When designing a multi-girder bridge deck, what specialized factors are employed to determine the portion of a vehicle's wheel load that a single interior girder is expected to resist?
When designing a multi-girder bridge deck, the specialized factors employed to determine the portion of a vehicle's wheel load that a single interior girder is expected to resist primarily involve the use of Load Distribution Factors. A Load Distribution Factor, or LDF, is a fraction that quantifies how much of the total live load effect (such as bending moment or shear force) from the design vehicle on the bridge deck is transferred to and resisted by a single longitudinal girder. This factor is crucial because the deck slab, being integral with the girders, and any transverse elements like diaphragms or cross-frames, cause the wheel loads to be distributed transversely across multiple girders, not just the one directly beneath the wheel. This composite action means no single girder carries the entire wheel load directly.
Two main approaches are used to determine these LDFs: approximate methods and refined methods.
Approximate methods, commonly found in bridge design specifications such as AASHTO LRFD, utilize empirical formulas derived from extensive research and calibrated to provide conservative and practical results for common bridge geometries. For interior girders, these formulas consider several specialized factors:
1. Girder Spacing (S): This is the center-to-center distance between adjacent longitudinal girders. Wider girder spacing generally results in a larger portion of the load being distributed to an individual girder, as there are fewer girders to share the load over a given width of the deck.
2. Span Length (L): The length of the bridge span significantly influences how moments and shears develop. Longer spans can affect the overall flexibility and the area over which loads are distributed.
3. Deck Slab Stiffness: The material properties (e.g., modulus of elasticity of concrete) and thickness of the deck slab contribute to its bending stiffness. A stiffer deck slab is more effective at distributing localized wheel loads transversely to adjacent girders.
4. Girder Stiffness: The relative stiffness of the longitudinal girders themselves plays a role. Girders with higher flexural rigidity (EI, where E is the modulus of elasticity and I is the moment of inertia) tend to attract a larger share of the load. The type of girder (e.g., steel I-girder, precast concrete bulb-tee) and its dimensions influence this.
5. Number of Design Lanes Loaded: Design specifications consider various scenarios for live load application, including simultaneous loading of multiple traffic lanes. The LDFs are calibrated based on whether one or more lanes are loaded, as this affects the total transverse distribution of the load.
6. Presence and Configuration of Cross-frames or Diaphragms: These are transverse members connecting the longitudinal girders. They act to stiffen the bridge deck transversely, significantly enhancing the load distribution capabilities between girders and preventing excessive differential deflection.
7. Support Conditions: Whether the bridge span is simply supported or continuous over multiple supports influences the moment and shear diagrams, which in turn affect the application and values of LDFs.
8. Bridge Configuration: Factors such as the skew angle of the bridge (if the girders are not perpendicular to the supports) or bridge curvature can also be incorporated into more sophisticated approximate LDF formulas or may necessitate refined analysis methods.
Once determined, the Load Distribution Factor is multiplied by the live load effect (e.g., maximum bending moment or shear force) calculated for a single design lane, to yield the design live load effect that a single interior girder must resist.
Refined methods are employed for complex bridge geometries, highly skewed bridges, or when approximate methods are deemed overly conservative or inadequate. These include:
1. Grillage Analysis: This method models the bridge deck as a grid of interconnected beam elements, representing the longitudinal girders and transverse elements (like diaphragms and equivalent strips of the deck slab). It allows for a more detailed analysis of load transfer within the grid.
2. Finite Element Analysis (FEA): A powerful numerical method where the entire bridge structure is discretized into a mesh of small elements. By applying material properties, boundary conditions, and loads to these elements, FEA can accurately determine stresses, strains, and deflections throughout the structure, providing a highly detailed and precise load distribution to each girder.