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

1. TALAT Lecture 2301
Design of Members
Torsion
Example 8.3 : Torsion constants for deck profile
3 pages
Advanced Level
prepared by Torsten Höglund, Royal Institute of Technology, Stockholm
Date of Issue: 1999
 EAA - European Aluminium Association
TALAT 2301 – Example 8.3 1

2. Example 8.3. Torsion constants for deck profile
This example is a simplification of an aluminium profile used in a bridge deck.
0 110.5 1.5 6.5
Nodes,
co-ordinates, 1 100 1.5 6.5
thickness
2 119.5 31.75 5.25
3 119.5 45.75 11
4 102.5 45.75 6.5
5 102.5 45.75 5
6 119.5 45.75 6.5
7 119.5 31.75 11
8 100 1.5 5.25
i 9 y 85.5 . mm z 1.5 . mm t 6.5 . mm
10 82.5 0 5
11 82.5 0 3.5
12 85.5 1.5 5
13 100 1.5 6.5
14 40 45.75 3.5
15 0 0 3.5
16 40 45.75 3.5
17 100 1.5 3.5
18 110.5 1.5 6.5
60
40
20
0
20
150 100 50 0 50 100 150
TALAT 2301 – Example 8.3 2

3. TALAT 2301 – Example 8.3 3

4. Nodes i 1 .. rows ( y ) 1
rows ( y ) 1 = 18
Area of cross
ti .
section 2 2
dAi yi yi 1 zi zi 1
elements
Cross rows ( y ) 1
section
A = 3.855 . 10 mm
3 2
area A dAi
i =1
First rows ( y ) 1
dAi Sy
moment Sy zi zi 1 . z gc
of area. 2 A
Gravity centre i =1
z gc = 24.932 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 = 1.468 . 10 mm
6 4
First rows ( y ) 1
dAi Sz
moment Sz yi yi 1 . y gc
of area. 2 A
Gravity centre i =1
y gc = 0 m
Second rows ( y ) 1
dAi
yi . yi 1 . A . y gc
moment 2 2 2
Iz yi yi 1 Iz Iz
of area 3
i =1
I z = 2.33 . 10 mm
7 4
When calculating torsion constants the interior branches are omitted
13
Area within
0.5 . yi yi 1 . zi A v = 1.039 . 10 mm
4 2
mid-line Av zi 1
i =2
13 2 2
yi yi 1 zi zi 1
Sum of l/t Dn if t i > 0 . mm , ,0 Dn = 116.407
ti
i =2
4 .A v
2
Torsion
I v = 3.711 . 10 mm
6 4
constant Iv
Dn
I vc 3.713 . 10 . mm
6 4
Correct value incl. branches:
i 0 .. 13 tm if t i > 0 . mm , t i , 100 . mm
Torsion i
resistance
2 . A v . min t m W v = 7.275 . 10 mm
4 3
Wv min t m = 3.5 mm
TALAT 2301 – Example 8.3 4