formate la rece 2

7/28/2019 Formate La Rece 2

1/10

Document Ref: SX023a-EN-EU Sheet 1 of 9Title

CALCULATION SHEET

Example: Calculation of effective section properties for a

cold-formed lipped channel section in compression

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 lipped channelsection 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 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 mm200=h

Total width of upper flange mm741 =b

Total width of bottom flange mm662 =b

Total width of edge fold mm8,20=c

Internal radius mm3=r

Nominal thickness mm2nom =t

Steel core thickness mm961,t= Basic yield strength

2

yb mmN350=f

Modulus of elasticity 2mmN210000=E

Poissons ratio 3,0=

Partial factor 01M0 ,=

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 upper flange mm72274nom1p1 === tbb

Width of bottom flange mm64266nom2p2 === tbb

Width of edge fold mm819228202nomp ,,tcc ===

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

CreatedonMonday,

March04,

2013

Thismaterialiscopyright-allrightsreserved.

Useofthisdocumentissu

bjecttothetermsandconditionsoftheAccessSteelLicenceAgreement
http://www.access-steel.com/discovery/linklookup.aspx?id=EC327http://www.access-steel.com/discovery/linklookup.aspx?id=EC327http://www.access-steel.com/discovery/linklookup.aspx?id=EC257http://www.access-steel.com/discovery/linklookup.aspx?id=EC257http://www.access-steel.com/discovery/linklookup.aspx?id=EC257http://www.access-steel.com/discovery/linklookup.aspx?id=EC257http://www.access-steel.com/discovery/linklookup.aspx?id=EC327http://www.access-steel.com/discovery/linklookup.aspx?id=EC327


2/10


CALCULATION SHEET






Checking of geometrical propor tions

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

are satisfied:

60tb 6075,3796,1741


3/10


CALCULATION SHEET






Effective width of the compressed flanges

The stress ratio: 1= (uniform compression), so the buckling factor is:

for internal compression element.4=k

yb235 f=

EN1993-1-3

5.5.2 and

EN1993-1-5

4.4

For the upper flange:

The relative slenderness:

78904350235428

96172428

p1b1p, ,

,,

k,

tb

===

The width reduction factor is:

( ) ( )9140

7890

13055078903055022

b1p,

b1p,

1 ,,

,,,=

+=

+=

The effective width is:

mm865729140p11eff1 ,,bb ===

mm9328655050 eff1e12e11 ,,,b,bb ====

For the bottom flange:


70204350235428

96164

428

p2

b2p, ,,

,

k,

tb=

==


( ) ( ) 97807020

13055070203055022

b2p,

b2p,

2 ,,

,,, =+=+=


mm662649780p22eff2 ,,bb ===

mm3316625050 eff2e22e21 ,,,b,bb ====


CreatedonMonday,

March04,

2013



http://www.access-steel.com/discovery/linklookup.aspx?id=EC313http://www.access-steel.com/discovery/linklookup.aspx?id=EC313http://www.access-steel.com/discovery/linklookup.aspx?id=EC167http://www.access-steel.com/discovery/linklookup.aspx?id=EC167http://www.access-steel.com/discovery/linklookup.aspx?id=EC167http://www.access-steel.com/discovery/linklookup.aspx?id=EC167http://www.access-steel.com/discovery/linklookup.aspx?id=EC313http://www.access-steel.com/discovery/linklookup.aspx?id=EC313


4/10


5/10


CALCULATION SHEET







mm81918192peff2 ,,cc ===

Effective area of the bottom edge stiffener:

( ) ( ) 2eff2e22s2 mm2100819331961 ,,,,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

s

scr,

2

A

IEK=

where:

Kis the spring stiffness per unit length,

Is is the effective second moment of area of the stiffener.

EN1993-1-3

5.5.3.2(7)

For the upper edge stiffener:

The spring stiffness is:

fp21

3

1p

2

1

2

3

15,0

1

)1(4 khbbbhb

tEK

++

=

with:

1b distance from the web to the centre of the effective area of the stiffener in

compression (upper flange)

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

29,3296,19,3272)(2

effe12

e12e12p11 =+

=+

=tcb

btbbb

EN1993-1-3

5.5.3.1(5)

2b distance from the web to the centre of the effective area of the stiffener

in compression (bottom flange)

mm41,5496,1)8,193,31(

23,3196,13,3164

)(

2

eff2e22

e22e22p22 =+

=

+=

tcb

btbbb


CreatedonMonday,

March04,

2013



http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC258http://www.access-steel.com/discovery/linklookup.aspx?id=EC258http://www.access-steel.com/discovery/linklookup.aspx?id=EC258http://www.access-steel.com/discovery/linklookup.aspx?id=EC258http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259


6/10


CALCULATION SHEET






9703103

2100

s1

s2f ,

,

,

A

Ak === for a member in axial compression

2

1 mmN331,0=K

The effective second moment of area:

( ) ( )

2

eff1e12

2

eff1eff1eff1

2

eff1e12

2

eff1e12

3

eff1

3

e12s1

2221212

++

+++=

cb

cctc

cb

ctb

tctbI

4

s1 mm3663=I so, the elastic critical buckling stress for the upper edge stiffener is

2

s1cr, mmN3093103

366321000033102=

=

,

,

For the bottom edge stiffener:

The spring stiffness is:

fp21

3

2p

2

2

2

3

2

5,0

1

)1(4 khbbbhb

tEK

++

=

,

2

2 mmN406,0=K

The effective second moment of area:

( ) ( )

2

eff2e22

2

eff2eff2eff2

2

eff2e22

2

eff2e22

3

eff2

3

e22s2

2221212

++

+++=

cb

cctc

cb

ctb

tctbI

4

s2 mm3618=I

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

2

s2cr, mmN73502100

361821000040602,

,

,=

=


CreatedonMonday,

March04,

2013





7/10


CALCULATION SHEET






Thickness reduction factord for the edge stiffener

For the upper edge stiffener:


0641309350s1cr,ybd1 ,f ===

The reduction factor will be:

if 650d , 01d ,=

if 381650 d ,,


8/10


CALCULATION SHEET






For the bottom edge stiffener:

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

7480d2 ,= 7440nd2,d2 ,==

mm331e22 ,b = mm32ne22,e22 == bb

mm819eff2 ,c = mm819neff2,eff2 ,cc ==

Final values of effective properties for flanges and lips in compression are:

For the upper flange and lip:

6830d1 ,= mm36e12 =b mm819eff1 ,c =

and mm93211e ,b =

For the bottom flange and lip:

7440d2 ,= mm32e22 =b mm819eff2 ,c =

and mm33121e ,b =

mm34.1683,096,1d1red,1 === tt

mm46,1744,096,1d2red,2 === tt

EN1993-1-3 5.5.3.2(12)

Effective section properties of the web

The stress ratio: 1= (uniform compression), so the buckling factor is:

for internal compression element.4=k

yb235 f=


17124350235428

961198

428

p

hp, ,,

,

k,

th=

==


( ) ( )4140

1712

13055017123055022

hp,

hp,,

,

,,,=

+=

+=

EN1993-1-3

5.5.2

and

EN1993-1-5

4.4


CreatedonMonday,

March04,

2013



http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC313http://www.access-steel.com/discovery/linklookup.aspx?id=EC313http://www.access-steel.com/discovery/linklookup.aspx?id=EC167http://www.access-steel.com/discovery/linklookup.aspx?id=EC167http://www.access-steel.com/discovery/linklookup.aspx?id=EC167http://www.access-steel.com/discovery/linklookup.aspx?id=EC167http://www.access-steel.com/discovery/linklookup.aspx?id=EC313http://www.access-steel.com/discovery/linklookup.aspx?id=EC313http://www.access-steel.com/discovery/linklookup.aspx?id=EC259http://www.access-steel.com/discovery/linklookup.aspx?id=EC259


9/10


CALCULATION SHEET






The effective width of the web is:

mm821984140peff === ,hh

mm41825050 effe2e1 ==== ,h,hh

Effective section properties

Effective cross-section area:

( ) ( )[ ]d2eff2e22d1eff1e12e2e1e21e11eff cbcbhhbbtA +++++++=

2

eff mm7436,A = Position of the centroidal axis with regard to the upper flange:

( )

eff

d1

2

eff1

2

e1e2pe2e21d2e22p

eff2pd2eff2

G1

2222

A

chhhhbbh

chct

z

++

+++

=

mm4498G1 ,z =

Position of the centroidal axis with regard to the bottom flange:

mm56994498198G1pG2 ,,zhz ===


CreatedonMonday,

March04,

2013





10/10

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

channel section in compression

SX023a-EN-EU.doc

Quality Record

RESOURCE TITLE Example: Calculation of effective section properties for a cold-formedlipped channel section in compression

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 Mller RWTH 11/4/06

5. Spain J Chica Labein 12/4/06

Resource approved by TechnicalCoordinator

G W Owens SCI 11/9/06

TRANSLATED DOCUMENT

This Translation made and checked by:

Translated resource approved by:

Page 10


CreatedonMonday,

March04,

2013




formate la rece 2

Documents