D12.A.6.4 Tube profile

Tube sections are rectangular or quadratic hollow uniform profiles. Critical stress is checked at 5 locations as shown in figure below.

Section Properties

A_x , I_x , I_y , and I_z are taken from the STAAD.Pro database.

where

Ay	=	2ht, similar as for wide flange profiles, see Section 5.2
Az	=	2(2/3)bt; (Ay and Az are not used in code checks)
Cw	=	$\frac{b^{2} h^{2} t {(h - b)}^{2}}{24 (h + b)}$ ref. NS app. C3

h₁ = h/2 - t

h₂ = h/2 - t/2

b₁ = b/2 - t

b₂ = b/2 - t/2

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

The general stress formulation is given in sec. 5.2.