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
Force Displ. RetroTopic Applicability
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
Force Displ. RetroTopic Applicability
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 Applicability
Three Observations
Force Displ. RetroTopic Applicability
Three Observations (cont)( )
Force Displ. RetroTopic Applicability
Three Observations (cont)( )
Force Displ. RetroTopic Applicability
Path to Plastic MechanismΔ
MomentDisplacement, Δ
Mp1
1 2 3Inertial Force
p
Mp2Plastic Hinge
(4 Total)( ota )
Mp shaft1 – First Hinges Form2 – Second Hinges Form3 – Deformation Capacity Reached
Force Displ. RetroTopic ApplicabilityExample Plastic
MechanismsMechanisms
Force Displ. RetroTopic Applicability
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.
f + f
columns
fspring + fdamping
The column shears include inelastic
Bent FBDTransverse Loading
include inelastic effects.
Force Displ. RetroTopic Applicability
Transverse ResponseTwo Span Continuous SuperstructureTwo-Span Continuous Superstructure
(If(If superstructurewere non-continuous,then center bent wouldresist much larger forces.)resist much larger forces.)
Force Displ. RetroTopic Applicability
Longitudinal ResponseTwo Span BridgeTwo-Span Bridge
Force Displ. RetroTopic Applicability
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
Force Displ. RetroTopic ApplicabilityEarthquake Resisting
Systems (ERS) (cont)Systems (ERS) (cont) Note: Concepts Valid for LRFD & Retrofit, Too.
Figure 3.3-1a Guide Specifications
Force Displ. RetroTopic ApplicabilityEarthquake Resisting
Elements (ERE)Elements (ERE) Note: Concepts Valid for LRFD & Retrofit, Too.
Permissible EREs:
Figure 3.3-1b Guide Specifications
Force Displ. RetroTopic ApplicabilityEarthquake Resisting
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
Force Displ. RetroTopic ApplicabilityEarthquake Resisting
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
Force Displ. RetroTopic Applicability
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.
Force Displ. RetroTopic Applicability
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 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))
Force Displ. RetroTopic Applicability
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 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
Fmax
ater
al F
o
1
2 3 4 Plastic Hinge
Fmax
La
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)
Force Displ. RetroTopic Applicability
Uniform Load Method (cont)( )
0.47
• Step 4
0
0.79 sec
AASHTO LRFD Interim 2008
Force Displ. RetroTopic Applicability
Uniform Load Method (cont)( )
Force Displ. RetroTopic Applicability
Uniform Load Method (cont)( )
Force Displ. RetroTopic ApplicabilitySingle-Mode Spectral
MethodMethod
Force Displ. RetroTopic ApplicabilitySingle-Mode Spectral
Method (cont)Method (cont)
Force Displ. RetroTopic ApplicabilitySingle-Mode Spectral
Method (cont)Method (cont)
Force Displ. RetroTopic ApplicabilitySingle-Mode Spectral
Method (cont)Method (cont)
Pe(x)
Force Displ. RetroTopic Applicability
Regular Bridgesg g
Force Displ. RetroTopic ApplicabilityAnalysis Method As
Function of RegularityFunction of Regularity
AASHTOLRFD 4th Ed.
Force Displ. RetroTopic Applicability
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 Applicability
Seismic Model Optionsp
Force Displ. RetroTopic Applicability
Spine Modelp
Force Displ. RetroTopic Applicability
Geometry Issuesy
Force Displ. RetroTopic Applicability
Example Bridge Slide 1 of 4p g
Force Displ. RetroTopic Applicability
Example Bridge Slide 2 of 4p g
Force Displ. RetroTopic Applicability
Example Bridge Slide 3 of 4p g
Force Displ. RetroTopic Applicability
Example Bridge Slide 4 of 4p g
Force Displ. RetroTopic Applicability
Example Spine Modelp p
Force Displ. RetroTopic Applicability
Substructure Model
Force Displ. RetroTopic ApplicabilityEffective Stiffness
Reinforced ConcreteReinforced Concrete
Priestley, Seible and Calvi, 1996
Force Displ. RetroTopic Applicability
Support Conditionspp
Force Displ. RetroTopic Applicability
Foundation Flexibilityy
Force Displ. RetroTopic Applicability
Foundation Flexibility (cont)y ( )
Force Displ. RetroTopic Applicability
Weight Distributiong
Force Displ. RetroTopic Applicability
Special Considerationsp
Force Displ. RetroTopic Applicability
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 Applicability
Multimode Analysisy
Force Displ. RetroTopic Applicability
Modal Participationp
Force Displ. RetroTopic Applicability
Modal Participation (cont)p ( )
Force Displ. RetroTopic Applicability
Participating Massp g
Force Displ. RetroTopic ApplicabilityExample
Participating MassParticipating Mass
X - LongitudinalY - VerticalZ - TransverseZ Transverse
Force Displ. RetroTopic ApplicabilityExample
Participating Mass (cont)Participating Mass (cont)
Force Displ. RetroTopic ApplicabilityExample
Participating Mass (cont)Participating Mass (cont)
Force Displ. RetroTopic ApplicabilityExample
Participating Mass (cont)Participating Mass (cont)
Force Displ. RetroTopic ApplicabilityExample
Participating Mass (cont)Participating Mass (cont)
Force Displ. RetroTopic ApplicabilityExample
Participating Mass (cont)Participating Mass (cont)
Force Displ. RetroTopic Applicability
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
sm,
C
Force Displ. RetroTopic Applicability
Modal Combinations
Force Displ. RetroTopic Applicability
Modal Combinations (cont)( )
Force Displ. RetroTopic Applicability
Modal Combinations (cont)( )
Force Displ. RetroTopic Applicability
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 Applicability
Directional Combinations
Force Displ. RetroTopic Applicability
Directional Combinations
Force Displ. RetroTopic Applicability
Directional Load Combos
Force Displ. RetroTopic Applicability
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 Applicability
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