D12.A.6.6 Angle profile type RA (reverse angle)

For angle profiles the von Mises check is checked at 8 stress points as shown in figure below.

Axes y and z are principal axes.

Axes u and w are local axes.

Cross section properties

where

A_x , I_x , I_y , and I_z	=	taken from the STAAD.Pro database
A_y	=	$\frac{2}{3} h t$ , applied in STAAD.Pro print option `PRINT MEMBER STRESSES`
A_z	=	$\frac{2}{3} b t$ (Az is not used in code checks)
τ_y	=	$\frac{F_{x}}{A_{y}}$
τ_z	=	$\frac{F_{x}}{A_{z}}$
h₂	=	0.5h₁ = t
f	=	h₁e
d	=	$\frac{t h_{1} h_{2} + 0.5 t^{2} b}{A_{x}}$
g	=	$\frac{t^{2} h_{1} + t b^{2}}{2 A_{x}}$
I_u	=	$\frac{h_{1} t^{3}}{12} + h t k^{2} + \frac{t b^{3}}{12} + t b {(\frac{b}{2} - g)}^{2}$
I_w	=	$\frac{t h_{1}^{3}}{12} + h_{1} t {(h_{2} - d)}^{2} + \frac{b t^{3}}{12} + b t {(d - \frac{t}{2})}^{2}$
I_wu	=	$\frac{(d - \frac{1}{2}) t}{2} (g^{2} - j^{2}) - \frac{k t}{2} (e^{2} - f^{2})$
α	=	$0.5 \tan^{- 1} (\frac{2 I_{u w}}{I_{u} + I_{w}})$

The section forces from the STAAD.Pro analysis are about the principle axis y and z.

The second moment of area (Ty L TZ):

T_y = A Z

T_z = A Y

Point No	σ_x	σ_by	σ_bz	τ_x	τ_y	τ_z
1	$\frac{F_{x}}{A_{x}}$	$- \frac{M_{y} Z 1}{I_{y}}$	$- \frac{M_{z} Y 1}{I_{z}}$	$\frac{M_{x}}{I_{x}} t$	0	0
2		0	$- \frac{M_{z} Y 2}{I_{z}}$		$\frac{F_{y} T_{z}}{I_{z} t}$	$\frac{F_{z} T_{y}}{I_{y} t}$
3		$\frac{M_{y} Z 3}{I_{y}}$	$- \frac{M_{z} Y 3}{I_{z}}$
4		$\frac{M_{y} Z 4}{I_{y}}$	$- \frac{M_{z} Y 4}{I_{z}}$
5		$\frac{M_{y} Z 5}{I_{y}}$	$\frac{M_{z} Y 5}{I_{z}}$
6		0	$\frac{M_{z} Y 6}{I_{z}}$
7		$- \frac{M_{y} Z 7}{I_{y}}$	$\frac{M_{z} Y 7}{I_{z}}$
8		$\frac{M_{y} Z 8}{I_{y}}$	0		0	0

An additional torsional moment is calculated based on:

M_T = F_y Z4

M_T = F_z Y4

This torsion moment is included in M_x if F_y and F_Z exist.

Note: The order of the joint numbers in the member incidence command specifies the direction of the local x-axis.