Introduction to Plate Girders
Plate girders, first gaining popularity in the late 1800s, were widely used in the construction of railroad bridges. Initially, these girders were assembled using riveted and bolted plates to form the desired girder size. By the 1950s, welded plate girders replaced their riveted counterparts in many developed countries due to their superior quality, aesthetic appeal, and economic advantages. Welded plate girders offered enhanced efficiency in manufacturing and better performance under load.
These structural components have become integral to bridge design, particularly for large-scale, heavy-duty transportation bridges. The main advantage of using plate girders in bridge construction is the designer’s ability to choose the most efficient and cost-effective girder for the specific structural needs, such as long spans or heavy loads.
Types of Plate Girder Bridges
Plate girder bridges come in various configurations, with the choice of bridge type depending largely on the specific site conditions, design requirements, and economic factors.
- Half-Through Plate Girder Bridges:
A half-through plate girder bridge is ideal when large embankment fills are necessary at the bridge approaches. This configuration allows the bridge to meet the minimum headroom clearance required, making it particularly useful in situations where the maximum approach gradient is low, such as in railway bridges. The structure of a half-through bridge involves a girder configuration where the top flange remains within the depth of the bridge, while the lower flange extends below the roadway. The lateral buckling of the compression flange is prevented by a U-frame system, which consists of floor beams and vertical stiffness, all connected through a moment-resisting joint. This system helps keep the structure stable, especially under dynamic loads from trains or vehicles. - Deck-Type Plate Girder Bridges:
A deck-type bridge is preferred when the construction depth is not a critical design constraint. In this type of bridge, the girders are located beneath the deck, and the compression flange is restrained against lateral buckling by the bracing system. This design is effective in distributing forces evenly and ensuring stability, especially for highway bridges where large loads are expected.
Main Plate Girders in Bridge Design
In bridge design, the main plate girders support the primary load-carrying function of the structure. These girders often require web stiffening (either transverse or both transverse and longitudinal) to improve their efficiency. Web stiffeners reduce the potential for buckling and increase the girder’s strength by resisting shear forces and bending moments.
Additionally, the design of plate girders must consider variations in flange thickness to optimize the girder’s performance for varying bending moments. For example, regions experiencing higher bending moments may require thicker flanges, which can be achieved either by welding additional cover plates or by using thicker flange plates in those areas.
In long-span bridges, particularly those with spans greater than 50 meters, variable-depth plate girders may be more economical, as they reduce material usage while maintaining structural integrity. The initial design of these girders often follows rules of thumb based on experience, allowing for a quick estimate of the dead load and dimensions of the girder.
Design Criteria for Main Plate Girders
When designing plate girders for bridges, there are several key criteria to consider. Some common thumb rules help guide the design process:
- Overall Depth (D):
For highway bridges, the depth typically falls within the range l/18l/18 to l/12l/12 (where ll is the span length), while for railway bridges, it ranges from l/10l/10 to l/7l/7. - Flange Width (2b):
The flange width is generally between D/4D/4 and D/3D/3. - Flange Thickness (T):
The flange thickness is commonly between b/12b/12 and b/5b/5. - Web Thickness (t):
The web thickness is usually between t=D/125t = D/125.
Once these preliminary dimensions are established, the detailed design process involves ensuring the girder satisfies various design criteria, including strength, stability, fatigue resistance, and dynamic behavior.
Recent advancements in optimum design methods have allowed for more direct and precise design of girder bridges, with a focus on minimizing weight and cost while maximizing performance.
Detailed Design of Main Plate Girders
When designing plate girders for bridge construction, it’s crucial to evaluate the load effects on the structure, such as bending moments and shear forces. These load effects are typically assessed using individual and un-factored load cases, which are then combined based on various load factors to determine the total design load.
Bridges are also subjected to cyclic loading, which can lead to fatigue and potentially cause structural failure over time. Therefore, bridge design must account for the following failure modes:
- Local Buckling:
Plate girder sections, especially those in the compression zone, must have sufficient thickness to avoid premature buckling before the section reaches its full plastic moment capacity. - Lateral Torsional Buckling:
Lateral torsional buckling occurs when a portion of the girder, especially its compression flange, is unrestrained laterally. In such cases, the girder may fail due to the twisting motion induced by the bending moments. The design of the girder must ensure proper lateral restraint to prevent this type of failure. - Web Buckling:
The web of the plate girder also needs to be designed to resist buckling under high shear forces. In some cases, additional web stiffeners are used to improve stability. - Fatigue Effects:
Bridges experience repeated loading, which can lead to fatigue failure if not properly accounted for in the design. The material selection and structural configuration must ensure that fatigue effects are minimized.
Shape Limitations for Plate Girders
Plate girders can be classified as compact or non-compact sections based on the thickness of the components. A compact section is one in which the thickness of the compression zone elements is sufficient to prevent local buckling before the section reaches its full plastic moment capacity. Conversely, non-compact sections may buckle locally before reaching full plastic capacity, and as a result, they are designed using a triangular stress block model.
For both compact and non-compact sections, specific formulas are used to evaluate the moment capacity. It is important to note that plastic analysis, which involves redistribution of moments, is not allowed under cyclic loading conditions. This is to prevent repeated plasticity and subsequent low-cycle fatigue failure, which could compromise the bridge’s long-term integrity.
Lateral Torsional Buckling
Lateral torsional buckling is a critical failure mode for plate girder bridges. This type of instability occurs when the compression flange of a girder is unrestrained over a certain length, causing the girder to twist and buckle laterally. The risk of this failure mode depends on factors such as the unrestrained length of the compression flange, the geometry of the girder, and the gradient of the bending moment.
Calculating the limiting compressive stress that the girder can safely withstand is crucial for determining the girder’s ability to resist lateral torsional buckling. Several design methods exist to estimate this stress, depending on the specific conditions and configuration of the girder.
Lateral Bracing for Plate Girders
Because plate girders are relatively flexible and have low torsional stiffness, they are highly susceptible to lateral-torsional instability. To mitigate this, lateral bracing is provided, typically in the form of cross frames or bracing systems located at the compression flange. These braces prevent lateral displacement and twisting of the girder under load.
For bridges that experience significant wind loads or other transverse forces, the design of lateral bracing becomes even more critical. The depth of the girder also plays a role; deeper girders present a larger surface area for wind loads to act on, exacerbating the potential for instability.
In deck-type plate girder bridges, triangulated bracing systems are commonly used to stabilize the compression flange. However, in half-through or through girder bridges, the bracing must be carefully designed to avoid interference with the bridge functions. In these cases, the deck itself provides lateral restraint, and U-frame action stabilizes the compression flange.
Conclusion
The design of plate girder bridges requires careful consideration of multiple factors, including structural efficiency, material strength, and stability under various loading conditions. Choosing the appropriate girder configuration and design method is essential for optimizing performance and minimizing costs. By addressing issues such as local buckling, lateral torsional buckling, and fatigue effects, engineers can design bridges that are not only strong and stable but also cost-effective and durable for long-term use.