D12.A.6.1 Double symmetric wide flange profile

The von Mises stress is checked at four stress points as shown in figure below.

Stress points checked for a wide flange section

Section Properties

A_x , I_x , I_y, and I_z are taken from STAAD.Pro database
A_y = h × s Applied in STAAD.Pro print option PRINT MEMBER STRESSES

A_z = (2/3)· b · t · 2

τ_y = F_y/A_y

τ_z = F_z/A_z

A_y and A_z are not used in the code check
$C_{w} = \frac{{(h - t)}^{2} b^{3} t}{24}$ ref. NS app. C3

T_y = dA × z

T_z = dA × y

Stress calculation

General stresses are calculated as:

σ = σ_{x} + σ_{b y} + σ_{b z} = \frac{F_{x}}{A_{x}} + \frac{M_{y}}{I_{y}} z + \frac{M_{z}}{I_{z}} y

τ = τ_{x} + τ_{y} + τ_{z} = \frac{M_{x}}{I_{x}} c + \frac{V_{y} T_{z}}{I_{z} t} + \frac{V_{z} T_{y}}{I_{y} t}

Where the component stresses are calculated as shown in the following table:

Table 1. Stress calculations at selected stress points for a wide flange section.
h₁ = ½(h - 2 t)

h₂ = ½ (h - t)
Point No	σ_x	σ_by	σ_bz	τ_x	τ_y	τ_z
1	$\frac{F_{x}}{A_{x}}$	$\frac{M_{y}}{I_{y}} \frac{b}{2}$	$\frac{M_{z}}{I_{z}} \frac{b}{2}$	$\frac{M_{x}}{I_{x}} t$	0	0
2		0	$\frac{M_{z}}{I_{z}} \frac{b}{2}$	$\frac{M_{x}}{I_{x}} t$	$\frac{F_{y}}{I_{z}} \frac{b t h_{2}}{2 t}$	$\frac{F_{z}}{I_{y}} \frac{t b^{2}}{8 t}$
3		0	$\frac{M_{z}}{I_{z}} h_{1}$	$\frac{M_{x}}{I_{x}} s$	$\frac{F_{y}}{I_{z}} \frac{b t h_{2}}{s}$	0
4		0	0	$\frac{M_{x}}{I_{x}} s$	$\frac{F_{y}}{I_{z}} \frac{(b t h_{2} + 0.5 h_{1}^{2} s)}{s}$	0

In general wide flange profiles are not suitable for large torsional moments. The reported torsional stresses are indicative only. For members with major torsional stresses a separate evaluation has to be carried out. Actual torsional stress distribution is largely dependent on surface curvature at stress point and warping resistance.