Formulas: torsional and flexural-torsional buckling of single angles and members without slender elements

Formula 1

In addition, Section E4 applies to single angles with $b / t>0.71 \sqrt{E / F_{y}}$ , although there are no ASTM A36/A36M hot-rolled angles for which this applies; for angles with $F_{y}=50 \mathrm{ksi}(345 \mathrm{MPa})$ and greater, this section may apply.

b / t>0.71 \sqrt{E / F_{y}}

Formula 2

For doubly symmetric shapes, the geometric centroid and shear center coincide resulting in $x_{o}=y_{o}=0$ .

x_{o}=y_{o}=0

Equation C-E4-1

Bracing offset along the minor axis by an amount $a$ [see Figure C-E4.2(a)] as follows:

F_{e}=\omega\left[\frac{\pi^{2} E I_{y}\left(\frac{h_{o}^{2}}{4}+a^{2}\right)}{\left(L_{c z}\right)^{2}}+G J \frac{1}{A r_{o}^{2}}\right]

Equation C-E4-2

Bracing offset along the major axis by an amount $b$ [see Figure C-E4.2(b)] as fol- lows:

F_{e}=\omega\left[\frac{\pi^{2} E I_{y}}{\left(L_{c z}\right)^{2}}\left(\frac{h_{o}^{2}}{4}+\frac{I_{x}}{I_{y}} b^{2}\right)+G J\right] \frac{1}{A r_{o}^{2}}

where

the polar radius of gyration is given by the following expression:

Equation C-E4-3

where the polar radius of gyration is given by the following expression:

r_{o}^{2}=\left(r_{x}^{2}+r_{y}^{2}+a^{2}+b^{2}\right)

Found in

TORSIONAL AND FLEXURAL-TORSIONAL BUCKLING OF SINGLE ANGLES AND MEMBERS WITHOUT SLENDER ELEMENTS