulum System
SAKHALIN II PLATFORMS PROTOTYPE BEARING PR1, LOAD=6925kN, DISPLACEMENT=240mm, VELOCITY=0.9 m/sec
EPS BEARING TESTING MACHINE, OCTOBER 2005 Courtesy of M. Constantinou
95
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4. Friction Pendulum System
• Electrical 3-phase disconnect switch isolated by friction pendulum system
UNIV. AT BUFFALO,
2006
96
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• Double curvature friction pendulum system – Combination of two friction pendulum systems
97
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4. Friction Pendulum System
• Double curvature friction pendulum system
TWO CONCAVE PLATES, EACH WITH EQUAL RADII
OF CURVATURE AND EQUAL COEFFICIENTS OF FRICTION
BEHAVIOR NEARLY IDENTICAL TO
SINGLE CONCAVE FP BEARING- RIGID-LINEAR HYSTERETIC
BUT OFFERS ADVANTAGE OF LARGE DISPLACEMENT CAPACITY
Courtesy of M. Constantinou
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4. Friction Pendulum System
• Double curvature friction pendulum system
TWO CONCAVE PLATES, EACH WITH EQUAL RADII
OF CURVATURE AND UNEQUAL COEFFICIENTS
OF FRICTION
RIGID-BILINEAR HYSTERETIC BEHAVIOR
OFFERS ADVANTAGE OF REDUCTION OF SECONDARY SYSTEM
RESPONSE
Courtesy of M. Constantinou
99
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4. Friction Pendulum System • Double curvature friction pendulum system
UNIV. AT BUFFALO, 2004 Courtesy of M. Constantinou
100
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4. Friction Pendulum System • Triple curvature friction pendulum system
Courtesy of M. Constantinou
101
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Triple curvature friction pendulum system 4. Friction Pendulum System
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Triple curvature friction pendulum system
Regime Description Force-Displacement Relationship
I Sliding on surfaces 2 and 3 only
2 2 3 3
2 3 2 3
f eff f eff
eff eff eff eff
F R F RWF uR R R R
+= +
+ +
Valid until: 1fF F= , ( ) ( )1 2 2 1 3 3eff effu u R R∗= = µ − µ + µ − µ
II
Motion stops on surface 2; Sliding on surfaces 1 and 3
( )1 1 2 2 2 3 3
1 3 1 3
f eff eff f eff f eff
eff eff eff eff
F R R F R F RWF uR R R R
− + += +
+ +
Valid until: 4fF F= , ( )( )4 1 1 3eff effu u u R R∗∗ ∗= = + µ − µ +
III
Motion is stopped on surfaces 2 and 3; Sliding on surfaces 1 and 4
( ) ( )1 4
1 1 2 2 2 3 3 4 4 3
1 4
eff eff
f eff eff f eff f eff f eff eff
eff eff
WF uR R
F R R F R F R F R RR R
= ++
− + + + −
+
Valid until:
*1 1 1
1dr f
eff
WF F d FR
= = + ,
( ) ( )4*1 1 4 1 1 4
1
1 effdr eff eff
eff
Ru u u d R R
R∗∗
= = + + − µ − µ +
Assumptions: (1) 1 4 2 3eff eff eff effR R R R= = , (2) 2 3 1 4µ = µ < µ < µ , (3) ( )*1 4 1 1effd R> µ − µ ,
(4) ( )*2 1 2 2effd R> µ − µ , (5) ( )*
3 4 3 3effd R> µ − µ
4. Friction Pendulum System
103
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Triple curvature friction pendulum system
ff
IV
Slider contacts restrainer on surface 1; Motion remains stopped on surface 3; Sliding on surfaces 2 and 4
( ) *1 1 1
2 4 1dr f
eff eff eff
W WF u u d FR R R
= − + ++
Valid until:
*4 4 4
4dr f
eff
WF F d FR
= = + ,
( )* *4 1
4 1 4 1 2 44 1
dr dr eff effeff eff
d du u u R RR R
= = + + µ − + µ +
V
Slider bears on restrainer of surface 1 and 4; Sliding on surfaces 2 and 3
( ) *4 4 4
2 3 4dr f
eff eff eff
W WF u u d FR R R
= − + ++
Regime Description Force-Displacement Relationship
Assumptions: (1) 1 4 2 3eff eff eff effR R R R= = , (2) 2 3 1 4µ = µ < µ < µ , (3) ( )*1 4 1 1effd R> µ − µ ,
(4) ( )*2 1 2 2effd R> µ − µ , (5) ( )*
3 4 3 3effd R> µ − µ
4. Friction Pendulum System
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4. Friction Pendulum System Shake table tests of a full-scale 5-story steel moment frame building (PI: K. Ryan, Reno; S. Mahin, Berkeley; G. Mosqueda, San Diego)
triple friction pendulum isolators lead rubber bearing/cross linear
slider Fixed base o Simulations designed to impose large
displacement demands in isolation systems
o Simulations both with and without vertical component of ground motion
o 4th and 5th floor included nonstructural systems
106
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4. Friction Pendulum System
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4. Friction Pendulum System
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E-Defense Experiments: 5 story steel moment frame Measured response
4. Friction Pendulum System L
evel
Peak Acceleration Profile
Peak Acc. (g)
50 60 70 80 90 100
-0.5
0
0.5
-0.48446
-0.11864
0.14598
Fixed BaseTPB IsolatedLRB Isolated
50 60 70 80 90 100
-0.5
0
0.5 0.5844
0.14362
-0.23067
Base Shear Coefficient
X-d
irec
tion
Y-di
rect
ion
Time (sec) 109
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5. Other Seismic Isolation Systems
• Seismic Isolation Systems Incorporating Metallic Dampers – The Uniform Moment Bending-Beam Damper
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5. Other Seismic Isolation Systems
• Seismic Isolation Systems Incorporating Metallic Dampers – The Tapered-Cantilever Bending-Beam Damper
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5. Other Seismic Isolation Systems
• Seismic Isolation Systems Incorporating Metallic Dampers – The Tapered-Cantilever Bending-Beam Damper
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• Seismic Isolation Systems Incorporating Metallic Dampers – The Tapered-Cantilever Bending-Beam Damper
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5. Other Seismic Isolation Systems
• Seismic Isolation Systems Incorporating Metallic Dampers – The Tapered-Cantilever Bending-Beam Damper
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5. Other Seismic Isolation Systems
• Seismic Isolation Systems Incorporating Metallic Dampers – The Torsional-Beam Damper
115
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5. Other Seismic Isolation Systems • Seismic Isolation Systems Incorporating
Metallic Dampers – The Torsional-Beam Damper
• South Rangitikei River Railroad Bridge, New Zealand, built in 1981
116
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5. Other Seismic Isolation Systems
• Seismic Isolation Systems Incorporating Metallic Dampers – Lead-Extrusion Bearings
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5. Other Seismic Isolation Systems
• Seismic Isolation Systems Incorporating Metallic Dampers – Sliding Bearing with C-Shaped Yielding Steel Devices -
ALGA
C-element
118
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5. Other Seismic Isolation Systems
• Seismic Isolation Systems Incorporating Metallic Dampers – Sliding Bearing with C-Shaped Yielding Steel
Devices - ALGA
119
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5. Other Seismic Isolation Systems
• Seismic Isolation Systems Incorporating Metallic Dampers – Sliding Bearing with C-Shaped Yielding Steel
Devices - ALGA
Courtesy of M. Constantinou
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• Seismic Isolation Systems Incorporating Metallic Dampers – Sliding Bearing with C-Shaped Yielding Steel
Devices - ALGA
BOLU VIADUCT, TURKEY
2.3 km LONG DAMAGED IN DUCZE EARTHQUAKE OF NOV. 1999
CROSSED BY ANATOLIAN FAULT BEARING DISPL. CAPACITY 210 mm
REQUIRED CAPACITY PER AASHTO OVER 1000 mm LIKELY DEMAND IN EARTHQUAKE ≥1400mm
Courtesy of M. Constantinou 121
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5. Other Seismic Isolation Systems
• Seismic Isolation Systems Incorporating Metallic Dampers – Rubber Bearings and U-Shaped Yielding Steel
Devices
122
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6. Example of adequacy assessment of a lead-rubber bearing under
Maximum Credible Earthquake (MCE)
123
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Circular bolted bearing. Factored axial load:
= 6000 kN Lateral displacement under MCE:
Lateral displacement caused by rotation is negligible.
Effective bounded diameter: D = 813 mm
29 rubber layers, each 7 mm thick Rubber moduli:
G = 0.5 MPa K = 2000 MPa
Steel shims: Probable yield strength: Fye =380 MPa Thickness: 3.04 mm
Bearing Description and Loading Conditions
MCE MCEu D D SL EP P P Pγ= + +
( ) mm5555.0 =+=++=MCEMCEcyst ESESS ΔγΔΔΔΔγΔ
124
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Assess the adequacy of the bearing for the Maximum Considered Earthquake (MCE). See Section 2.
Design Requirements
125
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Ar
∆
Calculation of reduced overlapping area, Ar Ar = Overlapping area for a displacement, ∆, equal to:
( ) mm5555.0 =+=++=MCEMCEcyst ESESS ΔγΔΔΔΔγΔ
( ) ( ) 222
11
mm9401056388.1sin6388.14
813sin4
6388.1mm813mm555cos2cos2
=−=−=
=
=
∆
= −−
δδ
δ
DA
D
r
Adequacy Assessment for MCE
126
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Ar
∆
Shear strains calculations Shear strain due to lateral deformation:
0.5MCE
MCE
S EuS
rTγ
γ∆ + ∆
=
( )
73.2mm203mm555
mm203mm729
==
==
uS
r
MCE
T
γ
Adequacy Assessment for MCE
127
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Ar
∆
Buckling load calculation Buckling load at MCE lateral displacement:
' 0.15MCE
rcr cr cr
AP P PA
= ≥
( )
( )( )
( )( )( )( )
( ) cr'cr
cr
rcr
r
P
mmNP
mmAIr
tDS
TGSArP
AA
MCE0.15kN1037kN515352.0P
kN35515mm203
mm25.203mm12451929/5.025.2
25.203mm124519
64mm813
29mm74mm813
4
25.2
20.0mm124519mm940105
4mm813mm940105
22
2
4
2
2
2
2
≥==
==
===
===
=
=
===
π
π
λ
λπ
π
Adequacy Assessment for MCE
128
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Ar
∆
Shear strains calculations Shear strain due to compression:
1MCE
u uC
r
P fA GS
γ = ⋅ f1
S K/G 2000 4000 6000 ∞
5 1.02 1.01 1.01 1.00 7.5 1.05 1.03 1.02 1.00 10 1.10 1.05 1.03 1.00
12.5 1.15 1.08 1.05 1.00 15 1.20 1.11 1.07 1.00
17.5 1.27 1.14 1.10 1.00 20 1.34 1.18 1.13 1.00
22.5 1.41 1.23 1.16 1.00 25 1.49 1.27 1.19 1.00
27.5 1.57 1.32 1.23 1.00 30 1.66 1.37 1.26 1.00 ( )( )( ) ( ) 27.535.1
29N/mm5.0mm940105N0000006
35.1
22
1
==
=
uCMCE
f
γ
Adequacy Assessment for MCE
129
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Ar
∆
Verification of total shear strain A bearing design is considered adequate if:
0.25 9.0C SMCE MCE
u u ursγ γ γ+ + ≤
0.90.8073.227.5 ≤=++
Adequacy Assessment for MCE
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Ar
∆
Stability verification A bearing design is considered adequate if:
'
1.1MCEcr
u
PP
≥
1.118.1kN0006kN1037
≥=
Adequacy Assessment for MCE
131
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Ar
∆
Minimum steel shims thickness. The thickness of the steel shims, ts, must be at least:
( )
( )
mm2.2mm3.04
mm1.9mm2.22
N0000006mm940105N/mm3801.08
mm765.12
2
≥
≥=−
≥st
Adequacy Assessment for MCE
132
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Questions/Discussions
133