proracun - example cold formed steel

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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 sectionproperties for a cold-formed l ipped channelsection 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 softwareor 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 mm200h

Total width of flange in compression mm741 b

Total width of flange in tension mm662 b

Total width of edge fold mm8,20c

Internal radius mm3r

Nominal thickness mm2nom t

Steel core thickness mm96,1t

Basic yield strength 2yb mm N350 f

Modulus of elasticity2

mm N210000 E

Poisson’s ratio 3,0

Partial factor 00,1M0

EN1993-1-3

§ 3.2.4(3)

EN1993-1-3

§ 2(3)

The dimensions of the section centre line are:

Web height mm1982200nom p t hh

Width of flange in compression mm72274nom1 p1 t bb

Width of flange in tension mm64266nom2 p2 t bb

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

C r

e a t e d o n W e d n e s d a y ,

J u l y 1 8 ,

2 0 1 2

T h

i s m a t e r i a l i s c o p y r i g h t - a l l r i g h t s r e s e r v e d .

U s e o f t h

i s d o c u m e n t i s s u b j e c t t o t h e t e r m s a n d c o n d i t i o n s o f t h e A c c e s s S t e e l L i c e n c e A g r e e m e n t


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Title

CALCULATION SHEET






Width of edge fold mm8,19228,202nom p t cc

Checking of geometrical proportions

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

are satisfied:

60t b 6075,3796,1741 t b – OK

50t c 5061,1096,18,20 t c – OK

500t h 50004,10296,1200 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:

6,02,0 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 t r – OK

10,0 p br 10,004,07231 p br – OK

10,005,06432 p br – OK

EN1993-1-3

§ 5.1(3)

Gross section properties

2 p p2 p1 p br

mm73219864728,19296,12 hbbct A

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

mm88,96222 br

2 p

2 p p p2 p p p

b1

A

t chhbchc z


C r e a t e d o n W e d n e s d a y ,

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Title

CALCULATION SHEET






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 isnot reduced ( 0ybEd com, / M f ).

EN1993-1-3

§ 5.5.3.2 (3)

Effective width of the compressed flange

The stress ratio: 1 (uniform compression), so

the buckling factor is: for internal compression element.4 k

yb235 f

The relative slenderness:

789,043502354,28

96,172

4,28

p1

b p, k

t b

The width reduction factor is:

914,0

789,0

13055,0789,03055,022

b p,

b p,

The effective width is:

mm865729140 p1eff , ,bb

mm9328655050 eff e2e1 , , ,b ,bb

EN1993-1-3

§ 5.5.2

and

EN1993-1-5

§ 4.4



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Effective width of the edge fold

The buckling factor is:

if 35,0 p1c p, bb : 5,0 k

if 6,035,0 p1c p, bb : 3 2 p1c p, 35,083,05,0 bbk

35,0275,0728,19 p1c p, bb so 5,0 k

EN1993-1-3

§ 5.5.3.2 (5a)


614,05,03502354,28

96,18,19

4,28

p

p,c k

t c

EN1993-1-5

§ 4.4


13,1614,0

188,0614,0188,022

c p,

c p,

but 1 so 1

The effective width is:

mm8,198,191 peff cc

Effective area of the edge stiffener:

2eff e2s

mm3,1038,199,3296,1 cbt 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

scr A

I E K 2,

where:

EN1993-1-3

§ 5.5.3.2 (7)



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Title

CALCULATION SHEET






K is the spring stiffness per unit length:

f p21

3

1 p

2

1

2

3

5,0

1

)1(4 k hbbbhb

t E K

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

eff e2

e2e2 p11

t cb

bt bbb

0f k for bending about the y-y axis

mm N439,0K

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

e2s

2221212

cb

cct c

cb

ct b

t ct b I

4

s mm3663 I

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

2

scr, mm N78,3553,103

3663210000439,02



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Title

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Thickness reduction factor d for the edge stiffener


992,078,355350scr,ybd f

The reduction factor will be:

if 65,0d 0,1d

if 38,165,0 d d d 723,047,1

if 38,1d

d d 66,0

38,1992,065,0 d so 753,0992,0723,047,1d

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 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 obtained using:

M0ybd iEd,com, f and d pred p,

The iteration stops when the reduction factor converges.

EN1993-1-3

§ 5.5.3.2 (10)

Initial values (iteration 1): Final values (iteration n):

753,0d 737,0nd,d

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 mm9,35e2 b mm8,19eff c

and mm9,32e1 b



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Title

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mm44,1737,096,1d red 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 e2e1 p p2 p

d

2

eff

2

p p p2 p p p

c

222

cbbhbc

chhbchch

mm6,101c h

The stress ratio:

949,06,1011986,101

c

pc

h

hh

The buckling factor: 2

78,929,681,7 k 58,22 k


914,058,223502354,28

96,1198

4,28

p

h p,

k

t h

EN1993-1-5

§ 4.4

(Table 4.1)


959,0

914,0

949,03055,0914,03055,022

h p,

h p,



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Title

CALCULATION SHEET






The effective width of the zone in compression of the web is:

mm5,976,101959,0ceff hh

Near the flange in compression:

mm395,974,04,0 eff e1 hh

Near the neutral axis:

mm5,585,976,06,0 eff e2 hh

The effective width of the web is:

Near the flange in compression:

mm39e11 hh

Near the flange in tension:

mm9,1545,586,101198e2c p2 hhhh

Effective section properties

Effective cross-section area:

])([ d eff 2e1e212 p peff cbbhhbct A

737,08,199,359,329,15439648,1996,1eff A

2

eff mm2,689 A

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

eff

d

2

eff

2

12 p2 p p2 p p pc

2222

A

chhhhhbchct z

mm3,102c z



J u l y 1 8 ,

2 0 1 2

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

mm7,953,102198c pt zh z

Second moment of area:

2

eff cd eff

2

cd e2

2

ce1

2

1c1

2

2t2

2

t2 p

2

pt p

d

3

eff

3

d e2

3

e1

3

p

3

p23

2

3

1yeff,

)2)(()(

)2()2()2(

12

)(

12

)(

1212121212

c zt c zt b zt b

h zt hh zt htzbc zt c

t ct bt bt ct bt ht h I

4yeff, mm4140000 I

Effective section modulus:

- with regard to the flange in compression

3

c

yeff,

cy,eff, mm404603,102

4140000

z

I W

- with regard to the flange in tension

3

t

yeff,

ty,eff, mm432607,95

4140000

z

I W

E x a m p l e : C a l c u l a t

C

r

e

a

t

e

d

o

n

W

e

d

n

e

s

d

a

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J

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T

h

i

s

m

a

t

e

r

i

a

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Example: Calculation of effective section properties for a cold-formed lippedchannel section in bending

SX022a-EN-EU.doc

Quality Record

RESOURCE TITLE Example: Calculation of effective section properties for a cold-formedlipped 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 thefollowing 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 TechnicalCoordinator

G W Owens SCI 23/08/06

TRANSLATED DOCUMENT

This Translation made and checked by:

Translated resource approved by:



J u l y 1 8 ,

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