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
 Ax , Ix , Iy , and Iz = taken from the STAAD.Pro database Ay = $2 3 h t$, applied in STAAD.Pro print option PRINT MEMBER STRESSES Az = $2 3 b t$, Az are not used in code checks τy = $F x A y$ τz = $F x A z$ h2 = 0.5h1 = t f = h1e d = $t h 1 h 2 + 0.5 t 2 b A x$ g = $t 2 h 1 + t b 2 2 A x$ Iu = $h 1 t 3 12 + h t k 2 + t b 3 12 + t b ( b 2 − g ) 2$ Iw = $t h 1 3 12 + h 1 t ( h 2 − d ) 2 + b t 3 12 + b t ( d − t 2 ) 2$ Iwu = $( d − 1 2 ) t 2 ( g 2 − j 2 ) − k t 2 ( e 2 − f 2 )$ α = $0.5 tan − 1 ( 2 I u w I u + I w ) ⁡$

Section forces

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

The second moment of area (Ty L TZ):

Ty = A Z

Tz = A Y

Stress calculation at selected stress points

Point No σx σby σbz τx τy τz
1 $F x A x$ $− M y Z 1 I y$ $− M z Y 1 I z$ $M x I x t$ 0 0
2 " 0 $− M z Y 2 I z$ " $F y T z I z t$ $F z T y I y t$
3 " $M y Z 3 I y$ $− M z Y 3 I z$ " " "
4 " $M y Z 4 I y$ $− M z Y 4 I z$ " " "
5 " $M y Z 5 I y$ $M z Y 5 I z$ " " "
6 " 0 $M z Y 6 I z$ " " "
7 " $− M y Z 7 I y$ $M z Y 7 I z$ " " "
8 " $M y Z 8 I y$ 0 " 0 0

An additional torsional moment is calculated based on:

MT = Fy Z4

MT = Fz Y4

This torsion moment is included in Mx if Fy and FZ exist.

Beta-rotation of equal & unequal legged angles

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