Singularities in Design of Reinforced Concrete Surfaces

Technical Article

Singularities occur in a limited area due to the concentration of the stress-dependent result values. They are conditioned by the FEA methodology. In theory, the stiffness and/or the stress in an infinite size concentrate on an infinitesimal small area.

In reality, the singularities or the resulting stress concentrations do not occur to the extent as they appear in the model. Basically, a result evaluation in singularity locations is not reasonable. However, examining and questioning singularity is very reasonable as the singularity locations can indicate problems in the real model. A practical example in concrete design would be the analysis of a punching risk in the area of singularity locations.

In the case of concrete design in RFEM and RF‑CONCRETE, singularities often cause failed design.

Where can singularities occur?

  • Point-like supports or load introduction
  • Reentrant corners or corners of openings
  • Stiffness jumps (jump in plate thickness, for example)
  • Start and end of ribs
  • Start and end of line supports or walls

Detecting Singularities

Singularity locations can be identified in the FEA by refining the mesh at the corresponding location in the model using the FE mesh refinement. If the stress-dependent result value in the considered area increases, but the respective area decreases, it is very likely a singularity location.

Preventing Singularities

In RFEM and the reinforced concrete design with RF‑CONCRETE, the singularities and the accompanying design failure can be prevented in various ways.

Average Region

In RFEM, average regions are available that can be used to smooth the maximum result values or set to zero. An average region can be created by clicking the corresponding option under “Results” in the menu bar. When averaging, the basic region must be determined. For example, by using the option “Set internal forces to zero,” the cross‑section of a connected column can be used as the range (see Figure 01).

Integrated Surface

As an alternative to the average region with the column cross‑section dimensions, it is possible to model surfaces and integrate them to the existing surfaces. These surfaces are then excluded from the design in RF‑CONCRETE Surfaces (see Figure 01).

Figure 01 - Exemplary Display of Singularity and Countermeasure

The option of using the averaged internal forces or the internal forces set to zero must be activated in Details of RF‑CONCRETE Surfaces (see Figure 02).

Figure 02 - Activating Averaged Internal Forces in RF‑CONCRETE Surfaces

Both methods (average region and integrated surface) can be used for both columns and reentrant corners. In general, average regions are sufficient. However, the average regions do not have the desired effect for a nonlinear calculation as the internal forces can be rearranged during the calculation and new singularity effects may arise.

Design Method for Walls

When designing walls, singularities can occur due to the high axial forces, for example, due to singular supports. In addition, the design method can have a significant impact on the singularity effects or design failure. Therefore, it is recommended to deactivate the optimization of design internal forces in RF‑CONCRETE Surfaces in the case of walls (see Figure 03).

Figure 03 - Design Method in RF-CONCRETE Surfaces

Distributed Load Introduction

To avoid the singularity effects, concentrated or line loads can be converted to surface loads. This option can be found in the shortcut menu, for example (see Figure 04).

Figure 04 - Convert Nodal Load to Surface Load

Rounding Reentrant Corners

In the case of reentrant corners and corners at openings, it is possible to round the corner using the “Create Round or Angled Corner” function, if necessary. This function can be selected in the menu bar under “Tools.” However, many singularity effects can be sufficiently prevented by using averaged regions.


Preventing singularities on nodal and line supports is explained in this article.


[1]   Rombach, G. (2000). Anwendung der Finite-Elemente-Methode im Betonbau. Berlin: Wilhelm Ernst & Sohn.



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