Principles of Earthquake Engineering of Bridges Part 1: Principles & Approach by Dr. Mark A. Ketchum, OPAC Consulting Engineers for the EERI 100 th Anniversary Earthquake Conference, April 17, 2006
Presentation Outline Introduction Performance Criteria Fundamental Principles Ground Motions Structural Design Demand Analysis Capacity Analysis Detailing Advanced Topics
Introduction Part 1: Principles & Approach Part 2: Structural Analysis Types of Structures AASHTO Methodology California Methodology
Types of Structures Ordinary Bridges Special Bridges
Special Bridges
Ordinary Bridges
Typical California Bridge
AASHTO Methodology Force-based Conformance Checking Response Modification Factors Importance Classification I: Essential Bridges II: Other Bridges Seismic Performance Category (SPC) Importance Classification Peak Ground Acceleration Categories A, B, C, D
AASHTO Design Requirements Ground Motion Minimum 0.2g Static Lateral Load Seismic Response Coefficient Hazard, Soil, and Frequency dependent Site-specific spectra & motions allowed Analysis Static Lateral Load Single & Multi Mode Spectral Analysis Time History Analysis Force D/C with Response Modification Factors
California Methodology Displacement Ductility Approach Pre-determined Damage Locations Hazard & Soil Dependent Motions Category (influences performance requirements) Ordinary Important (Post-EQ Service Required) Classification (influences analysis / design requirements) Geometry (multilevel / curved / skew) Framing (stiffness / strength distribution) Geotechnical (near fault / soft soil / liquefaction)
California Performance Criteria Ground Motions Ordinary Bridge Safety Event 1000-2000 year Return Period Maximum Credible Limited Service Significant Damage Functional Event Higher Probability 150-500 year Return Period Immediate Service Repairable Damage Important Bridge Immediate Service Repairable Damage Immediate Service Minimal Damage
Fundamental Principles Strength Analysis under Design Ground Motions Capacity Controlled Components Redundancy Stiffness Balance with a Frame Frequency Balance between Frames Ductility Capacity > Demand Minimum Ductility regardless of Demand
Design Ground Motion Site Specific Assessment for Important Bridges Probabilistic Seismic Hazard Assessment Deterministic Seismic Hazard Assessment Rock Motion Spectra Rock Motion Histories Site Response Analysis Soil / Foundation / Structure Interaction Analysis Simplified Procedures for Ordinary Bridges
Design Ground Motion Simplified Procedures for Ordinary Bridges EQ Magnitude from Seismic Map PGA from Seismic Map Select Representative Standard Soil Profile Response Spectra for EQ / PGA / Soil Profile
California Seismic Map
California Seismic Map
Soil Profile Classifications
Response Spectra
Response Spectra
Response Spectra
Structural Design Proportioning Minimum Column Dimensions & Lateral Loads Balanced Stiffnesses and Frequencies Redundancy Demand Controlled Elements Columns / Bents Foundations Capacity Protected Elements Bent Caps / Girders Pile Caps / Footings
Structural Design
Seismic Demand Analysis
Seismic Demand Analysis 3D Model of Bridge Dynamic Elastic, Cracked (usually) Inelastic (special cases) Response Spectra Analysis Time History Analysis in special cases Directional Combination of Ground Motions Horizontal Motions Vertical Motions Displacement & Force Demands
Prototype Design
3D Elastic Dynamic Model
Displacement Demands
Displacement Demands
Force Demands Demand Controlled Elements Columns / Bents Plastic Capacities Capacity Protected Elements Column Shear / Bent Caps / Girders / Footings Overstrength Capacity of Controlling Elements
Seismic Capacity Analysis Inelastic (Nonlinear) Analysis Displacement Capacities of Components (e.g. columns) Subsystems (e.g. frames / bents) Curvature Capacities of Sections By Moment vs. Curvature Analysis Strain Capacities of Materials Steel Concrete
Strain Capacities of Materials Mild Steel Prestressing Steel Concrete Confined Unconfined
Mild Steel
Prestressing Steel
Concrete
Curvature Capacities of Sections Inelastic Analysis of a R/C Cross Section
Displacement Capacity Pushover Analysis single-column system
Displacement Capacity Pushover Analysis multi-column system
Displacement Capacity Pushover Analysis complex system
Unified Demand & Capacity Global Inelastic Time History Analysis
Unified Demand & Capacity Global Inelastic Time History Analysis
Capacity Protected Elements Superstructures Bent Caps Footings Designed to direct inelastic damage into the columns, pier walls, and abutments Strength > connecting elements
Detailing Column confinement Ductile column connections Joint shear Hinge restrainers Abutments
Influence on Cost Model Structure Type Geometry Deck Width* Deck Depth Span Arrangement Bent Columns Column Type (Estimated Size) Column Height 1 CIP/PS box Straight 39 6 120 +150 +150 +150 +120 1 5.5 x8.25 oblong 22 2 CIP/PS box Straight 68 6 120 +150 +150 +150 +120 3 5.5 circular 22 3 CIP/PS box Straight 39 4 80 +100 +100 +100 +80 1 4 x6 oblong 22 4 CIP/PS box Straight 68 4 80 +100 +100 +100 +80 3 4 circular 22 5 PC/PS girder Straight 39 5-2 80 +100 +100 +100 +80 1 4 x6 oblong 22 6 PC/PS girder Straight 68 5-2 80 +100 +100 +100 +80 3 4 circular 22 7 PC/PS girder Straight 39 6-2 120 +120 1 4 x6 oblong 22 8 PC/PS girder Straight 68 6-2 120 +120 3 4 circular 22 9 CIP/PS box 1000 radius 27 6 120 +150 +150 +150 +120 1 5.5 x8.25 oblong 22 10 CIP/PS box 30 skew 68 6 120 +150 +150 +150 +120 3 5.5 circular 22 11 CIP/PS box Straight 39 6 120 +150 +150 +150 +120 1 5.5 circular 50
Cost Trends Cost/SF vs. PGA for Magnitude 7.25 Earthquake $180.00 $170.00 $160.00 $150.00 $140.00 $130.00 $120.00 Type 1 Type 3 Type 4 Type 6 Type 9 Type 10 Type 11 $110.00 Cost/SF ($/SF) $100.00 $90.00 $80.00 $70.00 $60.00 $50.00 $40.00 $30.00 $20.00 $10.00 $0.00 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 PGA (%g)
Summary Documented Approach Supported by Theory & Testing Directly applicable to standard bridges Approach applicable to special bridges Performance basis Details
Part 2: Structural Analysis Robert Dameron