Calculation of the Shear Stresses from Torsion and Lateral Force

The simplified approaches for determining the stresses in beams as a result of torsion and lateral force assume thin-walled profiles with a constant stress distribution across the section.

The method implemented in the InfoCAD program system calculates the distribution of the stresses across the section of any profile.

To determine the stressing as a result of St. Venant torsion, the differential equation of the warping function is solved, and to establish the stressing as a result of lateral force, the differential equation of the so-called shear warping is solved.

In the following, the stress distribution at the elastic limit moment is calculated and presented for an IPE 100 rolled section.

The limit stress of 240 MN/m² is reached at a torsional moment of Mt = 0.177 kNm.
The associated stress distribution over the section as well as the boundary stresses are illustrated.

The stress concentrations at the rounded inner corners and in the flange above the bar can be seen clearly.

When performing a simplified calculation for the same load, the result is a constant shear stress of only 146 MN/m². This corresponds to the stress that occurs in the central area of the flange sides. The limit moment of 0.291 kNm is approximately 64% higher than the actual value.

If you are interested in reading a more detailed account on this topic, we recommend, among others

Herr Prof. Dr.-Ing. habil. Werner Wagner and
Herr Prof. Dr.-Ing. habil. Friedich Gruttmann

and their contribution to the communications of the 'Institut für Baustatik' of the Universität Karlsruhe (TH)

http://www.bs.uni-karlsruhe.de/

Mitteilung (communication) 09/2002

W. Wagner, F. Gruttmann Genaue Berechnung der elastischen Grenzmomente von Walzprofilen bei Torsionsbelastung (Exact Calculation of the Elastic Limit Moment of Rolled Sections under Torsional Load)

or

Herr Prof. Dr.-Ing. Rolf Kindmann,
Lehrstuhl für Stahl- und Verbundbau der Ruhr-Universität Bochum (Professor for Steel and Composite Construction of the Ruhr-University, Bochum)

Stahlbau (Steel Construction) 75 (2006), Issue 5

Rolf Kindmann Neue Berechnungsformel für das IT von Walzprofilen und Berechnung der Schubspannungen (New Calculation Formula for IT of Rolled Sections and Calculation of the Shear Stresses)