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Seismic Analysis and

Response Fundamentals

Lee MarshSenior Project Manager

BERGER/ABAM Engineers, Inc

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Force Displ. Retro

Topic Applicability

L rnin m

Identify Earthquake Inertial Forces/Loadings

Describe the Interrelation Between the Plastic

Mechanism Concept and Capacity Design

List Extreme Event I Load Combination, Including Load

Factors

e ne o a e sm c es gn ra egy an en y

Earthquake Resisting Systems/Elements

s ypes o e sm c na ys s ec n ques

Define Regular vs. Non-Regular Bridges

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Force Displ. Retro

Topic Applicability

Presentation Roadma

Seismic Design Concepts and Strategies

Bridge Modeling Guidelines

Models, Stiffness and Mass

Modal Anal sis

Combining Directional Response

Summary

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Force Displ. Retro

Topic Applicability

Dynamic Equilibrium /

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Force Displ. Retro

Topic Applicability

Ground Excitation vs

Dynamic

Amplification

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Force Displ. Retro

Topic Applicability

Presentation Roadma




Modal Anal sis


Summary

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Force Displ. Retro

Topic Applicability

Three Observations

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Force Displ. Retro

Topic Applicability

Three Observations cont

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Force Displ. Retro

Topic Applicability

Three Observations cont

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Force Displ. Retro

Topic Applicability

Path to Plastic Mechanism

MomentDisplacement,

M1

1 2 3Inertial Force

Mp2

Plastic Hinge4 Total

Mp shaft1 First Hinges Form2 Second Hinges Form

3 Deformation Capacity Reached

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Force Displ. Retro

Topic Applicability

Example Plastic

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Force Displ. Retro

Topic Applicability

Ca acit Desi n Princi les Concept Underpins Modern Seismic Design

Establish Capacity and Plastic Mechanism Identify the Elements of the Structure That Should Behave

Inelastically and Design Them to Yield.

Provide Ductility

Imposed by the Design Earthquake.

Capacity Protect the Rest

Design All Other Elements to be Strong Enough That TheyDo Not Behave Inelastically, and Provide Articulation to

Permit Mobilization of the Plastic Mechanism.

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Force Displ. Retro

Topic Applicability

System Load vs Deflection

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Force Displ. Retro

Topic Applicability

Dynamic Equilibrium

finertial = m (agnd + arel) = Earthquake Load

Inertial force is limited to sum ofsuperstructure

column shears to satisfy equilibrim.columns

spring damping

The column shearsBent FBD

Transverse Loading

effects.

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Force Displ. Retro

Topic Applicability

Transverse Response-

superstructure

were non-continuous,

then center bent would

resist much lar er forces.

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Force Displ. Retro

Topic Applicability

Longitudinal Response-

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Force Displ. Retro

Topic Applicability

Balanced Stiffness

Guide Specification Isolation Casing

(example techniqueHighest Category

SDC D

to alter stiffness)

Column Stiffness Bent Stiffness

Frame Period

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Force Displ. Retro

Topic Applicability

Earthquake Resisting

Note: Concepts Valid for LRFD & Retrofit, Too.

Figure 3.3-1a Guide Specifications

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Force Displ. Retro

Topic Applicability


Note: Concepts Valid for LRFD& Retrofit, Too.

Figure 3.3-1a

Guide Specifications

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Force Displ. Retro

Topic Applicability


Note: Concepts Valid for LRFD

& Retrofit, Too.

Permissible EREs:

Figure 3.3-1b


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Force Displ. Retro

Topic Applicability



& Retrofit, Although Uninspectable Damage

is Not Explicitly Permitted in LRFD.Permissible EREs with Owners Approval:

Figure 3.3-2


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Force Displ. Retro

Topic Applicability



& Retrofit, Too.

EREs Not Recommended for New Bridges:

-.


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Force Displ. Retro

Topic Applicability

Global Desi n Strate ies T e 1 Ductile

Note: Concepts Valid, Except Types

2 & 3 Not Addressed in LRFD

Substructure, ElasticSuperstructure Type 2

ype as c

Substructure, Ductile

SuperstructureType 3

Type 3 Elastic Sub- &

Superstructure, Fusing

Type 1

Figure 7.1-1 Guide SpecificationsFigure shows all three types;

but use only one at a time.

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Force Displ. Retro

Topic Applicability

Presentation Roadma




Modal Anal sis


Summary

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Force Displ. Retro

Topic Applicability

AASHTO

Consider permanent loads, live load is special case

LRFD Extreme Event I p(DC+DD+DW+EH+EV+ES+EL+PS+CR+SH)+EQ

(LL+IM+CE+BR+PL+LS)+WA+FR+EQ

- =

Guide Specification Use load factors of 1.0 for all permanent loads.

Equivalent to p = 1.0 simplification appropriate for pushover Live load EQ up to engineer, per commentary (e.g. high ADTT,

etc

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Force Displ. Retro

Topic Applicability

Presentation Roadma




Modal Anal sis


Summary

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Force Displ. Retro

Topic Applicability

System Demand

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Force Displ. Retro

Topic ApplicabilityLocal Capacity Analysis Force Displ. Retro

Topic Applicability

Note: Concept Valid for LRFD, But Not Used.

rce

FEQ

EQActual Response

F

teralF

12 3 4 Plastic Hinge

L

sp acemen -

Actual Response Milestones

1 - First-yield Point, Previous Nonlinearity Due to Foundation Flexibility2 Maximum Allowable Plastic Deformation

3 Onset of Collapse

-

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Force Displ. Retro

Topic Applicability

Example

(L = 242 ft)

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Force Displ. Retro

Topic Applicability

Uniform Load Method cont

0.47

Step 4

0.79 sec

AASHTO LRFD Interim 2008

T i A li bilit

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Force Displ. Retro

Topic Applicability


T i A li bilit

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Force Displ. Retro

Topic Applicability


Topic Applicability

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Force Displ. Retro

Topic Applicability

Single-Mode Spectral

Topic Applicability

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Force Displ. Retro

Topic Applicability


Topic Applicability

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Force Displ. Retro

Topic Applicability


Topic Applicability

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Force Displ. Retro

Topic Applicability


Pe(x)

Topic Applicability

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Force Displ. Retro

Topic Applicability

Re ular Brid es

Topic Applicability

A l i M h d A

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Force Displ. Retro

Topic Applicability

Analysis Method As

AASHTO

LRFD 4th Ed.

Topic Applicability

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Force Displ. Retro

op c pp cab y

Presentation Roadma




Modal Anal sis


Summary

Topic Applicability

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Force Displ. Retro

p pp y

Seismic Model O tions

Topic Applicability

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Force Displ. Retro

p pp y

S ine Model

Topic Applicability

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Force Displ. Retro

Geometr Issues

Topic Applicability

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Exam le Brid e Slide 1 of 4

Topic Applicability

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Force Displ. Retro


F Di l R t

Topic Applicability

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Force Displ. Retro


F Di l R t

Topic Applicability

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Force Displ. Retro


Force Displ Retro

Topic Applicability

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Force Displ. Retro

Exam le S ine Model

Force Displ Retro

Topic Applicability

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Force Displ. Retro

Substructure Model

Force Displ Retro

Topic Applicability

Effective Stiffness

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Force Displ. Retro

Effective Stiffness

Priestley, Seible and Calvi, 1996

Force Displ Retro

Topic Applicability

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Force Displ. Retro

Su ort Conditions

Force Displ Retro

Topic Applicability

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Force Displ. Retro

Foundation Flexibilit

Force Displ. Retro

Topic Applicability

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Force Displ. Retro

Foundation Flexibilit cont

Force Displ. Retro

Topic Applicability

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p

Wei ht Distribution

Force Displ. Retro

Topic Applicability

S i l C id ti

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p

S ecial Considerations

Force Displ. Retro

Topic Applicability

P t ti R d

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p

Presentation Roadma




Modal Anal sis


Summary

Force Displ. Retro

Topic Applicability

M lti d A l i

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Multimode Anal sis

Force Displ. Retro

Topic Applicability

M d l P ti i ti

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Modal Partici ation

Force Displ. Retro

Topic Applicability

Modal Partici ation cont

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Modal Partici ation cont

Force Displ. Retro

Topic Applicability

Partici atin Mass

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Partici atin Mass

Force Displ. Retro

Topic Applicability

Example

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p

X - LongitudinalY - Vertical

-

Force Displ. Retro

Topic Applicability

Example

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p

Force Displ. Retro

Topic Applicability

Example

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Force Displ. Retro

Topic Applicability

Example

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Force Displ. Retro

Topic Applicability

Example

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Force Displ. Retro

Topic Applicability

Modal Anal sis Loadin

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Modal Anal sis Loadin

Loading is Mode-by-Mode

Process is Directly Analogous to Single-Mode Method

=

Force Displ. Retro

Topic Applicability

Response Spectrum

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sm,

Force Displ. Retro

Topic Applicability

Modal Combinations

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Modal Combinations

Force Displ. Retro

Topic Applicability

Modal Combinations cont

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Force Displ. Retro

Topic Applicability


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Force Displ. Retro

Topic Applicability

Presentation Roadma

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Presentation Roadma




Modal Anal sis

Combining Directional Response Summary

Force Displ. Retro

Topic Applicability

Directional Combinations

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Force Displ. Retro

Topic Applicability

Directional Combinations

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Force Displ. Retro

Topic Applicability

Directional Load Combos

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Force Displ. Retro

Topic Applicability

Presentation Roadma

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Modal Anal sis

Combining Directional Response Summary

Force Displ. Retro

Topic Applicability

Summar and Look Ahead

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Summary

Plastic Mechanism and Capacity Design Earth uake Resistin Elements and S stems

Demand Modeling

Look Ahead Force-Based Design

Displacement-Based Design

Detailing for Ductility Geotechnical Considerations

04 Marsh

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