Averaging strips

 

This functionality provides automatic averaging of peak results around defined points or along defined line strips on slabs. The users can define several styles how to calculate the averaged values. The averaging can be applied to internal forces on slabs and to required reinforcement areas used in the design of reinforcement in concrete slabs.

The averaging algorithm uses only the FE nodes that are located inside the averaging strip. This may cause certain inaccuracies especially in the combination with larger finite elements. Therefore, it is recommended to redefine mesh or define internal edges along the averaging strips. This ensures that finite element nodes are generated along the edge of the averaging strip, which may significantly improve the accuracy.

Averaging may be calculated in one or both directions:

Longitudinal

The averaging is done along the defined strip. We can imagine that the strip represents a 1D member and we want the program to smooth the distribution of the result along that 1D member.

Perpendicular

The averaging is performed in the direction that is perpendicular to the length of the strip. This option is for special purposes only.

Both

The averaging is made in both directions. Again, this option is for special purposes only, e.g. heads of columns.

None

No averaging is made. This option may be useful if one (or several) defined averaging strip(s) should be temporarily ignored while other strips are still required to be used.

We can demonstrate the functionality on a simple example. Let’s create a 4x4 meters concrete slab with thickness of 200mm, made of concrete C20/25. It will be supported according to the picture and subject to self weight. The mesh size is set to 1 meter. Two meter wide averaging strip was input in the Y direction with the averaging direction set to ‘Perpendicular’.

Non-averaged result of moment my with location parameter set to In nodes, no avg.

Results of moment my averaged with averaging strip, with location parameter set to In nodes, no avg.

Manual verification

Create sections perpendicular to the inputted averaging direction. In this example, the averaging was set to ‘perpendicular’ => create sections in longitudinal direction.

  • 2D section A is input just outside the strip from (0;3,001) to (4;3,001)
  • 2D section B is input just inside the strip from (0;2,999) to (4;2,999)
  • 2D section C is input in the middle of the slab from (0; 2) to (4;2)

Non averaged result of moment my on 2D sections with location parameter set to In nodes, no avg. Parameter course is set to Precise possibility.

Non averaged result of moment my on 2D sections with location parameter set to In nodes, no avg. Parameter course changed to Uniform possibility.

The conclusion is that in 2D section A the moment my has value -1,38 KNm, in 2D section B -4,45 KNm and in 2D section C -7 KNm.

Numerical results of moment my averaged with averaging strip, with location parameter set to In nodes, no avg.

Conclusion

Now if we compare this averaged numerical results in mesh nodes and the non averaged results on 2D sections, we come to the conclusion that the values are equal.

Basic size of the averaging strip should be, in general, sum of the width of the support and thickness of the slab doubled. Nevertheless, the final size of the averaging strip should be always checked by an experienced engineer.

Jiří Porada

01/06/2012