This example provides calculations on torsion of members based on Eurocode 9.

1. TALAT Lecture 2301
Design of Members
Torsion
Example 8.2 : Torsion constants for hollow cross
section
3 pages
Advanced Level
prepared by Torsten Höglund, Royal Institute of Technology, Stockholm
Date of Issue: 1999
 EAA - European Aluminium Association
TALAT 2301 – Example 8.2 1

2. Example 8.2. Torsion constants for hollow cross section
a) Polygon
b
Half width b 50 . mm Half width of a a = 20.711 mm
flat parts
Thickness s 6 . mm 1 2
Nodes no., 0 b a s
co-ordinates,
1 a b s
thickness
2 a b s
3 b a s
i 4 y b z a t s
5 a b s
6 a b s
7 b a s
8 b a s 50
0
Nodes i 1 .. rows ( y ) 1
z 0
0
Area of cross mm
ti .
section 2 2
dAi yi yi 1 zi zi 1
elements
50
Cross rows ( y ) 1
section 50 0 50
area A dAi y
i =1 mm
First rows ( y ) 1
dAi Sy
moment Sy zi zi 1 . z gc
of area. 2 A
i =1
Gravity centre z gc = 1.704 . 10
15
mm
Second rows ( y ) 1
dAi
zi . zi 1 . A . z gc
moment 2 2 2
Iy zi zi 1 Iy Iy
of area 3
i =1
I y = 2.627 . 10 mm
6 4
rows ( y ) 1
Area within
0.5 . yi yi 1 . zi A v = 8.284 . 10 mm
3 2
mid-line Av zi 1
Check:
i =1
( 2 .b ) 2 .( b a ) = 8.284 . 10 mm
2 2 3 2
Sum of l/t rows ( y ) 1
4 .A v
2 2 2
yi yi 1 zi zi 1
Torsion Dn Dn = 55.228 Iv
ti Dn
constant i =1
I v = 4.971 . 10 mm
6 4
Torsion
2 . A v . min ( t ) W v = 9.941 . 10 mm
4 3
resistance Wv min ( t ) = 6 mm
TALAT 2301 – Example 8.2 2

3. TALAT 2301 – Example 8.2 3

4. b) Symmetric hollow extrusion
Half width b 50 . mm
Indent c 10 . mm
Half width of a 20 . mm
flat parts
Thickness s 6 . mm
Nodes no.,
co-ordinates, 0 b a s
thickness
1 b c a s
2 a b c s
3 a b s
4 a b s
5 a b c s
6 b c a s
7 b a s
i 8 y b z a t s
9 b c a s
10 a b c s
11 a b s
12 a b s
13 a b c s 50
14 b c a s 0
15 b a s
z 0
16 b a s 0
mm
50
50 0 50
Nodes i 1 .. rows ( y ) 1 y
mm
rows ( y ) 1
Area within
0.5 . yi yi 1 . zi A v = 7.2 . 10 mm
3 2
mid-line Av zi 1
i =1
rows ( y ) 1 2 2
yi yi 1 zi zi 1
Sum of l/t Dn Dn = 58.856
ti
i =1
4 .A v
2
Torsion
I v = 3.523 . 10 mm
6 4
constant Iv
Dn
2 . A v . min ( t ) W v = 8.64 . 10 mm
4 3
Torsion Wv min ( t ) = 6 mm
resistance
TALAT 2301 – Example 8.2 4