10.2 Girder and frame analysis and design

Bridge girders and frames are the backbone of superstructure design. They transfer loads from the deck to the substructure through bending, shear, and axial forces. Understanding their behavior is crucial for creating safe, efficient bridges.

Girder analysis involves load distribution, dynamic effects, and internal force calculations. Design considerations include composite action, stability, and construction staging. Mastering these concepts is key to developing optimal bridge superstructures that meet performance and durability requirements.

Bridge Girder Behavior and Load Transfer

Load Transfer Mechanisms in Bridge Structures

Top images from around the web for Load Transfer Mechanisms in Bridge Structures

• 

  Frontiers | Bridge Load Rating Through Proof Load Testing for Shear at Dapped Ends of ... View original

  Is this image relevant?

• 

  Frontiers | Bridge Load Rating Through Proof Load Testing for Shear at Dapped Ends of ... View original

  Is this image relevant?

• 

  Frontiers | Bridge Load Rating Through Proof Load Testing for Shear at Dapped Ends of ... View original

  Is this image relevant?

• 

  Frontiers | Bridge Load Rating Through Proof Load Testing for Shear at Dapped Ends of ... View original

  Is this image relevant?

1 of 2

Top images from around the web for Load Transfer Mechanisms in Bridge Structures

• 

  Frontiers | Bridge Load Rating Through Proof Load Testing for Shear at Dapped Ends of ... View original

  Is this image relevant?

• 

  Frontiers | Bridge Load Rating Through Proof Load Testing for Shear at Dapped Ends of ... View original

  Is this image relevant?

• 

  Frontiers | Bridge Load Rating Through Proof Load Testing for Shear at Dapped Ends of ... View original

  Is this image relevant?

• 

  Frontiers | Bridge Load Rating Through Proof Load Testing for Shear at Dapped Ends of ... View original

  Is this image relevant?

1 of 2

• Bridge girders and frames transfer loads from deck to substructure through bending, shear, and axial forces
• Girder bridges use longitudinal beams supporting a deck slab
• Frame bridges incorporate rigid connections between superstructure and substructure elements
• Load distribution in girder bridges depends on girder spacing, deck stiffness, and diaphragm placement
• Frame action in integral bridges allows moment transfer between superstructure and substructure
  • Reduces mid-span moments
  • Increases end moments
• Torsional effects require special consideration in curved girders and skewed bridges
• Effective width determines the portion of deck acting compositely with girders
• Dynamic load allowance (impact factor) accounts for amplification of static loads from moving vehicles
  • Must be included in load transfer calculations

Factors Influencing Girder Behavior

• Girder spacing affects load distribution and deck span capabilities
  • Closer spacing generally results in more uniform load distribution
  • Wider spacing may require thicker deck or additional reinforcement
• Deck stiffness influences load sharing between adjacent girders
  • Stiffer decks distribute loads more evenly (concrete decks)
  • More flexible decks concentrate loads on nearest girders (orthotropic steel decks)
• Diaphragm placement provides lateral stability and improves load distribution
  • End diaphragms transfer loads to bearings and substructure
  • Intermediate diaphragms enhance girder stability and reduce differential deflections
• Skew angle impacts load distribution and introduces additional torsional effects
  • Increases in skew angle lead to more complex load paths
  • May require special detailing for bearings and cross-frames
• Curvature in horizontal alignment introduces torsion and warping effects
  • Requires consideration of out-of-plane bending in girder flanges
  • May necessitate closed-section girders (box girders) for high curvatures

Internal Forces in Bridge Girders

Analysis Methods for Continuous and Integral Girders

• Continuous girders distribute moments more efficiently than simple spans
  • Reduces positive moments in spans
  • Increases negative moments at interior supports
• Method of consistent deformations analyzes indeterminate structures (continuous girders)
  • Utilizes compatibility equations to solve for redundant forces
  • Allows for consideration of support settlements and thermal effects
• Moment distribution method (Hardy Cross) iteratively analyzes continuous beams and frames
  • Starts with assumed moment distribution and iterates to equilibrium
  • Particularly useful for hand calculations and understanding moment flow
• Influence lines determine critical loading positions and maximum internal forces
  • Graphical representation of force effect at a point due to unit load
  • Essential for identifying worst-case loading scenarios (live loads)
• Matrix methods (direct stiffness method) enable computer-aided analysis of complex systems
  • Assembles global stiffness matrix from element stiffness matrices
  • Efficiently solves for displacements and internal forces in large structures
• Support settlements and thermal gradients affect internal force distribution
  • Differential settlement can induce additional moments and shears
  • Temperature differentials between top and bottom flanges cause bending effects

Advanced Analysis Considerations

• Shear lag effects in wide-flanged and box girders require effective flange width calculations
  • Accounts for non-uniform stress distribution across flange width
  • AASHTO LRFD provides guidelines for determining effective width
• Second-order effects (P-Delta) may be significant in tall or slender bridge piers
  • Considers additional moments due to axial loads acting on deflected shape
  • Particularly important for integral abutment bridges
• Dynamic analysis may be necessary for long-span or lightweight bridges
  • Considers bridge natural frequencies and mode shapes
  • Evaluates potential for resonance under traffic or wind loads
• Finite element analysis allows for detailed modeling of complex geometries
  • Can account for local stress concentrations and connection details
  • Useful for analyzing deck-girder interaction and load distribution

Bridge Girder Design for Flexure, Shear, and Stability

Steel Girder Design Considerations

• AASHTO LRFD Bridge Design Specifications govern design in the United States
• Composite action between deck and girders enhances flexural capacity
  • Accounts for creep and shrinkage effects in concrete decks
  • Requires proper design of shear connectors (shear studs)
• Lateral-torsional buckling addressed through proper sizing and bracing
  • Unbraced length affects capacity of compression flange
  • Cross-frames and diaphragms provide lateral support
• Web buckling prevented by sizing and stiffening components
  • Transverse stiffeners increase shear capacity
  • Longitudinal stiffeners enhance bending resistance of slender webs
• Shear design includes web yielding and web crippling considerations
  • Web thickness and stiffener spacing affect shear capacity
  • End panels may require closer stiffener spacing or thicker webs
• Fatigue evaluation requires analysis of stress ranges and connection details
  • Category-based approach for various connection types
  • Considers cumulative damage over bridge lifespan
• Fracture-critical members require special attention and redundancy measures
  • Typically includes tension flanges in two-girder systems
  • May necessitate higher material toughness requirements

Prestressed Concrete Girder Design Principles

• Strand patterns and prestressing forces selected to satisfy limit states
  • Service limit state controls cracking and deflections
  • Strength limit state ensures ultimate capacity
• Shear design accounts for concrete, stirrup, and prestressing contributions
  • Vertical component of prestressing force enhances shear capacity
  • Stirrup spacing varies along girder length based on shear demand
• End zone reinforcement crucial for anchorage zone stress management
  • Bursting and spalling stresses require special detailing
  • Confinement reinforcement improves concrete performance
• Camber and deflection calculations consider time-dependent effects
  • Elastic shortening, creep, and shrinkage influence long-term behavior
  • Proper estimation important for setting haunch heights and deck profile
• Transfer and development length of prestressing strands must be considered
  • Affects stress distribution at girder ends
  • Impacts shear and moment capacity in end regions
• Debonding and harping of strands used to optimize stress profiles
  • Reduces excessive tensile stresses at girder ends
  • Allows for increased eccentricity at midspan

Construction Staging vs Composite Action in Girder Design

Impact of Construction Sequence on Load Distribution

• Construction staging affects dead load distribution and internal force development
  • Non-composite dead loads distinguished from composite dead loads
  • Separate analysis required for each construction stage
• Concrete deck placement sequence influences moment and shear distribution
  • Positive moment regions typically cast first
  • Negative moment regions cast last to minimize cracking
• Temporary support conditions may differ from final configuration
  • False work and temporary shoring alter load paths
  • Staged construction of continuous spans requires careful analysis
• Time-dependent effects (creep and shrinkage) influence long-term composite behavior
  • Differential shrinkage between precast girders and cast-in-place decks induces stresses
  • Creep causes redistribution of moments in continuous structures
• Shear connector design ensures full composite action between deck and girders
  • Partial composite action may be considered for rehabilitation projects
  • Fatigue considerations often govern shear stud spacing and size

Optimization Strategies for Composite Girder Systems

• Post-tensioning after deck placement optimizes stress distribution
  • Reduces cracking potential in negative moment regions
  • Can be used to address camber and deflection issues
• Staged post-tensioning allows for better control of time-dependent effects
  • Initial stage counteracts girder self-weight
  • Final stage applied after composite action develops
• Haunched girders in continuous spans improve moment capacity at supports
  • Reduces required prestressing force in midspan regions
  • Enhances overall structural efficiency
• Use of high-performance materials can reduce girder size and weight
  • High-strength concrete allows for longer spans or shallower sections
  • High-performance steel enables more slender girder designs
• Integral abutments eliminate expansion joints and reduce maintenance
  • Requires consideration of soil-structure interaction effects
  • Thermal movements accommodated through abutment and pile flexibility