Example: Calculation of effective section properties for a cold-formed lipped channel section in bending
CALCULATION SHEET Document Ref: Sheet of
SX022a-EN-EU 1 8
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
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 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 h = 200 mm
Total width of flange in compression b1 = 74 mm
Total width of flange in tension 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 = 1,00
M0
The dimensions of the section centre line are:
Web height hp = h - tnom = 200 - 2 = 198 mm
Width of flange in compression bp1 = b1 - tnom = 74 - 2 = 72 mm
Width of flange in tension bp2 = b2 - tnom = 66 - 2 = 64 mm
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
CALCULATION SHEET Document Ref: Sheet of
SX022a-EN-EU 2 8
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
Width of edge fold cp = c - tnom 2 = 20,8 - 2 2 = 19,8 mm
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 neutral axis with respect to the flange in compression:
2 2
[cp(hp - cp 2)+ bp2hp + hp 2 + cp 2]t
zb1 = = 96,88 mm
Abr
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
CALCULATION SHEET Document Ref: Sheet of
SX022a-EN-EU 3 8
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
Effective section properties of the flange and lip 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 stiffener using effective widths EN1993-1-3
of the flange determined by assuming that the compressed flange is doubly ż 5.5.3.2 (3)
supported, the stiffener gives full restraint ( K = " ) and that design strength is
not reduced (�com,Ed = fyb / ł ).
M 0
Effective width of the compressed flange
The stress ratio: � = 1 (uniform compression), so EN1993-1-3
ż 5.5.2
the buckling factor is: k� = 4 for internal compression element.
and
� = 235 fyb
EN1993-1-5
ż 4.4
The relative slenderness:
bp1 t
72 1,96
p,b = = = 0,789
28,4� k� 28,4� 235 350 � 4
The width reduction factor is:
p,b - 0,055(3 +� )
0,789 - 0,055�(3 +1)
� = = = 0,914
0,7892
p,b2
The effective width is:
beff = � bp1= 0,914 � 72 = 65,8 mm
be1 = be2 = 0,5beff = 0,5� 65,8 = 32,9 mm
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
CALCULATION SHEET Document Ref: Sheet of
SX022a-EN-EU 4 8
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
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
The buckling factor is:
EN1993-1-3
ż 5.5.3.2 (5a)
if bp,c bp1 d" 0,35 : k� = 0,5
2
3
if 0,35 < bp,c bp1 d" 0,6 : k� = 0,5 + 0,83 (bp,c bp1 - 0,35)
bp,c bp1 = 19,8 72 = 0,275 < 0,35 so k� = 0,5
The relative slenderness: EN1993-1-5
ż 4.4
cp t
19,8 1,96
p,c = = = 0,614
28,4� k� 28,4� 235 350 � 0,5
The width reduction factor is:
p,c - 0,188
0,614 - 0,188
� = = = 1,13
0,6142
p,c2
but � d" 1 so � = 1
The effective width is: EN1993-1-3
ż 5.5.3.2 (5a)
ceff = � cp = 1�19,8 = 19,8 mm
Effective area of the edge stiffener:
ż 5.5.3.2 (6)
As = t(be2 + ceff )= 1,96�(32,9 +19,8)= 103,3 mm2
Step 2:
Use the initial effective cross-section of the stiffener to determine the EN1993-1-3
reduction factor, allowing for the effects of the continuous spring restraint. ż 5.5.3.2 (3)
The elastic critical buckling stress for the edge stiffener is EN1993-1-3
ż 5.5.3.2 (7)
2 K E Is
� =
cr,s
As
where:
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
CALCULATION SHEET Document Ref: Sheet of
SX022a-EN-EU 5 8
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
K is the spring stiffness per unit length: EN1993-1-3
ż 5.5.3.1(5)
E t3 1
K = �"
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)
be2t be2 2 32,9�1,96� 32,9 2
b1 = bp1 - = 72 - = 61,73 mm
(be2 + ceff )t (32,9 +19,8) �1,96
kf = 0 for bending about the y-y axis
K = 0,439 N mm
Is is the effective second moment of area of the stiffener:
2 2
Ą# Ą#ceff ceff 2 ń#
be2 t3 ceff 3 t ceff 2 ń#
Is = + + be2 tó# -
12 12 (be2 )Ą# + ceff tó# 2 2(be2 + ceff )Ą#
Ł#2 + ceff Ś# Ł# Ś#
Is = 3663 mm4
so, the elastic critical buckling stress for the edge stiffener is
2� 0,439� 210000�3663
�cr,s = = 355,78 N mm2
103,3
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
CALCULATION SHEET Document Ref: Sheet of
SX022a-EN-EU 6 8
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
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)
The relative slenderness:
Figure 5.10d
d = fyb � = 350 355,78 = 0,992
cr,s
The reduction factor will be:
EN1993-1-3
ż 5.5.3.1 (7)
if d d" 0,65 �d =1,0
if 0,65 < d < 1,38 �d = 1,47 - 0,723d
EN1993-1-5
ż 4.4 (2)
if d e" 1,38 �d = 0,66 d
0,65 < d = 0,992 < 1,38 so �d =1,47 - 0,723� 0,992 = 0,753
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
�com,Ed,i = �d fyb ł and p,red = p �d
M0
ż 5.5.3.2 (10)
The iteration stops when the reduction factor � converges.
Initial values (iteration 1): Final values (iteration n):
�d = 0,753 �d = �d,n = 0,737
be2 = 32,9 mm be2 = be2,n = 35,9 mm
ceff =19,8 mm ceff = ceff,n = 19,8 mm
Final values of effective properties for flange and lip in compression are:
�d = 0,737 be2 = 35,9 mm ceff =19,8 mm
and be1 = 32,9 mm
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
CALCULATION SHEET Document Ref: Sheet of
SX022a-EN-EU 7 8
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
EN1993-1-3
tred = t�d =1,96� 0,737 =1,44 mm
ż 5.5.3.2 (12)
Effective section properties of the web
The position of the neutral axis with regard to the flange in compression:
cp(hp - cp 2)+ bp2 hp + hp2 2 + ceff 2 �d 2
hc = hc =101,6 mm
cp + bp2 + hp + be1 + (be2 + ceff )�d
The stress ratio:
hc - hp
101,6 -198
� = = = -0,949
hc 101,6
2
EN1993-1-5
The buckling factor: k� = 7,81- 6,29� + 9,78� k� = 22,58
ż 4.4
The relative slenderness:
(Table 4.1)
hp t
198 1,96
p,h = = = 0,914
28,4� k� 28,4� 235 350 � 22,58
The width reduction factor is:
p,h - 0,055(3 +� )
0,914 - 0,055�(3 - 0,949)
� = = = 0,959
0,9142
p,h 2
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
CALCULATION SHEET Document Ref: Sheet of
SX022a-EN-EU 8 8
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
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 zone in compression of the web is:
heff = � hc = 0,959�101,6 = 97,5 mm
Near the flange in compression:
he1 = 0,4heff = 0,4�97,5 = 39 mm
Near the neutral axis:
he2 = 0,6heff = 0,6�97,5 = 58,5 mm
The effective width of the web is:
Near the flange in compression:
h1 = he1 = 39 mm
Near the flange in tension:
h2 = hp - (hc - he2) = 198 - (101,6 - 58,5) = 154,9 mm
Effective section properties
Effective cross-section area:
Aeff = t[cp + bp2 + h1 + h2 + be1 + (be2 + ceff )�d ]
Aeff = 1,96�[19,8 + 64 + 39 +154,9 + 32,9 + (35,9 +19,8)�0,737]
Aeff = 689,2 mm2
Position of the neutral axis with regard to the flange in compression:
t[cp(hp - cp 2)+ bp2hp + h2(hp - h2 2)+ h12 2 + ceff 2�d 2]
zc =
Aeff
zc =102,3 mm
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.
E x a m p l e : C a l c u l a t
CALCULATION SHEET Document Ref: Sheet of
SX022a-EN-EU 9 8
Title
Example: Calculation of effective section properties for a
cold-formed lipped channel section in bending
Eurocode Ref
EN 1993-1-3
Made by Date
V. Ungureanu, A. Ruff Dec 2005
Checked by Date
D. Dubina Dec 2005
Position of the neutral axis with regard to the flange in tension:
zt = hp - zc = 198 -102,3 = 95,7mm
Second moment of area:
bp2t3 cp3t
h13t h23t be1t3 be2(�dt)3 ceff 3(�dt)
Ieff,y = + + + + + + +
12 12 12 12 12 12 12
+ cp t(zt - cp 2)2 + bp2tzt 2 + h2t(zt - h2 2)2 + h1t(zc - h1 2)2 +
+ be1t zc2 + be2(�dt) zc2 + ceff (�dt)(zc - ceff 2)2
Ieff,y = 4140000 mm4
Effective section modulus:
- with regard to the flange in compression
Ieff,y 4140000
Weff,y,c = = = 40460 mm3
zc 102,3
- with regard to the flange in tension
Ieff,y 4140000
Weff,y,t = = = 43260 mm3
zt 95,7
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Example: Calculation of effective section properties for a cold-formed lipped channel section in bending
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, 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 23/08/06
Coordinator
TRANSLATED DOCUMENT
This Translation made and checked by:
Translated resource approved by:
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.