13.3 Seismic analysis methods for bridges

Seismic analysis methods for bridges are crucial for ensuring safety during earthquakes. From simple static approaches to complex dynamic simulations, these techniques help engineers predict how bridges will respond to seismic forces. The choice of method depends on the bridge's complexity and importance.

Understanding these analysis methods is key to designing earthquake-resistant bridges. They allow engineers to identify potential weaknesses, optimize structural components, and implement effective seismic protection measures. This knowledge is essential for creating resilient infrastructure in earthquake-prone regions.

Seismic Analysis Methods for Bridges

Static vs Dynamic Analysis

Top images from around the web for Static vs Dynamic Analysis

• 

  Frontiers | Seismic Performance Evaluation of Shape Memory Alloy (SMA) Reinforced Concrete ... View original

  Is this image relevant?

• 

  Frontiers | Multi-Hazard Assessment of Bridges in Case of Hazard Chain: State of Play and ... View original

  Is this image relevant?

• 

  Frontiers | Structural Health Monitoring of a Cable-Stayed Bridge Using Regularly Conducted ... View original

  Is this image relevant?

• 

  Frontiers | Seismic Performance Evaluation of Shape Memory Alloy (SMA) Reinforced Concrete ... View original

  Is this image relevant?

• 

  Frontiers | Multi-Hazard Assessment of Bridges in Case of Hazard Chain: State of Play and ... View original

  Is this image relevant?

1 of 3

Top images from around the web for Static vs Dynamic Analysis

• 

  Frontiers | Seismic Performance Evaluation of Shape Memory Alloy (SMA) Reinforced Concrete ... View original

  Is this image relevant?

• 

  Frontiers | Multi-Hazard Assessment of Bridges in Case of Hazard Chain: State of Play and ... View original

  Is this image relevant?

• 

  Frontiers | Structural Health Monitoring of a Cable-Stayed Bridge Using Regularly Conducted ... View original

  Is this image relevant?

• 

  Frontiers | Seismic Performance Evaluation of Shape Memory Alloy (SMA) Reinforced Concrete ... View original

  Is this image relevant?

• 

  Frontiers | Multi-Hazard Assessment of Bridges in Case of Hazard Chain: State of Play and ... View original

  Is this image relevant?

1 of 3

• Seismic analysis methods for bridges categorized into equivalent static analysis and dynamic analysis
• Equivalent static analysis simplifies seismic loads into static forces applied to the bridge structure (suitable for regular bridges with predictable behavior)
• Dynamic analysis methods include response spectrum analysis and time history analysis
  • Account for the structure's dynamic properties and earthquake characteristics
  • Provide more accurate representation of complex bridge behavior
• Choice of analysis method depends on bridge importance, structural complexity, and seismic hazard level
  • Simple, regular bridges often analyzed using equivalent static methods
  • Complex or critical bridges require more sophisticated dynamic analysis techniques

Response Spectrum and Time History Analysis

• Response spectrum analysis uses structure's mode shapes and natural frequencies to determine maximum responses
  • Combines modal responses using methods like SRSS (Square Root of Sum of Squares) or CQC (Complete Quadratic Combination)
  • Efficient for design purposes but does not provide time-dependent response information
• Time history analysis applies acceleration time histories to the bridge model
  • Provides detailed representation of structural behavior over time
  • Involves solving equations of motion numerically (Newmark-β or Wilson-θ methods)
  • Offers most comprehensive assessment but computationally intensive
• Nonlinear analysis techniques used for more accurate predictions under extreme seismic events
  • Pushover analysis identifies potential failure mechanisms
  • Nonlinear time history analysis captures inelastic behavior throughout earthquake duration

Bridge Response to Earthquake Loading

Mathematical Modeling and Seismic Hazard Characterization

• Develop mathematical model representing bridge's mass, stiffness, and damping characteristics
  • Include all significant structural components (deck, columns, bearings, foundations)
  • Model soil-structure interaction effects for accurate response prediction
• Characterize seismic hazard at bridge site
  • Design response spectra based on probabilistic or deterministic seismic hazard analysis
  • Select appropriate ground motion time histories for time history analysis
    • Consider factors like magnitude, distance, and site conditions
• Apply lateral forces to bridge model in equivalent static analysis
  • Magnitude and distribution based on structure's mass and assumed mode shape
  • Typically applied at deck level or center of mass of superstructure

Analysis Procedures and Demand Evaluation

• Perform modal analysis to determine natural frequencies and mode shapes
  • Identify dominant modes of vibration and their contribution to overall response
• Execute chosen analysis method (equivalent static, response spectrum, or time history)
  • For response spectrum analysis, combine modal responses to estimate maximum demands
  • In time history analysis, integrate equations of motion step-by-step
• Evaluate seismic demands on critical bridge components
  • Columns: bending moments, shear forces, and axial loads
  • Bearings: displacements and forces
  • Foundations: overturning moments and soil pressures
• Compare demands to component capacities to assess performance
  • Consider strength, ductility, and displacement limits
  • Identify potential vulnerabilities or areas requiring design refinement

Seismic Analysis Results for Bridge Design

Dynamic Behavior and Performance Metrics

• Interpret analysis results to understand bridge's dynamic behavior
  • Natural frequencies indicate structure's stiffness and mass distribution
  • Mode shapes reveal deformation patterns under seismic excitation
  • Participation factors quantify contribution of each mode to overall response
• Evaluate maximum displacements and drift ratios
  • Ensure compliance with code-specified limits (typically 2-4% for columns)
  • Assess potential for pounding between adjacent spans or abutments
• Analyze internal forces and moments in bridge elements
  • Use for designing and detailing structural components (columns, cap beams, foundations)
  • Determine reinforcement requirements and member sizes
• Assess seismic demands on bearings and expansion joints
  • Size and detail these components to accommodate expected movements
  • Consider use of seismic isolation bearings for improved performance

Design Decisions and Retrofitting Strategies

• Inform selection and design of seismic isolation and energy dissipation devices
  • Lead-rubber bearings or friction pendulum systems for isolation
  • Viscous dampers or buckling-restrained braces for energy dissipation
• Guide implementation of seismic retrofitting measures for existing bridges
  • Column jacketing to increase strength and ductility
  • Installation of restrainer cables to prevent unseating
  • Foundation strengthening to improve overall stability
• Evaluate capacity-to-demand ratios for critical elements
  • Ensure sufficient strength and ductility under design-level earthquakes
  • Identify potential weak links in the structural system
• Use analysis results to optimize bridge configuration and component design
  • Adjust column heights or deck mass distribution to improve dynamic characteristics
  • Modify foundation design to reduce seismic demands on superstructure

Seismic Analysis Methods: Advantages vs Limitations

Comparison of Analysis Techniques

• Equivalent static analysis offers computational simplicity
  • Suitable for regular bridges with predictable behavior
  • May not capture higher mode effects or complex dynamic behavior
  • Typically used for preliminary design or low seismic regions
• Response spectrum analysis accounts for multiple modes of vibration
  • Efficient for design purposes and captures dynamic amplification
  • Does not provide time-dependent response information
  • Well-suited for medium-span bridges in moderate seismic regions
• Time history analysis provides most detailed representation of seismic response
  • Offers insights into time-varying demands and cumulative damage
  • Requires careful selection of input ground motions
  • Computationally intensive but necessary for critical or complex bridges

Applicability to Different Bridge Types

• Nonlinear static (pushover) analysis captures inelastic behavior
  • Identifies potential failure mechanisms and collapse sequence
  • May not accurately represent dynamic effects or higher mode contributions
  • Useful for vulnerability assessment of existing bridges
• Nonlinear time history analysis provides most comprehensive assessment
  • Captures material and geometric nonlinearities throughout earthquake duration
  • Complex, time-consuming, and sensitive to modeling assumptions
  • Required for bridges with seismic isolation or energy dissipation devices
• Applicability varies with bridge type and structural regularity
  • Simple span bridges often amenable to equivalent static or response spectrum methods
  • Cable-stayed or long-span bridges require more sophisticated dynamic analysis
  • Irregular bridges with significant mass or stiffness discontinuities need careful consideration
• Choice of analysis method balances accuracy, computational effort, and project requirements
  • Consider bridge importance, seismic hazard level, and design stage
  • Regulatory requirements may dictate minimum analysis complexity for certain bridge categories
  • Progressive increase in analysis sophistication from conceptual design to final verification