Local coordinate system

Each shape is defined in its own local coordinate system, which by default, is assumed to coincide with the global coordinate system. If a fixed frame, FrameName, is defined, the shape's local coordinate system coincides with this fixed frame. This option allows the section to be translated and rotated freely. For instance, an H-section is obtained through the rotation of an I-section.

The global and local coordinate systems coincide

If no FrameName is defined, or equivalently, if FrameName = FXDFRAME_INERTIAL, the local coordinate system is assumed to coincide with the global coordinate system. For instance, fig. 1 illustrates an I-Section defined with FrameName = FXDFRAME_INERTIAL. Note that the origin of the global axis system, indicated by a purple circle, is at the middle of the web, which extends along the global vertical direction, i.e., along unit vector b3 and unit vector b2 is along the horizontal. Clearly, the global and local coordinate systems coincide.

Figure 1. Configuration of the I-Section when defined in its own, local coordinate system.
The origin of the inertial coordinate system is indicated by the purple circle.

The global and local coordinate systems differ: Example 1

The following geometric objects are now added to the input file.

In this example, the fixed frame is defined by a point and a triad, but any alternative definition the fixed frame can be used. Note that point PointX1 is at a unit distance along the horizontal and triad TriadAt90 defines a 90 degree rotation of the global system. The detailed definition of these geometric objects is listed below.

@POINT_DEFINITION {
@POINT_NAME {PointX1} {
@COORDINATES {0.0, 1.0, 0.0}
}
}
@TRIAD_DEFINITION {
@TRIAD_NAME {TriadAt90} {
@ORIENTATION_DEFINITION_TYPE {VECTORS_E2_E3}
@ORIENTATION_E2 {0.0, 0.0, 1.0}
@ORIENTATION_E3 {0.0,-1.0, 0.0}
}
}
@FIXED_FRAME_DEFINITION {
@FIXED_FRAME_NAME {LocalFrame90} {
@POINT1_NAME {PointX1}
@TRIAD_NAME {TriadAt90}
}
}

If FrameName = LocalFrame90, the configuration of the I-Section now becomes that shown in fig. 2. Note that the midpoint of the web has now moved horizontally by one unit of distance from the origin of the global coordinate system (due to the definition of point PointX1) and the local unit vectors have rotated by 90 degrees (due to the definition of triad TriadAt90). In the local coordinate system, the shape of the I-section remains unchanged, but this local coordinate system has now been translated and rotated with respect the global coordinate system.

Figure 2. Configuration of the I-Section when FrameName = LocalFrame90.
The origin of the inertial coordinate system is indicated by the purple circle.

The global and local coordinate systems differ: Example 2

The following geometric objects are now added to the input file.

Note that point PointX2 is at a unit distance along the vertical and triad TriadAt45 defines a 45 degree rotation of the global system. The detailed definition of these geometric objects is listed below.

@POINT_DEFINITION {
@POINT_NAME {PointX2} {
@COORDINATES {0.0, 0.0, 1.0}
}
}
@TRIAD_DEFINITION {
@TRIAD_NAME {TriadAt45} {
@ORIENTATION_DEFINITION_TYPE {VECTORS_E2_E3}
@ORIENTATION_E2 {0.0, 0.7071, 0.7071}
@ORIENTATION_E3 {0.0,-0.7071, 0.7071}
}
}
@FIXED_FRAME_DEFINITION {
@FIXED_FRAME_NAME {LocalFrame45} {
@POINT1_NAME {PointX2}
@TRIAD_NAME {TriadAt45}
}
}

If FrameName = LocalFrame45, the configuration of the I-Section now becomes that shown in fig. 3. Note that the midpoint of the web has now moved vertically by one unit of distance from the origin of the global coordinate system (due to the definition of point PointX2) and the local unit vectors have rotated by 90 degrees (due to the definition of triad TriadAt45). In the local coordinate system, the shape of the I-section remains unchanged, but this local coordinate system has now been translated and rotated with respect the global coordinate system.

Figure 3. Configuration of the I-Section when FrameName = LocalFrame45.
The origin of the inertial coordinate system is indicated by the purple circle.