17.2 Load and Resistance Factor Design (LRFD) philosophy

Bridge codes are evolving to use Load and Resistance Factor Design (LRFD). This approach separates uncertainties in loads and resistances, leading to more consistent safety across different bridge components. LRFD uses factors to increase loads and decrease resistances, aiming for a target reliability.

LRFD offers advantages over older methods. It provides better safety, efficiency, and flexibility in design. The approach can easily adapt to new research and materials. It also helps standardize design practices globally, making it easier for engineers to collaborate across borders.

Load and Resistance Factor Design

Fundamental Principles of LRFD

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• Reliability-based design approach uses separate factors for loads and resistances accounting for uncertainties in the design process
• Fundamental LRFD equation states factored resistance must be greater than or equal to sum of factored load effects
  • Expressed mathematically as: $\phi R_n \geq \sum \gamma_i Q_i$
    • Where $\phi$ is the resistance factor
    • $R_n$ is the nominal resistance
    • $\gamma_i$ are load factors
    • $Q_i$ are nominal load effects
• Load factors in LRFD account for variability and uncertainty in load estimation
  • Typically increase nominal load values
  • Example: Dead load factor of 1.25 increases the nominal dead load by 25%
• Resistance factors in LRFD account for uncertainties in material properties, fabrication, and analysis methods
  • Typically reduce nominal resistance values
  • Example: Resistance factor of 0.9 for steel flexural members reduces the nominal moment capacity by 10%

Calibration and Reliability in LRFD

• LRFD aims to achieve consistent and acceptable level of reliability across different structural components and systems
  • Target reliability index (β) typically ranges from 3.0 to 3.5 for bridge components
• Calibration of load and resistance factors based on probabilistic methods and statistical data from structural performance
  • Utilizes techniques (Monte Carlo simulation, First-Order Reliability Method)
• Incorporates variability in material properties, loading conditions, and analysis methods
  • Example: Concrete compressive strength variability considered in resistance factor calibration

Advantages of LRFD

Enhanced Safety and Efficiency

• Provides more consistent level of safety and reliability across different structural elements and bridge types compared to allowable stress design (ASD) methods
  • Example: LRFD accounts for different variabilities in dead and live loads, unlike ASD which uses a single factor of safety
• Separation of load and resistance factors allows for more accurate consideration of individual uncertainties associated with loads and resistances
  • Leads to more efficient designs in many cases
  • Example: In areas with high seismic activity, LRFD can more accurately account for the uncertainty in earthquake loads

Flexibility and Adaptability

• Better accounts for variability in different load combinations
  • Example: LRFD can more easily handle unique load combinations (wind + live load) by applying specific factors to each load type
• Probabilistic basis allows for easier incorporation of new research findings and advancements in material properties and structural behavior
  • Example: New high-strength steel can be integrated into LRFD codes by adjusting resistance factors based on its statistical properties
• Facilitates integration of risk analysis and performance-based design concepts in bridge engineering
  • Allows engineers to design for specific performance objectives (limiting damage during moderate earthquakes)

Standardization and Collaboration

• Promotes harmonization of design practices across different countries and design codes
  • Enhances international collaboration in bridge engineering
  • Example: AASHTO LRFD Bridge Design Specifications align closely with Canadian Highway Bridge Design Code, facilitating North American collaboration

LRFD Principles in Bridge Design

Calculating Factored Loads and Resistances

• Calculate factored load effects by applying appropriate load factors to nominal loads
  • Consider different load combinations specified in design codes
  • Example: Strength I combination for typical vehicular loads: $1.25DC + 1.75LL + 1.0WA$
    • Where DC is dead load, LL is live load, and WA is water load
• Determine required nominal resistance of bridge components by dividing factored load effects by appropriate resistance factor
  • Example: For a steel girder in flexure with a factored moment of 1000 kN-m and a resistance factor of 0.9, the required nominal moment capacity would be: $M_n = 1000 / 0.9 = 1111 kN-m$

Limit States and Design Considerations

• Analyze and design bridge components to meet both strength and serviceability limit states as defined in LRFD specifications
  • Strength limit states ensure safety against structural failure
  • Serviceability limit states ensure acceptable performance under normal operating conditions
• Apply load modifiers to account for ductility, redundancy, and operational importance in LRFD design process
  • Example: A non-redundant bridge component may have an increased load factor to ensure higher reliability
• Utilize statistical data and reliability analysis techniques to evaluate probability of failure for critical bridge components
  • Example: Monte Carlo simulation to assess failure probability of a bridge pier under extreme flood conditions
• Implement iterative design procedures to optimize bridge components while satisfying LRFD requirements for strength and serviceability
  • Example: Adjusting girder sizes to meet both strength requirements and deflection limits

Load and Resistance Factors in Codes

Load Factors in Bridge Design

• Identify specific load factors for different types of loads in relevant bridge design codes and standards
  • Dead load (DC): typically 1.25 for components and 1.50 for wearing surfaces
  • Live load (LL): typically 1.75 for vehicular loads
  • Environmental loads (wind, earthquake): vary based on return period and importance
• Understand variation in load factors for different load combinations and limit states as specified in LRFD bridge design manuals
  • Example: Strength I (basic load combination) vs. Extreme Event I (earthquake)
• Evaluate rationale behind selection of specific load factors based on statistical data and target reliability indices
  • Example: Live load factor of 1.75 accounts for uncertainties in traffic patterns and vehicle weights

Resistance Factors in Bridge Design

• Recognize differences in resistance factors for various materials and structural elements in LRFD specifications
  • Steel: typically 0.95 for tension members, 0.90 for flexure in compact sections
  • Concrete: typically 0.90 for flexure, 0.75 for shear
  • Connections: often lower factors (0.65 - 0.80) due to higher variability
• Analyze impact of different resistance factors on design of tension members, compression members, flexural members, and shear elements in bridge structures
  • Example: Lower resistance factor for concrete in shear (0.75) compared to flexure (0.90) results in more conservative shear design
• Understand process of updating load and resistance factors in design codes as new research and performance data become available
  • Example: Adjustment of resistance factors for high-performance concrete based on field performance data
• Compare and contrast load and resistance factors across different international bridge design codes and standards
  • Example: AASHTO LRFD vs. Eurocode 1 for traffic loads on bridges