Seismic Analysis and Response...

Seismic Analysis andResponse Fundamentals

Lee MarshSSenior Project ManagerBERGER/ABAM Engineers, Inc

Force Displ. RetroTopic Applicability

Learning OutcomesLearning OutcomesIdentify Earthquake Inertial Forces/Loadings

Describe the Interrelation Between the Plastic Mechanism Concept and Capacity Design

Li t E t E t I L d C bi ti I l di L dList Extreme Event I Load Combination, Including Load Factors

D fi Gl b l S i i D i St t d Id tifDefine Global Seismic Design Strategy and Identify Earthquake Resisting Systems/Elements

Li t T f S i i A l i T h iList Types of Seismic Analysis Techniques

Define Regular vs. Non-Regular Bridges

Presentation Roadmapp

Earthquake LoadingsEarthquake LoadingsSeismic Design Concepts and StrategiesExtreme Event Earthquake LoadingExtreme Event Earthquake LoadingBridge Modeling Guidelines

Analysis MethodsAnalysis MethodsModels, Stiffness and MassModal AnalysisyCombining Directional Response

Summary

Force Displ. RetroTopic ApplicabilityDynamic Equilibrium /

Free VibrationFree Vibration

Force Displ. RetroTopic ApplicabilityGround Excitation vs

Earthquake ‘Loading’Earthquake ‘Loading’

IncludesIncludesDynamicAmplification

Summary

Three Observations

Three Observations (cont)( )

Path to Plastic MechanismΔ

MomentDisplacement, Δ

1 2 3Inertial Force

Mp2Plastic Hinge

(4 Total)( ota )

Mp shaft1 – First Hinges Form2 – Second Hinges Form3 – Deformation Capacity Reached

Force Displ. RetroTopic ApplicabilityExample Plastic

MechanismsMechanisms

Capacity Design Principlesp y g p

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 Ensure Those Elements Can Tolerate the Inelastic DemandsEnsure Those Elements Can Tolerate the Inelastic Demands Imposed by the Design Earthquake.

Capacity Protect the RestD i All O h El b S E h Th ThDesign All Other Elements to be Strong Enough That They Do Not Behave Inelastically, and Provide Articulation to Permit Mobilization of the Plastic Mechanism.

Force Displ. RetroTopic ApplicabilitySystem Load vs Deflection

Pushover CurvePushover Curve

Force Displ. RetroTopic ApplicabilityDynamic Equilibrium

Revisted: Including YieldingRevisted: Including Yielding

finertial = m (agnd + arel) = ‘Earthquake Load’

Inertial force is limited to sum ofsuperstructurecolumn shears to satisfy equilibrim.

columns

fspring + fdamping

The column shears include inelastic

Bent FBDTransverse Loading

include inelastic effects.

Transverse ResponseTwo Span Continuous SuperstructureTwo-Span Continuous Superstructure

(If(If superstructurewere non-continuous,then center bent wouldresist much larger forces.)resist much larger forces.)

Longitudinal ResponseTwo Span BridgeTwo-Span Bridge

Balanced Stiffness

Guide Specification Isolation Casing(example technique

Highest Category –SDC D

Control Relative:

to alter stiffness)

Control Relative:• Column Stiffness• Bent Stiffness• Frame Period

Force Displ. RetroTopic ApplicabilityEarthquake Resisting

Systems (ERS)Systems (ERS) Note: Concepts Valid for LRFD & Retrofit, Too.

Figure 3.3-1a Guide Specifications

Systems (ERS) (cont)Systems (ERS) (cont) Note: Concepts Valid for LRFD & Retrofit, Too.

Figure 3.3-1a Guide Specifications

Elements (ERE)Elements (ERE) Note: Concepts Valid for LRFD & Retrofit, Too.

Permissible EREs:

Figure 3.3-1b Guide Specifications

Elements (ERE)Elements (ERE) Note: Concepts Valid for LRFD & Retrofit, Although Uninspectable Damage is Not Explicitly Permitted in LRFD.Permissible EREs with Owner’s Approval:

Figure 3.3-2 Guide Specifications

Elements (ERE)Elements (ERE) Note: Concepts Valid for LRFD & Retrofit, Too.

EREs Not Recommended for New Bridges:

Figure 3 3-3Figure 3.3-3 Guide Specifications

Global Design Strategiesg g

Type 1 – Ductile

Note: Concepts Valid, Except Types2 & 3 Not Addressed in LRFD

ypSubstructure, Elastic SuperstructureT 2 El ti

Type 2

Type 2 – Elastic Substructure, Ductile Superstructure

Type 3

Type 3 – Elastic Sub- & Superstructure, Fusing Interface

Type 1

Interface

Figure 7.1-1 Guide SpecificationsFigure shows all three types; but use only one at a time.

Summary

Force Displ. RetroTopic ApplicabilityAASHTO

Earthquake Load CaseEarthquake Load CaseGeneralGeneral

Consider permanent loads, live load is special case

LRFD – Extreme Event Iγp(DC+DD+DW+EH+EV+ES+EL+PS+CR+SH)+γEQ(LL+IM+CE+BR+PL+LS)+WA+FR+EQγp – see Table 3.4.1-2 / γEQ = 0.50, but no consensusγp see Table 3.4.1 2 / γEQ 0.50, but no consensus

Guide Specification“Use load factors of 1.0 for all permanent loads.”Equivalent to γp = 1.0 … simplification – appropriate for pushover Live load γEQ up to engineer, per commentary (e.g. high ADTT, etc))

Summary

Force Displ. RetroTopic ApplicabilitySystem Demand

Analysis MethodsAnalysis Methods

Force Displ. RetroTopic ApplicabilityLocal Capacity Analysis

PushoverForce Displ. RetroTopic Applicability

Note: Concept Valid for LRFD, But Not Used.Pushoveror

ce FEQ

ΔEQActual Response

2 3 4 Plastic Hinge

Displacement ΔDisplacement - Δ

Actual Response Milestones1 - First-yield Point, Previous Nonlinearity Due to Foundation Flexibility2 – Maximum Allowable Plastic Deformation3 – Onset of Collapse4 - Collapse4 Collapse

Force Displ. RetroTopic ApplicabilityExample

Uniform Load MethodUniform Load Method

(L = 242 ft)

Uniform Load Method (cont)( )

• Step 4

0.79 sec

AASHTO LRFD Interim 2008

Force Displ. RetroTopic ApplicabilitySingle-Mode Spectral

MethodMethod

Method (cont)Method (cont)

Regular Bridgesg g

Force Displ. RetroTopic ApplicabilityAnalysis Method As

Function of RegularityFunction of Regularity

AASHTOLRFD 4th Ed.

Summary

Seismic Model Optionsp

Spine Modelp

Geometry Issuesy

Example Bridge Slide 1 of 4p g

Example Spine Modelp p

Substructure Model

Force Displ. RetroTopic ApplicabilityEffective Stiffness

Reinforced ConcreteReinforced Concrete

Priestley, Seible and Calvi, 1996

Support Conditionspp

Foundation Flexibilityy

Foundation Flexibility (cont)y ( )

Weight Distributiong

Special Considerationsp

Summary

Multimode Analysisy

Modal Participationp

Modal Participation (cont)p ( )

Participating Massp g

Participating MassParticipating Mass

X - LongitudinalY - VerticalZ - TransverseZ Transverse

Participating Mass (cont)Participating Mass (cont)

Modal Analysis Loadingy gLoading is Mode-by-ModeEach Mode is ‘Analyzed’ IndividuallyEach Mode is Analyzed IndividuallyProcess is Directly Analogous to Single-Mode Method

fi = Earthquake Loading With Dynamic Amplificationfi Earthquake Loading With Dynamic Amplification

Force Displ. RetroTopic ApplicabilityResponse Spectrum

LoadingLoadingC

Modal Combinations

Modal Combinations (cont)( )

Summary

Directional Combinations

Directional Load Combos

Summary

Summary and ‘Look Ahead’ySummary

Earthquake LoadingEarthquake LoadingPlastic Mechanism and Capacity DesignEarthquake Resisting Elements and Systemsq g yDemand Modeling

Look AheadLook AheadForce-Based Design Displacement-Based Design Detailing for DuctilityGeotechnical Considerations

Seismic Analysis and Response...

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