31 July 2019

FAQ 003376 EN

# Which formula is used for the calculation of the elastic torsional buckling force for torsional buckling Ncr,T in RF‑/STEEL EC3?

The elastic torsional buckling force for torsional buckling Ncr,T is calculated as follows:

${\mathrm N}_{\mathrm{cr},\mathrm T}\;=\frac1{{\mathrm i}_{\mathrm M}^2}\;\cdot\;\left(\frac{\mathrm\pi^2\;\cdot\;\mathrm E\;\cdot\;{\mathrm I}_{\mathrm w}}{{\mathrm L}_{\mathrm T}^2}\;+\;\mathrm G\;\cdot\;{\mathrm I}_{\mathrm t}\right)$

${\mathrm i}_{\mathrm M}\;=\;\sqrt{{\mathrm i}_{\mathrm u}^2\;+\;{\mathrm i}_{\mathrm v}^2\;+\;{\mathrm u}_{\mathrm M}^2\;+\;{\mathrm v}_{\mathrm M}^2}$

where

 E is the modulus of elasticity, G is the shear modulus, Iw is the warping constant of cross-section, It is the torsional constant, iu, iv are the principal radii of gyration, um, vm are the coordinates the shear center in the principal axis system, LT is the torsional buckling length.

#### Reference

 [1] Roik, K.; Carl, J.; Lindner, J. (1972). Biegetorsionsprobleme gerader dünnwandiger Stäbe. Berlin: Ernst & Sohn.