# Calculation of warping springs for consideration in the lateral -torsional buckling analysis for open cross -sections

## Technical Article on the Topic Structural Analysis Using Dlubal Software

### Technical Article

In the case of open cross -sections, the torsional load is removed mainly via secondary torsion, since the St. Venant torsional stiffness is low compared to the warping stiffness. Therefore, warping stiffeners in the cross -section are particularly interesting for the lateral -torsional buckling analysis, as they can significantly reduce the rotation. For this, end plates or welded stiffeners and sections are suitable.

#### Calculation of the warp spring

If a warping stress is applied, this corresponds to the complete restraint of the cross -section warping, for example via a rigid end plate. In reality, however, this full restraint is usually not given because the end plates are not infinitely rigid, but also deformable. When entering the nodal supports, the design modules for steel and aluminum structures allow for a direct calculation of the warping springs from the variants presented below according to [1] .

#### End plate

The warping restraint of the end plate results from the torsional stiffness of the connected plate.

$$Cω = 13 · G · b · h · t³$$

 G Shear modulus b width of end plate

#### Channel and angle sections

The warping restraint by torsional stiffness transverse bulkheads is significantly greater than by end plates and beam overhang due to the higher torsional stiffness. U- or L-stiffeners welded on one side together with the web form a box girder; if arranged on both sides, a box girder with larger dimensions results.

$$Cω = G · hm · 4 · Am2∑liti$$

#### Connecting column

The warping restraint by a connected column results from the torsional stiffness of the column cross -section. The prerequisite for its effectiveness is the arrangement of stiffeners as an extension of the flanges in the column.

$$Cω = G · IT · hm$$

#### Cantilevered portion

$$Cω = G · IT · 1λ · tan h (λ · lk)$$

#### Dipl.-Ing. Oliver Müller

Product Engineering & Customer Support

Mr. Müller is responsible for the development of the add-on modules for steel structures and provides technical support for our customers.

#### Reference

 [1] Petersen, C.: Statik und Stabilität der Baukonstruktionen, 2. Auflage. Wiesbaden: Vieweg, 1982

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• Updated 27 April 2021

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