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 mm200=h

Total width of flange in compression mm741 =b

Total width of flange in tension mm662 =b Total width of edge fold mm8,20=c Internal radius mm3=r

Nominal thickness mm2nom =t

Steel core thickness mm96,1=t

Basic yield strength 2yb mmN350=f

Modulus of elasticity 2mmN210000=E Poisson’s ratio 3,0=ν

Partial factor 00,1M0 =γ

EN1993-1-3 § 3.2.4(3) EN1993-1-3 § 2(3)

The dimensions of the section centre line are:

Web height mm1982200nomp =−=−= thh

Width of flange in compression mm72274nom1p1 =−=−= tbb

Width of flange in tension mm64266nom2p2 =−=−= tbb

Example: Calculation of effective section properties for a cold-formed lipped channel section in bendingC

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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 mm8,19228,202nomp =−=−= tcc

Checking of geometrical proportions

The design method of EN1993-1-3 can be applied if the following conditions are satisfied:

60≤tb 6075,3796,1741 <==tb – OK

50≤tc 5061,1096,18,20 <==tc – OK

500≤th 50004,10296,1200 <==th – 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:

6,02,0 ≤≤ bc 28,0748,201 ==bc 0,60,280,2 << – OK

32,0668,202 ==bc 0,60,320,2 << – OK

The influence of rounding of the corners is neglected if:

5tr ≤ 553,196,13 <==tr – OK

10,0p ≤br 10,004,07231p <==br – OK

10,005,06432p <==br – OK

EN1993-1-3 § 5.1(3)

Gross section properties

( ) ( ) 2pp2p1pbr mm73219864728,19296,12 =+++××=+++= hbbctA

Position of the neutral axis with respect to the flange in compression:

( )[ ]mm88,96

222

br

2p

2ppp2ppp

b1 =+++−

=A

tchhbchcz

Example: Calculation of effective section properties for a cold-formed lipped channel section in bendingC

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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 ( 0ybEdcom, / Mf γσ = ).

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. 4σ =k

yb235 f=ε

The relative slenderness:

789,043502354,28

96,1724,28 σ

p1bp, =

××==

ktb

ελ

The width reduction factor is:

( ) ( ) 914,0789,0

13055,0789,03055,022

bp,

bp, =+×−

=+−

=λ

ψλρ

The effective width is: mm865729140p1eff ,,bb =×== ρ

mm9328655050 effe2e1 ,,,b,bb =×===

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 bendingC

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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 35,0p1cp, ≤bb : 5,0σ =k

if 6,035,0 p1cp, ≤< bb : ( )3 2p1cp,σ 35,083,05,0 −+= bbk

35,0275,0728,19p1cp, <==bb so 5,0σ =k

EN1993-1-3 § 5.5.3.2 (5a)

The relative slenderness:

614,05,03502354,28

96,18,194,28 σ

pp,c =

××==

ktc

ελ

EN1993-1-5 § 4.4

The width reduction factor is:

13,1614,0

188,0614,0188,022

cp,

cp, =−

=−

=λ

λρ

but 1≤ρ so 1=ρ

The effective width is:

mm8,198,191peff =×== cc ρ

Effective area of the edge stiffener:

( ) ( ) 2effe2s mm3,1038,199,3296,1 =+×=+= cbtA

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

sscr A

IEK2, =σ

where:

EN1993-1-3 § 5.5.3.2 (7)

Example: Calculation of effective section properties for a cold-formed lipped channel section in bendingC

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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:

fp213

1p2

12

3

5,01

)1(4 khbbbhbtEK

++⋅

−=

ν

with:

1b – 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)

mm73,6196,1)8,199,32(

29,3296,19,3272)(2

effe2

e2e2p11 =

×+××

−=+

−=tcb

btbbb

0f =k for bending about the y-y axis

mmN439,0=K

sI is the effective second moment of area of the stiffener:

( ) ( )

2

effe2

2effeff

eff

2

effe2

2eff

e2

3eff

3e2

s 2221212 ⎥⎦

⎤⎢⎣

⎡+

−+⎥⎦

⎤⎢⎣

⎡+

++=cb

cctccb

ctbtctbI

4s mm3663=I

so, the elastic critical buckling stress for the edge stiffener is

2scr, mmN78,355

3,1033663210000439,02

=×××

=σ

Example: Calculation of effective section properties for a cold-formed lipped channel section in bendingC

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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 χd for the edge stiffener

The relative slenderness:

992,078,355350scr,ybd === σλ f

The reduction factor will be:

if 65,0d ≤λ 0,1d =χ

if 38,165,0 d << λ dd 723,047,1 λχ −=

if 38,1d ≥λ dd 66,0 λχ =

38,1992,065,0 d <=< λ so 753,0992,0723,047,1d =×−=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 χd < 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:

M0ybdiEd,com, γχσ f= and dpredp, χλλ =

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):

753,0d =χ 737,0nd,d == χχ

mm9,32e2 =b mm9,35ne2,e2 == bb

mm8,19eff =c mm8,19neff,eff == cc

Final values of effective properties for flange and lip in compression are:

737,0d =χ mm9,35e2 =b mm8,19eff =c

and mm9,32e1 =b

Example: Calculation of effective section properties for a cold-formed lipped channel section in bendingC

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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 44,1737,096,1dred =×== χtt 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:

( )( ) deffe2e1pp2p

d2

eff2

ppp2pppc

222χχ

cbbhbcchhbchc

h+++++

+++−= mm6,101c =h

The stress ratio:

949,06,1011986,101

c

pc −=−

=−

=h

hhψ

The buckling factor: 2σ 78,929,681,7 ψψ +−=k 58,22σ =k

The relative slenderness:

914,058,223502354,28

96,11984,28 σ

php, =

××==

kth

ελ

EN1993-1-5 § 4.4

(Table 4.1)

The width reduction factor is:

( ) ( ) 959,0914,0

949,03055,0914,03055,022

hp,

hp, =−×−

=+−

=λ

ψλρ

Example: Calculation of effective section properties for a cold-formed lipped channel section in bendingC

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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:

mm5,976,101959,0ceff =×== hh ρ

Near the flange in compression:

mm395,974,04,0 effe1 =×== hh

Near the neutral axis:

mm5,585,976,06,0 effe2 =×== hh

The effective width of the web is:

Near the flange in compression:

mm39e11 == hh

Near the flange in tension:

( ) ( ) mm9,1545,586,101198e2cp2 =−−=−−= hhhh

Effective section properties

Effective cross-section area:

])([ deff2e1e212ppeff χcbbhhbctA ++++++=

( )[ ]737,08,199,359,329,15439648,1996,1eff ×++++++×=A

2eff mm2,689=A

Position of the neutral axis with regard to the flange in compression:

( ) ( )[ ]eff

d2

eff2

12p2pp2pppc

2222A

chhhhhbchctz

χ++−++−=

mm3,102c =z

Example: Calculation of effective section properties for a cold-formed lipped channel section in bendingC

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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:

mm7,953,102198cpt =−=−= zhz

Second moment of area:

2effcdeff

2cde2

2ce1

21c1

22t2

2t2p

2ptp

d3

eff3

de23

e13

p3

p23

23

1yeff,

)2)(()(

)2()2()2(12

)(12

)(1212121212

cztcztbztb

hzthhzthtzbcztc

tctbtbtctbththI

−+++

+−+−++−+

+++++++=

χχ

χχ

4yeff, mm4140000=I

Effective section modulus:

- with regard to the flange in compression

3

c

yeff,cy,eff, mm 40460

3,1024140000

===z

IW

- with regard to the flange in tension

3

t

yeff,ty,eff, mm 43260

7,954140000

===z

IW

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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 bendingC

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ed o

n M

onda

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term

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ons

of th

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