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000585

2021-02-15

Calculation of Warping Springs for Consideration in Lateral-Torsional Buckling Analysis for Open Cross-Sections

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 Warping 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

Warping Restraint via End Plate

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

C_{ω} = \frac{1}{3} \cdot G \cdot b \cdot h \cdot t ³

C_ω	Wölbfeder
G	Schubmodul
b	Breite der Stirnplatte
h	Höhe der Stirnplatte
t	Dicke der Stirnplatte

Warping Spring for Warping Restraint via End Plate

Channel and Angle Sections

Warping Restraint via Welded Channel Section

Warping Restraint via Welded Angle Section

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.

C_{ω} = G \cdot h_{m} \cdot \frac{4 \cdot A_{m}^{2}}{\sum \frac{l_{i}}{t_{i}}}

C_ω	Wölbfeder
G	Schubmodul
h_m	Abstand der Mittelebenen der Flansche des Trägers
A_m	Von der Mittellinie eingeschlossene Fläche
l_i	Seitenlänge
t_i	Blechdicke

Warping Spring for Warping Restraint via Welded Channel or Angle Section

Connecting Column

Warping Restraint via Connecting Column

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 \cdot I_{T} \cdot h_{m}

C_ω	Wölbfeder
G	Schubmodul
I_T	Torsionsträgheitsmoment
h_m	Abstand der Flanschmittellinien

Warping Spring for Warping Restraint via Connecting Column

Cantilevered Portion

Warping Restraint via Beam Cantilever

C_{ω} = G \cdot I_{T} \cdot \frac{1}{λ} \cdot \tan h (λ \cdot l_{k})

C_ω	Wölbfeder
G	Schubmodul
I_T	Torsionsträgheitsmoment des überstehenden Trägers
λ	√[(G ⋅ I_T) / (E ⋅ I_ω)]
l_k	Überstandslänge
I_ω	Wölbwiderstand des überstehenden Trägers

Warping Spring for Warping Restraint via Beam Cantilever

Knowledge Base

KB 000585 | Calculation of Warping Springs for Consideration in Lateral-Torsional Buckling Analysis ...

Links

Structural Analysis Software for Steel Structures

References

Petersen, C. (1982). Statik und Stabilität der Baukonstruktionen, (2nd ed.). Wiesbaden: Vieweg.

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