Seismic Analysis and Response Fundamentals Lee Marsh Senior Project Manager BERGER/ABAM Engineers, Inc
Learning Outcomes 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 Define Global l Seismic i Design Strategy t and Identify Earthquake Resisting Systems/Elements List Types of Seismic i Analysis Techniques Define Regular vs. Non-Regular Bridges
Presentation Roadmap Earthquake Loadings Seismic Design Concepts and Strategies Extreme Event Earthquake Loading Bridge Modeling Guidelines Analysis Methods Models, Stiffness and Mass Modal Analysis Combining Directional Response Summary
Dynamic Equilibrium / Free Vibration
Ground Excitation vs Earthquake Loading Includes Dynamic Amplification
Presentation Roadmap Earthquake Loadings Seismic Design Concepts and Strategies Extreme Event Earthquake Loading Bridge Modeling Guidelines Analysis Methods Models, Stiffness and Mass Modal Analysis Combining Directional Response Summary
Three Observations
Three Observations (cont)
Three Observations (cont)
Path to Plastic Mechanism Δ Inertial Force 1 Displacement, Δ 1 2 3 Moment M p Plastic Hinge (4 Total) ota) 2 M p 1 First Hinges Form 2 Second Hinges Form 3 Deformation Capacity Reached M pshaft
Example Plastic Mechanisms
Capacity Design Principles 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 Demands Imposed by the Design Earthquake. Capacity Protect the Rest Design All Other Elements to be Strong Enough That They Do Not Behave Inelastically, and Provide Articulation to Permit Mobilization of the Plastic Mechanism.
System Load vs Deflection Pushover Curve
Dynamic Equilibrium Revisted: Including Yielding f inertial = m (a gnd + a rel ) = Earthquake Load superstructure columns Inertial force is limited to sum of column shears to satisfy equilibrim. Bent FBD Transverse Loading f spring +f damping The column shears include inelastic effects.
Transverse Response Two-Span Continuous Superstructure (If superstructure were non-continuous, then center bent would resist much larger forces.)
Longitudinal Response Two-Span Bridge
Balanced Stiffness Guide Specification Highest Category SDC D Isolation Casing (example technique to alter stiffness) Control Relative: Column Stiffness Bent Stiffness Frame Period
Earthquake Resisting Systems (ERS) Note: Concepts Valid for LRFD & Retrofit, Too. Figure 3.3-1a Guide Specifications
Earthquake Resisting Systems (ERS) (cont) Note: Concepts Valid for LRFD & Retrofit, Too. Figure 3.3-1a Guide Specifications
Earthquake Resisting Elements (ERE) Note: Concepts Valid for LRFD & Retrofit, Too. Permissible EREs: Figure 3.3-1b Guide Specifications
Earthquake Resisting Elements (ERE) Permissible EREs with Owner s Approval: Note: Concepts Valid for LRFD & Retrofit, Although Uninspectable Damage is Not Explicitly Permitted in LRFD. Figure 3.3-2 Guide Specifications
Earthquake Resisting Elements (ERE) EREs Not Recommended for New Bridges: Note: Concepts Valid for LRFD & Retrofit, Too. Figure 3 3-3 Figure 3.3-3 Guide Specifications
Global Design Strategies Note: Concepts Valid, Except Types 2 & 3 Not Addressed in LRFD Type 1 Ductile Substructure, Elastic Superstructure Type 2 Elastic Substructure, Ductile Superstructure Type 3 Elastic Sub- & Superstructure, Fusing Interface Type 2 Type 1 Type 3 Figure shows all three types; but use only one at a time. Figure 7.1-1 Guide Specifications
Presentation Roadmap Earthquake Loadings Seismic Design Concepts and Strategies Extreme Event Earthquake Loading Bridge Modeling Guidelines Analysis Methods Models, Stiffness and Mass Modal Analysis Combining Directional Response Summary
AASHTO Earthquake Load Case General Consider permanent loads, live load is special case LRFD Extreme Event I γ p (DC+DD+DW+EH+EV+ES+EL+PS+CR+SH)+γ EQ (LL+IM+CE+BR+PL+LS)+WA+FR+EQ γ p see Table 3.4.1-2 / γ EQ = 0.50, but no consensus Guide Specification Use load factors of 1.0 for all permanent loads. Equivalent to γ p = 1.0 simplification appropriate for pushover Live load γ EQ up to engineer, per commentary (e.g. high ADTT, etc)
Presentation Roadmap Earthquake Loadings Seismic Design Concepts and Strategies Extreme Event Earthquake Loading Bridge Modeling Guidelines Analysis Methods Models, Stiffness and Mass Modal Analysis Combining Directional Response Summary
System Demand Analysis Methods
Local Capacity Analysis Pushover La ateral Fo orce Note: Concept Valid for LRFD, But Not Used. Actual Response F F EQ max 2 3 4 Plastic Hinge 1 Δ EQ Displacement - Δ Actual Response Milestones 1 - First-yield Point, Previous Nonlinearity Due to Foundation Flexibility 2 Maximum Allowable Plastic Deformation 3 Onset of Collapse 4 - Collapse
Example Uniform Load Method (L = 242 ft)
Uniform Load Method (cont) Step 4 0.47 0.79 sec AASHTO LRFD Interim 2008
Uniform Load Method (cont)
Uniform Load Method (cont)
Single-Mode Spectral Method
Single-Mode Spectral Method (cont)
Single-Mode Spectral Method (cont)
Single-Mode Spectral Method (cont) P e (x)
Regular Bridges
Analysis Method As Function of Regularity AASHTO LRFD 4 th Ed.
Presentation Roadmap Earthquake Loadings Seismic Design Concepts and Strategies Extreme Event Earthquake Loading Bridge Modeling Guidelines Analysis Methods Models, Stiffness and Mass Modal Analysis Combining Directional Response Summary
Seismic Model Options
Spine Model
Geometry Issues
Example Bridge Slide 1 of 4
Example Bridge Slide 2 of 4
Example Bridge Slide 3 of 4
Example Bridge Slide 4 of 4
Example Spine Model
Substructure Model
Effective Stiffness Reinforced Concrete Priestley, Seible and Calvi, 1996
Support Conditions
Foundation Flexibility
Foundation Flexibility y( (cont)
Weight Distribution
Special Considerations
Presentation Roadmap Earthquake Loadings Seismic Design Concepts and Strategies Extreme Event Earthquake Loading Bridge Modeling Guidelines Analysis Methods Models, Stiffness and Mass Modal Analysis Combining Directional Response Summary
Multimode Analysis
Modal Participation
Modal Participation (cont)
Participating Mass
Example Participating Mass X - Longitudinal Y - Vertical Z - Transverse
Example Participating Mass (cont)
Example Participating Mass (cont)
Example Participating Mass (cont)
Example Participating Mass (cont)
Example Participating Mass (cont)
Modal Analysis Loading Loading is Mode-by-Mode Each Mode is Analyzed Individually Process is Directly Analogous to Single-Mode Method f i = Earthquake Loading With Dynamic Amplification
Response Spectrum Loading C sm,
Modal Combinations
Modal Combinations (cont)
Modal Combinations (cont)
Presentation Roadmap Earthquake Loadings Seismic Design Concepts and Strategies Extreme Event Earthquake Loading Bridge Modeling Guidelines Analysis Methods Models, Stiffness and Mass Modal Analysis Combining Directional Response Summary
Directional Combinations
Directional Combinations
Directional Load Combos
Presentation Roadmap Earthquake Loadings Seismic Design Concepts and Strategies Extreme Event Earthquake Loading Bridge Modeling Guidelines Analysis Methods Models, Stiffness and Mass Modal Analysis Combining Directional Response Summary
Summary and Look Ahead Summary Earthquake Loading Plastic Mechanism and Capacity Design Earthquake Resisting Elements and Systems Demand Modeling Look Ahead Force-Based Design Displacement-Based Design Detailing for Ductility Geotechnical Considerations