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
The warping restraint of the end plate results from the torsional stiffness of the connected plate.
| Cω | Warping spring |
| G | Shear modulus |
| b | Width of the end plate |
| h | Height of the end plate |
| t | Thickness of the 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 | Warping spring |
| G | Shear modulus |
| hm | Distance between center planes of the beam flanges |
| Am | Area enclosed by center line |
| li | Side length |
| ti | Plate thickness |
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 | Warping spring |
| G | Shear modulus |
| IT | Torsion moment of inertia |
| hm | Distance between the flange center lines |
Cantilevered Portion
| Cω | Warping spring |
| G | Shear modulus |
| IT | Torsional moment of inertia of the extended beam |
| λ | √[(G ⋅ IT) / (E ⋅ Iω)] |
| lk | Excess length |
| Iω | Warping resistance of the extended beam |
