Steel bar shell model

1. General

In finite element analysis beams and columns are usually analyzed using bar elements. This is often the best approach. It allows to find the deformations, internal forces and stresses quickly and do the needed design calculations based on formulas and these previously found results. This approach is much like we would do in hand-calculation. Sometimes this is not enough and more precision is needed.

In FEM-Design, we can do the bar element analysis, but we can also convert some bar elements into shell elements. This means that we no longer calculate the whole beam as one bar, but instead we have a separate shell elements for flanges and webs.

This kind of shell model gives us better accuracy in some situations – especially with stability of parts of the beam and utilization checks like flexural or lateral torsional buckling. Moreover, it allows some special cases which are not possible with bar model: mainly modelling of holes and stiffeners in specific locations.

The shell model is available only for steel bars. Also, it can be used with different section shapes but not for all shapes. Please refer to this article about section shapes for more information: Steel Design sections


2. Definition

To define the beam or column with shell model, we first need to define the bar model. Make sure that the element has the correct material set, because the shell model takes all it’s materials from the bar. In this example, we use the HEA profile beam, since it is possible to convert that shape to shell model.

Open the beam tool and define the beam as a normal bar. 
Figure 1. Beam bar model to shell model conversion


Then select “Analytical model” tool from the beam toolbar (number 1 in Figure 1) and use the “Shell model” option right next to it (number 2 in Figure 1). Now, we need to select the beam we want to convert and right click on it. FEM-Design will convert the bar element to a series of shell elements that represent the original shape. We had the option “Generate fictitious bars to the boundary of shell model” turned on, so we got some fictitious bars made at both ends of the beam. These will guarantee continuous connection to other objects like point supports and point loads.

The shell model is now complete. The shells are made of “plates” not “walls”. We cannot manually change the plates properties, though. 

Note. The stiffness of the fictitious bars can be changed with “Fictitious bar” tool.
Note. We can convert the shell model back to the bar model with the “Bar model” option (number 2 in Figure 2).

Figure 2. Turn shell model back to bar model
Note. Everything mentioned about the beam also applies to columns.



3. Holes, supports, stiffeners and loads

We can cut holes into the shell model as we would in every other plate element. Easiest way is to use the tools on “Modify region” toolbar. Below is a picture about cutting a hole in the web of the beam for example:  
Figure 3. Cutting holes into shell model


When adding supports to the shell model, we can use point supports, line supports or even surface supports. It depends on the actual model and the results we are looking for.

Note. We can also add stiffeners to the shell model with regular plate tool. Make sure that the stiffeners are made from steel and the thickness is correct. We cannot design the stiffeners, but they will affect the buckling shapes of the beam!

Figure 4. Beam with stiffeners made from plates

Loads can be applied to the shell model as line or point load (as we would do for a regular bar model), but we can choose where the load is acting on – whether it is the top or bottom part of the beam. Also, the load can be applied as a surface load to simulate the uniform loading on the flange, for example.

Figure 5. Different loading options on a shell model


4. Mesh and analysis results

Since the shell model is made from shells, then there will be finite element mesh generated on it before the analysis. As with any plate, the mesh can be adjusted and modified to our liking. 
Figure 6. Finite element mesh on a shell model


Standard analysis can be made to obtain the deformation, internal forces and stresses in the shells. Also, Steel design can be made, but the special “Steel bar, shell model” function needs to be selected (number 2 in Figure 7).

Figure 7. Design has a special function for shell model


Here are some results for this beam after the analysis: 
Figure 8. Analysis results like deformation and stresses


After the design check, the utilization of the shell model can be shown and there is also possibility to see the detailed results of the design calculations. 
Figure 9. Utilization view and detailed results of the design calculations.

S
Stojan is the author of this solution article.

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