Bridge Modelling: The benefits of section for resultant forces with plate elements

1. Introduction

Figure 1. Dubai Water Canal Bridge

When it comes to designing and building bridges, accurate modelling is essential. Even small errors in the modelling process can lead to significant problems down the line, including structural weaknesses, safety hazards, and increased costs. Advanced software programs like Midas Civil are used by many civil and structural engineers to model and analyse their bridge designs. One of the key features of Midas Civil is plate elements, which are used for structural analysis modelling, resulting in reliable and accurate results. In this article, we will delve deeper into plate elements and the benefits of section for resultant forces in Midas Civil.

2. Plate Elements for Structural Analysis Modelling

Plate elements are a type of finite element used in structural analysis modelling, particularly for thin and flat structures such as plates, shells, and slabs. They offer several advantages over other types of elements such as beam elements or solid elements.

One of the significant benefits of plate elements is their ability to accurately model complex shapes. With modern-day needs for sustainability, resilience, and climate change adaptation, bridge geometries can be intricate and challenging to model accurately. Plate elements can capture these details with precision, including the curved box-girder bridges and bridges with unique section geometries. Additionally, plate elements can handle both bending and membrane stress, making them a critical tool for accurately modelling bridge designs.

Another advantage of plate elements is their efficiency. While it does require more computational resources than simpler models such as grillage models. However, plate elements can be used to model complex structural geometries, which lead to an increase in computational efficiency by reducing the need for additional elements or produce local plate models to conduct extra structural analysis for detailed design checks. Additionally, in comparison to solid elements, plate elements can greatly reduce the number of elements required to model the structure while still maintaining accuracy. This reduction in elements leads to a higher overall efficiency.

Figure 2. Fenton Street Footbridge, Auckland New Zealand

3. Section for resultant forces in Midas Civil

Section for resultant forces is a technique used in structural engineering analysis to determine the internal forces and stresses in a specific section of a structure. In Midas Civil, the section for resultant forces feature allows engineers to analyse a cross-section of a bridge and determine the stresses and forces acting on it. This feature can be used to analyse a range of cross-sectional shapes, including circular, rectangular, and irregular shapes, and can be applied to different types of structures, including bridges, buildings, and towers.

The section for resultant forces features in Midas Civil works by first dividing the structure into smaller sections, which are then analysed individually to determine the internal forces and stresses acting on them. These individual section groups are then combined to create an overall demand profile of the structure through virtual beams. Thus, allows user to visually understand the demand profiles such as bending moment, axial and shear forces acted on the structure under different load combinations. With this function, engineers no longer need to create a separate grillage model to then undertake specific design checks.

Figure 3. Midas Civil - Section for Resultant Forces Demonstration

4. Application and consideration

The Midas Civil Section Resultant Force function proves to be highly effective in designing structures with irregular forms, such as horizontally or vertically curved bridges as the section resultant force function builds grillage model within the plate element model by the concept called virtual beam (Refer to Section 3).

Steel box-girder and viaduct bridge are some common types that designers choose plate element model over grillage or spine models at detailed design level.

Here are some factors to consider when determining whether to adopt this approach:

• Structural form:
  Assess whether the bridge has a conventional or bespoke design, as the suitability of the approach may vary depending on the complexity of the structural form.

• Design stage:
  Consider the stage of the design process, whether it is at the concept stage or the detailed design stage, as this can impact the applicability and usefulness of the approach.

• Demand type:
  Evaluate the specific demands to be analysed, such as moments and forces or stresses, as the approach may excel in certain types of analyses.

• Material type:
  Consider the materials used in the bridge, such as reinforced concrete, pre-stressed concrete, or steel and steel composites, as this may influence the effectiveness and accuracy of the approach.

These considerations will help in determining whether the proposed approach is suitable for a given bridge design and analysis scenario.

5. How to apply and view the results?

To apply section for resultant forces in Midas Civil, engineers must first create the geometry of the bridge with consideration to level of complexity, curvature, section offset and account for efforts in future modification to the model. Then, setup the boundary conditions and test the behaviour of the model by analyse with dead loads. Once the engineer verified the model, they can then setup each section group along the bridge segments.

Note: Recommend using polygon select function for complex bridge geometry. Additionally, it is important to review the section group one by one to ensure that they have been set up properly. This includes checking the position of each group and ensuring that the plate elements inside the group are properly defined.

Please watch this demo from Midas Civil on how to apply section for resultant force in a simple composite steel I-section girder bridge superstructure. link to video

6. Limitations and Precautions

While the Midas Civil Section Resultant Force function offers numerous benefits in analysis, it is equally important to be mindful of its limitations and take the necessary precautions when utilising this tool.

Midas Civil Section Resultant Force function is a relatively new which meant it is not user friendly as the others. As a user, you will need to constantly iterate and cross check that the virtual beam has been created correctly by visualising demands and the respective values. Because the application highly dependent on the selected sections, the orientation on how its been selected (similar to the right hand local axis rule) and the order of section groups which determines the start and end nodes for each virtual beams. Therefore, it is essential to constantly check and communicate with Midas Civil team through their support desk.

While section resultant force gave plate element model the benefits of global demand visualisation that comes from grillage model, the plate element model itself still have limitation such as application of differential temperature demands.

Figure 4. NZ Bridge Manual Temperature variation with depth

This is because plate element model doesn’t come with section datum reference like grillage model. Currently, the solution is adding dummy beams for applying the respective temperature demands, however this method is not viable for complex section form and curved bridge form. Therefore, it requires designer to create a separate grillage model with differential temperature loading to examine the magnitude of the demands in comparison to others. Below are some illustrations to explain this limitation.

Figure 5. Plate element box girder with dummy beams for differential temperature application

Figure 6. Illustration of the limitation of applying differential temperature in plate element model

7. Conclusion

Bridge modelling requires accuracy, and advanced software programs such as Midas Civil provide engineers with reliable results. Plate elements and section for resultant forces are key features in Midas Civil that help engineers produce accurate and reliable results while offer the same benefits as grillage modelling, enabling engineers to review the behaviour at both local and global level. Having a robust structural model enhance engineer’s workflow. Making it easier to identify potential weak areas, optimise the bridge's design, and ensure the bridge's reliability, safety, and efficient.

Reference

• MIDAS IT Co., Ltd. Midas Civil User Manual

• Engineering Standards, Waka Kotahi NZ Transport Agency. (2022). Bridge manual SP/M/022. Waka Kotahi NZ Transport Agency.

• Image Source: City Rail Link. "Normanby Road and Fenton Street Bridges Update." January 31, 2023. Connecting Mt Eden one bridge at a time — City Rail Link

• Image Source: "Section for Resultant Forces." Midas Customer Online Support. MIDAS Customer Online Support - [PROPERTIES]   How to use Section for Resultant Forces - Knowledge base 

About the Editor

Alice Xu

Senior Structural Engineer

Alice is a chartered senior engineer. She has more than 5 years of
experiences in civil structures design and management on a range of small to mega scale projects in New Zealand, Hong Kong SAR and Malaysia.

Most notably City Rail Link, KVMRT3 and Auckland Light Rail.

 

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