Talat Lecture 2301: Design Of Members Example 8.3: Torsion Constants For Deck Profile
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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
Example 8.3. Torsion constants for deck profile This example is a simplification of an aluminium profile used in a bridge deck.
Nodes, co-ordinates, thickness
i
0
110.5
1.5
6.5
1
100
1.5
6.5
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 y
9
85.5
5.25
1.5 . mm z
. mm
1.5
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
TALAT 2301 – Example 8.3
50
0
2
50
100
150
TALAT 2301 – Example 8.3
3
Nodes
i
Area of cross section elements
dAi
Cross section area
1 .. rows ( y ) ti .
1
yi
2
yi 1
rows ( y )
1 = 18
rows ( y ) zi
zi 1
2
1 A = 3.855 . 10 mm 3
dAi
A
2
i =1 First moment of area. Gravity centre
Second moment of area
First moment of area. Gravity centre
Second moment of area
rows ( y )
1
dAi zi 1 . 2
zi
Sy
z gc
i =1
Sy A
z gc = 24.932 mm
rows ( y )
1
Iy
zi
2
zi 1
2
dAi zi . zi 1 . 3
Iy
i =1
Iy
A . z gc
2
I y = 1.468 . 10 mm 6
rows ( y )
1
dAi yi 1 . 2
yi
Sz
y gc
i =1
4
Sz A
y gc = 0 m
rows ( y )
1 yi
Iz
2
yi 1
2
dAi yi . yi 1 . 3
Iz
i =1
Iz
A . y gc
2
I z = 2.33 . 10 mm 7
4
When calculating torsion constants the interior branches are omitted 13 Area within mid-line
0.5 . yi
Av
yi 1 . zi
A v = 1.039 . 10 mm 4
zi 1
2
i =2 13 Sum of l/t
if t i > 0 . mm ,
Dn i =2
Torsion constant
4 .A v
Iv
yi
yi 1
2
zi
zi 1
ti
i
Wv
Dn = 116.407
I v = 3.711 . 10 mm 6
Dn
0 .. 13
,0
2 4
6 4 I vc 3.713 . 10 . mm
Correct value incl. branches:
Torsion resistance
2
tm
i
2 . A v . min t m
TALAT 2301 – Example 8.3
if t i > 0 . mm , t i , 100 . mm min t m = 3.5 mm
4
W v = 7.275 . 10 mm 4
3
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
Example 8.3. Torsion constants for deck profile This example is a simplification of an aluminium profile used in a bridge deck.
Nodes, co-ordinates, thickness
i
0
110.5
1.5
6.5
1
100
1.5
6.5
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 y
9
85.5
5.25
1.5 . mm z
. mm
1.5
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
TALAT 2301 – Example 8.3
50
0
2
50
100
150
TALAT 2301 – Example 8.3
3
Nodes
i
Area of cross section elements
dAi
Cross section area
1 .. rows ( y ) ti .
1
yi
2
yi 1
rows ( y )
1 = 18
rows ( y ) zi
zi 1
2
1 A = 3.855 . 10 mm 3
dAi
A
2
i =1 First moment of area. Gravity centre
Second moment of area
First moment of area. Gravity centre
Second moment of area
rows ( y )
1
dAi zi 1 . 2
zi
Sy
z gc
i =1
Sy A
z gc = 24.932 mm
rows ( y )
1
Iy
zi
2
zi 1
2
dAi zi . zi 1 . 3
Iy
i =1
Iy
A . z gc
2
I y = 1.468 . 10 mm 6
rows ( y )
1
dAi yi 1 . 2
yi
Sz
y gc
i =1
4
Sz A
y gc = 0 m
rows ( y )
1 yi
Iz
2
yi 1
2
dAi yi . yi 1 . 3
Iz
i =1
Iz
A . y gc
2
I z = 2.33 . 10 mm 7
4
When calculating torsion constants the interior branches are omitted 13 Area within mid-line
0.5 . yi
Av
yi 1 . zi
A v = 1.039 . 10 mm 4
zi 1
2
i =2 13 Sum of l/t
if t i > 0 . mm ,
Dn i =2
Torsion constant
4 .A v
Iv
yi
yi 1
2
zi
zi 1
ti
i
Wv
Dn = 116.407
I v = 3.711 . 10 mm 6
Dn
0 .. 13
,0
2 4
6 4 I vc 3.713 . 10 . mm
Correct value incl. branches:
Torsion resistance
2
tm
i
2 . A v . min t m
TALAT 2301 – Example 8.3
if t i > 0 . mm , t i , 100 . mm min t m = 3.5 mm
4
W v = 7.275 . 10 mm 4
3
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