Design of Bridge Superstructures
The superstructure is the visible portion of a bridge that directly carries the traffic loads and spans the obstacle. Its design is critical for safety, serviceability, and economy. This module explores the primary components of typical girder bridge superstructures: the deck and the supporting girders.
Bridge Decks
The deck is the physical surface over which vehicles and pedestrians travel. It serves two primary structural functions: providing a smooth riding surface and distributing the localized wheel loads to the underlying supporting members (girders or stringers).
Common Types of Bridge Decks
- Cast-in-Place (CIP) Reinforced Concrete Slabs: The most common type for short to medium spans. The concrete is poured directly onto formwork supported by the girders. They are durable but construction can be slow and weather-dependent.
- Precast Concrete Deck Panels: Manufactured off-site and transported to the bridge. They offer faster construction and better quality control. They are often used as stay-in-place forms topped with a CIP concrete wearing surface to provide continuity.
- Orthotropic Steel Decks: Consist of a flat steel plate stiffened longitudinally and transversely by welded ribs. They are exceptionally light and strong, making them ideal for very long-span bridges (like suspension or cable-stayed bridges) where minimizing dead load is crucial. However, they are expensive and prone to fatigue cracking.
- Timber Decks: Used primarily on rural, low-volume roads, temporary bridges, or historic structures. They are lightweight but require frequent maintenance and have a shorter lifespan compared to concrete or steel.
- Open Grid Steel Decks: Extremely lightweight and self-draining (snow and rain fall through). Often used on movable bridges (bascule, vertical lift) to reduce the weight that machinery must lift. They can be noisy and slippery when wet.
Concrete Deck Design Methods
AASHTO LRFD specifies different methodologies for designing the reinforcing steel within a concrete bridge deck to resist localized wheel loads.
- Traditional Design (Approximate Strip Method): Assumes the deck acts as a continuous transverse beam spanning between the supporting longitudinal girders. It calculates bending moments based on assumed transverse strips loaded by a single wheel axle. It generally results in heavy, conservative reinforcement detailing.
- Empirical Design Method: Based on extensive physical testing and observation rather than rigid structural mechanics. Testing showed that most deck slabs fail in "punching shear" rather than flexure due to an internal compressive arching action that develops within the concrete. If a deck meets specific geometric criteria (girder spacing, deck thickness), this method allows for significantly less reinforcement than the traditional method, reducing costs and the potential for corrosion while maintaining safety.
- Yield Line Analysis: A sophisticated plastic analysis technique. It calculates the ultimate load capacity of the deck slab by analyzing the specific pattern of plastic hinge lines (yield lines) that form just before total collapse. This approach is highly efficient for complex deck geometries or severe skew angles.
Composite Action
A crucial design concept in modern bridge engineering. When a concrete deck is rigidly connected to the supporting steel or concrete girders (using shear connectors like headed studs), they act together as a single structural unit to resist bending.
- Benefits: Significantly increases the stiffness and flexural strength of the superstructure. The concrete deck effectively acts as the top flange of the girder, resisting compressive forces, while the bottom flange of the steel girder resists tension. This allows for lighter girders and longer spans.
Orthotropic Steel Decks
Used primarily on extremely long-span bridges (like suspension or cable-stayed bridges) or movable bridges where minimizing dead weight is absolutely critical.
Orthotropic Deck Features
Instead of a heavy concrete slab, the deck consists of a relatively thin steel plate stiffened by a complex grid of longitudinal ribs and transverse floor beams welded underneath. "Orthotropic" means it has different stiffness properties in orthogonal (perpendicular) directions. They are incredibly lightweight but very expensive to fabricate and fatigue-prone if not designed perfectly.
Bridge Girders (Main Supporting Members)
Girders are the primary longitudinal load-carrying members. They span between the substructure supports (piers and abutments) and support the deck.
Types of Girder Materials and Shapes
- Rolled Steel Beams: Standard I-shaped steel sections (e.g., W-shapes) produced in steel mills. Used for relatively short spans due to limited available depths. Economical and quick to erect.
- Steel Plate Girders: Custom-fabricated by welding steel plates together to form an I-shape. They allow for much deeper sections and variable flange thicknesses along the span to optimize material usage where bending moments are highest. Used for medium to long spans.
- Steel Box Girders: Closed, hollow rectangular or trapezoidal cross-sections fabricated from steel plates. They offer excellent torsional stiffness (resistance to twisting), making them ideal for curved bridges. They are aesthetically pleasing but more expensive to fabricate and inspect internally.
- Prestressed Concrete Girders: Concrete beams containing high-strength steel tendons that are tensioned before or after the concrete is cast. This pre-compression counteracts the tensile stresses caused by service loads, preventing cracking and allowing for longer spans than conventional reinforced concrete.
- Standard Precast Shapes: Commonly used standard shapes include AASHTO I-Beams (traditional standard for short/medium spans) and Bulb-Tees (feature a wide top flange for better stability and deck support, very efficient for longer spans).
- Pre-tensioned: Tendons tensioned before concrete is poured (typical for I-girders and bulb-tees manufactured in a plant).
- Post-tensioned: Tendons tensioned after concrete has cured (often used for cast-in-place box girders or splicing precast segments).
- Concrete Box Girders: Hollow concrete cross-sections, often constructed segmentally (precast or cast-in-place). Similar to steel box girders, they provide high torsional rigidity and are frequently used for long, curved highway interchanges.
Concrete Girders: Prestressed and Post-Tensioned
Concrete is strong in compression but weak in tension. To overcome this, bridge girders are actively compressed before everyday loads are applied.
Prestressing and Post-Tensioning
- Pre-Tensioned Concrete: High-strength steel strands are stretched taut in a casting bed. Concrete is poured around them. Once the concrete cures, the strands are cut, and their tendency to shrink back transfers a massive compressive force into the concrete. This is typically done in precast plants for standard girders (I-beams, bulb-tees).
- Post-Tensioned Concrete: Hollow ducts are cast into the concrete. After the concrete cures on-site, steel tendons are threaded through the ducts, pulled tight by hydraulic jacks against the hardened concrete, and anchored at the ends. The ducts are then grouted. This method allows for curved tendons (draped profiles) and is essential for continuous spans and segmental bridge construction.
Steel Girders and Composite Action
Modern steel bridges almost universally rely on "composite action" to maximize structural efficiency.
How Composite Action Works
- Non-Composite (Historical): The concrete deck simply rests on top of the steel girder. When loaded, the deck and girder bend independently, sliding past each other at their interface.
- Composite Design: Steel shear studs are welded to the top flange of the steel girder and embedded into the cast-in-place concrete deck. These studs act like "nails," preventing the deck from sliding over the girder.
- Structural Benefit: The concrete deck and the steel girder are forced to bend together as a single, massive "T-beam." The concrete deck handles the compressive forces at the top, while the massive steel girder handles the tension at the bottom. This dramatically increases the girder's stiffness and load-carrying capacity, allowing for longer spans with shallower steel sections.
Load Distribution Factors (LDF)
When a heavy truck tire presses down on a bridge deck, the deck bends and distributes that localized load laterally to multiple supporting girders underneath. Not just one single girder carries the entire wheel weight.
Determining Load Distribution
Because a bridge superstructure is a complex three-dimensional system, analyzing the exact load path of every truck wheel is computationally heavy. Instead, engineers rely on simplified methods.
- The Concept: A "Load Distribution Factor" (LDF) simplifies a 3D problem into a 1D analysis. If a girder's calculated LDF is , the engineer applies the entire design truck load to a simple 1D line model of a single girder and multiplies the resulting maximum moments and shears by to find the design force for that specific girder.
- AASHTO Empirical Formulas: AASHTO provides complex empirical equations to calculate LDFs for interior girders. These formulas depend heavily on the girder spacing (), the span length (), the stiffness of the deck relative to the girder, and the number of loaded traffic lanes. Wider girder spacing generally results in higher LDFs (each girder carries a larger share).
- The Lever Rule: A statics-based method primarily used to calculate the distribution factor for exterior (fascia) girders. It assumes the bridge deck acts as a series of simple spans hinged over the interior girders. The engineer places the wheel loads transversely across the deck and uses simple statics (sum of moments) to calculate the reaction on the exterior girder.
- Refined Methods: For complex bridges (highly skewed, sharply curved, or unusual cross-sections where simple formulas fail), a full 3D Finite Element Analysis (FEA) or grillage analysis is required to determine the exact distribution of forces.
Single Girder Design Moment Equation
Calculates the maximum bending moment (or shear) for a single specific girder by converting the 3D bridge load into a 1D equivalent using the Load Distribution Factor (LDF) and Dynamic Load Allowance (IM). Use cases: Sizing the longitudinal girders for an entire bridge superstructure, Determining the maximum shear forces for girder web design.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Maximum design bending moment for the individual girder | kN·m or kip-ft | |
| Maximum bending moment caused by a single design truck on a simple 1D line | kN·m or kip-ft | |
| Load Distribution Factor (fraction of the truck carried by the girder) | - | |
| Dynamic Load Allowance (expressed as a decimal fraction) | - |
Superstructure Design Considerations
The structural design of the superstructure involves more than simply sizing the girders for strength.
Key Design Aspects
- Flexure (Bending): The primary mode of behavior. Girders must have sufficient flexural capacity (moment resistance) to withstand the maximum positive bending moments (usually at midspan) and negative bending moments (over continuous supports).
- Shear: The vertical forces trying to slice the girder near the supports. Steel plate girders often require transverse stiffeners (vertical plates welded to the web) to prevent the thin web from buckling under shear forces. Concrete girders rely on shear reinforcement (stirrups).
- Deflection (Camber): Bridges are designed with an initial upward curve, called camber, so that under dead load (and sometimes a portion of live load), the deck becomes flat or follows the intended highway profile. Excessive deflection can cause a bumpy ride and drainage issues.
- Fatigue: As heavy trucks cross the bridge, the stress in the girders fluctuates. Over millions of cycles, these stress variations can initiate microscopic cracks, particularly at welded details or sharp changes in section geometry. Fatigue design limits these stress ranges.
- Bracing and Diaphragms: Cross-frames or solid diaphragms placed between longitudinal girders. They provide lateral stability during construction, distribute wind and seismic loads to the bearings, and help distribute live loads across multiple girders.
Continuous vs. Simple Spans
- Simple Spans: A girder supported only at its ends. The bending moment is zero at the supports and maximum near midspan. They are structurally determinate and easier to analyze and construct.
- Continuous Spans: A girder resting on three or more supports without joints over the intermediate piers. This arrangement significantly reduces the maximum positive bending moments in the spans, allowing for shallower girders and fewer expansion joints (which are sources of maintenance problems). However, they develop large negative moments over the piers and are sensitive to uneven settlement of the foundations.
Key Takeaways
- The deck provides the riding surface and distributes wheel loads; design methodologies include the traditional strip method, the highly efficient Empirical Design (relying on arching action), and Yield Line Analysis.
- Composite action structurally connects the deck and girders, significantly increasing efficiency and strength.
- Girders (steel or prestressed concrete) carry the primary longitudinal loads. Standard concrete shapes like AASHTO I-Beams and Bulb-Tees are industry standards for efficiency.
- Load Distribution Factors (LDFs) and the Lever Rule simplify complex 3D wheel load distributions into 1D girder analyses.
- Steel Box Girders and Concrete Box Girders offer superior torsional stiffness, essential for curved bridges. Design must address flexure, shear, deflection (camber), and fatigue limit states.
- Continuous spans are generally more efficient than simple spans but require careful design for negative moments and potential settlement.