ahmadizadeh/courses/strcontrol... · Supplemental Damping and Seismic Isolation Chapter 10 –Seismic Isolation SystemsSeismic Isolation Systems CIE 626 - Structural Control Chapter

Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems

CIE 626 - Structural Control Chapter 9 – Seismic Isolation Systems


Chapter 9 Seismic Isolation Systems

1



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



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

3



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.

4



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




Photo: Courtesy of M. Constantinou

6




Image T. Saito

7




• Elastomeric Bearings for Sakhalin I Orlan Platform. • Tested at University at Buffalo.

Photos: Courtesy of M. Constantinou

8



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



2. Laminated Rubber Bearings • Full-Scale Isolated Bridge Testing

Video

10



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



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.

12



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.

13




• Gravity Load Carrying Capacity of Laminated-Rubber Bearings.

14


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 − ∆=


15



Gravity Load Carrying Capacity Overlapping Area Rectangular bearings:

Ar

∆( )rA B L= − ∆


B

L

∆

16



Gravity Load Carrying Capacity Overlapping Area Cylindrical hollow bearings:

Ar

∆

( sin )rAA

δ δπ

−≈

12cos ( )D

δ − ∆=

o


17



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 = ⋅


18



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 = ⋅


circular

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 = ⋅


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:

20



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.


21

Mehdi

Text Box

A measure of the compressibility of rubber



Gravity Load Carrying Capacity Coefficient f1 for rectangular bearings:

K is the bulk modulus of rubber ( ≈ 2000 MPa).

1cP f

AGSγ = ⋅


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


22





1cP f

AGSγ = ⋅


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


23





1cP f

AGSγ = ⋅


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


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1cP f

AGSγ = ⋅


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


25



Gravity Load Carrying Capacity Coefficient f1 for cylindrical hollow bearings:


1cP f

AGSγ = ⋅


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


26



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=


27



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

− −

+

=


28



Gravity Load Carrying Capacity Critical displacement for simply supported bearings Instability by overturning occurs when the overturning

moment is larger than the stabilizing moment.


29



Gravity Load Carrying Capacity Critical displacement for simply supported bearings Critical displacement, Dcr, causing overturning:

If Dcr ≤ D1:

If Dcr > D1:


30



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 :


31



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


32



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 = ⋅


33



Rotations between the top and bottom of bearings Coefficient f2 for circular bearings:


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.


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Rotations between the top and bottom of bearings Coefficient f2 rectangular 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


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Rotations between the top and bottom of bearings Coefficient f2 for rectangular bearings:


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


36






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


37





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


38



Rotations between the top and bottom of bearings Coefficient f2 for cylindrical hollow bearings:


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


39



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 ∆=


40



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.


41



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.


42



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

≥−


43




• Lateral Stiffness of Laminated Rubber Bearings

44




• Natural Period of Vibration of Laminated-Rubber Bearings Supporting a Rigid Structure

45




• 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




• 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




• Vertical Stiffness of Laminated Rubber Bearings

48



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


49



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).


50



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= + +


51



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+

= ⋅


52



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

=


53



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


54



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

≥ ≥−

+ +


55



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 = ⋅


56



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∆ = ∆ + ∆


57



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


58



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

≥ ≥−


59



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 ++=


60



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= ∆ + ∆


61




(MCE) Critical buckling load at the MCE lateral displacement:

' 0.15MCE

rcr cr cr

AP P PA

= ≥

MCEEs ΔγΔ.Δ += 50


62



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


s

urγ

'

1.1MCEcr

u

PP

≥


63




(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

≥ ≥−


64



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




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.

66




• 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




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


Courtesy of Ridg-U-Rak Inc.

68




• Seismic Isolation of Pallet-Type Steel Storage Racks with Laminated Rubber Bearings

108

31

31

31

64


108

31

31

31

64


Steel Plate

Rubber Layers

Rubber Durometer Horizontal Stiffness (kN/m) Equivalent Viscous Damping Ratio

40 47 0.20 60 93 0.22

69




• Seismic Isolation of Pallet-Type Steel Storage Racks with Laminated Rubber Bearings

Courtesy of Ridg-U-Rak Inc

70




Racks with Laminated Rubber Bearings

Courtesy of Ridg-U-Rak Inc

Isolated Rack Conventional Rack Video 71



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.


72



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



3. Lead-rubber Bearings • Properties of Lead-Rubber Bearings

74



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



3. Lead-rubber Bearings • SRMD Testing Machine, UC-San Diego

DIS LR Bearing, 400% strain

76



3. Lead-rubber Bearings • Failure Test, NIED, Tsukuba, Japan

77




• Modeling of Lead-Rubber Bearings

k1

k2 Fy

78





k1

k2 Fy

79





k1

k2 Fy

80





81



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



4. Friction Pendulum System

• General Description – Articulated friction slider traveling on spherical

concave lining surface.

83





84




• 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




– 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).


86



FPS Isolator, Vertical Load = 3490 kips, Displacement = 29 in, velocity = 53 in/s

87




New International Terminal San Francisco International Airport

88




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




KODIAK, ALASKA COLD TEMPERATURE APPLICATION -40 DEG TEMPERATURE, STRONG WIND


90



• Properties of Frictionless Pendulum System

91



• Properties of Frictionless Pendulum System

92



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)


93



• Properties of Pendulum System including Friction 4. Friction Pendulum System

94




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




• Electrical 3-phase disconnect switch isolated by friction pendulum system

UNIV. AT BUFFALO,

2006

96



• Double curvature friction pendulum system – Combination of two friction pendulum systems

97




• 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


98




• 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


99



4. Friction Pendulum System • Double curvature friction pendulum system

UNIV. AT BUFFALO, 2004 Courtesy of M. Constantinou

100



4. Friction Pendulum System • Triple curvature friction pendulum system


101



Triple curvature friction pendulum system 4. Friction Pendulum System

102



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


103



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


104



http://www.earthquakeprotection.com/index.html



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




107




108



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



5. Other Seismic Isolation Systems

• Seismic Isolation Systems Incorporating Metallic Dampers – The Uniform Moment Bending-Beam Damper

110




• Seismic Isolation Systems Incorporating Metallic Dampers – The Tapered-Cantilever Bending-Beam Damper

111





112




113





114




• Seismic Isolation Systems Incorporating Metallic Dampers – The Torsional-Beam Damper

115



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




• Seismic Isolation Systems Incorporating Metallic Dampers – Lead-Extrusion Bearings

117




• Seismic Isolation Systems Incorporating Metallic Dampers – Sliding Bearing with C-Shaped Yielding Steel Devices -

ALGA

C-element

118




• Seismic Isolation Systems Incorporating Metallic Dampers – Sliding Bearing with C-Shaped Yielding Steel

Devices - ALGA

119





Devices - ALGA


120




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




• Seismic Isolation Systems Incorporating Metallic Dampers – Rubber Bearings and U-Shaped Yielding Steel

Devices

122




6. Example of adequacy assessment of a lead-rubber bearing under

Maximum Credible Earthquake (MCE)

123



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



Assess the adequacy of the bearing for the Maximum Considered Earthquake (MCE). See Section 2.

Design Requirements

125



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



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


127



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


128



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


129



Ar

∆

Verification of total shear strain A bearing design is considered adequate if:

0.25 9.0C SMCE MCE


0.90.8073.227.5 ≤=++


130



Ar

∆

Stability verification A bearing design is considered adequate if:

'

1.1MCEcr

u

PP

≥

1.118.1kN0006kN1037

≥=


131



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


132



Questions/Discussions

133

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ahmadizadeh/courses/strcontrol... · Supplemental Damping and Seismic Isolation Chapter 10 –Seismic Isolation SystemsSeismic Isolation Systems CIE 626 - Structural Control Chapter