cadru portal cu o deschidere

8/10/2019 Cadru Portal Cu o Deschidere

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Document Ref: SX029a-EN-EU Sheet 1 of 28Title Example: Elastic analysis of a single bay portal frame

Eurocode Ref

Made by Valrie Lemaire Date April 2006

CALCULATION SHEET

Checked by Alain Bureau Date April 2006

Example: Elastic analysis of a single bay portalframe

A single bay portal frame made of rolled profiles is designed according to EN 1993-1-1. This worked example includes the elastic analysis of the frame using first order theory, and all the verifications of the membersunder ULS combinations.

30,00

5 , 9

8 8

[m]

7, 2 0

7 , 3

0 7 2, 0 0

1 Basic data Total length : b = 72,00 m Spacing: s = 7,20 m Bay width : d = 30,00 m Height (max): h = 7,30 m Roof slope: = 5,0

1

3,00 3,00 3,00 3,00 3,00

1 : Torsional restraints

Example: Elastic analysis of a single bay portal frame

C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

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

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CALCULATION SHEET


2 LoadsEN 1991-1-1

2.1 Permanent loads self-weight of the beam roofing with purlins G = 0,30 kN/m 2

for an internal frame: G = 0,30 7,20 = 2,16 kN/ml

2.2 Snow loads EN 1991-1-3Characteristic values for snow loading on the roof in [kN/m]

S = 0,8 1,0 1,0 0,772 = 0,618 kN/m

for an internal frame: S = 0,618 7,20 = 4,45 kN/m

7 , 3

0

30,00

s = 4,45 kN/m

[m]


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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b j e c t

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CALCULATION SHEET


4 Sections

hw

y y

z

z

t f

t w

b

h

4.1 ColumnTry IPE 600 Steel grade S275

Depth h = 600 mm

Web Depth hw = 562 mm

Depth of straight portion of the web

d w = 514 mm

Width b = 220 mm

Web thickness t w = 12 mm

Flange thickness t = 19 mm f

Fillet r = 24 mm

Mass 122,4 kg/m

Section area A = 156 cm 2

Second moment of area /yy I y = 92080 cm 4

Second moment of area /zz I z = 3386cm 4

Torsion constant I = 165,4 cm 4t

Warping constant I w = 2845500 cm 6

Elastic modulus /yy W el,y = 3069 cm 3

Plastic modulus /yy W pl,y = 3512 cm 3

Elastic modulus /zz W = 307,80 cm 3el,z

Plastic modulus /zz W pl,z = 485,60 cm 3


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


t i s s u

b j e c t

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CALCULATION SHEET


4.2 RafterTry IPE 500 Steel grade S275

Depth h = 500 mm

Web Depth hw = 468 mm

Depth of straight portion of the web

d w = 426 mm

Width b = 200 mm

Web thickness t w = 10,2 mm

Flange thickness t f = 16 mm

Fillet r = 21 mm

Mass 90,7 kg/m

Section area A = 115,50 cm 2


Second moment of area /zz I z = 2141 cm 4

Torsion constant I t = 89,29 cm 4

Warping constant I w = 1249400 cm 6


Plastic modulus /yy W pl,y = 2194 cm 3

Elastic modulus /zz W el,z = 214,1 cm 3

Plastic modulus /zz W pl,z = 335,90 cm 3

5 Global analysisThe joints are assumed to be:

pinned for column bases rigid for beam to column.

EN 1993-1-1 5.2

The frame has been modelled using the EFFEL program.


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


t i s s u

b j e c t

t o t h e

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5.1 Buckling amplification factor EN 1993-1-1cr 5.2.1In order to evaluate the sensitivity of the frame to 2 nd order effects, a buckling

analysis is performed to calculate the buckling amplification factor cr for theload combination giving the highest vertical load: G + max Q QS (combination 101).

For this combination, the amplification factor is: cr = 14,57

The first buckling mode is shown hereafter.

EN 1993-1-1So : cr = 14,57 > 10 5.2.1First order elastic analysis may be used. (3)

5.2 Effects of imperfections EN 1993-1-1 5.3.2The global initial sway imperfection may be determined from (3)

310204,3866,0740,0200

1 = = 0 h =m

where 0 = 1/200

740,030,7

22 ==h

h =

866,0)1

1(5,0 =+m

m = 2 (number of columns)= m

Sway imperfections may be disregarded where H 0,15 V EN 1993-1-1Ed Ed. 5.3.2The effects of initial sway imperfection may be replaced by equivalent

horizontal forces:(4)

H = V in the combination where H < 0,15 V eq Ed Ed Ed


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


t i s s u

b j e c t

t o t h e

t e r m s a n

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Eurocode Ref


CALCULATION SHEET


The following table gives the reactions at supports.

Left column 1 Right column 2 TotalULS

Comb. H Ed,1

kN

V Ed,1

kN

H Ed,2

Kn

V Ed,2

kN

H Ed

kN

V Ed

kN

0,15 V Ed

101 -125,5 -172,4 125,5 -172,4 0 -344,70 51,70

102 95,16 80,74 -24,47 58,19 70,69 138,9 20,83

103 -47,06 -91,77 89,48 -105,3 42,42 -197,1 29,56

104 -34,59 -73,03 77,01 -86,56 42,42 -159,6 23,93

105 43,97 11,97 26,72 -10,57 70,69 1,40 0,21

106 56,44 30,71 14,25 8,17 70,69 38,88 5,83

The sway imperfection has only to be taken into for the combination 101:

V EdkN

H eq = .V EdkN

172,4 0,552

Modelling with H eq for the combination 101

EN 1993-1-1 5.3.2 (7)

5.3 Results of the elastic analysis5.3.1 Serviceability limit s tatesCombinations and limits should be specified for each project or in NationalAnnex.

For this example, the deflections obtained by modeling are as follows:

EN 1993-1-1 7 and

EN 1990

Vertical deflections :

G + Snow: Dy = 124 mm = L/241

Snow only: Dy = 73 mm = L/408

Horizontal deflections:Deflection at the top of column by wind only

D x = 28 mm = h/214


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t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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CALCULATION SHEET


5.3.2 Ultimate limit statesMoment diagram in kNm

Combination 101:

Combination 102:

Combination 103:

Combination 104:


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d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


t i s s u

b j e c t

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CALCULATION SHEET


Combination 105:

Combination 106:

6 Column verificationProfile IPE 600 - S275 ( = 0,92)

The verification of the member is carried out for the combination 101 :

N = 161,5 kN (assumed to be constant along the column)Ed = 122,4 kN (assumed to be constant along the column) V Ed

M = 755 kNm (at the top of the column)Ed

6.1 Classif ication of the cross section

Web: The web slenderness is c / t w = 42,83 EN 1993-1-1 5.5

mm94,4827512

161500

yw

Ed N =

== f t

N d

548,05142

94,485142 w

Nw =+=+=

d d d

> 0,50

49,591548,013

92,0396 =

The limit for Class 1 is : 396 / (13 1) =

Then : c / t w = 42,83 < 59,49 The web is class 1.


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t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


t i s s u

b j e c

t t o t h e

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CALCULATION SHEET


Flange: The flange slenderness is c / t f = 80 / 19 = 4,74 The limit for Class 1 is : 9 = 9 0,92 = 8,28Then : c / t = 4,74 < 8,28 The flange is Class 1 f

So the section is Class 1. The verification of the member will be based onthe plastic resistance of the cross-section.

6.2 Resistance of cross sectionVerification for shear force

Shear area : A = A - 2bt v f + ( t w+2r )t > .hf w.t EN 1993-1-1w 6.2.6 may be conservatively taken equal to 1 (3)

838019)24212(19220215600 =++=v A mm 2 > .hw.t w = 6744 mm 2

V pl,Rd = Av (f y / 3 ) /M0 = (8380 275/ 3 ).10 -3

V = 1330 kN pl,Rd

V / V Ed pl,Rd = 122,40/1330 = 0,092 < 0,50

The effect of the shear force on the moment resistance may be neglected.

Verification to axial force EN 1993-1-1 6.2.4-3 N = A f pl,Rd y / = (15600 275/1,0).10M0 N = 4290 kN pl,Rd N = 161,5 kN < 0,25 N Ed pl ,Rd = 4290 x 0,25 = 1073 kNEN 1993-1-1

and N Ed = 161,5 kN < 3,92710001

275125625,05,0

M0

yww =

=

f t h

6.2.8kN (2)

The effect of the axial force on the moment resistance may be neglected.

Verification to bending moment EN 1993-1-1 6.2.5-3 M = W pl,y,Rd pl,y f y / = (3512 275/1,0).10M0

M = 965,8 kNm pl,y,Rd

M y,Ed = 755 kNm < M = 965,8 kNm pl,y,Rd


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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

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CALCULATION SHEET


6.3 Buckling resistanceThe buckling resistance of the column is sufficient if the following conditionsare fulfilled (no bending about the weak axis, M

EN 1993-1-1z,Ed = 0): 6.3.3

1

M1

Rk y,LT

Edy,yy

M1

Rk y

Ed +

M M

k N

N

1

M1

Rk y,LT

Edy,zy

M1

Rk y

Ed +

M M

k N

N

The k and k yy zy factors will be calculated using the Annex A of EN 1993-1-1.

The frame is not sensitive to second order effects ( cr = 14,57 > 10). Then the buckling length for in-plane buckling may be taken equal to the system length.

EN 1993-1-1 5.2.2

(7)

Lcr,y = 5,99 m

Note: For a single bay symmetrical frame that is not sensitive to second ordereffects, the check for in-plane buckling is generally not relevant. Theverification of the cross-sectional resistance at the top of the column will bedeterminant for the design .

Regarding the out-of-plane buckling, the member is laterally restrained at bothends only. Then :

L = 5,99 m for buckling about the weak axiscr,z L = 5,99 m for torsional bucklingcr,T

and L = 5,99 m for lateral torsional bucklingcr,LT

Buckling about yy Lcr,y = 5,99 m

EN 1993-1-1 Buckling curve : a ( y = 0,21) 6.3.1.2

10005990

10000920802100002

22

ycr,

y2ycr,

== L

EI N

(2)=53190kN Table 6.1

284,0

10.5319027515600

3ycr,

yy =

== N

Af EN 1993-1-1

6.3.1.3 (1)


C r e a

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F e

b r u a r y

2 4

, 2 0 1 1

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l l r i g

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d .

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CALCULATION SHEET


( ) ( )[ ]22yyy 284,02,0284,021,015,02,015,0 ++=++= EN 1993-1-1= 0,5491 6.3.1.2 (1)9813,0

284,05491,05491,0

11222

y2

yy

y =+

=+

=

Buckling about zz L = 5,99 m EN 1993-1-1cr,z 6.3.1.2 Buckling curve : b ( z = 0,34)

(2)

Table 6.1

10005990

1000033862100002

22

zcr,

z2zcr,

== L

EI N = 1956 kN

EN 1993-1-1481,1

10.195627515600

3zcr,

yz =

== N

Af 6.3.1.3 (1)

( ) ( )[ ]22zzz 481,12,0481,134,015,02,015,0 ++=++= EN 1993-1-1= 1,814 6.3.1.2 (1)3495,0

481,1814,1814,1

11222

z2zz

z =+=

+=

Lateral torsional buckling Lcr,LT = 5,99 m

EN 1993-1-1 Buckling curve : c ( LT = 0,49) 6.3.2.3 Moment diagram with linear variation : = 0 C 1 = 1,77Table 6.5

Z2

t2

LTcr,

Z

W2

LTcr,

Z2

1cr EI

GI L

I I

L EI

C M

+= NCCISN003

42

42

4

6

62

2

cr

10.3386210000

10.4,165807705990

10.3386

10.2845500

105990

10000338621000077,1

+

=

M

M cr = 1351 kNm

8455,010.1351

27510.35126

3

cr

yy pl,LT ===

M

f W

( ) 2LTLT,0LTLTLT 15,0 ++= EN 1993-1-1 6.3.2.3 (1)and =0,7540,0LT,0 = with


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t e d o n

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2 4

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t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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CALCULATION SHEET


( )[ ] 8772,08455,075,04,08455,049,015,0 2LT =++=

7352,08455,075,08772,08772,0

11222

LT2LTLT

LT =+

=+

=

7519,033,033,1

1 =

EN 1993-1-1k ( = 0)c = 6.3.2.3

( )2LTc 8,021)1(5,01 = k f (2)

Table 6.6

( ) 8765,08,08455,021)7519,01(5,01 2 == f < 1

8388,08765,07352,0 ==

f LT LT,mod = < 1

and k Calculation of the factors k yy zy according to Annex A of EN 1993-1-1 EN 1993-1-1Annex A

9999,0

531905,161

9813,01

531905,161

1

1

1

ycr,

Edy

ycr,

Ed

y =

=

=

N N

N N

9447,0

19565,161

3495,01

19565,161

1

1

1

zcr,

Edz

zcr,

Ed

z =

=

=

N N

N N

EN 1993-1-1144,1

30693512

yel,

y pl,y === W

W w < 1,5 Annex A

578,18,307 6,485zel,z pl,z === W

W w > 1,5 wz = 1,5

NCCICritical axial force in the torsional buckling mode

SN003)( 2

Tcr,

w2

t0

Tcr, L

EI GI

I A

N +=

For a doubly symmetrical section,

cm 495466338692080)( 2020zy0 =+=+++= A z y I I I


C r e a

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b r u a r y

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, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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b j e c t

t o t h e

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d c o n

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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
http://www.access-steel.com/discovery/linklookup.aspx?id=EC080http://www.access-steel.com/discovery/linklookup.aspx?id=EC080http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=SN003http://www.access-steel.com/discovery/linklookup.aspx?id=SN003http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC080http://www.access-steel.com/discovery/linklookup.aspx?id=EC080


14/29


15/29


Eurocode Ref


CALCULATION SHEET


Calculation of the factor C my,0

EN 1993-1-1

ycr,

Edyymy,0 )33,0(36,021,079,0 N

N C ++= Annex A

Table A2

ycr,

Edmy,0 1188,079,0 N

N C = = 0,78960y =

Calculation of the factors C and C my m,LT :

LTy

LTymy,0my,0my

1)1(

a

aC C C +

+=

9641,09982,076,231

9982,076,23)7896,01(7896,0C my =+

+=

EN 1993-1-11

)1)(1(Tcr,

Ed

zcr,

Ed

LT2mymLT

=

N N

N N

aC C Annex A

9843,0

)4869

5,1611)(

19565,161

1(

9982,09641,0 2mLT =

=C < 1

C = 1mLT

Calculation of the factors C yy and C : EN 1993-1-1zyAnnex A

y pl,

yel,LT pl

2max

2my

y

max2my

yyyy ])

6,16,12)[(1(1

W

W bnC

wC

wwC +=

03765,01/27515600

161500/ M1Rk Ed

pl ===

N N

n

M z,Ed = 0 and0LT =b 0LT =d 4810,1zmax ==

]03765,0)481,19641,0144,1

6,1481,19641,0

144,16,1

2[()1144,1(1 222yy +=C

8739,035123069

y pl,

yel, ==>W

W C yy = 0,9849


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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
http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139


16/29


Eurocode Ref


CALCULATION SHEET


y pl,

yel,

z

yLT pl

2max

2my5

yyzy 6,0])

142)[(1(1

W

W

w

wd nC

wwC +=

9318,0]03765,0)481,19641,0144,114

2)[(1144,1(1 225zy =+=C

4579,035123069

5,1144,1

6,06,0y pl,

yel,

z

y ==W

W

w

w>= 9318,0zyC

Calculation of the factors kyy

and kzy

: EN 1993-1-1Annex A

yy

ycr,

Ed

ymLTmyyy

1

1 C N N

C C k

=

9818,09849,01

531905,161

1

9999,019641,0yy =

=k

z

y

zy

ycr,

Ed

zmLTmyzy 6,0

1

1 w

w

C N N C C k =

5138,050,1

144,16,0

9318,01

531905,161

1

9447,019641,0zy =

=k

Verification with interaction formulae

EN 1993-1-1 1

M1

Rk y,LT

Edy,

M1

Rk y

Ed +

M

M k

N

N yy 6.3.3

9534,0

127510.3512

8388,0

10.7559818,0

127515600

9813,0

1615003

6

=

+


17/29


Eurocode Ref


CALCULATION SHEET


5867,0

127510.3512

8388,0

10.7555138,0

127515600

3495,0

1615003

6=

+

0,5

c / t w = 41,76 < 38,581557,013

92,0396113

396 =

=

class 1

EN 1993-1-1 5.5

Flangesb = 200 mmt f = 16 mmr = 21 mm c / t f = 4,44 c = 71 mm

part to compression

c / t f < 9 = 8,28 (S275 = 0,92 )

c / t = 4,44 class 1f

So the section is Class 1. The verification of the member will be based onthe plastic resistance of the cross-section.


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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


18/29


Eurocode Ref


CALCULATION SHEET


7.2 Resis tance of cross-section

Verification with maximum moment along the member in cross-section of IPE500:

Combination 101Maximum force in IPE 500 at the end of the haunch:

N = 136,00 kNEd V = 118,50 kNEd

M = 349,10 kNmy,Ed

305,23 kNm

349,10 kNm

754,98 kNm

Combination 101: Bending moment diagram along the rafter

Shear V = 118,50 kN EN 1993-1-1Ed 6.2 A = A - 2 bt v f + ( t w+2 r )t = 1f

598516)2122,10(16200211550 =++=v A mm 2EN 1993-1-1

Av > .hw.t w = 468 10,2 = 4774mm 2

6.2.8 (2)

3 3V pl,Rd = Av (f / ) / = 5985 275/ /1000 = 950,3 kNy M0V / V Ed pl ,Rd = 118,5/950,3 = 0,125 < 0,50

its effect on the moment resistance may be neglected!

Compression EN 1993-1-1 6.2.4 N pl, = 11550 x 275/1000 = 3176 kNRd

N = 136 kN < 0,25 NEd pl , = 3176 0,25 = 794,1 kNRd andEN 1993-1-1

kN4,65610001

2752,104685,05,0

M0

yww =

=

f t h 6.2.8 N Ed = 136 kN < (2)

its effect on the moment resistance may be neglected!


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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


19/29


Eurocode Ref


CALCULATION SHEET


Bending EN 1993-1-1 6.2.5 M = 2194 275/1000 = 603,4 kNm pl,y,Rd M = 349,10 kNm < M y,Ed pl,y,Rd = 603,4 kNm

7.3 Buckling resistanceUniform members in bending and axial compression EN 1993-1-1

6.3.3Verification with interaction formulae

1

M1

Rk y,LT

Edy,yy

M1

Rk y

Ed +

M M

k N

N and 1

M1

Rk y,LT

Edy,zy

M1

Rk z

Ed +

M

M k

N N

Buckling about yy:

For the determination of the buckling length about yy, a buckling analysisis performed to calculate the buckling amplification factor cr for the loadcombination giving the highest vertical load, with a fictitious restraint attop of column :

EN 1993-1-1 6.3.1.2 (2)

Table 6.1Combination 101 cr = 37,37

EN 1993-1-1 6.3.1.3 (1)

EN 1993-1-1Buckling curve : a (h/b>2) y = 0,21 6.3.1.2

kN N N 508213637,37Edcr ycr, === (2)

Table 6.1

7906,010.508227511550

3ycr,

yy =

== N

Af


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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
http://www.access-steel.com/discovery/linklookup.aspx?id=EC008http://www.access-steel.com/discovery/linklookup.aspx?id=EC008http://www.access-steel.com/discovery/linklookup.aspx?id=EC013http://www.access-steel.com/discovery/linklookup.aspx?id=EC013http://www.access-steel.com/discovery/linklookup.aspx?id=EC137http://www.access-steel.com/discovery/linklookup.aspx?id=EC137http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=EC137http://www.access-steel.com/discovery/linklookup.aspx?id=EC137http://www.access-steel.com/discovery/linklookup.aspx?id=EC137http://www.access-steel.com/discovery/linklookup.aspx?id=EC137http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=EC137http://www.access-steel.com/discovery/linklookup.aspx?id=EC137http://www.access-steel.com/discovery/linklookup.aspx?id=EC013http://www.access-steel.com/discovery/linklookup.aspx?id=EC013http://www.access-steel.com/discovery/linklookup.aspx?id=EC008http://www.access-steel.com/discovery/linklookup.aspx?id=EC008


20/29


Eurocode Ref


CALCULATION SHEET


( ) ++=2yyy 2,015,0

= 0,8745( )[ ]2y 7906,02,07906,021,015,0 ++=

8011,07906,08745,08745,0

11222

y2

yy

y =+=

+=

Buckling about zz:

For buckling about zz and for lateral torsional buckling, the bucklinglength is taken as the distance between torsional restraints:

Lcr = 6,00m

Note: the intermediate purlin is a lateral restraint of the upper flange only.Its influence could be taken into account but it is conservatively neglectedin the following.

Flexural buckling EN 1993-1-1L = 6,00 m 6.3.1.3cr,z

10006000100002141210000 222

zcr,

z2zcr, == L EI N = 1233kN

NCCITorsional buckling

Lcr,T = 6,00 m SN003

)( 2Tcr,

w2

t0

Tcr, L

EI GI

I A

N +=

with y o = 0 and z o = 0 (doubly symmetrical section)

cm 450340214148199)( 2020zy0 =+=+++= A z y I I I

)

600010.1249370210000

10.29,8980770(100010.50340

115502

624

4Tcr,

+

= N

N cr,T = 3305 kN

N cr = min ( N ; N cr,z cr,T ) = 1233 kN EN 1993-1-1 6.3.1.3

605,110.1233

275115503cr

yz =

== N

Af

(1)


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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
http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=SN003http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=SN003http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=EC143


21/29


Eurocode Ref


CALCULATION SHEET


Buckling curve : b EN 1993-1-1 6.3.1.2 z = 0,34 (1)

( ) 2zzz 2,015,0 ++=Table 6.1

( )[ ]2z 605,12,0605,134,015,0 ++= =2,0273063,0

605,1027,2027,2

11222

z2zz

z =+=

+=

Lateral torsional buckling : EN 1993-1-1 6.3.1.3 L , = 6,00 mcr LT Table 6.5= 0,49Buckling curve : c LT

Moment diagram along the part of rafter between restraints:

Combination 101

NCCICalculation of the critical moment:

SN003 = - 0,487

qL8

2

q = - 9,56 kN/m = = - 0,123

C 1 = 2,75

NCCI

Z2

t2

LTcr,

Z

W2

LTcr,

Z2

1cr EI

GI L

I I

L

EI C M

+=

42

42

4

6

62

42

cr 10.214121000010.29,89807706000

10.214110.1249400

106000102141210000

75,2+

=

M

M cr = 1159 kNm


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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
http://www.access-steel.com/discovery/linklookup.aspx?id=EC137http://www.access-steel.com/discovery/linklookup.aspx?id=EC137http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=SN003http://www.access-steel.com/discovery/linklookup.aspx?id=SN003http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=EC143http://www.access-steel.com/discovery/linklookup.aspx?id=EC137http://www.access-steel.com/discovery/linklookup.aspx?id=EC137


22/29


Eurocode Ref


CALCULATION SHEET


7215,010.1159

27510.21956

3

cr

yy pl,LT ===

M

f W

( ) 2LTLT,0LTLTLT 15,0 ++=

EN 1993-1-1 6.3.2.3with 40,0LT,0 = and =0,75 (1)

( )[ ] 7740,07215,075,04,07215,049,015,0 2LT =++=

8125,0

7215,075,07740,07740,0

11222

LT2LTLT

LT =

+

=

+

=

k c = 0,91

( )28,021)1(5,01 = LT ck f EN 1993-1-1 6.3.2.3

( ) 9556,08,07215,021)91,01(5,01 2 == f (2)

< 1 Table 6.6

8503,09556,08125,0 ==

f LT LT,mod = < 1

Combination 101 N = 136 kN compressionEd

M = 349,10 kNmy,Ed

M z,Ed = 0

Section class1 M = 0 et M y,Ed z,Ed = 0

EN 1993-1-1 6.3.3

1

M1

Rk y,LT

Edy,yy

M1

Rk y

Ed +

M M

k N

N 1

M1

Rk y,LT

Edy,zy

M1

Rk z

Ed +

M

M k

N N


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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


23/29


Eurocode Ref


CALCULATION SHEET


EN 1993-1-1

9946,0

5082136

8011,01

5082136

1

1

1

ycr,

Edy

ycr,

Ed

y =

=

=

N N

N N

Annex A

9208,0

1233136

3063,01

1233136

1

1

1

zcr,

Edz

zcr,

Ed

z =

=

=

N N

N N

EN 1993-1-1138,1

19282194

yel,

y pl,y === W

W w < 1,50 Annex A

569,11,2149,335

zel,

z pl,z === W

W w > 1,50 w = 1,5 z

NCCI

Z2

t2

LTcr,

Z

W2

LTcr,

Z2

1cr,0 EI

GI L

I I

L

EI C M

+= SN003

0 M cr,0 is the critical moment for the calculation of for uniform bendingmoment as specified in Annex A.

C 1 = 1

42

42

4

6

62

42

cr,010.2141210000

10.29,89807706000

10.2141

10.1249400

106000

10.21412100001

+

=

M

kNm M 5,421ocr, =

EN 1993-1-16

3

ocr,

yy pl,0

10.5,42127510.2195 ==

M f W = 1,196 Annex A

4

TFcr,

Ed

zcr,

Ed1lim0 )1)(1(2,0 N

N N N

C = with C 1 = 2,75

with N = N cr,TF cr,T ( doubly symmetrical section)

4lim0 )3305136

1)(1233136

1(75,22,0 = = 0,3187

0 =1,196 > lim0 =0,3187


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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
http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=SN003http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=SN003http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139


24/29


Eurocode Ref


CALCULATION SHEET


EN 1993-1-1

LTy

LTymy,0my,0my

1)1(

a

aC C C

++= Annex A

with 36

yel,Ed

Edy,y 101928

11550136000

10.10,349

==W A

N

M =15,38 (class 1)

and48200

29,8911

y

tLT == I

I a = 0,9981

Calculation of the factor C EN 1993-1-1my,0 Annex AMoment diagram along the rafter:Table A2

M y,Ed = maximum momentalong the rafter = 755kNm

= maximum displacementalong the rafter = 179mm30m

ycr,

Ed

Edy,2

xy

2

my,0 11 N N

M L EI C

+=

5082136

11075530000

17910482002100001 62

42

my,0

+= C =0,9803

Calculation of the factors C and C my m,LT :

LTy

LTymy,0my,0my

1)1(

a

aC C C

++=

996,09982,038,151

9982,038,15)9803,01(9803,0my =+

+=C


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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
http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC158http://www.access-steel.com/discovery/linklookup.aspx?id=EC158http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139http://www.access-steel.com/discovery/linklookup.aspx?id=EC139


25/29


Eurocode Ref


CALCULATION SHEET


EN 1993-1-11)1)(1(

Tcr,

Ed

zcr,

Ed

LT2mymLT

=

N N

N N

aC C Annex A

072,1)

3305136

1)(1233136

1(

9981,0996,0 2mLT =

=C > 1

Calculation of the factors C yy and C EN 1993-1-1zyAnnex A

y pl,

yel,LT pl

2max

2my

y

max2my

yyyy ])6,16,12)[(1(1 W

W bnC w

C w

wC +=

0428,01/27511550

136000/ M1Rk Ed

pl ===

N N

n

M 605,1max == z z,Ed = 0 and0LT =b 0LT =d

]0428,0)605,1996,0138,1

6,1605,1996,0

138,16,1

2)[(1138,1(1 222yy +=C

C yy = 0,9774

y pl,

yel,

z

yLT pl

2max

2my5

yyzy 6,0])

142)[(1(1

W

W

w

wd nC

wwC +=

9011,0]0428,0)605,1996,0138,114

2)[(1138,1(1 225zy =+=C

Calculation of the factors kyy and kzy : EN 1993-1-1Annex A

yy

ycr,

Ed

ymLTmyyy

1

1 C N N C C k =

116,19774,01

5082136

1

9946,0072,1996,0yy =

=k


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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


26/29


Eurocode Ref


CALCULATION SHEET


z

y

zy

ycr,

Ed

zmLTmyzy 6,0

1

1 w

w

C N N

C C k

=

5859,050,1

138,16,0

9011,01

5082136

1

9208,0072,1996,0zy =

=k

Verification with interaction formulae EN 1993-1-1 6.3.3

1

M1

Rk y,LT

Edy,yy

M1

Rk y

Ed +

M M k N N (6.61)

8131,0

127510.2194

8503,0

10.1,349116,1

127511550

8011,0

1360003

6

=

+ < 1 OK

1

M1

Rk y,LT

Edy,zy

M1

Rk z

Ed +

M

M k

N N

(6.62)

5385,0

127510.2194

8503,0

10.1,3495859,0

127511550

3063,0

1360003

6

=

+< 1 OK

8 Haunch verification

For the verification of the haunch, the compression part of the cross-section isconsidered as alone with a length of buckling about the zz-axis equal to 3,00m(length between the top of column and the first restraint).

Maximum forces and moments in the haunch :

N = 139,2 kNEdV = 151,3 kN Ed

M = 755 kNmEd


C r e a

t e d o n

T h u r s

d a y ,

F e

b r u a r y

2 4

, 2 0 1 1

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


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


27/29


Eurocode Ref


CALCULATION SHEET


Properties of the whole section:The calculation of elastic section properties for this case is approximate,ignoring the middle flange.

1000 mm

200 mm

Section area A = 160,80 cm 2


Second moment of area /zz I z = 2141 cm 4


Elastic modulus /zz W = 214 cm 3el,z

Properties of the compression part :

Section at the mid-length of the haunch including 1/6th of the web depth

Section area A = 44 cm 2 120 mm

Second moment of area /yy I y = 554 cm4

Second moment of area /zz I z =1068 cm 4

cmi 93,444

1068z == 200 mm

7044,039,8630,49

3000

1z

f z =

==

i L z

Buckling of welded I section with h/b > 2 :

curve d = 0,76

( ) ( )[ ] 9397,07044,02,07044,076,015,02,015,0 22zzz =++=++= 640,0

7044,09397,09397,0

11222

z2zz

z =+=

+=


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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


28/29


Eurocode Ref


CALCULATION SHEET


Compression in the bottom flange:

kN N 7604400100010.4610

1000755000160804400

24,139 3f Ed, =+=

Verification of buckling resistance of the bottom flange:

981,02754400640,0

760000

Rk z

f Ed, =

= N

N

< 1 OK


C r e a

t e d o n

T h u r s

d a y , F e

b r u a r y

2 4

, 2 0 1 1

T h i s m a

t e r i a


t - a

l l r i g

h t s r e s e r v e

d .

U s e o


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


29/29

Example: Elastic analysis of a single bay portal frameSX029a-EN-EU

Quality Record

Example: Elastic analysis of a single bay portal frameRESOURCE TITLE

Reference(s) T2703

ORIGINAL DOCUMENT

Name Company Date

Created by Valrie LEMAIRE CTICM 25/10/2005

Technical content checked by Alain BUREAU CTICM 26/10/2005

Editorial content checked by

Technical content endorsed by the

following STEEL Partners:1. UK G W Owens SCI 10/04/06

2. France A Bureau CTICM 10/04/06

3. Sweden B Uppfeldt SBI 10/04/06

4. Germany C Muller RWTH 10/04/06

5. Spain J Chica Labein 10/04/06

Resource approved by TechnicalCoordinator

G W Owens SCI 18/09/06

TRANSLATED DOCUMENT

This Translation made and checked by :

Translated resource approved by:


r s d a y , F e

b r u a r y

2 4

, 2 0 1 1

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


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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