5 Design of Isolated Bridges

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(5)??????? (5) Design of Isolated Bridges
?????? ???? Kazuhiko Kawashima Tokyo Institute of
Technology
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Very Brief Introduction on Seismic Design of
Bridges ???????(????)
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Force Reduction Factor ??????
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Force Reduction Factor ??????
Elastic Inertia Force
Inertia Force considering nonlinear behavior of a
structure
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When a structure undergoes inelastic response
under a strong ground motion, how does the
structure response?
Response
Ground Acceleration
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Ductility Factor ????
Bilinear Hysteresis
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Target Ductility Factor ??????

• Target ductility factor is a response ductility
  factor which is anticipated to occur in design
• If response ductility factor is less than the
  target ductility factor, designed structure must
  show expected performance
• If response ductility factor is larger than the
  target ductility factor, designed structure does
  not have expected performance.

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Linear Nonlinear Response of a SDOF Oscillator
Natural Period0.5s, Target Ductility Factor 4,
Yield Displacement 53.3mm
Acceleration (m/sec2)
Displacement (m)
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Force Reduction Factor ??????
A basic parameter in the force-based seismic
design
Target ductility factor
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How is the Force Reduction Factor used in
Seismic Design?
Elastic force can be estimated approximately as
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Force Reduction Factor
A basic parameter in the Force-based Seismic
Design

• Force reduction factor
• Response modification factor
• q-factor
• R-factor
• ..

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Limited number of research on the force reduction
factors in spite of its importance

• Newmark Hall (1973)
• Nassar Krawinkler (1991)
• Miranda Bertero (1994)
• Watanabe Kawashima (2002)

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Significant Scattering of Force Reduction Factors
Depending on Ground Motions
Moderate Soils
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Approximate Estimates of the Force Reduction
Factors ??????????
Equal Displacement Assumption ?????
Equal Energy Assumption ????????
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Evaluation of Force Reduction Factor Taking the
Large Scattering into Account
Moderate Soils
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Evaluation of Modal Damping Ratio of a
Bridge ???????????????
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How can we determine the modal damping ratios by
assigning damping ratios of each structural
components?

• Theoretically, damping ratio is defined for a
  SDOF system. If we can assume the oscillation of
  each structural component as a SDOF system, it
  may be possible to assign a damping ratio for
  each structural component.

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How can we determine the modal damping ratios by
assigning damping ratios of each structural
components? (continued)

• There is not a single method which is exact and
  easy for implementation for design purpose.
• Following empirical methods are frequently used
• Strain energy proportional method
• Kinematic energy proportional method

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Strain Energy Proportional Method ?????????????
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Because
Strain energy of m-th element for k-th mode is
Therefore, the total energy dissipation of the
system is
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Kinematic Energy Proportional Damping
Ratio ??????????
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Which is better for determining modal damping
ratios between the strain energy proportional
method and kinematic energy proportional method?

• Damping ratios of the structural components where
  large strain energy is developed are emphasized
  in the strain energy proportional method.

Plastic deformation of columns
Plastic deformation of foundations soils

• Strain energy proportional method is better in a
• system in which hysteretic energy dissipation is
  predominant

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Which is better for determining modal damping
ratios between the strain energy proportional
method and kinematic energy proportional method?

• Damping ratios of the structural components with
  larger kinematic energy are emphasized in the
  kinematic energy proportional method.

• Kinematic energy proportional method is better in
  a
• system in which hysteretic energy dissipation is
  less significant

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Where do we consider the damping characteristics
of the bridge in the static design?
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How should we incorporate the damping ratio of
the bridge in the static seismic design?
Dynamic Analysis
Static Analysis
Ground Accelerations
Response Acceleration
Dynamic Response Analysis
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How can we estimate the damping ratio of bridges?

• Empirical relation on the damping ratio vs.
  fundamental natural period of bridges
• This is based on force excitation tests on
  bridges supported by various types of foundations

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Why is the damping ratio inversely proportional
to the fundamental natural period?
Radiational energy dissipation
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How should we incorporate the damping ratio of
the bridge in the static seismic design?
Damping ratio of the bridge should be
incorporated in the evaluation of response
accelerations used in the static analysis
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How should we incorporate the damping ratio of
the bridge in the static seismic design?
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How should we incorporate the damping ratio of
the bridge in the static seismic design?
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Response Acceleration used in Static Design by
taking account of Damping Ratio of a Bridge
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Response Acceleration used in Static Design by
taking account of Damping Ratio of a Bridge
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Japanese Practice in the Evaluation of Design
Seismic Forces

• Explicit Two Level Design Forces are used
• Near field GMs and Middle field GMs resulted
  from M 8 EQs are used for the safety
  evaluation GMs
• Importance is accounted for not in the evaluation
  of design ground motions but in the evaluation of
  design ductility factors
• A damping force vs. natural period relation is
  included in the design seismic forces for static
  analysis

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Static Inelastic Design for Seismic Isolated
Bridges
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Evaluation of Demand for a Fixed Base
Bridge ????????????????
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Static Inelastic Analysis ??????????
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Static Inelastic Analysis
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Design of Isolators and Dampers ???????
Equivalent Damping Ratio ??????
Equivalent Stiffness ????
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Static Inelastic Analysis
Response Modification Factor resulting from
Enhanced Energy Dissipation Capacity
1.0
1.11
1.25
1.43
Evaluation of First Mode Damping Ratio based on
Energy Proportion Damping
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Static Inelastic Analysis
Evaluation of First Mode Damping Ratio based on
Energy Proportion Damping
Structural Component
Deck
0.03-0.05
Isolators
Equivalent damping ratio
Piers
0.05-0.1
Foundations
0.1-0.3
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Approximated Estimation of System Damping Ratio
based on Energy Proportional Method ??????????????
????????????????
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Approximated Estimation of System Damping Ratio
based on Energy Proportional Method

• Determine the system damping ratio for the
  fundamental mode from the damping ratio of the
  column and the damping ratio of the isolator.
• Disregard the deformation and energy dissipation
• Fundamental mode shape can be approximated as

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Strain energy of the column and the isolator
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Based on the strain energy proportional method,
the system damping ratio for the 1st mode becomes
as
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Evaluation of Design Ductility Factor of RC
Columns ??????(??????)
Design response ductility factor of a pier
Fixed-base Bridge ????
Isolated Bridge ???
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Design of Isolators and Dampers ???????
Design Requirements for Devices

• Displacement computed in design lt /-10
• from the assumed design displacement
• Shear strain in the device subjected to design
  lateral force
• lt 250
• Local shear strain resulting from the seismic
  effect, dead weight, rotation and other effects
  lt Rupture Strain / 1.2
• Lateral capacity gt Lateral force demand

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Design of Isolators and Dampers
Design Requirements for Devices

• Devices with positive tangential stiffness at any
  displacement within the design displacement uB
  should be used to prevent shake down.
• Devices have to be designed fabricated so that
  scatter of stiffness equivalent damping ratio
  are within 10 of the design values
• Devices have to be stable for at least 50 15
  lateral load reversals with the design
  displacement uB for Type I Type II ground
  motions, respectively.

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Design Requirements for Devices (continued)

• A deck should return to the rest position after
  it is subjected to design ground motions.
  Residual displacement lt 10 x design
  displacement.
• The stiffness and damping ratio should be stable
  for a change of load condition and natural
  environment

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Damage Control of Columns in Isolated Bridges
Limit response ductility factor of a pier
Fixed-base
Isolated
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?????????? Effect of Column Deformation
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Effect of Isolator Deformation on the System
Ductility Factor
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Effect of Isolator Deformation on the System
Ductility Factor
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System Ductility Factor vs. Column Ductility
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Response Modification Factor should be Evaluated
using System Ductility Factor
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Isolator-Column Interaction
1.85m
Longitudinal reinforcement ratios

• 0.95
• 0.99
• 1.58

Tie reinforcement ratios
0.8
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Yield Strength of Column and Isolator
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Isolator-Column Interaction (continued)
d95mm
d75mm
d45mm
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Seismic Isolation with Limited Increase of
Natural Period (Menshin Design)
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Menshin Design
Seismic Isolation
Menshin Design
Limited increase of the natural period
Increase of the natural period
Increase of the energy dissipation
Increase of the energy dissipation
Distribute lateral force to as many substructures
as possible
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Favorable Implementations of Menshin Design

• Super multi-span continuous bridges
• Damage control of bearings and piers
• Seismic retrofit of existing bridges
• Deck connection to make simply supported decks to
  multi-span decks

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Design Codes for Menshin Design

• 1989 Guideline for Menshin Design of Highway
  Bridges
• 1992 Manual of Menshin Design of Highway Bridges
• 1995 Guide Specifications for Design of Highway
  Bridges that suffered Damage in the 1995
  Hyogo-ken nanbu Earthquake
• 1996 Part V Seismic Design, Design
  Specifications of Highway Bridges
• First stipulations in the mandate code
• 2002 Part V Seismic Design, Design
  Specifications of Highway Bridges

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Part V Seismic Design Design Specifications of
Highway Bridges
Japan Roads Association, 1996
Highway bridges with span length less than 200m
About 2000-3000 new bridges per year

• Part I Common Part
• Part II Steel Bridges
• Part III Concrete Bridges
• Part IV Foundations
• Part V Seismic Design

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Part V Seismic Design Design Specifications of
Highway Bridges
Chapter 8 Menshin Design
8.1 General 8.2 Menshin Design 8.3 Design Lateral
Force 8.4 Design of Isolator and Energy
Dissipator 8.4.1 Basic Principle 8.4.2
Evaluation of Safety of Isolator 8.4.3 Design
Displacement of Isolator 8.4.4 Equivalent
Stiffness Damping Ratio 8.4.5 Dynamic
Performance of Bearings 8.5 Evaluation of Natural
Period 8.6 Evaluation of Damping Ratio of Bridge
System 8.7 Design Details 8.7.1 Distance
between Decks 8.7.2 Expansion Joints