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D12.A.6.5 Channel profile

For channel profiles the von Mises stress is checked at 6 locations as shown in the figure below.

Cross section properties

where

A_x , S_y , S_z , I_x , I_y , and I_z	=	taken from the STAAD.Pro database
A_y	=	2ht, similar as for wide flange profiles
A_z	=	2×(2/3)bt (Ay and Az are not used in code checks)
e	=	b×(I_y/S_y)
x	=	h-t
y	=	b-t/2
C_w	=	$\frac{x^{2} y^{3} t}{12} \frac{(2 x t + 3 y t)}{(x t + 6 y t)}$ , ref.[4] tab. 21, case 1

Stress calculations at selected stress points

h₁ = h/2 - t

h₂ = h/2 - t/2

b₁ = e - t

b₂ = e - t/2

Point No	σ_x	σ_by	σ_bz	τ_x	τ_y	τ_z
1	$\frac{F_{x}}{A_{x}}$	$\frac{M_{y}}{I_{y}} (b - e)$	$\frac{M_{z}}{I_{z}} h_{2}$	$\frac{M_{x}}{I_{x}} t$	0	0
2		0	$\frac{M_{z}}{I_{z}} h_{2}$	$\frac{M_{x}}{I_{x}} t$	$\frac{F_{y}}{I_{z}} \frac{(b - e) t h_{2}}{t}$	$\frac{F_{z}}{I_{y}} \frac{0.5 {(b - e)}^{2} t}{t}$
3		$\frac{M_{y}}{I_{y}} b_{1}$	$\frac{M_{z}}{I_{z}} h_{2}$	$\frac{M_{x}}{I_{x}} t$	$\frac{F_{y}}{I_{z}} \frac{(b - t) t h_{2}}{t}$	$\frac{F_{z}}{I_{y}} \frac{(b - t) t [0.5 (b + t) - e]}{t}$
4		$\frac{M_{y}}{I_{y}} b_{2}$	$\frac{M_{z}}{I_{z}} h_{2}$	$\frac{M_{x}}{I_{x}} t$	$\frac{F_{y}}{I_{z}} \frac{(b - 0.5 t) t h_{2}}{t}$	$\frac{F_{z}}{I_{y}} \frac{(b - \frac{t}{2}) t [0.5 (b + \frac{t}{2}) - e]}{t}$
5		$\frac{M_{y}}{I_{y}} b_{2}$	$\frac{M_{z}}{I_{z}} h_{1}$	$\frac{M_{x}}{I_{x}} t$	$\frac{F_{y}}{I_{z}} \frac{b t h_{2}}{t}$	$\frac{F_{z}}{I_{y}} \frac{b t (\frac{b}{2} - e)}{t}$
6		$\frac{M_{y}}{I_{y}} b_{2}$	0	$\frac{M_{x}}{I_{x}} t$	$\frac{F_{y}}{I_{z}} \frac{b t h_{2} + 0.5 t h_{1}^{2}}{t}$	0

The general stress formulation is given in sec. 5.2.f