D14.C.6.4 Torsional or Torsional-Flexural Buckling

Per section 13.3.2, the factored compressive resistance, C_r , of asymmetric, singly symmetric, and cruciform or other bisymmetric sections not covered under 13.3.1 shall be computed using the expressions given in 13.3.1 with a value of n = 1.34 and the value of f_e taken as lesser of F_ex and F_eyz for single symmetric section, with the y axis taken as the axis of symmetry.

f_{e y z} = \frac{f_{e y} + f_{e z}}{2 Ω} [1 - \sqrt{1 - \frac{4 f_{e y} f_{e z} Ω}{{(f_{e y} + f_{e z})}^{2}}}]

where

f_ey	=	$\frac{π^{2} E}{{(\frac{K_{y} L_{y}}{r_{y}})}^{2}}$
f_ez	=	$(\frac{π^{2} E C_{w}}{K_{Z}^{2} L_{Z}^{2}} + G J) \frac{1}{A {\bar{r}}_{0}^{2}}$
Ω	=	$1 - (\frac{x_{0}^{2} + y_{0}^{2}}{{\bar{r}}_{0}^{2}})$
x₀ ,y₀	=	= the principal coordinates of the shear center with respect to the centroid of the cross-section.
${\bar{r}}_{0}^{2}$	=	$= x_{0}^{2} + y_{0}^{2} + r_{x}^{2} + r_{y}^{2}$

For asymmetric sections, f_e is the smallest root of:

(f_{e} - f_{e x}) (f_{e} - f_{e y}) (f_{e} - f_{e z}) - f_{e}^{2} (f_{e} - f_{e y}) {(\frac{x_{0}}{{\bar{r}}_{0}})}^{2} - f_{e}^{2} (f_{e} - f_{e x}) {(\frac{y_{0}}{{\bar{r}}_{0}})}^{2} = 0

where

f_ex

\frac{π^{2} E}{{(\frac{K_{x} L_{x}}{r_{x}})}^{2}}

The parameters KY, LY, KZ, and LZ are applicable for this.