FAQ: Coordinate System & PGL
- Cagin Yakar
- Melis Ceylan
When using OpenBrIM, a thorough understanding of the coordinate systems is essential for various purposes, such as accurately modeling bridge elements, interpreting results correctly, and performing other tasks.
OpenBrIM uses three coordinate systems:
1.Global Coordinate System: The axis directions can be viewed using the cube symbol located in the top-right corner of the application.
2.Alignment Coordinate System: In OpenBrIM, any node or point assigned to an alignment will have local X-Y-Z values in the alignment coordinate system. In this system, moving upstation and downstation along the PGL will change the local X value of points or nodes. For instance, in the case of a curved alignment, the X-axis follows the horizontal curve, so local X values displayed at nodes or points can be interpreted as station values. The Y values, in this case, represent the transverse direction and are perpendicular to the PGL, with the positive Y-axis pointing to the right when looking upstation along the PGL and negative values pointing to the left. The Z value is 0 at the PGL, with positive Z values pointing upwards and negative Z values pointing downwards from the PGL.
3.Finite Element’s Local Coordinate System: The element's local axes can be viewed directly by activating 'Display Local Axis.' The line representing the element's direction corresponds to the X-axis, the second line represents the Y-axis, and the third line represents the Z-axis, as shown in the figure below.
To display the local axes of the elements, the steps are as follows:
1.Switch to the FEA View - Model
2.Click the Settings icon and choose 'Display Local Axis'
Then, the local axes for each element will be displayed, and the size can be adjusted via the FEA View settings, which can be accessed through the Settings icon.
Coordinate systems utilized for FEA results can be summarized as follows:
An node’s coordinate system can be viewed in the FEA tab of the workflow, under Geometry > Nodes (when the lock icon is clicked), in the 'Coordinate System' column.
Node Displacements (Local):
Node displacements are presented with respect to the node's associated coordinate system. Typically, for most bridge workflows, nodes follow the alignment coordinate system. However, for bearing nodes, if the bearing rotation is defined, this parameter will directly affect the node's coordinate system by rotating the axes according to the bearing rotation definition. Refer to the screenshot provided below for further clarification.
Node Reactions (Local):
Node reactions are presented to the user based on the node's local coordinate system. In most cases, this coordinate system aligns with the alignment coordinate system. However, if the bearing rotation parameter is defined with a value other than zero, the node's coordinate system will rotate accordingly, and the reactions will follow the updated orientation.
For example:
Force X: Represents the longitudinal alignment direction.
Positive values: Indicate forces resisting movement in the downstation direction.
Negative values: Indicate forces resisting movement in the upstation direction.
Force Y: Represents the transverse direction, perpendicular to the alignment.
Positive values: Indicate forces resisting movement to the left when looking upstation.
Negative values: Indicate forces resisting movement to the right when looking upstation.
Force Z: Represents the vertical direction.
Positive values: Indicate forces resisting downward movement, often corresponding to compressive reactions.
Negative values: Indicate forces resisting upward movement, often corresponding to uplift or tension.
Node Reactions (Global):
Node reactions in this section are presented to the user with respect to the global coordinate system.
Element End Forces (External - Local):
The forces at the ends of each FELine and FESurface are presented to the user in this section with respect to the element's local coordinate system.
If the user intends to use these forces or Element End Forces (External - Global) for design purposes, they should exercise caution, as the sign convention for element end forces is opposite with respect to the element's local coordinate system. For example, a positive axial force at one end of the element will appear as a negative axial force at the opposite end. This reversal is inherent to how forces are represented and must be accounted for during the design process to avoid errors. Alternatively, using FELine internal forces may provide a simpler approach.
Element End Forces (External - Global):
The forces at the ends of each FELine and FESurface generated are presented to the user with respect to the global coordinate system in this section.
Composite Element Forces (Sectional):
FEComposite forces represent the combined effects of internal forces across multiple finite elements that make up a composite structure or a group of connected elements.
These forces are calculated by summing or integrating the internal forces (e.g., axial forces, shear forces, and bending moments) from all contributing finite elements along the path of the composite element. The resulting forces provide a simplified and consolidated representation of the overall structural behavior, making it easier to interpret and use for design and analysis purposes.
Summation of Forces:
The forces from all finite elements within the composite structure are aggregated to produce a single resultant value for each force component (e.g., axial, shear, and moment).
Simplified Interpretation:
Instead of analyzing individual element forces, FEComposite forces provide a macro-level understanding of the force distribution within the entire structure or substructure.
Applications in Bridge Engineering:
Useful for analyzing composite sections such as girders, deck slabs, or combined bridge components where the contribution of multiple elements needs to be evaluated as a whole.
The path of a typical FEComposite force for bridge elements is illustrated in the figures below.
In the case of the Footing's path of composite elements, users are given the option to specify the number of paths to be used in filtering composite element forces (sectional results). Users can specify the Minimum Number of Strips in the Longitudinal and Transverse directions on the Footing object from the FEM tab. The results will then be presented according to the defined paths.
For girders, the composite force follows the girder's physical path along its centerline.
Fx (Axial Force): Represents the force along the girder's longitudinal axis. For example, a positive Fx indicates tensile forces, while a negative Fx indicates compressive forces.
Fy (Shear Force in the Y-Direction): Represents the transverse shear force acting perpendicular to the girder's length.
Fz (Shear Force in the Z-Direction): Represents the vertical shear force acting in the vertical plane of the girder.
Mx (Torsional Moment): Represents twisting along the girder's axis.
My (Bending Moment about the Y-Axis): Represents major-axis bending, typically caused by vertical loads.
Mz (Bending Moment about the Z-Axis): Represents minor-axis bending, typically caused by lateral forces.
FELine Forces (Internal):
FELine internal forces are displayed in this section along the local axes of the FELine element. These forces include axial, shear, and bending components:
Force X: Represents the axial force within the element. Negative values indicate compression, while positive values indicate tension.
Force Y: Represents the shear force in the local Y-axis direction, perpendicular to the element's axis.
Force Z: Represents the shear force in the local Z-axis direction, also perpendicular to the element's axis.
Moment X: Represents the torsional moment about the local X-axis.
Moment Y: Represents the bending moment about the local Y-axis, where positive and negative values indicate different bending directions.
Moment Z: Represents the bending moment about the local Z-axis, following the same convention as Moment Y.
FELine Stresses:
Stresses calculated for FELines can be viewed under this section.
FESpring Forces (Global):
The spring forces at each node are displayed in this section. The results for each node are reported based on the node's coordinate system, which, in most cases, aligns with the alignment coordinate system.
In a typical bridge workflow, if the bearing rotation angle is 0:
X-axis: Represents the longitudinal direction of the alignment.
Positive values: Indicate forces acting in the upstation direction.
Negative values: Indicate forces acting in the downstation direction.
Y-axis: Represents the transverse direction, perpendicular to the alignment.
Positive values: Indicate forces acting to the left when looking upstation.
Negative values: Indicate forces acting to the right when looking upstation.
Z-axis: Represents the vertical direction.
Positive values: Indicate upward forces.
Negative values: Indicate downward forces, often corresponding to compressive reactions.
FESurface Forces (Internal):
Composite Element Stresses:
Why do the node coordinates show a negative y direction even though the positive transverse offset is going in the right direction looking ahead station in most bridge workflows?
In a typical 3D coordinate system, there are three mutually perpendicular axes: X, Y, and Z. The positive direction of the x-axis points to the right, the Z-axis is vertical and the positive direction of the Z-axis points upwards, and the Y-axis is horizontal and pointing away from you. However, in the context of bridge engineering, positive transverse offset values are typically used in the right direction when looking ahead at a station. To ensure consistency with how bridge engineers think, many library components in OpenBrIM Platform convert +Y values to -Y and -Y values to +Y in their input parameters.