1. General
In FEM-Design, regular forces (point, line and surface) can be placed either on the theoretical eccentric axis or a physical (center of gravity) axis of an element. Depending on the settings this can produce various results. In this article we look at a few examples of beams with various conditions.
2. Where are the settings?
The eccentricity settings of bar elements are in the “End conditions” tab.
Figure 1. Beam eccentricity settings
Here we have multiple options. First, we have the selection between whether the end releases are applied to the theoretical eccentric axis (away from the element) (1) or on the physical axis (at section’s center of gravity) (2).
For concrete elements, there is an option to consider the eccentricity caused by cracking in the Cracked section analysis (special type of analysis) (3).
Then we can select if both ends of the element are the same, or if we want to have different conditions on Start and End of the element (4).
We can also select the Releases’ stiffnesses for the selected end (either Start, End or both ends) (5).
And finally, we can set an eccentricity either by manually typing in the number or clicking on the green dots in the icon on the right (6).
For loads, the settings of eccentricity are in the Default settings dialogue of the relevant load:
Figure 2. Load eccentricity settings
3. On to the examples
In the examples, we use a 4m long beam, section shape HEA200, material S355. It has no self-weight applied. It has a uniformly distributed force of 10kN/m and an axial force of 20kN. We use elastic 1st order analysis. We show both the result of the bar model and next to it a theoretical illustration of what it could look like in real life (in shell model).
Figure 3. Beam loading schema
In the examples, we use the simply supported analytical schema. The stiffnesses of the supports are as follows:
Figure 4. Beam support stiffnesses
Example 1: Centric beam with centric load (reference).
In the first example, we use the centric beam with the centric loada (the so-called “normal” case). Here you can expect the results be as for any simply supported beam. This is a reference case that we can compare against.
Figure 5. Centric beam, translational deformations
Figure 6. Centric beam, reactions
Figure 7. Centric beam, internal forces
Figure 8. Centric beam, all displacements
The theoretical illustrative reference shell model would look like this
Figure 9. Centric beam, illustrative shell model
Figure 10. Centric beam, illustrative shell model's translational deformations
Example 2: Centric beam with eccentric load
If we would turn on the eccentricity for the loads, then it would look exactly like the reference example 1 above. Since there is no eccentricity set for the beam, the eccentric load option has no effect and the load acts as if it is centric.
Example 3: Eccentric beam with load applied onto physical axis
In this example, we add an eccentricity of 200mm to the beam. The section settings look like this:
Figure 11. Beam eccentricity used in the examples
The load will be applied to physical axis (center of gravity). This means that we DO NOT check the box “Apply on the eccentric axis/surface” option. The load will be centric to the beam itself, but it will actually be eccentric to the supports (since the beam is also eccentric to the supports). It is better to visualize this when looking at the shell model below.
Here are the results for the beam calculations
Figure 12. Eccentric beam - centric load, translational deformations
Figure 13. Eccentric beam - centric load, reactions
Figure 14. Eccentric beam - centric load, internal forces
Figure 15. Eccentric beam - centric load, all displacements
The theoretical illustrative reference shell model would look like this
Figure 16. Eccentric beam - centric load, illustrative shell model
Figure 17. Eccentric beam - centric load, illustrative shell model's translational deformations
With this illustrative shell model, it is easy to see why the beam had torsion Mt or why there is a contant Mz’ moment in the beam. Also, all the displacements that we saw on the beam’s results are visible here.
Example 4: Eccentric beam with eccentric load
In this example, we use the same eccentric beam from the previous example, but both of the loads will be applied to eccentric axis this time. This means that we CHECK the box “Apply on the eccentric axis/surface” option.
Figure 18. Eccentric beam - ecccentric load, translational deformations
Figure 19. Eccentric beam - ecccentric load, reactions
Figure 20. Eccentric beam - ecccentric load, internal forces
Figure 21. Eccentric beam - ecccentric load, all displacements
The theoretical illustrative reference shell model would look like this
Figure 22. Eccentric beam - ecccentric load, illustrative shell model
Figure 23. Eccentric beam - ecccentric load, illustrative shell model's translational deformations
With this illustrative shell model, it is again easy to see why the beam had variable torsion Mt and how the beam is twisted in the middle. Also, all the other displacements that we saw on the beam’s results are visible here.