Beam Bar Elements Shear Center Effect
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Building on the last post, beam and bar elements, in this post we will discuss beam bar elements shear center effect.
We learned what is a shear center in the Stress Engineering Interview Questions Part 3 blog post, so check that out first. In the figure below, we can see the shear centers represented by the orange stars.
Let us recap the definition of “Shear Center” here:
A point on the cross sectional plane of a beam or a section coincident with its planes of symmetry, through which any applied transverse shear load (including oblique shear load) will cause bending without any twisting of the beam, such a point is called a ‘shear center’.
Figure 1: Beam Vs Bar Element Shear Centers (TOP), Effect of in Plane Load on a Stiffened Plate With Offset Beam and Bar Elements (BOTTOM), Cross Section Views
Figure 1 TOP:
Beam: Whenever we define a beam element property in FEM, by default, the element nodes are placed at the shear center axis of the end cross sections. The neutral axis is then offset from the shear center axis. Each axis (shear center, neutral and non structural mass) can be defied with different offsets in a beam element property.
Bar: Whenever we define a bar element in FEM, by default, all axes are the same, viz., the shear center axis, the neutral axis and the non structural mass axis.
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Figure 1 BOTTOM:
Thus, care should be taken when defining the element types for aircraft structure such as the stiffened plate (light blue plate) shown above.
Effect of Element Type:
Assume the stiffened plate is a cantilever beam fixed at the other end of the view in Figure 1. If beam elements with the offsets shown in Figure 1 are used to model the attached C-Channel, then the in plane load F at the visible end shown above would produce a counter clockwise twisting moment about the shear center. On the other hand if bar elements are used, then the moment would be a clockwise twisting moment or torque about the shear center/neutral axis of the bar elements.
Figure 2: Effect of In-Plane Load on a Stiffened Plate With Offset Beam Elements, Twisting
Therefore, the beam element must be used in this case to accurately represent the actual deformation behavior. This will help you understand Beam Bar Elements Shear Center Effect on a cantilever stiffened plate as shown above in Figure 2.
Using Plate Elements to Represent the C-Channel:
Another way to represent the same model (although a slightly larger model) would be to use shell elements to model the C-Channel. In this case it is best to limit the shell elements to represent relatively thin cross sections. Thus the shear center and neutral axis are accounted for by virtue of the shell 'mesh' of the C-Channel. However, when connecting the C-Channel plate element nodes to the top plate mid line nodes, the best approach is to use RBE3 elements.
So there you have it, I hope you found this useful and learned more about Beam Bar Elements Shear Center Effect.