Spliced U-Girder Bridge

Introduction

This tutorial outlines the recommended steps to model a curved spliced U-girder bridge using SOFiSTiK for Grasshopper. The example is based on guidelines issued by the Florida Department of Transportation. The guidelines, including drawings and presentations, can be found here: Curved Precast Spliced U-Girder Bridges.

The tutorial bridge example uses a hybrid modelling approach, where the girders are modelled using composite beam elements and the deck is modelled using orthotropic shell elements.

Units

Imperial units

Project files

Latest version: spliced-u-girder-bridge-2025-1.zip

• Version History

Note

Following texts and images refer to the Rhino-Interface 2025-1.

Objectives

• Structure of parametric project files

• Defining the bridge axis input

• Axis definition

• Superstructure analytical model

• Defining the substructure

• Substructure placement

• SOFiSTiK model generation

Figure 1. Geometric and analitical models of the splice U-girder bridge

Figure 2. Superstructure of the bridge

Figure 3. An extract from the Master Assembly script

Structure of parametric project files

The parametric project file structure for the bridge is organized into distinct Component Scripts and a Master Assembly. Both parts rely on external files, including Excel and JSON data.

Each bridge model component, such as Road Alignment, Foundations, and Substructure is developed in a separate Grasshopper file, that together are referred to as Component Scripts. These scripts generate outputs in a form of GHData files which are then used by the Master Assembly script to integrate all components into a cohesive model. Within the Master Assembly, a script is also included to create the superstructure of the bridge.

The Master Assembly file serves as the foundation for both the SOFiSTiK analytical model and the volumetric BIM model, ensuring a seamless transition from design to analysis and construction documentation.

That approach offers the advantage of a better project organization, enabling project engineers to work simultaneously. It also contributes to a faster runtime of the Grasshopper software.

Note

To simplify the tutorial, only the substructure of the bridge and the support towers will be introduced as separate Component Scripts.

Defining the bridge axis input

Road alignment curve

The bridge axis geometry is created with the Alignment component, which uses horizontal and vertical alignment data to create a 3D curve. The 3D alignment curve has a horizontal radius of 1500 ft and a vertical profile with a radius of 8000 ft.

Figure 4. 3D road alignment definition

Axis placements definition

The Axis Placement component defines placements, i.e. points of interest along the axis, such as the start and the end of the bridge or the location of substructure components and splices. Placement types can indicate the beginning (B) or the end (E) of the structure, supports (S) and intermediate stations (I). Placements of type Begin (B), End (E) and Support (S) define the bridge span layout that allows further model inputs using relative stationing (e.g. “1.5” = 50% of span 1).

Figure 5. Axis Placement definition

Variable Distribution

In this tutorial example the Variability Distribution is not included.

Cross sections

The superstructure sections were defined using the JSON file format (Section Definition In Json Format) and consist of the following parts:

• Deck [in].

• Tub Girder [in].

• Spliced Girder [in].

The JSON files are included in the project folder.

The deck cross-section is used to obtain the deck geometric model. It can also be used as a basis for the deck structural area model (see chapter Deck structural area). The girder locations are defined through interpolation of cross section points G1 and G2. These points are used as a basis for the girder axes (see chapter Axis definition).

The girder composite cross sections are used to model the beam structural lines. They include U-Girder and effective deck parts. The Tub Girder also includes a lid slab part.

Figure 6. Definition of the deck cross section

Figure 7. Preview of the deck cross section

Figure 8. Definition of the girder cross sections

Figure 9. Preview of the Tub girder section (left) and the Spliced girde section (right)

The change of sections along the girder axes is achieved using the Section Sequence component.

Figure 10. Merging girder sections using the Section Sequence component.

Axis definition

For multi-girder bridges it is recommended to separate the main bridge axis from the individual girder axes and use the Axis Definition component to define them. The main bridge axis uses the road alignment curve, deck section and placements as input data. Interpolating curves through cross section points G1 and G2 provide geometry data for the girder axes. The individual girder axes require placements and section sequence components as input data.

Figure 11. Preview of the axes definition

Figure 12. Preview of the superstructure cross section

Figure 13. Preview of the deck and girder axes

Superstructure analytical model

Note

The group numbers of the structural elements are assigned to reflect the intended construction sequence.

Deck structural area

The deck analytical model is defined as a set of Structural Areas, where the surface geometry is provided using the Interpolate Surface component. This component uses deck cross section points to create curves along the road axis, which are then extrapolated into surfaces.

Note

Since the girder composite sections already include the deck, the weight of the structural area material should be set to zero to avoid doubling the deck self-weight in the analysis. This can be done in the SSD by modifying properties of the material assigned to the deck structural areas.

Figure 14. Modifying material properties in the SOFiSTiK Structural Desktop (SSD)

Figure 15. Definition of the deck structural area

Figure 16. Preview of the deck structural area

Girder structural lines

The superstructure girders are defined as Structural Lines. The geometry of those structural lines is provided by the Interpolate Curves component which obtains relevant information from the girder axes. To assign group numbers to a list of structural lines more conveniently, the curve list should be shifted to the one data tree level lower.

Figure 17. Defining the girder structural lines

Figure 18. Preview of the girder structural lines

Tendon definition

This bridge example utilizes two types of girder post-tensioning profiles: segmental tendons in the girder bottom slabs and continuity tendons in the girder webs.

The tendon geometry is defined using the PT Geometry | Profile component.

• For the bottom slab tendons, the profile is aligned vertically with the cross section point “BOT” and distributed horizontally using a list of perpendicular offsets. Based on that geometry, tendons are defined in segments alongside other tensioning attributes using the component Tendon Definition. The start and end stations of tendon segments are defined by selecting placement names using the wildcards.

Figure 19. Segmental tendons’ definition

Figure 20. Preview of the segmental tendons

• The profiles of the web tendons are defined using the PT Profile | Spline component which creates profiles in a 2D plane based on vertical offsets and stations. The position of the profiles for both webs are managed by one PT Geometry | Profile component. The profiles are projected onto the web aligned with segments defined by two pair of cross sectional points (TFL with BSL and TFR with BSR). Since the web tendons are continuous, there is no need to provide end stations in the Tendon Definition component.

Figure 21. Continuity tendons’ definition

Figure 22. Preview of the continuity tendons

Support conditions

Three sets of supports are defined to account for the bridge’s construction sequence and layout: bearings, temporary falsework towers and temporary casting yard supports. Each definition involves using a Rigid Link between the top and bottom of the girder, as well as the Bridge Bearing component.

• A Rigid Link is created between TOP and BOT points of girder axes at abutment and bent stations. The points are retrieved through the Evaluate Section component. To avoid unnecessary offsets due to the vertical curvature of the bridge, within the Interpolation Attributes the PlcOrient can be set as False and the Alignment Type as Vertical. For the Bearings , the BOT of Girder points are lowered by 0.45 feet which represents the height of the elastomeric bearing pads. To provide enough torsional support to the girders the CMX value is set to 1.0e+7.

Figure 23. Definition of the support conditions at abutments and bents

Figure 24. Preview of the support conditions at abutments and bents

• Girders are supported on the falsework towers during the assembly. Therefore, the points for the Rigid Link as well as for Bearings are retrieved at the Splice start and end stations. The rest of the properties should follow the previous step.

Figure 25. Definition of the falsework tower supports

Figure 26. Preview of the falsework tower supports

• For temporary casting yard supports the points for the Evaluate Section are selected at the ends of the girders. The remaining properties should be applied as previously shown, with the difference that Bearing are created based on a one single point.

Figure 27. Definition of the casting yard support

Figure 28. Preview of the casting yard support

Defining the substructure

Elements included in this chapter are defined in separate Grasshopper scripts within Component Scripts. Subsequently, their output will be transferred to the Master Assembly using ghdata files.

Note

The substructure cross sections are defined in the SSD file.

Bent

For the bent structure, the script contains Structural Lines representing the cap and the columns, Rigid Link between the structural elements as well as a Structural Point serving as a fixed support. The Local Z direction needs to be set along the global X vector to align with the local coordinates of the bridge.

It is important to model the top of bent substructure at the origin point of the global coordinate system which will be reflected within bridge model axis later on.

Finally, the data of the structural elements is sent using the .ghdata file with help of the Data Output grasshopper component and saved in the ghdata folder.

Figure 29. Definition of the bent structural elements

Figure 30. Preview of the bent substructure at global origin point

Falsework tower

The Falsework Tower is created in a separate grasshopper script. The structure consists of truss-type Structural Lines for columns, bracings and horizontal members as well as Structural Points representing hinge supports. The Local Z direction of columns is set along the global X direction and the entire tower is based in the global origin point.

As previously, the data is saved in the ghdata folder.

Figure 31. Definition of the Falsework Tower structural elements

Figure 32. Preview of the Falsework Tower at the origin point of global coordinate system

Substructure placement

Within the Master Assembly script, all the ghdata files which come from Components Scripts are supplied by Data Input component. The substructures, generated at the global origin position are then transformed to the appropriate locations using Placement Transform and the Grasshopper Transform component.

• The origin of the base plane for the Bent substructure needs to include the distance to the Deck Axis (girder and bearing pad height) at the Abutments and Bents stations.

• The Falsework Tower should be located within the same base plane as bent substructure, but it must be positioned in the middle of spliced girder segments, as one tower supports both girder elements.

Thanks to the transformations obtained from the Placement Transform and the use of the Transform component, the substructures are oriented to the specific locations along the bridge axis.

Figure 33. Definition of the substructure placement

Figure 34. Preview of the substructures at the origin plane and along the bridge axis

SOFiSTiK model generation

Export the SOFiSTiK data

In order to export the model from Grasshopper to SOFiSTiK the relevant data is saved by the Text File components in the project folder. The following data text files are exported:

• AQUA - exports data regarding materials and cross-sections.

• SOFiMSHC - exports information about structural objects for meshing.

• TENDON - exports information about tendons elements and their attributes.

Note

The loads are not included in this tutorial example.

Figure 35. Definition of the SOFiSTiK data

Read in the SOFiSTiK data

In the SSD the SOFiSTiK text files are imported using the #include command in the Text Editor Task for the Sections, Structure and Tendons data.

Figure 36. Reading the SOFiSTiK data exported from Grasshopper in the SSD

Analysis

The Construction Stage Manager is integrated into the SSD model, defining the construction sequence and its analysis parameters by activating elements based on group numbers.

Figure 37. SOFiSTiK construction stages

Once exporting the data from Grasshopper has concluded, the structural model is ready for further processing and analysis.

Figure 38. Model View in the SOFiSTiK Viewer