Example: Calculation of effective section properties for a cold-formed lipped channel section in compression
CALCULATION SHEET Document Ref: Sheet of
SX023a-EN-EU 1 9
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina 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 h = 200 mm
Total width of upper flange b1 = 74 mm
Total width of bottom flange b2 = 66 mm
Total width of edge fold c = 20,8 mm
Internal radius r = 3 mm
Nominal thickness tnom = 2 mm
EN1993-1-3
Steel core thickness t = 1,96 mm
ż 3.2.4(3)
Basic yield strength fyb = 350 N mm2
Modulus of elasticity E = 210000 N mm2
EN1993-1-3
Poisson s ratio � = 0,3
ż 2(3)
Partial factor ł = 1,0
M0
The dimensions of the section centre line are:
Web height hp = h - tnom = 200 - 2 = 198 mm
Width of upper flange bp1 = b1 - tnom = 74 - 2 = 72 mm
Width of bottom flange bp2 = b2 - tnom = 66 - 2 = 64 mm
Width of edge fold cp = c - tnom 2 = 20,8 - 2 2 = 19,8 mm
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
CALCULATION SHEET Document Ref: Sheet of
SX023a-EN-EU 2 9
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
Checking of geometrical proportions
The design method of EN1993-1-3 can be applied if the following conditions EN1993-1-3
are satisfied: ż 5.2
b t d" 60 b1 t = 74 1,96 = 37,75 < 60  OK
c t d" 50 c t = 20,8 1,96 =10,61 < 50  OK
h t d" 500 h t = 200 1,96 =102,04 < 500  OK
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:
0,2 d" c b d" 0,6 c b1 = 20,8 74 = 0,28 0,2 < 0,28 < 0,6  OK
c b2 = 20,8 66 = 0,32 0,2 < 0,32 < 0,6  OK
The influence of rounding of the corners is neglected if: EN1993-1-3
ż 5.1(3)
r t d" 5 r t = 3 1,96 =1,53 < 5  OK
r bp d" 0,10 r bp1 = 3 72 = 0,04 < 0,10  OK
r bp2 = 3 64 = 0,05 < 0,10  OK
Gross section properties
Abr = t(2cp + bp1 + bp2 + hp)=1,96�(2�19,8 + 72 + 64 +198)= 732 mm2
Position of the centroidal axis with regard to the upper flange:
2 2
[cp(hp - cp 2)+ bp2hp + hp 2 + cp 2]t
zb1 = = 96,88 mm
Abr
Effective section properties of the flanges and lips in compression
The general (iterative) procedure is applied to calculate the effective EN1993-1-3
properties of the compressed flange and the lip (plane element with edge ż 5.5.3.2
stiffener). The calculation should be carried out in three steps:
Step 1:
Obtain an initial effective cross-section for the stiffeners using effective EN1993-1-3
widths of the flanges determined by assuming that the compressed flanges are ż 5.5.3.2 (3)
doubly supported, the stiffener gives full restraint ( K = " ) and that design
strength is not reduced (� = fyb / ł ).
com,Ed M 0
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
CALCULATION SHEET Document Ref: Sheet of
SX023a-EN-EU 3 9
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
Effective width of the compressed flanges
The stress ratio: � = 1 (uniform compression), so the buckling factor is: EN1993-1-3
ż 5.5.2 and
k� = 4 for internal compression element.
EN1993-1-5
� = 235 fyb
ż 4.4
For the upper flange:
The relative slenderness:
bp1 t
72 1,96
p,b1 = = = 0,789
28,4� k� 28,4 � 235 350 � 4
The width reduction factor is:
p,b1 - 0,055(3 +� )
0,789 - 0,055�(3 +1)
�1 = = = 0,914
0,7892
p,b12
The effective width is:
beff1 = �1bp1 = 0,914� 72 = 65,8 mm
be11 = be12 = 0,5beff1 = 0,5� 65,8 = 32,9 mm
For the bottom flange:
The relative slenderness:
bp2 t
64 1,96
p,b2 = = = 0,702
28,4� k� 28,4 � 235 350 � 4
The width reduction factor is:
p,b2 - 0,055(3 +� )
0,702 - 0,055�(3 +1)
�2 = = = 0,978
0,7022
p,b2 2
The effective width is:
beff2 = �2bp2 = 0,978 � 64 = 62,6 mm
be21 = be22 = 0,5beff2 = 0,5� 62,6 = 31,3 mm
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
CALCULATION SHEET Document Ref: Sheet of
SX023a-EN-EU 4 9
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
Effective width of the edge fold
For the upper edge fold: EN1993-1-3
ż 5.5.3.2(5a)
The buckling factor is:
if bp,c bp d" 0,35 : k� = 0,5
2
3
if 0,35 < bp,c bp d" 0,6 : k� = 0,5 + 0,83 (bp,c bp - 0,35)
bp,c bp1 = 19,8 72 = 0,275 < 0,35 so k�1 = 0,5
The relative slenderness:
EN1993-1-5
cp t
19,8 1,96
p,c1 = = = 0,614
ż 4.4
28,4� k�1 28,4 � 235 350 � 0,5
The width reduction factor is:
p,c1 - 0,188
0,614 - 0,188
�1 = = = 1,13 but � d" 1 so �1 = 1
0,6142
p,c12
The effective width is: EN1993-1-3
ż 5.5.3.2(5a)
ceff1 = cp�1 = 19,8 �1 = 19,8 mm
Effective area of the upper edge stiffener:
ż 5.5.3.2(6)
As1 = t(be12 + ceff1)= 1,96�(32,9 +19,8)= 103,3 mm2
For the bottom edge fold: EN1993-1-3
The buckling factor is: ż 5.5.3.2(5a)
bp,c bp2 = 19,8 64 = 0,309 < 0,35 so k�2 = 0,5
The relative slenderness:
cp t
19,8 1,96
EN1993-1-5
p,c2 = = = 0,614
ż 4.4
28,4� k�2 28,4 � 235 350 � 0,5
The width reduction factor is:
p,c2 - 0,188
0,614 - 0,188
�2 = = =1,13 but � d" 1 so �2 = 1
0,6142
p,c2 2
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
CALCULATION SHEET Document Ref: Sheet of
SX023a-EN-EU 5 9
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
The effective width is: EN1993-1-3
ż 5.5.3.2(5a)
ceff2 = cp�2 = 19,8 �1 = 19,8 mm
Effective area of the bottom edge stiffener:
ż 5.5.3.2(6)
As2 = t(be22 + ceff2)=1,96�(31,3 +19,8)= 100,2 mm2
Step 2: EN1993-1-3
Use the initial effective cross-section of the stiffener to determine the ż 5.5.3.2(3)
reduction factor, allowing for the effects of the continuous spring restraint.
The elastic critical buckling stress for the edge stiffener is:
EN1993-1-3
2 K E Is
�cr,s =
ż 5.5.3.2(7)
As
where:
K is the spring stiffness per unit length,
Is is the effective second moment of area of the stiffener.
For the upper edge stiffener: EN1993-1-3
ż 5.5.3.1(5)
The spring stiffness is:
E t3 1
K1 = �"
2
4(1-� )
b12 hp + b13 + 0,5b1 b2 hp kf
with:
b1  distance from the web to the centre of the effective area of the stiffener in
compression (upper flange)
be12 t be12 2 32,9 �1,96 � 32,9 2
b1 = bp1 - = 72 - = 61,73 mm
(be12 + ceff ) t (32,9 +19,8) �1,96
b2  distance from the web to the centre of the effective area of the stiffener
in compression (bottom flange)
be22 t be22 2 31,3�1,96 � 31,3 2
b2 = bp2 - = 64 - = 54,41 mm
(be22 + ceff2) t (31,3 +19,8) �1,96
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
CALCULATION SHEET Document Ref: Sheet of
SX023a-EN-EU 6 9
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
As2 100,2
kf = = = 0,97 for a member in axial compression
As1 103,3
K1 = 0,331 N mm2
The effective second moment of area:
2
2
Ą#ceff1
Ą# Ą#
be12 t3 ceff13 t ceff12 ń# ceff12 ń#ń#
Is1 = + + be12 tó# + ceff1 tó# -
ó#2
12 12 (be12 Ś# 2 (be12 + ceff1)Ą#Ą#
ó# Ą#
Ł#2 + ceff1)Ą# Ł# Ś#
Ł# Ś#
Is1 = 3663 mm4
so, the elastic critical buckling stress for the upper edge stiffener is
2� 0,331� 210000� 3663
�cr,s1 = = 309 N mm2
103,3
For the bottom edge stiffener:
The spring stiffness is:
E t3 1
K2 = �" ,
2
4(1-� )
b22 hp + b23 + 0,5b1 b2 hp kf
K2 = 0,406 N mm2
The effective second moment of area:
2
2
Ą#ceff2
Ą# Ą#
be22 t3 ceff23 t ceff22 ń# ceff22 ń#ń#
Is2 = + + be22 tó# + ceff2 tó# -
ó#2
12 12 (be22 Ś# 2 (be22 + ceff2)Ą#Ą#
ó# Ą#
Ł#2 + ceff2)Ą# Ł# Ś#
Ł# Ś#
Is2 = 3618 mm4
so, the elastic critical buckling stress for the bottom edge stiffener is
2� 0,406� 210000� 3618
�cr,s2 = = 350,7 N mm2
100,2
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
CALCULATION SHEET Document Ref: Sheet of
SX023a-EN-EU 7 9
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
Thickness reduction factor �d for the edge stiffener EN1993-1-3
ż 5.5.3.2(3)
For the upper edge stiffener:
Figure 5.10d
The relative slenderness:
d1 = fyb � = 350 309 = 1,064
cr,s1
EN1993-1-3
The reduction factor will be: ż 5.5.3.1(7)
if d d" 0,65 �d = 1,0
EN1993-1-5
if 0,65 < d < 1,38 �d = 1,47 - 0,723d
ż 4.4(2)
if d e" 1,38 �d = 0,66 d
0,65 < d1 = 1,064 < 1,38 so �d1 = 1,47 - 0,723�1,064 = 0,701
For the bottom edge stiffener:
The relative slenderness:
d2 = fyb � = 350 350,7 = 0,999
cr,s2
The reduction factor will be:
0,65 < d2 = 0,999 < 1,38 so �d2 = 1,47 - 0,723� 0,999 = 0,748
Step 3: EN1993-1-3
ż 5.5.3.2(3)
As the reduction factor for buckling of the stiffener is �d < 1, iterate to refine
the value of the reduction factor for buckling of the stiffener. Figure 5.10e
The iterations are carried out based on modified values of � obtained using: EN1993-1-3
ż 5.5.3.2 (10)
� = �d fyb ł and p,red = p �d
com,Ed,i M0
The iteration stops when the reduction factor � converges.
For the upper edge stiffener:
Initial values (iteration 1): Final values (iteration n):
�d1 = 0,701 �d1 = �d1,n = 0,683
be12 = 32,9 mm be12 = be12,n = 36 mm
ceff1 = 19,8 mm ceff1 = ceff1,n = 19,8 mm
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
CALCULATION SHEET Document Ref: Sheet of
SX023a-EN-EU 8 9
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
For the bottom edge stiffener:
Initial values (iteration 1): Final values (iteration n):
�d2 = 0,748 �d2 = �d2,n = 0,744
be22 = 31,3 mm be22 = be22,n = 32 mm
ceff2 = 19,8 mm ceff2 = ceff2,n = 19,8 mm
Final values of effective properties for flanges and lips in compression are:
For the upper flange and lip:
�d1 = 0,683 be12 = 36 mm ceff1 = 19,8 mm
and be11 = 32,9 mm
For the bottom flange and lip:
�d2 = 0,744 be22 = 32 mm ceff2 = 19,8 mm
and be21 = 31,3 mm
EN1993-1-3
tred,1 = t�d1 = 1,96 � 0,683 = 1.34 mm
ż 5.5.3.2(12)
tred,2 = t�d2 = 1,96 � 0,744 = 1,46 mm
Effective section properties of the web
The stress ratio: � = 1 (uniform compression), so the buckling factor is: EN1993-1-3
ż 5.5.2
k� = 4 for internal compression element.
and
� = 235 fyb
EN1993-1-5
ż 4.4
The relative slenderness:
hp t
198 1,96
p,h = = = 2,171
28,4� k� 28,4� 235 350 � 4
The width reduction factor is:
p,h - 0,055(3 +� )
2,171- 0,055�(3 +1)
� = = = 0,414
2,1712
p,h 2
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
CALCULATION SHEET Document Ref: Sheet of
SX023a-EN-EU 9 9
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in compression
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
The effective width of the web is:
heff = �hp = 0,414 �198 = 82 mm
he1 = he2 = 0,5heff = 0,5� 82 = 41 mm
Effective section properties
Effective cross-section area:
Aeff = t[be11 + be21 + he1 + he2 + (be12 + ceff1)�d1 + (be22 + ceff2)�d2]
Aeff = 436,7 mm2
Position of the centroidal axis with regard to the upper flange:
Ą#
ceff2 he2 he12 ceff12�d1 ń#
ś# ś#
tó#ceff2�d2�# hp - ź# ś#
+ hp(be22�d2 + be21)+ he2�# hp - ź#
+ +
ś#
Ą#
2 2 2 2
�# # �# #
Ł# Ś#
zG1 =
Aeff
zG1 = 98,44 mm
Position of the centroidal axis with regard to the bottom flange:
zG2 = hp - zG1 = 198 - 98,44 = 99,56 mm
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
Example: Calculation of effective section properties for a cold-formed lipped
channel section in compression
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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, 05/12/2005
Romania
Technical content checked by D. Dubina BRITT Ltd. Timisoara, 08/12/2005
Romania
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 M�ller RWTH 11/4/06
5. Spain J Chica Labein 12/4/06
Resource approved by Technical G W Owens SCI 11/9/06
Coordinator
TRANSLATED DOCUMENT
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Translated resource approved by:
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Created on Friday, April 30, 2010
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