Cold formed bending

7/22/2019 Cold formed bending

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Document Ref: T3704_T3706-DFE Sheet 1 of 6Title Example: Design and serviceabili ty limit state check of a

cold-formed steel member i n bending

Eurocode Ref EN 1993-1-3

Made by V. Ungureanu, A. Ruff Date Dec 2005

CALCULATION SHEET

Checked by D. Dubina Date Dec 2005

T3704_T3706-DFE.doc

Example: Design and serviceability limit statecheck of a cold-formed steel member in bending

This example considers the design of a simply supported lipped channel

section fl oor j oist. I t is assumed that the upper and bottom f langes are

continuously laterally restrained. Serviceability limit state check is also

considered.

Basic Data

Span of joist m5=L

Spacing between joists m6,0=S

Distributed loads applied to the joist:

self-weight of the beam mkN060beamG, ,q =

lightweight slab 2mkN680,

mkN41060680slabG, ,,,q ==

dead load mkN47,0slabG,beamG,G =+= qqq

imposed load 2mkN50,2

mkN50,16,050,2Q ==q

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 mm961,t=

Basic yield strength 2yb mmN350=f

Modulus of elasticity 2mmN210000=E

Poissons ratio 3,0=


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CALCULATION SHEET


T3704_T3706-DFE.doc

Partial factors 0,1M0 =

0,1M1=

35,1G = permanent loads

50,1Q = variable loads

EN1993-1-32(3)

EN1990

Design of the joist for Ultimate Limit State

Effective section properties at the ultimate limit state

Second moment of area of cold-formed lipped channel section subjected

to bending about its major axis: 4yeff, mm4139861=I

Position of the neutral axis:

- from the flange in compression: mm3102c ,z =

- from the flange in tension: mm795t ,z =

Effective section modulus:

- with respect to the flange in compression:

3

c

yeff,

y,ceff, mm404633,102

4139861===

z

IW

- with respect to the flange in tension:

3

t

yeff,

ty,eff, mm432647,95

4139861===

z

IW

( ) 3ty,eff,cy,eff,yeff, mm40463== W,WminW

T3701a

Applied loading on the joist at ULS

mkN89,250,150,147,035,1QQGGd =+=+= qqq

Maximum applied bending moment (at midspan) about the major axis y-y:

kNm039858928 22dEd ,,LqM ===

EN1990

Check of bending resistance at ULS

Design moment resistance of the cross-section for bending:

kNm161401103501040463 39

M0ybyeff,Rdc,

,,fWM === EN1993-1-36.1.4.1(1)


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CALCULATION SHEET


T3704_T3706-DFE.doc

Verification of bending resistance:

163801614

039

Rdc,

Ed

EN1993-1-3

6.1.5


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CALCULATION SHEET


T3704_T3706-DFE.doc

The relative slenderness w for webs without longitudinal stiffeners:

427,1210000

350

96,1

2200346,0

346,0346,0ybnomybw

w

=

=

==E

f

t

th

E

f

t

s

8304271w ,, >= so:

2wybbv mmN731174271350480480 ,,,f,f ===

( )

kN74501

10731171096190sin

102200 333

Rdb, ,,

,,

V =

=

Design shear resistance

( ) kN,7457,45;42,78Rdb,Rdpl,Rdc, === minV,VminV

Verification of shear resistance

11580745

2257

Rdc,

Ed


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CALCULATION SHEET


T3704_T3706-DFE.doc

The local transverse resistance of the web

The bearing length is: mm80s =s

For 60816,4096,180s


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CALCULATION SHEET


T3704_T3706-DFE.doc

Effective section properties at the serviceability limit state

Second moment of area for SLS:

( )( )effgrgr

grfic

IIII =

with:

4

gr mm4495921=I is the second moment of area of the gross cross-section

EN1993-1-3

7.1(3)

gr maximum compressive bending stress in SLS

mm8896grc, ,z = position of the centroidal axis with regard to the

compressed flange

26

grc,gr

serEd,

gr

serEd,

gr mmN7413288964495921

10166,

,

,

zI

M

W

M=

===

2

yb mmN350== f

( ) 4yeff,ff mm4139861==II e

( ) 4fic mm436088341398614495921350

741324495921 == ,I

Deflection check

Deflection of the joist:

mm51,174360883210000

500097,1

384

5

384

5 4

fic

4

serd, =

==

EI

Lq

The deflection is L/286 OK

Note1: the limits of deflection should be specified by the client. The

National Annex may specify some limits. Here the result may be considered

as fully satisfactory.

Note 2: concerning the vibration, the National Annex may specify limits

concerning the frequency. Here the total deflection is acceptably low, for this

reason there is no problem of vibration.

EN 1993-1-1

7.2.1

EN 1993-1-1

7.2.3


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Example: Design and serviceabili ty limi t state check of a cold-formed steel

member in bending

T3704_T3706-DFE.doc

Page 7

Quality Record

RESOURCE TITLE Example: Design and serviceability limit state check of a cold-formedsteel member in bending

Reference(s)

ORIGINAL DOCUMENT

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Created by

Technical content checked by

Editorial content checked by

Technical content endorsed by thefollowing STEEL Partners:

1. UK SCI

2. France CTICM

3. Sweden SBI

4. Germany RWTH

5. Spain Labein

Resource approved by TechnicalCoordinator

TRANSLATED DOCUMENT

This Translation made and checked by:

Translated resource approved by:


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Example: Design and serviceabili ty limi t state check of a cold-formed steel

member in bending

T3704_T3706-DFE.doc

Page 8

Wrapper InformationTitle* Example: Design and serviceability limit state check of a cold-formed steel member in

bending

Series

Description* This example considers the design of a simply supported lipped channel section floor joist. Itis assumed that the upper and bottom flanges are continuously laterally restrained.Serviceability limit state check is also considered.

Access Level* Expertise

Identifiers* Filename C:T3704_T3706-DFE.doc

Format Microsoft Office Word; 8 Pages; 589kb;

Resource Type Worked exampleCategory*

Viewpoint

Subject* Application Area(s) Residential buildings

Created Date 25/12/2005

Last Modified Date

Checked Date

Valid From

Dates

Valid To

Language(s)*

Author

Checked By

Approved by

Editor

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Keywords* Ultimate limit state, serviceability limit state, bending, lipped channel section, cold-formed,joist

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Cold formed bending

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