How to Specify Beam Orientation

A beam element is represented as a line. However, a line has no inherent orientation to represent the beam cross-section. For example, the web of an I-beam could lie in a vertical plane, a horizontal plane or some other plane. The orientation of the cross-section must be specified in order to specify the sectional properties of beam elements (such as the moments of inertia about the axes). Conveniently, the orientation of a linear beam cross-section is specified by the surface number of the line.

More specifically, the surface number of the line specifies a node in space, called the K-node. The two end nodes of the beam element (the I- and J-nodes) and the K-node define a plane (see Figure 1). Beam elements are defined by the local axes 1, 2 and 3, where:

Figure 1: Axis 2 lies in the plane of the I-, J- and K- nodes.

With the element axes known, the cross-sectional properties A, J1, I2, I3, S2, S3, Sa2 and Sa3 can be entered appropriately in the "Element Definition" dialog as shown in Figure 2. (For more information about sectional properties, see the ALGOR User's Guide.)

Figure 2: The cross-sectional properties of beam elements can be specified on the "Cross Section" tab of the "Element Definition" dialog.

The K-node for the beam elements will be assigned according to Table 1 below. The local 2 axis of each beam element is perpendicular to the beam and goes through the K-node. Table 1 is acceptable for beams that lie along one of the global axes.

Table 1 shows where the K-node occurs for various line surface numbers. The "first choice" location is where the K-node is created provided the I-, J- and K- nodes form a plane. If the beam element is colinear with the K-node, then a unique plane cannot be formed. In this case, the "second choice" location is used for that element.

Table 1: Correlation of surface number and K-node (axis 2 orientation). For linear beam elements only.

Surface Number	First Choice K-node Location	Second Choice K-node Location
1	1.0E14 in +Y	1.0E14 in -X
2	1.0E14 in +Z	1.0E14 in +Y
3	1.0E14 in +X	1.0E14 in +Z
4	1.0E14 in -Y	1.0E14 in +X
5	1.0E14 in -Z	1.0E14 in -Y
6	1.0E14 in -X	1.0E14 in -Z

Alternatively, on the "General" tab of the "Element Definition" dialog, the "Override surface-based orientation" option can be activated, which enables you to define the K-node manually for beams that do not lie along one of the global axes (see Figure 3). This manually defined K-node will be assigned for all beams in the part, regardless of surface number.

Figure 3: The X, Y and Z coordinates of the K-node can be defined manually on the "General" tab of the "Element Definition" dialog.

For example, Figure 4 shows part of two models, each containing a W10x45 I-beam. Note that both members have the same physical orientation; that is, the webs are parallel. However, the analyst chose to set the K-node above the beam element in model A and to the side of the beam element in model B. Even though the cross-sectional properties are the same, the moment of inertia about axis 2 (I2) and the moment of inertia about axis 3 (I3) need to be entered differently.

Figure 4: Determining the cross-sectional properties appropriate for the beam orientation.

In some situations, a global K-node location may not be suitable. In this case, add a circle on a surface number between 7 and 255 in Superdraw. The center of the circle will be the K-node for all beam elements of the same surface number.

In the Superview IV Results environment, the orientation of beam elements can be checked by using the "Display Options:Show Orientation Marks:Beam Orientations" command sequence. A line will be added at the midpoint of each beam element pointing in the direction of axis 2.

Thus, ALGOR software provides you with flexibility for defining and checking beam cross-section orientation.