Seismic Analysis and Response Fundamentals. Lee Marsh Senior Project Manager BERGER/ABAM Engineers, Inc

Transcription

1 Seismic Analysis and Response Fundamentals Lee Marsh Senior Project Manager BERGER/ABAM Engineers, Inc

2 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

3 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

4 Dynamic Equilibrium / Free Vibration

5 Ground Excitation vs Earthquake Loading Includes Dynamic Amplification

6 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

7 Three Observations

8 Three Observations (cont)

9 Three Observations (cont)

10 Path to Plastic Mechanism Δ Inertial Force 1 Displacement, Δ 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

11 Example Plastic Mechanisms

12 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.

13 System Load vs Deflection Pushover Curve

14 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.

15 Transverse Response Two-Span Continuous Superstructure (If superstructure were non-continuous, then center bent would resist much larger forces.)

16 Longitudinal Response Two-Span Bridge

17 Balanced Stiffness Guide Specification Highest Category SDC D Isolation Casing (example technique to alter stiffness) Control Relative: Column Stiffness Bent Stiffness Frame Period

18 Earthquake Resisting Systems (ERS) Note: Concepts Valid for LRFD & Retrofit, Too. Figure 3.3-1a Guide Specifications

19 Earthquake Resisting Systems (ERS) (cont) Note: Concepts Valid for LRFD & Retrofit, Too. Figure 3.3-1a Guide Specifications

20 Earthquake Resisting Elements (ERE) Note: Concepts Valid for LRFD & Retrofit, Too. Permissible EREs: Figure 3.3-1b Guide Specifications

21 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 Guide Specifications

22 Earthquake Resisting Elements (ERE) EREs Not Recommended for New Bridges: Note: Concepts Valid for LRFD & Retrofit, Too. Figure Figure Guide Specifications

23 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 Guide Specifications

24 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

25 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 / 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)

26 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

27 System Demand Analysis Methods

28 Local Capacity Analysis Pushover La ateral Fo orce Note: Concept Valid for LRFD, But Not Used. Actual Response F F EQ max 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

29 Example Uniform Load Method (L = 242 ft)

30 Uniform Load Method (cont) Step sec AASHTO LRFD Interim 2008

31 Uniform Load Method (cont)

32 Uniform Load Method (cont)

33 Single-Mode Spectral Method

34 Single-Mode Spectral Method (cont)

35 Single-Mode Spectral Method (cont)

36 Single-Mode Spectral Method (cont) P e (x)

37 Regular Bridges

38 Analysis Method As Function of Regularity AASHTO LRFD 4 th Ed.

39 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

40 Seismic Model Options

41 Spine Model

42 Geometry Issues

43 Example Bridge Slide 1 of 4

44 Example Bridge Slide 2 of 4

45 Example Bridge Slide 3 of 4

46 Example Bridge Slide 4 of 4

47 Example Spine Model

48 Substructure Model

49 Effective Stiffness Reinforced Concrete Priestley, Seible and Calvi, 1996

50 Support Conditions

51 Foundation Flexibility

52 Foundation Flexibility y( (cont)

53 Weight Distribution

54 Special Considerations

55 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

56 Multimode Analysis

57 Modal Participation

58 Modal Participation (cont)

59 Participating Mass

60 Example Participating Mass X - Longitudinal Y - Vertical Z - Transverse

61 Example Participating Mass (cont)

62 Example Participating Mass (cont)

63 Example Participating Mass (cont)

64 Example Participating Mass (cont)

65 Example Participating Mass (cont)

66 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

67 Response Spectrum Loading C sm,

68 Modal Combinations

69 Modal Combinations (cont)

70 Modal Combinations (cont)

71 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

72 Directional Combinations

73 Directional Combinations

74 Directional Load Combos

75 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

76 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