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Document Ref: SX029a-EN-EU Sheet 1 of 28Title Example: Elastic analysis of a single bay portal frame
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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
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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Document Ref: SX029a-EN-EU Sheet 2 of 28Title Example: Elastic analysis of a single bay portal frame
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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]
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
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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Document Ref: SX029a-EN-EU Sheet 4 of 28Title Example: Elastic analysis of a single bay portal frame
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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
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
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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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 /yy I y = 48200 cm 4
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
Elastic modulus /yy W el,y = 1928 cm 3
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.
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
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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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
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
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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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
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
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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5.3.2 Ultimate limit statesMoment diagram in kNm
Combination 101:
Combination 102:
Combination 103:
Combination 104:
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
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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Document Ref: SX029a-EN-EU Sheet 9 of 28Title Example: Elastic analysis of a single bay portal frame
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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.
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
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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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
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
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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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)
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
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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( ) ( )[ ]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
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
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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13/29
Document Ref: SX029a-EN-EU Sheet 13 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
( )[ ] 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
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
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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8/10/2019 Cadru Portal Cu o Deschidere
15/29
Document Ref: SX029a-EN-EU Sheet 15 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
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
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
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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Document Ref: SX029a-EN-EU Sheet 16 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
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
=
+
8/10/2019 Cadru Portal Cu o Deschidere
17/29
Document Ref: SX029a-EN-EU Sheet 17 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
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.
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
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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Document Ref: SX029a-EN-EU Sheet 18 of 28Title Example: Elastic analysis of a single bay portal frame
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CALCULATION SHEET
Checked by Alain Bureau Date April 2006
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!
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
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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19/29
Document Ref: SX029a-EN-EU Sheet 19 of 28Title Example: Elastic analysis of a single bay portal frame
Eurocode Ref
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CALCULATION SHEET
Checked by Alain Bureau Date April 2006
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
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
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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Document Ref: SX029a-EN-EU Sheet 20 of 28Title Example: Elastic analysis of a single bay portal frame
Eurocode Ref
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CALCULATION SHEET
Checked by Alain Bureau Date April 2006
( ) ++=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)
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
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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Document Ref: SX029a-EN-EU Sheet 21 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
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
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
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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Document Ref: SX029a-EN-EU Sheet 22 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
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
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
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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Document Ref: SX029a-EN-EU Sheet 23 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
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
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
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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24/29
Document Ref: SX029a-EN-EU Sheet 24 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
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
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
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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25/29
Document Ref: SX029a-EN-EU Sheet 25 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
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
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
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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26/29
Document Ref: SX029a-EN-EU Sheet 26 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
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
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
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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27/29
Document Ref: SX029a-EN-EU Sheet 27 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
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 /yy I y = 230520 cm 4
Second moment of area /zz I z = 2141 cm 4
Elastic modulus /yy W el,y = 4610 cm 3
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 =+=
+=
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
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
8/10/2019 Cadru Portal Cu o Deschidere
28/29
Document Ref: SX029a-EN-EU Sheet 28 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
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
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
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
8/10/2019 Cadru Portal Cu o Deschidere
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:
Example: Elastic analysis of a single bay portal frame
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
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