Document Ref:
SX022a-EN-EU
Sheet
1
of
8
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
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 bending
This example deals with the effective properties calculation of a cold-
formed lipped channel section subjected to bending about its major axis.
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 flange in compression
mm
74
1
=
b
Total width of flange in tension
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
00
,
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 flange in compression
mm
72
2
74
nom
1
p1
=
−
=
−
=
t
b
b
Width of flange in tension
mm
64
2
66
nom
2
p2
=
−
=
−
=
t
b
b
Example: Calculation of effective section properties for a cold-formed lipped channel section in bending
Utworzono 30 kwietnia 2010
Material ten jest objety prawem autorskim - wszystkie prawa zastrzezone. Uzycie tego dokumentu uzaleznione jest od warunków umowy licencyjnej z Access Steel.
Document Ref:
SX022a-EN-EU
Sheet
2
of
8
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
Width of edge fold
mm
8
,
19
2
2
8
,
20
2
nom
p
=
−
=
−
=
t
c
c
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
0,6
0,28
0,2
<
<
– OK
32
,
0
66
8
,
20
2
=
=
b
c
0,6
0,32
0,2
<
<
– 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 neutral axis with respect to the flange in compression:
(
)
[
]
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
Example: Calculation of effective section properties for a cold-formed lipped channel section in bending
Utworzono 30 kwietnia 2010
Material ten jest objety prawem autorskim - wszystkie prawa zastrzezone. Uzycie tego dokumentu uzaleznione jest od warunków umowy licencyjnej z Access Steel.
Document Ref:
SX022a-EN-EU
Sheet
3
of
8
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
Effective section properties of the flange and lip 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 stiffener using effective widths
of the flange determined by assuming that the compressed flange is 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)
Effective width of the compressed flange
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:
789
,
0
4
350
235
4
,
28
96
,
1
72
4
,
28
σ
p1
b
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
b
p,
b
p,
=
+
×
−
=
+
−
=
λ
ψ
λ
ρ
The effective width is:
mm
8
65
72
914
0
p1
eff
,
,
b
b
=
×
=
=
ρ
mm
9
32
8
65
5
0
5
0
eff
e2
e1
,
,
,
b
,
b
b
=
×
=
=
=
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 bending
Utworzono 30 kwietnia 2010
Material ten jest objety prawem autorskim - wszystkie prawa zastrzezone. Uzycie tego dokumentu uzaleznione jest od warunków umowy licencyjnej z Access Steel.
Document Ref:
SX022a-EN-EU
Sheet
4
of
8
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
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
The buckling factor is:
if
35
,
0
p1
c
p,
≤
b
b
:
5
,
0
σ
=
k
if
6
,
0
35
,
0
p1
c
p,
≤
<
b
b
:
(
)
3
2
p1
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
σ
=
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
σ
p
p,c
=
×
×
=
=
k
t
c
ε
λ
EN1993-1-5
§ 4.4
The width reduction factor is:
13
,
1
614
,
0
188
,
0
614
,
0
188
,
0
2
2
c
p,
c
p,
=
−
=
−
=
λ
λ
ρ
but
1
≤
ρ
so 1
=
ρ
The effective width is:
mm
8
,
19
8
,
19
1
p
eff
=
×
=
= c
c
ρ
Effective area of the edge stiffener:
(
)
(
)
2
eff
e2
s
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)
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
A
I
E
K
2
,
=
σ
where:
EN1993-1-3
§ 5.5.3.2
(7)
Example: Calculation of effective section properties for a cold-formed lipped channel section in bending
Utworzono 30 kwietnia 2010
Material ten jest objety prawem autorskim - wszystkie prawa zastrzezone. Uzycie tego dokumentu uzaleznione jest od warunków umowy licencyjnej z Access Steel.
Document Ref:
SX022a-EN-EU
Sheet
5
of
8
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
K
is the spring stiffness per unit length:
f
p
2
1
3
1
p
2
1
2
3
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)
EN1993-1-3
§ 5.5.3.1
(5)
mm
73
,
61
96
,
1
)
8
,
19
9
,
32
(
2
9
,
32
96
,
1
9
,
32
72
)
(
2
eff
e2
e2
e2
p1
1
=
×
+
×
×
−
=
+
−
=
t
c
b
b
t
b
b
b
0
f
=
k
for bending about the y-y axis
mm
N
439
,
0
=
K
s
I is the effective second moment of area of the stiffener:
(
)
(
)
2
eff
e2
2
eff
eff
eff
2
eff
e2
2
eff
e2
3
eff
3
e2
s
2
2
2
12
12
⎥
⎦
⎤
⎢
⎣
⎡
+
−
+
⎥
⎦
⎤
⎢
⎣
⎡
+
+
+
=
c
b
c
c
t
c
c
b
c
t
b
t
c
t
b
I
4
s
mm
3663
=
I
so, the elastic critical buckling stress for the edge stiffener is
2
s
cr,
mm
N
78
,
355
3
,
103
3663
210000
439
,
0
2
=
×
×
×
=
σ
Example: Calculation of effective section properties for a cold-formed lipped channel section in bending
Utworzono 30 kwietnia 2010
Material ten jest objety prawem autorskim - wszystkie prawa zastrzezone. Uzycie tego dokumentu uzaleznione jest od warunków umowy licencyjnej z Access Steel.
Document Ref:
SX022a-EN-EU
Sheet
6
of
8
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
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
The relative slenderness:
992
,
0
78
,
355
350
s
cr,
yb
d
=
=
=
σ
λ
f
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
992
,
0
65
,
0
d
<
=
<
λ
so
753
,
0
992
,
0
723
,
0
47
,
1
d
=
×
−
=
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)
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)
Initial values (iteration 1):
Final values (iteration n):
753
,
0
d
=
χ
737
,
0
n
d,
d
=
=
χ
χ
mm
9
,
32
e2
=
b
mm
9
,
35
n
e2,
e2
=
= b
b
mm
8
,
19
eff
=
c
mm
8
,
19
n
eff,
eff
=
= c
c
Final values of effective properties for flange and lip in compression are:
737
,
0
d
=
χ
mm
9
,
35
e2
=
b
mm
8
,
19
eff
=
c
and
mm
9
,
32
e1
=
b
Example: Calculation of effective section properties for a cold-formed lipped channel section in bending
Utworzono 30 kwietnia 2010
Material ten jest objety prawem autorskim - wszystkie prawa zastrzezone. Uzycie tego dokumentu uzaleznione jest od warunków umowy licencyjnej z Access Steel.
Document Ref:
SX022a-EN-EU
Sheet
7
of
8
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
mm
44
,
1
737
,
0
96
,
1
d
red
=
×
=
=
χ
t
t
EN1993-1-3
§ 5.5.3.2
(12)
Effective section properties of the web
The position of the neutral axis with regard to the flange in compression:
(
)
(
)
d
eff
e2
e1
p
p2
p
d
2
eff
2
p
p
p2
p
p
p
c
2
2
2
χ
χ
c
b
b
h
b
c
c
h
h
b
c
h
c
h
+
+
+
+
+
+
+
+
−
=
mm
6
,
101
c
=
h
The stress ratio:
949
,
0
6
,
101
198
6
,
101
c
p
c
−
=
−
=
−
=
h
h
h
ψ
The buckling factor:
2
σ
78
,
9
29
,
6
81
,
7
ψ
ψ
+
−
=
k
58
,
22
σ
=
k
The relative slenderness:
914
,
0
58
,
22
350
235
4
,
28
96
,
1
198
4
,
28
σ
p
h
p,
=
×
×
=
=
k
t
h
ε
λ
EN1993-1-5
§ 4.4
(Table 4.1)
The width reduction factor is:
(
)
(
)
959
,
0
914
,
0
949
,
0
3
055
,
0
914
,
0
3
055
,
0
2
2
h
p,
h
p,
=
−
×
−
=
+
−
=
λ
ψ
λ
ρ
Example: Calculation of effective section properties for a cold-formed lipped channel section in bending
Utworzono 30 kwietnia 2010
Material ten jest objety prawem autorskim - wszystkie prawa zastrzezone. Uzycie tego dokumentu uzaleznione jest od warunków umowy licencyjnej z Access Steel.
Document Ref:
SX022a-EN-EU
Sheet
8
of
8
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
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 zone in compression of the web is:
mm
5
,
97
6
,
101
959
,
0
c
eff
=
×
=
= h
h
ρ
Near the flange in compression:
mm
39
5
,
97
4
,
0
4
,
0
eff
e1
=
×
=
=
h
h
Near the neutral axis:
mm
5
,
58
5
,
97
6
,
0
6
,
0
eff
e2
=
×
=
=
h
h
The effective width of the web is:
Near the flange in compression:
mm
39
e1
1
=
= h
h
Near the flange in tension:
(
)
(
)
mm
9
,
154
5
,
58
6
,
101
198
e2
c
p
2
=
−
−
=
−
−
=
h
h
h
h
Effective section properties
Effective cross-section area:
]
)
(
[
d
eff
2
e
1
e
2
1
2
p
p
eff
χ
c
b
b
h
h
b
c
t
A
+
+
+
+
+
+
=
(
)
[
]
737
,
0
8
,
19
9
,
35
9
,
32
9
,
154
39
64
8
,
19
96
,
1
eff
×
+
+
+
+
+
+
×
=
A
2
eff
mm
2
,
689
=
A
Position of the neutral axis with regard to the flange in compression:
(
)
(
)
[
]
eff
d
2
eff
2
1
2
p
2
p
p2
p
p
p
c
2
2
2
2
A
c
h
h
h
h
h
b
c
h
c
t
z
χ
+
+
−
+
+
−
=
mm
3
,
102
c
=
z
Example: Calculation of effective section properties for a cold-formed lipped channel section in bending
Utworzono 30 kwietnia 2010
Material ten jest objety prawem autorskim - wszystkie prawa zastrzezone. Uzycie tego dokumentu uzaleznione jest od warunków umowy licencyjnej z Access Steel.
Document Ref:
SX022a-EN-EU
Sheet
9
of
8
Title
CALCULATION SHEET
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
Eurocode Ref
EN 1993-1-3
Made by
V. Ungureanu, A. Ruff
Date
Dec 2005
Checked by
D. Dubina
Date
Dec 2005
Position of the neutral axis with regard to the flange in tension:
mm
7
,
95
3
,
102
198
c
p
t
=
−
=
−
=
z
h
z
Second moment of area:
2
eff
c
d
eff
2
c
d
e2
2
c
e1
2
1
c
1
2
2
t
2
2
t
2
p
2
p
t
p
d
3
eff
3
d
e2
3
e1
3
p
3
p2
3
2
3
1
y
eff,
)
2
)(
(
)
(
)
2
(
)
2
(
)
2
(
12
)
(
12
)
(
12
12
12
12
12
c
z
t
c
z
t
b
z
t
b
h
z
t
h
h
z
t
h
tz
b
c
z
t
c
t
c
t
b
t
b
t
c
t
b
t
h
t
h
I
−
+
+
+
+
−
+
−
+
+
−
+
+
+
+
+
+
+
+
=
χ
χ
χ
χ
4
y
eff,
mm
4140000
=
I
Effective section modulus:
- with regard to the flange in compression
3
c
y
eff,
c
y,
eff,
mm
40460
3
,
102
4140000 =
=
=
z
I
W
- with regard to the flange in tension
3
t
y
eff,
t
y,
eff,
mm
43260
7
,
95
4140000 =
=
=
z
I
W
E
x
a
m
p
l
e
:
C
a
l
c
u
l
a
t
i
o
n
o
f
e
f
f
e
c
t
i
v
e
s
e
c
t
i
o
n
p
r
o
p
e
r
t
i
e
s
f
o
r
a
c
o
l
d
-
f
o
r
m
e
d
l
i
p
p
e
d
c
h
a
n
n
e
l
s
e
c
t
i
o
n
i
n
b
e
n
d
i
n
g
Utworzono 30 kwietnia 2010
Material ten jest objety prawem autorskim - wszystkie prawa zastrzezone. Uzycie tego dokumentu uzaleznione jest od warunków umowy licencyjnej z Access Steel.
Example: Calculation of effective section properties for a cold-formed lipped
channel section in bending
SX022a-EN-EU.doc
Quality Record
RESOURCE TITLE
Example: Calculation of effective section properties for a cold-formed
lipped channel section in bending
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
23/08/06
TRANSLATED DOCUMENT
This Translation made and checked by:
Translated resource approved by:
Example: Calculation of effective section properties for a cold-formed lipped channel section in bending
Utworzono 30 kwietnia 2010
Material ten jest objety prawem autorskim - wszystkie prawa zastrzezone. Uzycie tego dokumentu uzaleznione jest od warunków umowy licencyjnej z Access Steel.
Document Outline