Document Ref:
SX023a-EN-EU
Sheet
1
of
9
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
Example: Calculation of effective section
properties for a cold-formed lipped channel
section in compression
This example deals with the effective properties calculation of a cold-
formed lipped channel section subjected to compression.
For practical design of light gauge sections to EN1993, designers will normally use software
or refer to manufacturers’ data. This example is presented for illustrative purposes
Basic Data
The dimensions of the cross-section and the material properties are:
Total
height
mm
200
=
h
Total width of upper flange
mm
74
1
=
b
Total width of bottom flange
mm
66
2
=
b
Total width of edge fold
mm
8
,
20
=
c
Internal
radius
mm
3
=
r
Nominal
thickness
mm
2
nom
=
t
Steel core thickness
mm
96
1,
t
=
Basic yield strength
2
yb
mm
N
350
=
f
Modulus of elasticity
2
mm
N
210000
=
E
Poisson’s
ratio
3
,
0
=
ν
Partial
factor
0
1
M0
,
=
γ
EN1993-1-3
§ 3.2.4
(3)
EN1993-1-3
§ 2
(3)
The dimensions of the section centre line are:
Web height
mm
198
2
200
nom
p
=
−
=
−
=
t
h
h
Width of upper flange
mm
72
2
74
nom
1
p1
=
−
=
−
=
t
b
b
Width of bottom flange
mm
64
2
66
nom
2
p2
=
−
=
−
=
t
b
b
Width of edge fold
mm
8
19
2
2
8
20
2
nom
p
,
,
t
c
c
=
−
=
−
=
Example: Calculation of effective section properties for a cold-formed lipped channel section in compression
Created on Friday, April 30, 2010
This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement
Document Ref:
SX023a-EN-EU
Sheet
2
of
9
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
Checking of geometrical proportions
The design method of EN1993-1-3 can be applied if the following conditions
are satisfied:
60
≤
t
b
60
75
,
37
96
,
1
74
1
<
=
=
t
b
– OK
50
≤
t
c
50
61
,
10
96
,
1
8
,
20
<
=
=
t
c
– OK
500
≤
t
h
500
04
,
102
96
,
1
200
<
=
=
t
h
– OK
EN1993-1-3
§ 5.2
In order to provide sufficient stiffness and to avoid primary buckling of the
stiffener itself, the size of stiffener should be within the following range:
6
,
0
2
,
0
≤
≤ b
c
28
,
0
74
8
,
20
1
=
=
b
c
6
,
0
28
,
0
2
,
0
<
<
– OK
32
,
0
66
8
,
20
2
=
=
b
c
6
,
0
32
,
0
2
,
0
<
<
– OK
The influence of rounding of the corners is neglected if:
5
t
r
≤
5
53
,
1
96
,
1
3
<
=
=
t
r
– OK
10
,
0
p
≤
b
r
10
,
0
04
,
0
72
3
1
p
<
=
=
b
r
– OK
10
,
0
05
,
0
64
3
2
p
<
=
=
b
r
– OK
EN1993-1-3
§ 5.1
(3)
Gross section properties
(
)
(
)
2
p
p2
p1
p
br
mm
732
198
64
72
8
,
19
2
96
,
1
2
=
+
+
+
×
×
=
+
+
+
=
h
b
b
c
t
A
Position of the centroidal axis with regard to the upper flange:
(
)
[
]
mm
88
,
96
2
2
2
br
2
p
2
p
p
p2
p
p
p
b1
=
+
+
+
−
=
A
t
c
h
h
b
c
h
c
z
Effective section properties of the flanges and lips in compression
The general (iterative) procedure is applied to calculate the effective
properties of the compressed flange and the lip (plane element with edge
stiffener). The calculation should be carried out in three steps:
EN1993-1-3
§ 5.5.3.2
Step 1:
Obtain an initial effective cross-section for the stiffeners using effective
widths of the flanges determined by assuming that the compressed flanges are
doubly supported, the stiffener gives full restraint (
∞
=
K
) and that design
strength is not reduced (
0
yb
Ed
com,
/
M
f
γ
σ
=
).
EN1993-1-3
§ 5.5.3.2
(3)
Example: Calculation of effective section properties for a cold-formed lipped channel section in compression
Created on Friday, April 30, 2010
This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement
Document Ref:
SX023a-EN-EU
Sheet
3
of
9
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
Effective width of the compressed flanges
The stress ratio:
1
=
ψ
(uniform compression), so the buckling factor is:
for internal compression element.
4
σ
=
k
yb
235 f
=
ε
EN1993-1-3
§ 5.5.2
and
EN1993-1-5
§ 4.4
For the upper flange:
The relative slenderness:
789
0
4
350
235
4
28
96
1
72
4
28
σ
p1
b1
p,
,
,
,
k
,
t
b
=
×
×
=
=
ε
λ
The width reduction factor is:
(
)
(
)
914
0
789
0
1
3
055
0
789
0
3
055
0
2
2
b1
p,
b1
p,
1
,
,
,
,
,
=
+
×
−
=
+
−
=
λ
ψ
λ
ρ
The effective width is:
mm
8
65
72
914
0
p1
1
eff1
,
,
b
b
=
×
=
=
ρ
mm
9
32
8
65
5
0
5
0
eff1
e12
e11
,
,
,
b
,
b
b
=
×
=
=
=
For the bottom flange:
The relative slenderness:
702
0
4
350
235
4
28
96
1
64
4
28
σ
p2
b2
p,
,
,
,
k
,
t
b
=
×
×
=
=
ε
λ
The width reduction factor is:
(
)
(
)
978
0
702
0
1
3
055
0
702
0
3
055
0
2
2
b2
p,
b2
p,
2
,
,
,
,
,
=
+
×
−
=
+
−
=
λ
ψ
λ
ρ
The effective width is:
mm
6
62
64
978
0
p2
2
eff2
,
,
b
b
=
×
=
=
ρ
mm
3
31
6
62
5
0
5
0
eff2
e22
e21
,
,
,
b
,
b
b
=
×
=
=
=
Example: Calculation of effective section properties for a cold-formed lipped channel section in compression
Created on Friday, April 30, 2010
This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement
Document Ref:
SX023a-EN-EU
Sheet
4
of
9
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
Effective width of the edge fold
For the upper edge fold:
The buckling factor is:
if
35
0
p
c
p,
,
b
b
≤
:
5
0
σ
,
k
=
if
6
0
35
0
p
c
p,
,
b
b
,
≤
<
:
(
)
3
2
p
c
p,
σ
35
0
83
0
5
0
,
b
b
,
,
k
−
+
=
35
0
275
0
72
8
19
p1
c
p,
,
,
,
b
b
<
=
=
so
5
0
σ1
,
k
=
EN1993-1-3
§ 5.5.3.2
(5a)
The relative slenderness:
614
0
5
0
350
235
4
28
96
1
8
19
4
28
σ1
p
c1
p,
,
,
,
,
,
k
,
t
c
=
×
×
=
=
ε
λ
The width reduction factor is:
13
1
614
0
188
0
614
0
188
0
2
2
c1
p,
c1
p,
1
,
,
,
,
,
=
−
=
−
=
λ
λ
ρ
but
1
≤
ρ
so
1
1
=
ρ
EN1993-1-5
§ 4.4
The effective width is:
mm
8
19
1
8
19
1
p
eff1
,
,
c
c
=
×
=
=
ρ
Effective area of the upper edge stiffener:
(
)
(
)
2
eff1
e12
s1
mm
3
103
8
19
9
32
96
1
,
,
,
,
c
b
t
A
=
+
×
=
+
=
EN1993-1-3
§ 5.5.3.2
(5a)
§ 5.5.3.2
(6)
For the bottom edge fold:
The buckling factor is:
35
0
309
0
64
8
19
p2
c
p,
,
,
,
b
b
<
=
=
so
5
0
σ2
,
k
=
EN1993-1-3
§ 5.5.3.2
(5a)
The relative slenderness:
614
0
5
0
350
235
4
28
96
1
8
19
4
28
σ2
p
c2
p,
,
,
,
,
,
k
,
t
c
=
×
×
=
=
ε
λ
The width reduction factor is:
13
1
614
0
188
0
614
0
188
0
2
2
c2
p,
c2
p,
2
,
,
,
,
,
=
−
=
−
=
λ
λ
ρ
but
1
≤
ρ
so
1
2
=
ρ
EN1993-1-5
§ 4.4
Example: Calculation of effective section properties for a cold-formed lipped channel section in compression
Created on Friday, April 30, 2010
This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement
Document Ref:
SX023a-EN-EU
Sheet
5
of
9
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
The effective width is:
mm
8
19
1
8
19
2
p
eff2
,
,
c
c
=
×
=
=
ρ
Effective area of the bottom edge stiffener:
(
)
(
)
2
eff2
e22
s2
mm
2
100
8
19
3
31
96
1
,
,
,
,
c
b
t
A
=
+
×
=
+
=
EN1993-1-3
§ 5.5.3.2
(5a)
§ 5.5.3.2
(6)
Step 2:
Use the initial effective cross-section of the stiffener to determine the
reduction factor, allowing for the effects of the continuous spring restraint.
EN1993-1-3
§ 5.5.3.2
(3)
The elastic critical buckling stress for the edge stiffener is:
s
s
s
cr,
2
A
I
E
K
=
σ
where:
K is the spring stiffness per unit length,
I
s
is the effective second moment of area of the stiffener.
EN1993-1-3
§ 5.5.3.2
(7)
For the upper edge stiffener:
The spring stiffness is:
f
p
2
1
3
1
p
2
1
2
3
1
5
,
0
1
)
1
(
4
k
h
b
b
b
h
b
t
E
K
+
+
⋅
−
=
ν
with:
1
b – distance from the web to the centre of the effective area of the stiffener in
compression (upper flange)
mm
73
,
61
96
,
1
)
8
,
19
9
,
32
(
2
9
,
32
96
,
1
9
,
32
72
)
(
2
eff
e12
e12
e12
p1
1
=
×
+
×
×
−
=
+
−
=
t
c
b
b
t
b
b
b
EN1993-1-3
§ 5.5.3.1
(5)
2
b – distance from the web to the centre of the effective area of the stiffener
in compression (bottom flange)
mm
41
,
54
96
,
1
)
8
,
19
3
,
31
(
2
3
,
31
96
,
1
3
,
31
64
)
(
2
eff2
e22
e22
e22
p2
2
=
×
+
×
×
−
=
+
−
=
t
c
b
b
t
b
b
b
Example: Calculation of effective section properties for a cold-formed lipped channel section in compression
Created on Friday, April 30, 2010
This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement
Document Ref:
SX023a-EN-EU
Sheet
6
of
9
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
97
0
3
103
2
100
s1
s2
f
,
,
,
A
A
k
=
=
=
for a member in axial compression
2
1
mm
N
331
,
0
=
K
The effective second moment of area:
(
)
(
)
2
eff1
e12
2
eff1
eff1
eff1
2
eff1
e12
2
eff1
e12
3
eff1
3
e12
s1
2
2
2
12
12
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
+
−
+
⎥
⎦
⎤
⎢
⎣
⎡
+
+
+
=
c
b
c
c
t
c
c
b
c
t
b
t
c
t
b
I
4
s1
mm
3663
=
I
so, the elastic critical buckling stress for the upper edge stiffener is
2
s1
cr,
mm
N
309
3
103
3663
210000
331
0
2
=
×
×
×
=
,
,
σ
For the bottom edge stiffener:
The spring stiffness is:
f
p
2
1
3
2
p
2
2
2
3
2
5
,
0
1
)
1
(
4
k
h
b
b
b
h
b
t
E
K
+
+
⋅
−
=
ν
,
2
2
mm
N
406
,
0
=
K
The effective second moment of area:
(
)
(
)
2
eff2
e22
2
eff2
eff2
eff2
2
eff2
e22
2
eff2
e22
3
eff2
3
e22
s2
2
2
2
12
12
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
+
−
+
⎥
⎦
⎤
⎢
⎣
⎡
+
+
+
=
c
b
c
c
t
c
c
b
c
t
b
t
c
t
b
I
4
s2
mm
3618
=
I
so, the elastic critical buckling stress for the bottom edge stiffener is
2
s2
cr,
mm
N
7
350
2
100
3618
210000
406
0
2
,
,
,
=
×
×
×
=
σ
Example: Calculation of effective section properties for a cold-formed lipped channel section in compression
Created on Friday, April 30, 2010
This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement
Document Ref:
SX023a-EN-EU
Sheet
7
of
9
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
Thickness reduction factor χ
d
for the edge stiffener
For the upper edge stiffener:
The relative slenderness:
064
1
309
350
s1
cr,
yb
d1
,
f
=
=
=
σ
λ
The reduction factor will be:
if
65
0
d
,
≤
λ
0
1
d
,
=
χ
if
38
1
65
0
d
,
,
<
<
λ
d
d
723
0
47
1
λ
χ
,
,
−
=
if
38
1
d
,
≥
λ
d
d
66
0
λ
χ
,
=
38
1
064
1
65
0
d1
,
,
,
<
=
<
λ
so
701
0
064
1
723
0
47
1
d1
,
,
,
,
=
×
−
=
χ
EN1993-1-3
§ 5.5.3.2
(3)
Figure 5.10d
EN1993-1-3
§ 5.5.3.1
(7)
EN1993-1-5
§ 4.4
(2)
For the bottom edge stiffener:
The relative slenderness:
999
0
7
350
350
s2
cr,
yb
d2
,
,
f
=
=
=
σ
λ
The reduction factor will be:
38
1
999
0
65
0
d2
,
,
,
<
=
<
λ
so
748
0
999
0
723
0
47
1
d2
,
,
,
,
=
×
−
=
χ
Step 3:
As the reduction factor for buckling of the stiffener is χ
d
< 1, iterate to refine
the value of the reduction factor for buckling of the stiffener.
EN1993-1-3
§ 5.5.3.2
(3)
Figure 5.10e
The iterations are carried out based on modified values of
ρ
obtained using:
M0
yb
d
i
Ed,
com,
γ
χ
σ
f
=
and
d
p
red
p,
χ
λ
λ
=
The iteration stops when the reduction factor
χ
converges.
EN1993-1-3
§ 5.5.3.2
(10)
For the upper edge stiffener:
Initial values (iteration 1):
Final values (iteration n):
701
0
d1
,
=
χ
683
0
n
d1,
d1
,
=
=
χ
χ
mm
9
32
e12
,
b
=
mm
36
n
e12,
e12
=
= b
b
mm
8
19
eff1
,
c
=
mm
8
19
n
eff1,
eff1
,
c
c
=
=
Example: Calculation of effective section properties for a cold-formed lipped channel section in compression
Created on Friday, April 30, 2010
This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement
Document Ref:
SX023a-EN-EU
Sheet
8
of
9
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
For the bottom edge stiffener:
Initial values (iteration 1):
Final values (iteration n):
748
0
d2
,
=
χ
744
0
n
d2,
d2
,
=
=
χ
χ
mm
3
31
e22
,
b
=
mm
32
n
e22,
e22
=
= b
b
mm
8
19
eff2
,
c
=
mm
8
19
n
eff2,
eff2
,
c
c
=
=
Final values of effective properties for flanges and lips in compression are:
For the upper flange and lip:
683
0
d1
,
=
χ
mm
36
e12
=
b
mm
8
19
eff1
,
c
=
and
mm
9
32
11
e
,
b
=
For the bottom flange and lip:
744
0
d2
,
=
χ
mm
32
e22
=
b
mm
8
19
eff2
,
c
=
and
mm
3
31
21
e
,
b
=
mm
34
.
1
683
,
0
96
,
1
d1
red,1
=
×
=
=
χ
t
t
mm
46
,
1
744
,
0
96
,
1
d2
red,2
=
×
=
=
χ
t
t
EN1993-1-3
§ 5.5.3.2
(12)
Effective section properties of the web
The stress ratio:
1
=
ψ
(uniform compression), so the buckling factor is:
for internal compression element.
4
σ
=
k
yb
235 f
=
ε
The relative slenderness:
171
2
4
350
235
4
28
96
1
198
4
28
σ
p
h
p,
,
,
,
k
,
t
h
=
×
×
=
=
ε
λ
The width reduction factor is:
(
)
(
)
414
0
171
2
1
3
055
0
171
2
3
055
0
2
2
h
p,
h
p,
,
,
,
,
,
=
+
×
−
=
+
−
=
λ
ψ
λ
ρ
EN1993-1-3
§ 5.5.2
and
EN1993-1-5
§ 4.4
Example: Calculation of effective section properties for a cold-formed lipped channel section in compression
Created on Friday, April 30, 2010
This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement
Document Ref:
SX023a-EN-EU
Sheet
9
of
9
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
The effective width of the web is:
mm
82
198
414
0
p
eff
=
×
=
=
,
h
h
ρ
mm
41
82
5
0
5
0
eff
e2
e1
=
×
=
=
=
,
h
,
h
h
Effective section properties
Effective cross-section area:
(
)
(
)
[
]
d2
eff2
e22
d1
eff1
e12
e2
e1
e21
e11
eff
χ
χ
c
b
c
b
h
h
b
b
t
A
+
+
+
+
+
+
+
=
2
eff
mm
7
436,
A
=
Position of the centroidal axis with regard to the upper flange:
(
)
eff
d1
2
eff1
2
e1
e2
p
e2
e21
d2
e22
p
eff2
p
d2
eff2
G1
2
2
2
2
A
c
h
h
h
h
b
b
h
c
h
c
t
z
⎥
⎦
⎤
⎢
⎣
⎡
+
+
⎟
⎠
⎞
⎜
⎝
⎛ −
+
+
+
⎟
⎠
⎞
⎜
⎝
⎛ −
=
χ
χ
χ
mm
44
98
G1
,
z
=
Position of the centroidal axis with regard to the bottom flange:
mm
56
99
44
98
198
G1
p
G2
,
,
z
h
z
=
−
=
−
=
Example: Calculation of effective section properties for a cold-formed lipped channel section in compression
Created on Friday, April 30, 2010
This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement
Example: Calculation of effective section properties for a cold-formed lipped
channel section in compression
SX023a-EN-EU.doc
Quality Record
RESOURCE TITLE
Example: Calculation of effective section properties for a cold-formed
lipped channel section in compression
Reference(s)
ORIGINAL DOCUMENT
Name
Company
Date
Created by
V. Ungureanu, A. Ruff
BRITT Ltd. Timisoara,
Romania
05/12/2005
Technical content checked by
D. Dubina
BRITT Ltd. Timisoara,
Romania
08/12/2005
Editorial content checked by
Technical content endorsed by the
following STEEL Partners:
1. UK
G W Owens
SCI
12/4/06
2. France
A Bureau
CTICM
12/4/06
3. Sweden
B Uppfeldt
SBI
11/4/06
4. Germany
C Müller
RWTH
11/4/06
5. Spain
J Chica
Labein
12/4/06
Resource approved by Technical
Coordinator
G W Owens
SCI
11/9/06
TRANSLATED DOCUMENT
This Translation made and checked by:
Translated resource approved by:
Page 10
Example: Calculation of effective section properties for a cold-formed lipped channel section in compression
Created on Friday, April 30, 2010
This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement
Document Outline