Bridge design and analysis is a complex process that involves several technical steps to ensure safety, efficiency, and reliability. A bridge must be able to withstand various loads, including those caused by traffic, environmental conditions, and its own weight. The analytical process of designing a bridge can be broken down into six main steps. This article outlines these steps, offering insight into how engineers approach the task of creating safe and functional bridge structures.
1. Idealize the Structure
The first step in analyzing a bridge is to idealize the structure. This process involves simplifying the real bridge into a more manageable form. Since bridges are complex structures with various components, idealization is necessary to make the analysis feasible. For instance, beams in the real bridge are often represented as line elements in the analysis. These line elements have length and stiffness but no depth or breadth, thus simplifying the model for analysis.
While idealizing the structure, it’s crucial to keep in mind that this simplified model does not capture every detail of the physical bridge, such as the exact thickness of the beams, the type of reinforcement used, or the actual shape of the components. The idealization is only a representation of the bridge, and engineers must later use this model to determine the necessary reinforcement and check compliance with safety standards.
2. Form a Model
Once the structure has been idealized, the next step is to form a model. This step involves assigning stiffness and areas to the idealized elements of the bridge. The type of model chosen depends on the complexity of the bridge and the analysis required.
- For a 2D beam model, engineers calculate the bending stiffness and cross-sectional area.
- For a 2D grillage model (often used for bridge decks), bending and torsional stiffnesses are calculated, but there’s no need to calculate the area since there are no axial loads.
- For a more advanced 3D space frame model, bending and torsional stiffnesses are needed, along with areas in multiple directions.
The material’s elastic modulus also plays a key role, as it influences how the structure deforms under stress. Once these parameters are defined, the model can be analyzed to understand how it will behave under various loads.
3. Idealize the Loading
Bridges must be designed to withstand a variety of loads. Idealizing the loading is the next step, where the loads acting on the bridge are simplified for easier analysis.
In most cases, the load specifications are already provided in design codes, which include detailed information on standard loading conditions. For example, in the UK, the Highways Agency specifies HA and HB loading in the BD 37/88 code. These loadings represent typical traffic conditions, including the weight of vehicles and the way they move across the bridge.
However, loading in real life is not always simple. A typical office, for example, contains desks, chairs, cabinets, and people, each with different weights. Instead of analyzing each component separately, the loading is idealized as a uniform load. Similarly, vehicle loads on a bridge are represented by uniform line and point loads, which simplify the analysis without losing essential details.
Commercial analysis programs help in automating the process of converting real-world loads into idealized loads, making the process much more efficient. These programs typically come with pre-processors that automatically convert the standard HA and HB loads into node loads for each load case.
4. Solve the Resulting Equation
Once the idealized model and loading are in place, the next step is to solve the resulting equation. If the model is simple enough, engineers can solve the structural equations by hand using methods such as moment distribution or applying known coefficients (e.g., WL/8 for a simple beam). However, more complex models like grillage or finite element models require computational tools to solve the equations.
In such cases, computer programs are used to perform the necessary calculations, typically using the stiffness matrix method. This method is highly effective for handling large and complicated systems. The use of computers has revolutionized the design process, allowing engineers to tackle much larger and more intricate bridge designs without worrying about the time and effort required for manual computations.
5. Interpretation of the Idealized Results
After solving the equations, engineers obtain a set of results that typically include moments, shears, axial forces, torsions, deflections, and rotations. However, these results apply only to the idealized model of the bridge, not the real structure. The interpretation of the idealized results involves adjusting the results to reflect the real-world behavior of the bridge.
For example, slab moments and shears need to be averaged over a meter width to better represent how they occur in a real bridge. Additionally, grillage model results, which may appear “sawtooth” due to idealization, need to be smoothed out for a more accurate representation of actual bridge behavior.
This step is crucial because the model’s behavior might not exactly mirror that of the real structure. Engineers must reverse the idealization process, translating the idealized results back to more realistic values.
6. Checking the Results
The final step in the analysis process is to check the results. This step ensures the accuracy of the analysis and confirms that the model has been set up correctly. Simple hand checks are often sufficient to verify that the input data is correct, that all loads have been applied properly, and that the magnitude of the results makes sense.
For example, in a grillage analysis of a simply supported bridge deck, the total load applied to the model should equal the sum of the support reactions. If there is a significant discrepancy between the two, it indicates that there was an error in applying the load. Similarly, comparing moments and shears from an isolated longitudinal beam with those from the corresponding member in the grillage model can help identify any inconsistencies in the model.
By performing these simple checks, engineers can verify that their model is working as expected. Once they are confident in the results, they can proceed with using the model for further design and reinforcement calculations.
Conclusion
Analyzing a bridge involves a series of steps that transform a real-world, complex structure into a simplified model that can be studied and understood. From idealizing the structure and loading to solving equations and interpreting results, each step is critical to ensuring the safety and reliability of the final design. By carefully following these steps, engineers can create bridge designs that meet all the required standards while accounting for the complex forces at play.
Note on HA & HB Loading
In bridge design, HA and HB loadings are used to represent typical traffic conditions:
- HA Loading consists of uniformly distributed loads combined with line loads, representing standard vehicular traffic.
- HB Loading represents an abnormal vehicle, which can weigh up to 180 tonnes on each axle, used for situations involving exceptionally heavy traffic or transport vehicles.
Both of these loading types are essential for designing bridges that can withstand the dynamic forces exerted by traffic over time.