example design and serviceability limit state check of a cold-formed steel member in bending

Document Ref: SX026a-EN-EU Sheet 1 of 6 Title

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

CALCULATION SHEET

Eurocode Ref EN 1993-1-3 Made by V. Ungureanu, A. Ruff Date Dec 2005

Checked by D. Dubina Date Dec 2005


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

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

Span of joist m5=L

Spacing between joists m6,0=S

Distributed loads applied to the joist:

mkN060beamG, ,q = self-weight of the beam

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

mm741 =bTotal width of flange in compression

mm662 =bTotal width of flange in tension Total width of edge fold mm8,20=c

Internal radius mm3=r

mm2nom =tNominal thickness

Steel core thickness mm961,t =2

yb mmN350=fBasic yield strength 2mmN210000=EModulus of elasticity

Poisson’s ratio 3,0=ν

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

reat

ed o

n F

riday

, May

24,

201

3T

his

mat

eria

l is

copy

right

- a

ll rig

hts

rese

rved

. Use

of t

his

docu

men

t is

subj

ect t

o th

e te

rms

and

cond

ition

s of

the

Acc

ess

Ste

el L

icen

ce A

gree

men

t



CALCULATION SHEET



EN1993-1-3Partial factors 0,1M0 =γ §2(3) 0,1M1 =γ

EN1990 35,1G =γ – permanent loads

– variable loads 50,1Q =γ

Design of the joist for Ultimate Limit State

Effective section properties at the ultimate limit state SX022Second moment of area of cold-formed lipped channel section subjected

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

Position of the neutral axis:

mm3102c ,z =- from the flange in compression:

mm795t ,z =- from the flange in tension:

Effective section modulus:

- with respect to the flange in compression:

3

c

yeff,cy,eff, mm 40460

3,1024140000

===z

IW

- with respect to the flange in tension:

3

t

yeff,ty,eff, mm 43260

7,954140000

===z

IW

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

Applied loading on the joist at ULS

EN1990 mkN89,250,150,147,035,1QQGGd =×+×=+= qqq γγ

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

kNm039858928 22dEd ,,LqM =×==

Check of bending resistance at ULS

Design moment resistance of the cross-section for bending:

EN1993-1-3kNm161401103501040463 39M0ybyeff,Rdc, ,,fWM =×××== −γ

§6.1.4.1(1)


reat

ed o

n F

riday

, May

24,

201

3T

his

mat

eria

l is

copy

right

- a

ll rig

hts

rese

rved

. Use

of t

his

docu

men

t is

subj

ect t

o th

e te

rms

and

cond

ition

s of

the

Acc

ess

Ste

el L

icen

ce A

gree

men

t

http://www.access-steel.com/discovery/linklookup.aspx?id=EC257

http://www.access-steel.com/discovery/linklookup.aspx?id=SX022




CALCULATION SHEET



Verification of bending resistance: EN1993-1-1

163801614039

Rdc,

Ed <== ,,,

MM

§6.2.5(1) – OK

Check of shear resistance at ULS Design to shear force

Maximum applied shear force

kN225,72589,22dEd =×== LqV

Design plastic shear resistance

( ) ( )M0

yb

M0

ybvRdpl,

3sin3

γφ

γ

fthfA

V

w

==EN1993-1-1 §6.2.6(2)

where:

vA – is the shear area

nomw thh −= – is the web height

– is the slope of the web relative to the flanges. °= 90φ

( ) ( )kN4278

01

3103501096190

102200 333

Rdpl, ,,

,sinV =

××××°×−

=

−−

Design shear buckling resistance

M0

bvw

Rdb,sinγφ

tfh

V =

EN1993-1-3

§6.1.5

where:

bvf is the shear strength, considering buckling

For a web with stiffening at the support:

if ybbv 58,0 ff = 83,0w ≤λ

wybbv 48,0 λff = if 83,0w >λ


reat

ed o

n F

riday

, May

24,

201

3T

his

mat

eria

l is

copy

right

- a

ll rig

hts

rese

rved

. Use

of t

his

docu

men

t is

subj

ect t

o th

e te

rms

and

cond

ition

s of

the

Acc

ess

Ste

el L

icen

ce A

gree

men

t






CALCULATION SHEET



The relative slenderness for webs without longitudinal stiffeners: wλ

427,1210000

35096,1

2200346,0

346,0346,0 ybnomybww

=×−

×

=−

==Ef

tth

Ef

tsλ

so: 8304271w ,, >=λ

2wybbv mmN7,117427,135048,048,0 =×== λff

( )kN7,45

0,1

107,1171096,190sin

102200 333

Rdb, =××××

°×−

=

−−

V

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

Verification of shear resistance

EN1993-1-111580

7452257

Rdc,

Ed <== ,,

,VV – OK

§6.2.6(1)

Check of local transverse resistance at ULS Support reaction:

kN225,72589,22dEd =×== LqF

EN1993-1-3To obtain the local transverse resistance of the web for a cross section with a single unstiffened web, the following criteria should be satisfied:

§6.1.7.2 (1)

20002,10196,1198 <=200w ≤th – OK

6≤tr 653,196,13 <= – OK

°≤≤° 9045 φ

where φ is the slope of the web relative to the flanges: – OK °= 90φ


reat

ed o

n F

riday

, May

24,

201

3T

his

mat

eria

l is

copy

right

- a

ll rig

hts

rese

rved

. Use

of t

his

docu

men

t is

subj

ect t

o th

e te

rms

and

cond

ition

s of

the

Acc

ess

Ste

el L

icen

ce A

gree

men

t





CALCULATION SHEET



The local transverse resistance of the web The bearing length is: mm80s =s EN1993-1-3

§6.1.7.2 (2) 60816,4096,180s <==tsFor the local transverse resistance of the web

is: Figure 6.7

Rdw,R

M1

yb2sw

321

Rdw,

01,01132

92,5

γ

fttsthkkk

R⎥⎦⎤

⎢⎣⎡ +⎥⎦⎤

⎢⎣⎡ −

=

where:

EN1993-1-3kk 33,033,11 −= with 535,1228350228yb === fk §6.1.7.2(3)

823,0535,133,033,11 =×−=k

92,096,1315,015,115,015,12 =×−=−= trk

( ) ( ) 190903,07,0903,07,0 223 =×+=+= φk

N73960,1

35096,196,1

8001,01132

96,119892,5192,0823,0 2

Rdw, =××⎥⎦

⎤⎢⎣

⎡ ×+×⎥⎦⎤

⎢⎣⎡ −×××

=R

kN396,7Rdw, =R

Verification of local transverse force EN1993-1-3kN396,7kN225,7 Rdw,Ed =<= RF – OK

§6.1.7.1(1)

2 Verification for Serviceability Limit State

Applied loading on the joist at SLS (frequent combination)

mkN97,150,147,0QGserd, =+=+= qqqEN1990 The maximum applied bending moment:

kNm166859718 22serd,serEd, ,,LqM =×==

E x a m p l e : D e s i g n a n d s e r v i c e a b i l i t y l i m i t s t a t e c h e c k o f a c o l d - f o r m e d s t e e l m e m b e r i n b e n d i n gC

re

at

ed

o

n

Fr

id

ay

,

Ma

y

24

,

20

13

Th

is

m

at

er

ia

l

is

c

op

yr

ig

ht

-

a

ll

r

ig

ht

s

re

se

rv

ed

.

Us

e

of

t

hi

s

do

cu

me

nt

i

s

su

bj

ec

t

to

t

he

t

er

ms

a

nd

c

on

di

ti

on

s

of

t

he

A

cc

es

s

St

ee

l

Li

ce

nc

e

Ag

re

em

en

t






CALCULATION SHEET



Effective section properties at the serviceability limit state

Second moment of area for SLS:

( )( )effgr

grgrfic σ

σσ

IIII −−= EN1993-1-3

with: §7.1(3) 4

gr mm4496000=I – is the second moment of area of the gross cross-section

– maximum compressive bending stress in SLS grσ

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

26

grc,gr

serEd,

gr

serEd,gr mmN7,132

88,9644960001016,6

=×

===zI

MW

Mσ

2yb mmN350== fσ

( ) 4yeff,ff mm4140000== II eσ

( ) 4fic mm436100041400004496000

3507,1324496000 =−×−=I

Deflection check

Deflection of the joist:

mm51,174361000210000

500097,1384

5384

5 4

fic

4serd, =

××

×==EI

Lqδ

The deflection is L/286 – OK

Note 1: 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.

EN 1993-1-1 §7.2.1

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 §7.2.3


reat

ed o

n F

riday

, May

24,

201

3T

his

mat

eria

l is

copy

right

- a

ll rig

hts

rese

rved

. Use

of t

his

docu

men

t is

subj

ect t

o th

e te

rms

and

cond

ition

s of

the

Acc

ess

Ste

el L

icen

ce A

gree

men

t





SX026a-EN-EU

Quality Record

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

Reference(s)

ORIGINAL DOCUMENT

Name Company Date

Created by V. Ungureanu, A. Ruff BRITT Ltd. Timisoara, Romania

Technical content checked by D. Dubina BRITT Ltd. Timisoara, 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 Müller RWTH 11/4/06

5. Spain J Chica Labein 12/4/06

Resource approved by Technical Coordinator

G W Owens SCI 11/9/06


reat

ed o

n F

riday

, May

24,

201

3T

his

mat

eria

l is

copy

right

- a

ll rig

hts

rese

rved

. Use

of t

his

docu

men

t is

subj

ect t

o th

e te

rms

and

cond

ition

s of

the

Acc

ess

Ste

el L

icen

ce A

gree

men

t

example design and serviceability limit state check of a cold-formed steel member in bending

Documents