Design-support for MSH sections

Transcription

Umschlag_2007_engl
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Seite 28
VA L L O U R E C & M A N N E S M A N N T U B E S
VA L LO U R E C & M A N N E S M A N N T U B E S
Vallourec Group
V & M 3 B 0 0 11 - 8 G B
V & M DEUTSCHLAND GmbH
Theodorstraße 90
40472 Düsseldorf · Germany
Phone +49 (2 11) 9 60-35 80
Fax +49 (2 11) 9 60-23 73
E-Mail: info.service@vmtubes.de
www.vmtubes.com/msh
according to Eurocode 3,
DIN EN 1993-1-1: 2005
and
DIN EN 1993-1-8: 2005
Innenteil_2007_engl_02-21
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Design-Support for MSH sections according to Eurocode 3,
DIN EN 1993-1-1: 2005 and DIN EN 1993-1-8: 2005
in cooperation with
Prof. Dr.-Ing. R. Kindmann, Dr.-Ing. M. Kraus and Dipl.-Ing. J. Vette, University of Bochum,
Dipl.-Ing. O. Josat, Dipl.-Ing. J. Krampen and Dipl.-Ing. C. Remde, Vallourec & Mannesmann Tubes
VALLOUREC & MANNESMANN TUBES is world market leader in the manufacture of
seamless hot rolled steel tubes for all applications. The company operates 11 state-of-the-art
pipe mills worldwide, eight located in Europe (four plants at three locations in Germany and
four plants in France), two at a facility in Brazil and one in the USA. With an annual output of
up to three million tonnes the world’s largest and most comprehensive range of seamless steel
tubes is supplied.
Hot rolled circular, square and rectangular Mannesmann Structural Hollow
Sections of VALLOUREC & MANNESMANN TUBES have been used
successfully for several decades. Modern steel architecture, with its elegant
and transparent forms, would be practically impossible to create without them.
2
VALLOUREC & MANNESMANN TUBES
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Seite 3
Descriptions and basic informations
4
Classification of hollow cross sections
5
Calculation methods/Determination of internal forces
5
Resistance of cross sections
5
Buckling resistance of members
6
Design-support
for members in compression
Lattice girders
8
9
Joints of lattice girders 10
Design-support for K gap joints
with square MSH-chords (SHS) 12
Design-support for K joints
with circular MSH sections (CHS) 13
Design-support for K gap joints
with rectangular MSH-chords (RHS) 14
Design-support for K overlap joints with square
MSH-chords (SHS) 16
Calculation examples 18
Circular MSH sections
22
Square MSH sections
24
Rectangular MSH sections
26
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1 Descriptions and basic informations
Table 1 Descriptions and available dimensions
circular (CHS)
square (SHS)
rectangular (RHS)
21.3 mm
to
711 mm
40 x 40 mm
to
400 x 400 mm
50 x 30 mm
to
500 x 300 mm
Cross section
Outer measurement
d, b or h
Wall thickness t
2.3 mm to 100 mm
Available lengths
maximum 20 mm
up to 16 m; standard up to 12 m
This brochure for the design only covers hot-rolled MSH sections (according to DIN EN 10210).
Due to production differences they provide more favourable characteristics than cold formed profiles:
•
•
•
•
higher load-carrying capacity for columns and members in compression
larger cross section areas as a result of smaller corner radiuses
substantially better suitability for welding
in comparison to cold formed hollow profiles according to DIN EN 10219 there are no restrictions for the ability
of welding (DIN EN 1993-1-8:2005)
Table 2 Materials: Yield strength fy, tensile strength fu, impact energy KV and carbon equivalent CEV
Steel designation
DIN EN 10 027 /
EN 10 210-1
old
fy in N/mm2 fu in N/mm2
n. EN 1993 for t ≤ 40 mm
KV* in J at
test temp.
CEV* in % for
t ≤ 16 mm 16 < t ≤ 40 mm
Structural
steels
S 355 J0H 1. 0547
S 355 J2H 1. 0576
S 355 K2H 1. 0512
St 52-3U
St 52-3N
355
355
355
510
510
510
0 °C: 27
-20 °C: 27
-20 °C: 40
0.45
0.45
0.45
0.47
0.47
0.47
Normalised
fine grain
structual
steels
S 355 NH
S 355 NLH
S 460 NH
S 460 NLH
StE 355 N
TStE 355 N
StE 460 N
TStE 460 N
355
355
460
460
490
490
560
560
-20 °C: 40
-50 °C: 27
-20 °C: 40
-50 °C: 27
0.43
0.43
0.53
0.53
0.45
0.45
0.55
0.55
1. 0539
1. 0549
1. 8953
1. 8956
S 690 approval in each individual case
* according to DIN EN 10210-1
According to DIN EN 1993-1-1 the yield and tensile strengths fy and fu are either to be taken out of the product
standard (DIN EN 10210-1) or simplified from DIN EN 1993-1-1. The values in table 2 correspond to the simplified
specifications according to DIN EN 1993-1-1 for t ≤ 40 mm. The DIN EN 10210-1 demands a reduction of the yield
strength for wall thicknesses > 16 mm already as well as different tensile strengths. The yield strength according to
EC 3 specifies a nominal value for calculations, not the actual minimum value of the material.
Detailed information and brochures are available at: www.vmtubes.com
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2 Classification of hollow cross sections
By the classification of the cross sections the resistance and rotation capacity due to local buckling is supposed
to be determined.
Table 3 Classification on the bases of c/t- and d/t-ratios of cross section parts subjected to compression
Cross section
ε=
235/fy
fy in N/mm2
Class
Pure
compression
Pure
bending
1
c/t ≤ 33 ε
c/t ≤ 72 ε
2
c/t ≤ 38 ε
c/t ≤ 83 ε
3
c/t ≤ 42 ε
c/t ≤ 124 ε
1
d/t ≤ 50 ε2
2
d/t ≤ 70 ε2
3
d/t ≤ 90 ε2
fy
ε
ε2
235
1.00
1.00
275
0.92
0.85
355
0.81
0.66
Cross sections which do not
comply to the conditions of the
classes 1, 2 or 3 are classified as
class 4.
The tables of the sections 14 to
16 include details on the classification using the steel grade
S 355. The first digit describes
the classification for pure compression, the second for pure
bending.
420
0.75
0.56
460
0.71
0.51
3 Calculation methods/Determination of internal forces
Internal forces can be determined using an elastic or a plastic structural analysis. A plastic analysis can only be
performed, if the structure provides sufficient rotation capacity at the locations where plastic hinges occur. For the
structural analysis the design values of the loading have to be taken into consideration, which means that partial
safety factors γF and combination factors ψ have to be regarded for the actions. As a result the design values of the
internal forces NEd, VEd und MEd.
4 Resistance of cross sections
Class:
Tension:
NEd
≤ 1.0
Npl/γM0
all
Compression:
NEd
≤ 1.0
Npl/γM0
1, 2 or 3
NEd
≤ 1.0
Aeff · fy/γM0
4
MEd
≤ 1.0
Mpl/γM0
1 or 2
Bending moment:
MEd
Wel · fy/γM0
Shear:
≤ 1.0
VEd
≤ 1.0
Vpl/γM0
Partial safety factors:
According to DIN EN 1993-1-1
γM0 = γM1 = 1.00 is recommended. The definition will be stated
in the national annex, which is not
yet available.
Npl, Vpl and Mpl for fy
= 35.5 kN/cm2:
see tables in sections 14 to 16.
For a different yield strength the
values can be converted using the
ratio of the strengths.
3
no shear buckling!
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Bending moment and shear force:
The influence of the shear force on the bending moment resistance has to be taken into consideration if the shear
force VEd exceeds 0.5 · Vpl/γM0.In that case a reduced yield strength has to be regarded for the parts of the cross
section subjected to shear:
2
2 · VEd
–1
red fy = (1 – ρ) · fy where ρ =
Vpl/γM0
Bending moment and axial force:
For classes 1 and 2 cross sections the following criterion should be satisfied:
MEd ≤ MN,Rd
where MN,Rd is the design plastic moment resistance reduced by the axial force NEd.
For rectangular hollow sections the following approximation may be used:
MN,Rd =
1–n
Mpl
M
·
where: MN,Rd ≤ pl
γM0 1–0.5·aw
γM0
where: n =
NEd
Npl/γM0
2bt
but aw ≤ 0.5
A
For circular hollow cross sections EC 3 does not provide any specifications. Analogously the following condition is
obtained according to Kindmann/Frickel „Elastische und plastische Querschnittstragfähigkeit“ (Ernst & Sohn publishing, Berlin):
aw = 1–
2
MEd
NEd
+
· arc sin
π
Mpl/γM0
Npl/γM0
≤ 1.0
5 Buckling resistance of members
Buckling resistance of members in compression
Uniform members with class 1, 2 and 3 sections
shall be verified against buckling as follows:
NEd
≤ 1.0
χ · Npl/γM1
1
χ=
Φ+
–
Φ2 – λ2
aber χ ≤ 1.0
–
–
Φ = 0.5 · [1+α · (λ – 0.2) + λ2]
N =L ·
f ; N
i · π N
E
– =
λ
pl
cr
cr
y
cr
=
π2EI
L2cr
α = 0.21 for buckling curve a (S 235 to S 420)
α = 0.13 for buckling curve a0 (S 460)
Lcr: buckling length
6
_
λ
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
χ for curve
a
a0
1.000 1.000
0.989 0.993
0.977 0.986
0.966 0.978
0.953 0.970
0.939 0.961
0.924 0.951
0.908 0.940
0.890 0.928
0.870 0.913
0.848 0.896
0.823 0.876
0.796 0.853
0.766 0.827
0.734 0.796
0.700 0.762
0.666 0.725
0.631 0.687
0.596 0.648
0.562 0.610
0.530 0.573
0.499 0.538
0.470 0.505
_
λ
1.35
1.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
1.80
1.85
1.90
1.95
2.00
2.10
2.20
2.30
2.40
2.50
2.60
2.80
2.90
3.00
χ for curve
a
a0
0.443 0.475
0.418 0.446
0.394 0.420
0.372 0.395
0.352 0.373
0.333 0.352
0.316 0.333
0.299 0.315
0.284 0.299
0.270 0.283
0.257 0.269
0.245 0.256
0.234 0.244
0.223 0.232
0.204 0.212
0.187 0.194
0.172 0.178
0.159 0.164
0.147 0.151
0.136 0.140
0.118
0.122
0.111
0.114
0.104 0.106
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Buckling resistance of members in bending
Procedure for the verification of sufficient carrying capacity:
– Application of equivalent geometric imperfections
– Determination of internal bending moments using a second order theory analysis taking the equivalent geometric
imperfections into account (approximations see below)
– Verification of sufficient cross section carrying capacity according to section 4 for “bending and axial force”
Equivalent geometric imperfections:
a) Initial sway imperfections
b) Initial bow imperfections
φ = 1/200 · αh · αm
According to DIN EN 1993-1-1 the initial bow
imperfections are recommended as stated in the
following table. The definition will be stated in
the national annex, which is not available yet.
Reduction factor for height h [m] applicable to columns:
2
2
αh =
but
≤ αh ≤ 1.0
3
h
e0,d / L
Reduction factor for the number of columns in a row:
αm =
1
0.5 · 1 +
m
m is the number of columns in a row including only those
columns which carry a vertical load NEd not less than 50%
of the average value of the column in the vertical
plane considered.
Buckling
curve
Elastic
analysis
Plastic
analysis
a0
a
1/350
1/300
1/300
1/250
Equivalent loading
Equivalent loading
Approximations for the bending moment according to second order theory:
For the approximation the first
order theory
bending moment
is multiplied
by an enlargement factor α:
MII ≅ α · MI
α=
1+ δ · NEd /Ncr,d
Bending moment according to first order theory and correction factors δ for selected cases
Hog. moment: MI = - q · L2/2
δ = - 0.40
Hog. moment: MI = P · L
δ = - 0.18
Hog. moment: MI = - NEd·φ·L
δ = - 0.18
Sag. moment: MI = q · L2/8
δ = + 0.03
Sag. moment: MI = P · L/4
δ = - 0.18
Sag. moment: MI = NEd · e0,d
δ=0
1–NEd /Ncr,d
Ncr,d = Ncr / γΜ1
Condition: α ≤ 3
L = beam length
Hog. moment: MI = - q · L2/8
Hog. moment: MI = - 3 PL/16 Hog. moment: MI ≅ - NEd · e0,d
δ = - 0.37
δ = - 0.27
δ = - 0.33
Sag. moment at: 5/8 · L:
Sag. moment at: 5/8 · L:
I
2
I
M = 9 q L /128 Sag. moment: M = 5 PL/32
MI ≅ 0.6 NEd · e0,d
δ = + 0.10
δ = - 0.30
δ = + 0.07
Online verification against buckling at www.vmtubes.com (STACOM)
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6 Design-support for members in compression
Example 1, P.18
Example 5, P. 21
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7 Lattice girders
Lattice structures are often designed as single span girders with parallel chords, as for example roof girders of long
span constructions. Established structures in practice are:
- Warren truss
- small amount of work due
few joints
- long diagonals in compression
- few points of load application
at the upper chord
- Warren truss with vertical posts
- many points of load application at the upper chord
- many joints
- extensive joints at lower chord
and large amount of work
- Pratt truss
- short diagonals in compression
- many points of load application at upper chord
- many joints and therefore large
amount of work
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Compared to plate girders lattice girders with parallel chords using hollow members provide economic advantages
for span lengths greater than about 20 m. The split-up of the internal bending moment into tension and compression
forces leads to light roof constructions saving material. Additionally hollow profiles provide an ideal cross
section shape for centrical compression loading.
Support for the construction:
- Lattice girders with parallel chords usually have heights from 1/10 to 1/20 of the system lengths. As a guide
value for pre-design a girder height of 1/15 of the span length is appropriate.
- The angles between the chords and the brace members should be in-between 45° and 60°. In any case an
angle greater than 30° has to be chosen.
- Joints of lattice structures should be designed in a way that the centrelines of the members intersect in a
single point. In the case they show eccentricities chapter 5.1.5 of DIN EN 1993-1-8:2005 has to be regarded
(see section 8).
- Loadings, as for instance from purlins, should be introduced at the joints of the structure.
- Moments at the joints, caused by the actual rotational stiffness of the connections, may be neglected in the
design of the members and joints, provided that the range of validity for the joints are observed and the ratio
of the system length to the heights of the members is not less than 6.
The cross section carrying capacity has to be verified for each member and for those in compression the stability
as well. For connections the design joint resistance according to DIN EN 1993-1-8:2005 has to be verified.
8 Joints of lattice girders
Each member of a lattice structure is usually loaded by axial forces for which they have to be designed. At joints,
several members come together and the directions of force-actions have to be redistributed in order to fulfil the
equilibrium. Joints are highly stressed details of the structure for which the design joint resistance has to be determined and verified. Usually hollow profiles are welded at the connections; welds have to be verified separately
however. The ends of brace members may not be flattened or pressed together. The following types of joints are
often used:
K gap joint
K overlap joint
K joint with vertical post (N joint)
KT joint
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The following supports for design may be applied for mainly stationary loading. Moments resulting from eccentricities of the centrelines have to be regarded in the design of tension chord members and brace members as well as
the design of the connections if the following limits are not fulfilled:
CHS: – 0.55 · d0 ≤ e ≤ 0.25 · d0
resp.
RHS/SHS: – 0.55 · h0 ≤ e ≤ 0.25 · h0
In the design of compression chord members eccentricities usually have to be taken into account, even if they are
within the limits specified above. According to DIN EN 1993-1-8 a partial safety factor of γM5 = 1.00 is recommended for the design of the joints. The definition will be stated in the national annex, which is not available yet.
Definition and Notation
Table 4 Range of validity for K and N gap joints according to DIN EN 1993-1-8:2005
Circular MSH sections (CHS):
Rectangular MSH sections (RHS):
0.35
1. bi/b0 ≥ Max
0.1 + 0.01 · b0/t0
2.
3.
4.
5.
bi/ti ≤ 35 und hi/ti ≤ 35
b0/t0 ≤ 35 und h0/t0 ≤ 35
0.5 ≤ h0/b0 ≤ 2.0
0.5 ≤ hi/bi ≤ 2.0
6.
g ≥ Max
0.5 · b · (1–(h +t b+ t+ h + b )/(4 · b ))
(h + b + h + b )
If g ≥ 1.5 · b · 1 –
the joint has to
4·b
0
1
1
i
7.
1.
2.
3.
4.
5.
1
2
2
0
2
1
0
2
2
0
be treated as two separate Y and T joints
8.
9.
6.
0.2 ≤ di/d0 ≤ 1.0
10 ≤ d0/t0 ≤ 50
10 ≤ di/ti ≤ 50
Θi ≥ 30°
Class 2 sections in terms of pure
bending at least (see section 2)
g ≥ t1+t2
Class 2 sections in terms of pure bending at least
(see section 2)
Θi ≥ 30°
Square MSH sections (SHS):
Points 1-9 see RHS
10. 15 ≤ b0/t0 ≤ 35
11. 0.6 ≤
b1 + b2
≤ 1.3
2 · b1
Table 5 Range of validity for K and N overlap joints according to DIN EN 1993-1-8:2005
Rectangular and square MSH sections (RHP/QHP):
Circular MSH sections (CHS):
1.
2.
Points 1-5 see table 4
6. λ0V ≥ 25%
3.
4.
5.
6.
bi/b0 ≥ 0.25
Chord: 0.5 ≤ h0/b0 ≤ 2.0 and class 2 section in terms
of pure bending at least
Braces (in compression): class 1 sections (pure bending)
Braces (in tension): bi/ti ≤ 35 and hi/ti ≤ 35
25% ≤ λ0V ≤ 100% and bi/bj ≥ 0.75
Θi ≥ 30°
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9 Design-support for K gap joints with square
MSH-chords (SHS)
Preconditions:
– Joint has to be within the range of validity given in table 4!
– Same yield strength fy for all members
Design resistance of the joint
N1,Rd =
nRd · kn · Npl,0
sin θ1 · γM5
N2,Rd = N1,Rd ·
sin θ1
sin θ2
nRd see diagram below
Note:
For circular braces the design resistances
Ni,Rd have to be multiplied by the factor
π / 4. For that case bi = di is valid.
kn is obtained
sin Θ is given by:
θ
sin θ
30°
0.50
for compression chords by:
|No,d| · γM5
2 · b0
·
≤ 1.0
kn = 1.3 – 0.4 ·
Npl,0
b1 + b2
40°
0.64
45°
0.707
50°
0.77
for tension chords by: kn = 1.0
60°
0.87
Example:
- Chord member SHS 150x150x6.3 mm (tension)
- Brace members SHS 80x80x5 mm
- Gradient of the brace members 45° (e = 0 cm)
Check of the validity given in table 4:
1. bi/b0 = 8/15 = 0.533 ≥ 0.35
2. bi/ti = hi/ti = 80/5 = 16 ≤ 35
8
7.5 · 1– = 3.5 cm
8
15
6. g = 15 – sin 45° = 3.7 cm ≥ Max
1.0 cm
8
7. g = 15 – sin 45° = 3.7 cm ≤ 1.5 · 15 · (1–8/15) = 10.5 cm
8. Members are at least class 2 sections
9. Θ1 = Θ2 = 45° ≥ 30°
10. 15 ≤ b0/t0 = 150/6.3 = 23.8 ≤ 35
b1 + b2 8 + 8
11. 0.6 ≤ 2 · b = 2 · 8 = 1.0 ≤ 1.3
1
Determination of the design resistance:
b1
8
b0
15
With b = 15 = 0.533 and t = 0.63 = 23.8: nRd ≈ 0.18
0
0
The limit brace force for a tension chord is:
0.18 · 1.0 · 1270
N1,Rd =
0.707 · 1.0 = 323.3 kN
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10 Design-support for K joints
with circular MSH sections (CHS)
Preconditions:
– Joint has to be within the range of validity given in tables 4 and 5!
Conditions for design:
nRd · kp · Npl,0
sin θi · γM5
N1,Rd Min
≥ Ni,d
1 – Comp.
where i = 2 – Tension
di · kΘi · Npl,0
(d0 – t0) · γM5
nRd see diagram below
(Interim values may be interpolated)
Notes:
g<0: overlap joint (table 5)
g>0: gap joint (table 4)
kp is obtained
for compression chords by:
|minNo,d| · γM5
|minNo,d| · γM5
(1+
) ≤ 1.0
kp = 1 – 0.3 ·
Npl,0
Npl,0
kΘi is obtained by:
1+sin Θi
kΘi =
12
· sin2 Θi
for tension chords by: kp = 1.0
Example:
- Chord member: 101.6 x 6.3 mm (tension)
- Brace members: 60.3 x 5mm
- Gradient of the brace members: 45° (e = 0 cm)
Check of validity given in table 4:
1. 0.2 ≤ di/d0 = 60.3/101.6 = 0.594 ≤ 1.0
2. 10 ≤ d0/t0 = 101.6/6.3 = 16.1 ≤ 50
3. 10 ≤ di/ti = 60.3/5 = 12.1 ≤ 50
4. Θ1 = Θ2 = 45° ≥ 30°
6. g = 10.16 –
6.03
= 1.6 cm ≥ t1 + t2 = 1.0 cm
sin 45°
Θi
kΘi
35°
1.38
40°
1.15
45°
0.99
50°
0.87
60°
0.72
d1
d0
g
with
= 0.594, = 16.1 and
= 2.54 and by
t0
d0
t0
interpolation:
nRd ≈ 0.32 (g/t0 ≤ –4), nRd ≈ 0.26 (g/t0 ≥ 8)
nRd ≈ 0.26 + (0.32 – 0.26) · (8 – 2.54)/(4+8) = 0.287
The limit brace force for a tension chord is:
NRd = Min
0.287 · 669.6
0.707 · 1.0
6.03 · 0.99 · 669.6
(10.16–0.63) · 1.0
= 272
= 272 kN
= 419.4
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11 Design-support for K gap joints
with rectangular MSH-chords (RHS)
Preconditions:
– Brace members are equal profiles SHS/CHS
– The compression force in the chord shall satisfy:
|No,d|
γ
Npl,0 · M5 ≤ 0.5
(For small bi/b0-ratios and small compression forces or tension forces in the chord the exact verification according
to Eurocode can lead to favourable results)
Note:
For circular braces the design resistances Ni,Rd have to be multiplied by the factor π /4. For that case bi = di is valid.
Conditions for design:
1. Condition (Verification of the chord force)
N1,d · sin Θ1
· γM5
VEd =
Vpl,0
h0
kα = 0.2 b + 0.35
0
· k
n0,Rd = 1 – 1 – 1–v2Ed
N0,Rd =
α
n0,Rd · Npl,0
>N0,d
γM5
2. Condition (Verification of the brace force)
Ni,Rd = Min
n1,Rd · Npl,i
γM5
n2,Rd · Npl,0
sin Θi · γM5
> Ni,d
n1,Rd and n2,Rd see diagrams below
Diagram for n1,Rd:
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Diagrams for n2,Rd:
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Seite 16
12 Design-support for K overlap joints
with square MSH-chords (SHS)
Preconditions:
– Brace members are equal profiles SHS/CHS
Note:
For circular braces the design resistancese Ni,Rd have to be multiplied by the factor π / 4.
For that case bi = di is valid.
Design resistance of the joint:
The overlapping brace
n ·N
N1,Rd = Rd pl,1 member 2 does not have
γM5
to be verified.
Determination nRd taking into account:
λ0V = q/p · 100% ≥ 25% (see table 5)
With the overlap ratio λ0V
the following cases can be distinguished:
– Case 1: λ0V = 25%
– Case 2: 25% < λ0V < 50%
linear interpolation of nRd
using case 1 and case 3
– Case 3: 50% ≤ λ0V < 80%
– Case 4: 80% ≤ λ0V ≤ 100%
Diagrams for nRd in case 1 (λ0V = 25%):
16
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Seite 17
Diagrams for nRd in case 3 (50% < λ0V < 80%):
Diagrams for nRd in case 4 (80% ≤ λ0V ≤ 100%):
17
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Seite 18
13 Calculation examples
Example 1: Column with hinged supports (L = 6 m):
By considering Lcr = L = 6 m the following can directly be taken from the
design-support of section 6: CHS 406.4 x 16 NEd ≈ 6250 kN > 6000 kN
In comparison to that the verification against buckling according to sect. 5 is
carried out: I = 37449 cm4, Npl = 6966 kN (see section 14), buckling length:
Lcr = 600 cm (see section 5)
Npl
6966
–
π2 EI π2 21000 · 37449
= 21560 kN; λ = N = 21560 = 0.57
Ncr = 2 =
L cr
6002
cr
χ ≈ 0.9 (buckling curve a, see section 5)
Verification against buckling:
NEd
6000
=
= 0.96 < 1.0
χ · Npl/γM1 0.9 · 6966/1.0
Example 2: Column with fixed support (L = 4 m) and lateral loading:
The column shown in the figure has to be verified for stability. Due to the lateral
loading the verification will be achieved by a second order theory analysis
(ly = 9055 cm4).
The buckling length of the column is Lcr = 2L = 8 m.
Ncr =
π2 EI
π2 21000 · 9055
=
= 2932.4 kN
L2cr · γM1
8002 · 1.0
The bending moment at support due to the uniformly distributed load is (see sect. 5):
Mql = –15 ·
42
= –120 kNm
2
With δ = – 0.40 from the table of section 5 the enlargement factor α is determined as follows:
α=
1+δ · NEd/Ncr.d 1– 0.4 · 1300/2932.4
=
= 1.48 ≤ 3.0
1–NEd/Ncr,d
1–1300/2932.4
The second order theory moment is gained with the multiplication of the moment at support by the enlargement
factor α (see section 5).
Mllq = Mql · α = (–120) · 1.48 = –177.6 kNm
1
The initial sway imperfection is regarded with φ =
(for the application of equiv. geo. imperfections see section 5)
200
1300
= 6.5 kN;
Mϕl = –H0 · l = – 6.5 · 4 = –26 kNm
H0 = φ · NED =
200
With δ = – 0,18 (see section 5):
α=
1– 0.18 · 1300/2932.4
= 1.65 ≤ 3.0;
1–1300/2932.4
Mllϕ = (–26) · 1.65 = – 42.9 kNm
The internal forces according to the second order theory analysis may only be superposed, if the axial compression force
of the loading conditions is identical (limited superposition). In this example the axial compression force is regarded with
Nd = 1300 kN in combination with the uniformly distributed load qd as well as the sway imperfection φ.
ll = Mll Mll = –177.6 – 42.9 = –220.5 kNm
MEd
q+ ϕ
The bending moment resistance is determined according to section 4 with regard of the axial compression force
(since V/Vpl is smaller than 0.5, a reduction of the yield strength is not necessary):
n=
NEd
1300
=
= 0.386;
Npl/γM0 3370/1.0
MN,Rd =
18
aw = 1–
2·b·t
2 · 25 · 1.0
= 1–
= 0.473
A
94.93
1– n
302
1 – 0,386
Mpl
ll = 220.5 kNm
·
=
·
= 242.9 kNm ≥ MEd
γM0 1 – 0.5 · aw 1.0 1 – 0.5 · 0.473
Condition satisfied!
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Seite 19
Example 3: K gap joint with RHS-chord and SHS-brace members
Check of validity: (see section 8)
1. bi/b0 =
7
= 0.35 ≥ Max
20
0.35 ⇐ decisive
20
0.1 + 0.01 ·
= 0.3
1
2. bi/ti = hi/ti = 7/0.5 = 14 ≤ 35
3. b0/t0 = 20/1 = 20 ≤ 35
und h0/t0 = 10/1 = 10 ≤ 35
4. 0.5 ≤ h0/b0 = 10/20 = 0.5 ≤ 2.0
5. 0.5 ≤ hi/bi = 7/7 = 1 ≤ 2.0
10 + 2 · 2.5
7
6. g = tan 40° – sin 40° = 6.99 cm ≥ Max
2·7+2·7
7. g = 6.99 cm ≤ 1.5 · 20 · 1 –
4 · 20
0.5 · 20 · 1 –
2·7+2·7
4 · 20
= 6.5 cm ⇐ decisive
0.5 + 0.5 = 1.0 cm
= 19.5 cm
9. Θ1 = Θ2 = 40° ≥ 30°
Check of eccentricities:
e
2.5
– 0.55 ≤ h = 10 = 0.25 ≤ 0.25
0
Condition satisfied, which means, that the moments resulting from eccentricities may be neglected in the design of
the connection. The tension chord does not have to be verified for the moments of eccentricities as well.
1. Condition (Verification of the chord force)
Determination of the plastic shear resistance according to DIN EN 1993-1-1:2005:
A · h0
fy,d 54.93 · 10
35.5
= 10 + 20 · 1.0 ·
= 375.3 kN
Vpl,0,d = b + h ·
0
0
3
3
With ved =
350 · sin 40°
10
1 – 0.5992 · 0.45 = 0.910
= 0.599, kα = 0.2 · 20 + 0.35 = 0.45 and n0,Rd = 1 – 1 – 375.3
N0,Rd can be determined according to section 11 as follows:
1950
N0,Rd = 0.910 · 1.0 = 1774.5 kN ≥ N0,d = 950 kN Condition satisfied!
2. Condition (Verification of the brace force)
The following ratios are necessary for the use of the diagrams:
ti
5
bi
7
b0 20
h0 10
t0 = 10 = 0.5;
b0 = 20 = 0.35;
t0 = 1 = 20;
b0 = 20 = 0.5;
bi
7
ti = 0.5 = 14
With the diagrams n1,Rd ≈ 1,0 and for n2,Rd ≈ 0.135 is provided. The maximum brace force can be determined
as follows:
Ni,Rd =
1.0 · 452
= 452.0 kN
1,0
0.135 · 1950
= 409.5 kN ⇐ decisive
sin 40° · 1.0
Ni,Rd = 409.5 kN ≥ Ni,d = 350 kN Condition satisfied!
19
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Seite 20
Example 4: K overlap joint with SHS
Check of validity: (see table 5)
b1 b2
8
1. b = b = 14 = 0.57 ≥ 0.25
0
0
h0
= 1.0 and class 1 cross section
b0
bi hi
3. and 4.
=
= 20 ≤ 35 and class 1 cross section
ti
ti
2.
5. λ0V =
4.7 x 100
10.44 = 45% and
6. Θi >30
≥ 25 %
≤ 100 %
bi
and b = 1 ≥ 0.75
j
For λ0V = 0.45 case 2 is decisive. nRd has to be interpolated
using the cases 1 and 3. With the ratios
ti
4
b1 80
b0 140
t0 = 6.3 = 0.63 ≈ 0.6, b0 = 140 = 0.57 and t0 = 6.3 = 22.2 the diagrams provide:
Check of eccentricities:
Using the eccentricity e the ratio e/h0 can be deternRd,25 ≈ 0.56
nRd,50 ≈ 0.81
mined (see section 8):
Interpolation:
e = – 3.68 cm
(45 – 25)
= 0.76
nRd = 0.56 + (0.81 – 0.56) ·
25
425.6
= 323 kN
N1,Rd = 0.76 ·
1.0
Verification of the design joint resistance:
300
N1,Ed
=
= 0.93
323
N1,Rd
– 0.55 ≤
e –3.68
=
= – 0.26 ≤ 0.25
h0
14
Condition satisfied, which means, that the moments
resulting from eccentricities may be neglected in the
design of the connection. For the design of the compression chord the eccentricities have to be regarded.
Example 5: Lattice girder L = 40 m
Rectangular hollow sections made of S 355 J2H (hot
rolled). The example deals with a roof girder designed
as a warren truss. The single span girder is loaded by
the self-weight, snow and suction forces due to wind.
The loads are combined according to DIN EN
1990:2002. Afterwards the verifications against
buckling and for the joint resistances are carried out.
Loading table:
Load case Dead load G
P1
9.85 kN
P2
19.7 kN
Snow S
7.8 kN
15.6 kN
Wind (suction) Ws
–6.9 kN
–13.8 kN
(The dead load includes the self-weight of the girder.)
Decisive load combinations according to
DIN EN 1990:2002:
LCC 1: 1.35 * G + 1.5 * S
LCC 2: 0.9 * G + 1.5 * Ws
Internal forces
LCC 1:
Load at each node:
P1,d = 1.35 · 19.7 + 1.5 · 15.6 = 50 kN
P2,d = P1,d/2 = 25 kN
Ad = 3.5 · 50 + 25 = 200 kN
Bearing reaction:
LCC 2:
P1,d = –3 kN
P2,d = –1.5 kN
Ad = –3.5 · 3 – 1.5 = –12 kN
– (200 – 25) · 17.5 + 50 · (12.5 + 7.5 + 2.5)
= –775 kN
2.5
max. force in lower chord: UM = 775 + 50/2 = 800 kN
max. force in upper chord: OM =
max. force in braces:
20
D1 = ± (200 – 25) · 2 = ± 247.5 kN
OM = 46.5 kN
UM = – 48 kN
D1 = ± 14.9 kN
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Seite 21
Buckling of the upper chord member (SHS 140 x 8):
The nodes of the upper chords are fixed laterally.
Buckling length for hollow section chord members according to Annex BB.1.3 of DIN EN 1993-1-1: Lcr = 0.9 · 500
= 450 cm. Using the design-support of section 6 the required cross section can be chosen. With. NEd = –775 kN and
Lcr = 4.5 m follows a hollow profile 140 x 140 x 8: I = 1195 cm4, Npl = 1475 kN (see section 15).
Ncr =
–
π2 EI π2 21000 · 1195
=
= 1223 kN; λ =
L2cr
4502
N
1475
= 1223
N
pl
cr
NEd
Verification against buckling for OM: χ · N /γ
pl M1
= 1.1 ⇒ χ ≈ 0.596 (buckling curve a, see sect. 5)
775
= 0.596 · 1475/1.0 = 0.9 < 1.0
Buckling of the lower chord member (SHS 140 x 6.3) :
Perpendicular to the girder-plane the lower chord is fixed at the bearings and in mid-span by structural elements.
Buckling length for hollow section chord members according to Annex BB.1.3 of DIN EN 1993-1-1: Lcr = 0.9 · 2000
= 1800 cm
Ncr =
–
π2 EI π2 21000 · 983,9
=
= 62.9 kN; λ =
L2cr
18002
N
1181
= 62.9
N
pl
cr
NEd
46.5
Verification against buckling for UM: χ · N /γ = 0.051 · 1181/1.0 = 0.77 < 1.0
pl M1
Buckling of the brace members (SHS 80 x 5):
The brace members are welded continuously to the chord members.
Since bi = 0.8 cm < 0.6 · b0 = 0.6 · 14 = 8.4 cm and the connection to the chords is presumed as continuously welded
the buckling length for the brace members according to Annex BB.1.3 of DIN EN 1993-1-1 is:
Lcr = 0.75 · 250 · 2 = 265 cm
This length is valid for in-plane as well as out-of-plane buckling of the brace members.
2
2
–
Ncr = π 2EI = π 21000 2· 136.6 = 403 kN; λ =
L cr
265
N
523
= 403
N
pl
cr
NEd
247.5
Verification against buckling for D1: χ · N /γ =
= 0.84 < 1.0
0.562 · 523/1.0
pl M1
Design joint resistance of node 1:
1. bi/b0 = 8/14 = 0.57 ≥ 0.35
2. bi/ti = hi/ti = 8/0.5 = 16 ≤ 35
3. and 10. 15 ≤ b0/t0 = 14/0.63 = 22.2 ≤ 35
4. and 5. hi/bi = 1 (QHP)
8
≥ 0.5 · 14 · 1– 14 = 3.0 cm
6. and 7. g = 3.1 cm
where e = 2 mm
8
≤ 1.5 · 14 · 1–
= 9.0 cm
14 (The eccentricity is within the range according to section 8)
9. Θ1 = Θ2 = 45° ≥ 30°
b1 + b2 8 + 8
11. 0.6 ≤ 2 · b = 2 · 8 = 1 ≤ 1.3
1
Determination of Ni,Rd:
b1 + b2
With kn = 1.0 (tension chord) and 2 · b = 0.57 the diagram in section 9 provides:
0
0.20 · 1181
nRd ≈ 0.20
Ni,RD = 0.707 · 1.0 = 334 kN
Verification of the design joint resistance:
Ni,d
247.5
Ni,Rd = 334 = 0.74 < 1.0
21
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Seite 22
14 Circular MSH sections according DIN EN 10210
Dimensions
d
t
mm
mm
42.4
48.3
60.3
88.9
101.6
114.3
139.7
168.3
177.8
193.7
3.2
4
5
6.3
3.2
4
5
6.3
4
5
6.3
8
5
6.3
8
10
12.5
5
6.3
8
10
12.5
5
6.3
8
10
12.5
16
5
6.3
8
10
12.5
16
8
10
12.5
16
20
8
10
12.5
16
20
8
10
12.5
16
20
25
30
A
G
U
cm2
kg/m
m2/m
3.094
3.788
4.612
5.609
3.559
4.370
5.339
6.525
5.554
6.819
8.390
10.32
10.35
12.83
15.96
19.46
23.55
11.91
14.81
18.47
22.59
27.47
13.48
16.78
20.97
25.72
31.38
38.79
16.61
20.73
25.98
31.99
39.21
48.81
31.63
39.04
48.03
60.10
73.15
33.50
41.38
50.96
63.84
77.83
36.64
45.30
55.86
70.12
85.67
104.0
121.1
0.133
0.133
0.133
0.133
0.152
0.152
0.152
0.152
0.189
0.189
0.189
0.189
0.279
0.279
0.279
0.279
0.279
0.319
0.319
0.319
0.319
0.319
0.359
0.359
0.359
0.359
0.359
0.359
0.439
0.439
0.439
0.439
0.439
0.439
0.529
0.529
0.529
0.529
0.529
0.559
0.559
0.559
0.559
0.559
0.609
0.609
0.609
0.609
0.609
0.609
0.609
3.941
4.825
5.875
7.145
4.534
5.567
6.802
8.313
7.075
8.687
10.69
13.14
13.18
16.35
20.33
24.79
30.00
15.17
18.86
23.52
28.78
34.99
17.17
21.38
26.72
32.77
39.98
49.41
21.16
26.40
33.10
40.75
49.95
62.18
40.29
49.73
61.18
76.55
93.18
42.68
52.72
64.91
81.33
99.15
46.67
57.71
71.16
89.32
109.1
132.5
154.3
Bending and Torsion
l = lT/2 Wel
i max S
cm4
cm3
cm cm3
7.620
8.991
10.46
11.99
11.59
13.77
16.15
18.74
28.17
33.48
39.49
45.99
116.4
140.2
168.0
196.0
224.8
177.5
215.1
259.5
305.4
354.1
256.9
312.7
379.5
449.7
525.7
612.6
480.5
588.6
720.3
861.9
1 020
1 209
1 297
1 564
1 868
2 244
2 608
1 541
1 862
2 230
2 687
3 136
2 016
2 442
2 934
3 554
4 171
4 817
5 342
3.594
4.241
4.932
5.657
4.797
5.701
6.689
7.761
9.344
11.10
13.10
15.25
26.18
31.55
37.79
44.09
50.57
34.93
42.34
51.08
60.12
69.70
44.96
54.72
66.40
78.68
91.98
107.2
68.80
84.27
103.1
123.4
146.0
173.1
154.2
185.9
222.0
266.7
309.9
173.4
209.4
250.8
302.3
352.7
208.1
252.1
303.0
367.0
430.6
497.4
551.5
1.391
1.365
1.334
1.296
1.599
1.573
1.541
1.502
1.996
1.963
1.922
1.871
2.972
2.929
2.874
2.812
2.737
3.420
3.377
3.321
3.258
3.181
3.868
3.825
3.769
3.704
3.626
3.521
4.766
4.722
4.665
4.599
4.519
4.410
5.675
5.608
5.526
5.414
5.291
6.010
5.943
5.861
5.748
5.624
6.572
6.504
6.422
6.308
6.182
6.030
5.884
2.464
2.960
3.518
4.147
3.260
3.936
4.708
5.598
6.350
7.666
9.227
11.03
17.62
21.53
26.26
31.29
36.81
23.35
28.65
35.13
42.12
49.94
29.89
36.78
45.28
54.56
65.10
77.99
45.38
56.10
69.46
84.28
101.4
123.1
102.9
125.5
152.0
186.2
221.3
115.4
141.0
171.1
210.1
250.3
138.0
168.9
205.5
253.3
303.1
358.4
406.5
Npl
kN
139.9
171.3
208.6
253.6
161.0
197.6
241.5
295.1
251.2
308.4
379.4
466.6
467.9
580.4
721.8
879.9
1 065
538.7
669.6
835.1
1 022
1 242
609.5
758.8
948.4
1 163
1 419
1 754
751.1
937.3
1 175
1 446
1 773
2 207
1 430
1 765
2 172
2 718
3 308
1 515
1 871
2 304
2 887
3 520
1 657
2 049
2 526
3 171
3 874
4 704
5 477
fy = 35.5 kN/cm2
Vpl
Mpl
kN
kNm
51.42
62.96
76.65
93.23
59.16
72.64
88.75
108.5
92.31
113.3
139.5
171.5
172.0
213.3
265.3
323.4
391.5
198.0
246.1
306.9
375.5
456.5
224.0
278.9
348.6
427.5
521.6
644.7
276.1
344.5
431.9
531.7
651.8
811.3
525.7
648.9
798.3
998.9
1 216
556.8
687.8
847.0
1 061
1 294
609.0
753.0
928.5
1 165
1 424
1 729
2 013
1.750
2.101
2.498
2.944
2.315
2.794
3.343
3.975
4.509
5.443
6.551
7.829
12.51
15.29
18.65
22.22
26.13
16.58
20.34
24.94
29.90
35.46
21.22
26.12
32.15
38.74
46.22
55.37
32.22
39.83
49.32
59.84
72.03
87.40
73.04
89.08
107.9
132.2
157.1
81.94
100.1
121.5
149.2
177.7
98.00
119.9
145.9
179.8
215.2
254.4
288.6
Class
S 355
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
For further available dimensions see MSH technical information 1
22
Dimensions
d
t
mm
mm
219.1
244.5
273
323.9
355.6
406.4
457
508
10
12.5
16
20
25
30
8
10
12.5
16
20
25
30
10
12.5
16
20
25
30
36
40
8
10
12.5
16
20
25
30
36
40
10
12.5
16
20
25
30
36
40
10
12.5
16
20
25
30
36
40
10
12.5
16
20
10
12.5
16
20
15.01.2008
A
G
U
cm2
kg/m
m2/m
51.57
63.69
80.14
98.20
119.7
139.9
46.66
57.83
71.52
90.16
110.7
135.3
158.7
64.86
80.30
101.4
124.8
152.9
179.8
210.4
229.8
62.32
77.41
95.99
121.5
149.9
184.3
217.4
255.6
280.1
85.23
105.8
134.0
165.5
203.8
240.9
283.7
311.3
97.76
121.4
154.0
190.6
235.1
278.5
328.8
361.4
110.2
137.0
174.0
215.5
122.8
152.7
194.1
240.7
0.688
0.688
0.688
0.688
0.688
0.688
0.768
0.768
0.768
0.768
0.768
0.768
0.768
0.858
0.858
0.858
0.858
0.858
0.858
0.858
0.858
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.117
1.117
1.117
1.117
1.117
1.117
1.117
1.117
1.277
1.277
1.277
1.277
1.277
1.277
1.277
1.277
1.436
1.436
1.436
1.436
1.596
1.596
1.596
1.596
65.69
81.13
102.1
125.1
152.4
178.2
59.44
73.67
91.11
114.9
141.1
172.4
202.2
82.62
102.3
129.2
159.0
194.8
229.0
268.0
292.8
79.39
98.61
122.3
154.8
190.9
234.8
277.0
325.6
356.8
108.6
134.7
170.7
210.9
259.7
306.9
361.5
396.6
124.5
154.7
196.2
242.8
299.6
354.7
418.9
460.4
140.4
174.6
221.7
274.6
156.5
194.6
247.3
306.6
14:39 Uhr
Seite 23
Bending and Torsion
l = lT/2 Wel
i max S
cm4
cm3
cm cm3
3 598
4 345
5 297
6 261
7 298
8 167
4 160
5 073
6 147
7 533
8 957
10 517
11 854
7 154
8 697
10 707
12 798
15 127
17 162
19 254
20 455
9 910
12 158
14 847
18 390
22 139
26 400
30 219
34 263
36 657
16 223
19 852
24 663
29 792
35 677
41 011
46 737
50 171
24 476
30 031
37 449
45 432
54 702
63 224
72 520
78 186
35 091
43 145
53 959
65 681
48 520
59 755
74 909
91 428
328.5
396.6
483.5
571.5
666.2
745.5
340.3
415.0
502.9
616.2
732.7
860.3
969.7
524.1
637.2
784.4
937.6
1 108
1 257
1 411
1 499
611.9
750.7
916.7
1 136
1 367
1 630
1 866
2 116
2 263
912.5
1 117
1 387
1 676
2 007
2 307
2 629
2 822
1 205
1 478
1 843
2 236
2 692
3 111
3 569
3 848
1 536
1 888
2 361
2 874
1 910
2 353
2 949
3 600
7.401
7.318
7.203
7.075
6.919
6.769
8.366
8.298
8.214
8.098
7.969
7.811
7.658
9.305
9.221
9.104
8.973
8.813
8.657
8.475
8.358
11.17
11.10
11.02
10.90
10.77
10.60
10.44
10.26
10.14
12.22
12.14
12.02
11.89
11.72
11.56
11.37
11.25
14.02
13.93
13.81
13.68
13.51
13.35
13.16
13.03
15.81
15.72
15.60
15.47
17.61
17.52
17.40
17.27
218.8
267.1
330.7
397.7
473.5
540.9
223.8
275.1
336.7
418.4
505.3
604.9
694.7
346.0
424.5
529.1
641.4
771.4
890.2
1 019
1 096
399.3
492.8
606.4
759.1
924.9
1 119
1 300
1 500
1 623
597.4
736.1
923.3
1 128
1 369
1 595
1 846
2 003
785.8
970.1
1 220
1 494
1 821
2 130
2 477
2 696
999.2
1 235
1 557
1 911
1 240
1 535
1 937
2 383
Npl
kN
2 332
2 880
3 624
4 441
5 412
6 327
2 110
2 615
3 234
4 077
5 008
6 120
7 177
2 933
3 632
4 586
5 643
6 915
8 130
9 515
10 394
2 818
3 501
4 341
5 494
6 779
8 334
9 833
11 559
12 665
3 854
4 783
6 060
7 486
9 218
10 894
12 832
14 079
4 421
5 491
6 966
8 619
10 634
12 594
14 871
16 345
4 985
6 197
7 869
9 747
5 554
6 908
8 779
10 885
fy = 35.5 kN/cm2
Vpl
Mpl
kN
kNm
857.1
1 059
1 332
1 632
1 989
2 325
775.6
961.3
1 189
1 499
1 841
2 249
2 638
1 078
1 335
1 686
2 074
2 541
2 988
3 497
3 820
1 036
1 287
1 596
2 019
2 491
3 063
3 614
4 249
4 655
1 417
1 758
2 227
2 751
3 388
4 004
4 716
5 175
1 625
2 018
2 561
3 168
3 909
4 629
5 466
6 008
1 832
2 278
2 892
3 583
2 041
2 539
3 227
4 001
155.3
189.6
234.8
282.4
336.2
384.0
158.9
195.3
239.1
297.1
358.8
429.4
493.2
245.7
301.4
375.6
455.4
547.7
632.1
723.4
778.5
283.5
349.9
430.5
539.0
656.7
794.8
923.1
1 065
1 152
424.1
522.6
655.5
800.6
971.9
1 132
1 311
1 422
557.9
688.7
866.2
1 061
1 293
1 512
1 759
1 914
709.4
877.0
1 105
1 357
880.5
1 090
1 375
1 692
Class
S 355
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
3
2
1
1
23
15.01.2008
14:39 Uhr
Seite 24
15 Square MSH sections according DIN EN 10210
Dimensions
bxb
t
mm
mm
40 x 40
50 x 50
60 x 60
70 x 70
80 x 80
90 x 90
100 x 100
120 x 120
140 x 140
150 x 150
160 x 160
4.0
5.0
6.3
4.0
5.0
6.3
4.0
5.0
6.3
8.0
4.0
5.0
6.3
8.0
4.0
5.0
6.3
8.0
10.0
5.0
6.3
8.0
10.0
5.0
6.3
8.0
10.0
12.5
5.0
6.3
8.0
10.0
12.5
6.3
8.0
10.0
12.5
16.0
20.0
6.3
8.0
10.0
12.5
16.0
17.5
20.0
6.3
8.0
10.0
A
G
U
cm2
kg/m
m2/m
ly = lz
cm4
4.387
5.284
6.332
5.643
6.854
8.310
6.899
8.424
10.29
12.52
8.155
9.994
12.27
15.04
9.411
11.56
14.25
17.55
21.14
13.13
16.22
20.06
24.28
14.70
18.20
22.57
27.42
33.03
17.84
22.16
27.60
33.70
40.88
26.11
32.62
39.98
48.73
60.14
71.99
28.09
35.13
43.12
52.65
65.17
70.23
78.27
30.07
37.64
46.26
0.1497
0.1471
0.1438
0.1897
0.1871
0.1838
0.2297
0.2271
0.2238
0.2194
0.2697
0.2671
0.2638
0.2594
0.3097
0.3071
0.3038
0.2994
0.2942
0.3471
0.3438
0.3394
0.3342
0.3871
0.3838
0.3794
0.3742
0.3678
0.4671
0.4638
0.4594
0.4542
0.4478
0.5438
0.5394
0.5342
0.5278
0.5188
0.5085
0.5838
0.5794
0.5742
0.5678
0.5588
0.5549
0.5485
0.6238
0.6194
0.6142
11.83
13.37
14.68
24.97
28.88
32.76
45.39
53.26
61.65
69.73
74.69
88.50
103.8
119.8
114.5
136.6
161.9
189.3
213.9
199.6
238.3
281.5
322.3
279.4
335.6
399.6
462.1
522.2
497.7
602.9
726.3
852.1
981.8
983.9
1 195
1 416
1 653
1 916
2 128
1 223
1 491
1 773
2 080
2 430
2 553
2 724
1 499
1 831
2 186
5.588
6.732
8.067
7.188
8.732
10.59
8.788
10.73
13.11
15.95
10.39
12.73
15.63
19.15
11.99
14.73
18.15
22.35
26.93
16.73
20.67
25.55
30.93
18.73
23.19
28.75
34.93
42.07
22.73
28.23
35.15
42.93
52.07
33.27
41.55
50.93
62.07
76.61
91.71
35.79
44.75
54.93
67.07
83.01
89.46
99.71
38.31
47.95
58.93
Bending
Wel iy = iz
cm3
cm
5.915
6.684
7.339
9.990
11.55
13.10
15.13
17.75
20.55
23.24
21.34
25.29
29.67
34.22
28.61
34.15
40.47
47.32
53.47
44.35
52.95
62.55
71.61
55.89
67.11
79.92
92.42
104.4
82.95
100.5
121.1
142.0
163.6
140.6
170.7
202.3
236.1
273.7
304.0
163.1
198.7
236.4
277.4
324.0
340.4
363.2
187.4
228.9
273.2
1.45
1.41
1.35
1.86
1.82
1.76
2.27
2.23
2.17
2.09
2.68
2.64
2.58
2.50
3.09
3.05
2.99
2.91
2.82
3.45
3.40
3.32
3.23
3.86
3.80
3.73
3.64
3.52
4.68
4.62
4.55
4.46
4.34
5.44
5.36
5.27
5.16
5.00
4.82
5.85
5.77
5.68
5.57
5.41
5.34
5.23
6.26
6.18
6.09
lT
cm4
Npl
kN
19.48
22.50
25.36
40.39
47.56
55.19
72.51
86.40
102.0
118.2
118.2
142.0
169.5
199.7
180.0
217.4
261.5
311.7
360.0
315.5
381.8
459.0
536.0
439.4
534.2
646.2
761.0
879.0
776.5
950.2
1 160
1 382
1 623
1 540
1 892
2 272
2 696
3 196
3 634
1 909
2 351
2 832
3 375
4 026
4 267
4 617
2 333
2 880
3 478
198.4
239.0
286.4
255.2
310.0
375.8
312.0
381.0
465.3
566.3
368.8
452.0
554.7
679.9
425.6
523.0
644.2
793.5
955.9
594.0
733.7
907.1
1 098
665.0
823.1
1 021
1 240
1 494
807.0
1 002
1 248
1 524
1 849
1 181
1 475
1 808
2 204
2 720
3 256
1 270
1 589
1 950
2 381
2 947
3 176
3 540
1 360
1 702
2 092
fy = 35.5 kN/cm2
Vpl
Mpl
kN
kNm
57.27
68.99
82.67
73.67
89.48
108.5
90.06
110.0
134.3
163.5
106.5
130.5
160.1
196.3
122.9
151.0
186.0
229.1
275.9
171.5
211.8
261.9
316.9
192.0
237.6
294.7
357.9
431.2
233.0
289.3
360.2
439.9
533.6
340.9
425.8
521.9
636.1
785.1
939.8
366.7
458.6
562.9
687.4
850.7
916.8
1021
392.6
491.4
603.9
2.641
3.075
3.516
4.357
5.158
6.037
6.499
7.773
9.229
10.81
9.067
10.92
13.09
15.54
12.06
14.60
17.63
21.13
24.60
18.81
22.83
27.56
32.40
23.56
28.71
34.86
41.26
48.05
34.64
42.47
51.99
62.18
73.42
58.92
72.54
87.36
104.1
124.3
143.0
68.15
84.09
101.5
121.4
145.8
155.0
168.8
78.05
96.49
116.8
Class
S 355
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
24
Dimensions
bxb
t
mm
mm
160 x 160 12.5
16.0
17.5
20.0
180 x 180 6.3
8.0
10.0
12.5
16.0
17.5
20.0
200 x 200 6.3
8.0
10.0
12.5
16.0
17.5
20.0
220 x 220 6.3
8.0
10.0
12.5
16.0
17.5
20.0
250 x 250 8.0
10.0
12.5
16.0
17.5
20.0
260 x 260 8.0
10.0
12.5
16.0
17.5
20.0
300 x 300 8.0
10.0
12.5
16.0
17.5
20.0
350 x 350 10.0
12.5
16.0
400 x 400 10.0
12.5
16.0
20.0
15.01.2008
14:39 Uhr
A
G
U
cm2
kg/m
m2/m
ly = lz
cm4
56.58
70.19
75.72
84.55
34.03
42.67
52.54
64.43
80.24
86.71
97.11
37.98
47.69
58.82
72.28
90.29
97.70
109.7
41.94
52.7
65.10
80.13
100.3
108.7
122.2
60.25
74.52
91.90
115.4
125.2
141.1
62.76
77.66
95.83
120.4
130.7
147.4
72.81
90.22
111.5
140.5
152.7
172.5
105.9
131.2
165.7
121.6
150.8
190.8
235.3
0.6078
0.5988
0.5949
0.5885
0.7038
0.6994
0.6942
0.6878
0.6788
0.6749
0.6685
0.7838
0.7794
0.7742
0.7678
0.7588
0.7549
0.7485
0.8638
0.8594
0.8542
0.8478
0.8388
0.8349
0.8285
0.9794
0.9742
0.9678
0.9588
0.9549
0.9485
1.019
1.014
1.008
0.9988
0.9949
0.9885
1.179
1.174
1.168
1.159
1.155
1.148
1.374
1.368
1.359
1.574
1.568
1.559
1.548
2 576
3 028
3 191
3 422
2 168
2 661
3 193
3 790
4 504
4 768
5 156
3 011
3 709
4 471
5 336
6 394
6 794
7 393
4 049
5 002
6 050
7 254
8 749
9 324
10 198
7 455
9 055
10 915
13 267
14 187
15 609
8 423
10 242
12 365
15 061
16 121
17 766
13 128
16 026
19 442
23 850
25 608
28 371
25 884
31 541
38 942
39 128
47 839
59 344
71 535
72.07
89.41
96.46
107.7
43.35
54.35
66.93
82.07
102.2
110.5
123.7
48.39
60.75
74.93
92.07
115.0
124.5
139.7
53.43
67.15
82.93
102.1
127.8
138.5
155.7
76.75
94.93
117.1
147.0
159.5
179.7
79.95
98.93
122.1
153.4
166.5
187.7
92.75
114.9
142.1
179.0
194.5
219.7
134.9
167.1
211.0
154.9
192.1
243.0
299.7
Bending
Wel iy = iz
cm3
cm
322.0
378.5
398.9
427.8
240.9
295.6
354.8
421.1
500.4
529.8
572.9
301.1
370.9
447.1
533.6
639.4
679.4
739.3
368.1
454.7
550.0
659.5
795.3
847.6
927.0
596.4
724.4
873.2
1 061
1 135
1 249
647.9
787.9
951.1
1 159
1 240
1 367
875.2
1 068
1 296
1 590
1 707
1 891
1 479
1 802
2 225
1 956
2 392
2 967
3 577
Seite 25
lT
cm4
5.98 4 158
5.82 4 988
5.75 5 299
5.64 5 760
7.07 3 361
7.00 4 162
6.91 5 048
6.80 6 070
6.64 7 343
6.57 7 833
6.46 8 576
7.89 4 653
7.81 5 778
7.72 7 031
7.61 8 491
7.46 10 340
7.39 11 063
7.27 12 177
8.71 6240
8.63 7 765
8.54 9 473
8.43 11 481
8.27 14 054
8.21 15 072
8.09 16 658
9.86 11 525
9.77 14 106
9.66 17 164
9.50 21 138
9.43 22 732
9.32 25 244
10.3 13 006
10.2 15 932
10.1 19 409
9.91 23 942
9.84 25 766
9.73 28 650
11.9 20 194
11.8 24 807
11.7 30 333
11.5 37 622
11.5 40 587
11.4 45 318
13.9 39 886
13.7 48 934
13.6 60 990
15.9 60 092
15.8 73 906
15.6 92 442
15.4 112 489
Npl
kN
2 559
3 174
3 424
3 824
1 539
1 930
2 376
2 914
3 629
3 921
4 392
1 718
2 157
2 660
3 269
4 083
4 418
4 960
1 897
2 384
2 944
3 624
4 537
4 915
5 528
2 725
3 370
4 156
5 219
5 661
6 380
2 838
3 512
4 334
5 446
5 909
6 664
3 293
4 080
5 044
6 355
6 903
7 800
4 790
5 931
7 491
5 500
6 819
8 627
10 640
fy = 35.5 kN/cm2
Vpl
Mpl
kN
kNm
738.6
916.3
988.6
1 104
444.2
557.0
685.9
841.1
1 047
1 132
1 268
495.9
622.6
767.8
943.6
1 179
1 276
1 432
547.5
688.2
849.8
1 046
1 310
1 419
1 596
786.6
972.8
1 200
1 507
1 634
1 842
819.4
1 014
1 251
1 572
1 706
1 924
950.5
1 178
1 456
1 835
1 993
2 252
1383
1 712
2 162
1 588
1 968
2 490
491.4
140.1
169.0
180.1
196.8
99.87
123.9
150.5
181.5
220.5
235.8
259.2
124.4
154.6
188.5
228.1
278.8
298.9
330.1
151.5
188.8
230.7
280.1
344.0
369.5
409.5
246.5
302.0
368.1
454.5
489.3
544.6
267.4
327.9
400.1
494.7
533.0
594.0
359.6
442.2
541.3
672.7
726.4
812.4
608.9
747.8
933.5
802.3
987.6
1.237
1.508
Class
S 355
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
4
2
1
1
25
15.01.2008
14:39 Uhr
Seite 26
16 Rectangular MSH sections according DIN EN 10210
Dimensions
hxb
t
mm
mm
50 x 30
4.0
5.0
60 x 40
4.0
5.0
80 x 40
4.0
5.0
6.3
90 x 50
4.0
5.0
6.3
8.0
100 x 50
4.0
5.0
6.3
8.0
100 x 60
4.0
5.0
6.3
8.0
120 x 60
4.0
5.0
6.3
8.0
10.0
120 x 80
5.0
6.3
8.0
10.0
140 x 80
5.0
6.3
8.0
10.0
150 x 100 5.0
6.3
8.0
10.0
12.5
160 x 80
5.0
6.3
8.0
10.0
12.5
180 x 100 5.0
6.3
8.0
10.0
12.5
16.0
200 x 100 6.3
8.0
10.0
12.5
16.0
A
G
cm2
kg/m
ly
cm4
5.588
6.732
7.188
8.732
8.788
10.73
13.11
10.39
12.73
15.63
19.15
11.19
13.73
16.89
20.75
11.99
14.73
18.15
22.35
13.59
16.73
20.67
25.55
30.93
18.73
23.19
28.75
34.93
20.73
25.71
31.95
38.93
23.73
29.49
36.75
44.93
54.57
22.73
28.23
35.15
42.93
52.07
26.73
33.27
41.55
50.93
62.07
76.61
35.79
44.75
54.93
67.07
83.01
4.387
5.284
5.643
6.854
6.899
8.424
10.29
8.155
9.994
12.27
15.04
8.783
10.78
13.26
16.29
9.411
11.56
14.25
17.55
10.67
13.13
16.22
20.06
24.28
14.70
18.20
22.57
27.42
16.27
20.18
25.08
30.56
18.63
23.15
28.85
35.27
42.84
17.84
22.16
27.60
33.70
40.88
20.98
26.11
32.62
39.98
48.73
60.14
28.09
35.13
43.12
52.65
65.17
16.49
18.71
32.83
38.09
68.20
80.28
93.28
107.1
127.3
149.9
173.6
139.6
166.5
197.1
229.9
158.0
189.1
224.8
263.8
248.7
299.2
358.3
424.7
488.1
365.4
439.8
525.3
609.5
534.0
645.8
776.3
908.1
738.7
897.9
1 087
1 282
1 488
744.0
903.2
1 091
1 284
1 485
1 153
1 407
1 713
2 036
2 385
2 777
1 829
2 234
2 664
3 136
3 678
Bending strong and weak axis
Wel.y
iy
lz Wel.z
cm3
cm
cm4 cm3
6.596
7.486
10.94
12.70
17.05
20.07
23.32
23.80
28.28
33.30
38.57
27.92
33.30
39.42
45.98
31.61
37.82
44.96
52.77
41.46
49.87
59.71
70.79
81.36
60.90
73.30
87.54
101.6
76.28
92.26
110.9
129.7
98.50
119.7
144.9
171.0
198.4
93.00
112.9
136.4
160.6
185.7
128.1
156.4
190.4
226.2
265.0
308.6
182.9
223.4
266.4
313.6
367.8
1.72
1.67
2.14
2.09
2.79
2.74
2.67
3.21
3.16
3.10
3.01
3.53
3.48
3.42
3.33
3.63
3.58
3.52
3.44
4.28
4.23
4.16
4.08
3.97
4.42
4.36
4.27
4.18
5.08
5.01
4.93
4.83
5.58
5.52
5.44
5.34
5.22
5.72
5.66
5.57
5.47
5.34
6.57
6.50
6.42
6.32
6.20
6.02
7.15
7.06
6.96
6.84
6.66
7.084
7.888
17.03
19.53
22.24
25.70
29.16
41.95
49.21
56.99
64.58
46.19
54.30
63.05
71.72
70.52
83.59
98.15
113.3
83.09
98.76
116.4
135.1
151.5
192.9
230.5
272.6
312.6
221.1
264.8
314.2
361.9
392.3
474.1
569.3
665.4
763.1
249.3
299.1
355.8
411.2
464.7
460.1
557.2
671.1
787.4
907.6
1 033
612.5
739.0
868.8
1 004
1 147
4.722
5.258
8.517
9.767
11.12
12.85
14.58
16.78
19.69
22.80
25.83
18.48
21.72
25.22
28.69
23.51
27.86
32.72
37.78
27.70
32.92
38.80
45.05
50.51
48.24
57.62
68.14
78.14
55.28
66.20
78.55
90.47
78.47
94.81
113.9
133.1
152.6
62.32
74.78
88.96
102.8
116.2
92.02
111.4
134.2
157.5
181.5
206.6
122.5
147.8
173.8
200.8
229.5
iz
cm
lT
cm4
fy = 35.5 kN/cm2
Npl
Mpl.y Mpl.z
kN
kNm kNm
1.13
1.08
1.54
1.50
1.59
1.55
1.49
2.01
1.97
1.91
1.84
2.03
1.99
1.93
1.86
2.43
2.38
2.33
2.25
2.47
2.43
2.37
2.30
2.21
3.21
3.15
3.08
2.99
3.27
3.21
3.14
3.05
4.07
4.01
3.94
3.85
3.74
3.31
3.26
3.18
3.10
2.99
4.15
4.09
4.02
3.93
3.82
3.67
4.14
4.06
3.98
3.87
3.72
16.59
18.97
36.66
42.98
55.19
65.05
75.63
97.52
116.4
137.7
160.3
112.8
134.7
159.7
186.4
155.9
187.5
224.4
265.4
200.7
241.8
290.0
344.3
395.7
401.3
486.6
586.6
687.6
499.4
606.5
732.9
862.1
806.7
986.5
1 203
1 432
1 679
600.0
729.6
883.1
1 041
1 204
1 042
1 277
1 560
1 862
2 191
2 564
1 475
1 804
2 156
2 541
2 982
198.4
239.0
255.2
310.0
312.0
381.0
465.3
368.8
452.0
554.7
679.9
397.2
487.5
599.5
736.7
425.6
523.0
644.2
793.5
482.4
594.0
733.7
907.1
1 098
665.0
823.1
1 021
1 240
736.0
912.6
1 134
1 382
842.5
1 047
1 305
1 595
1 937
807.0
1 002
1 248
1 524
1 849
949.0
1 181
1 475
1 808
2 204
2 720
1 270
1 589
1 950
2 381
2 947
3.051
3.560
4.909
5.820
7.744
9.275
11.03
10.60
12.78
15.34
18.25
12.51
15.13
18.23
21.79
13.87
16.81
20.32
24.40
18.41
22.40
27.21
32.91
38.75
26.48
32.30
39.27
46.56
33.48
40.98
50.04
59.67
42.40
52.08
63.92
76.70
90.94
41.20
50.55
61.96
74.20
87.76
55.84
68.79
84.77
102.2
122.0
146.0
81.04
100.1
121.0
144.9
174.3
2.089
2.413
3.663
4.318
4.686
5.560
6.531
6.970
8.353
9.947
11.69
7.623
9.152
10.92
12.89
9.680
11.68
14.03
16.71
11.27
13.63
16.44
19.67
22.85
19.92
24.22
29.31
34.54
22.59
27.52
33.40
39.51
31.99
39.18
47.92
57.24
67.47
25.25
30.81
37.48
44.48
51.98
37.05
45.47
55.76
66.82
79.12
93.55
49.66
60.98
73.21
86.88
103.1
Class
S 355
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
1-1
2-1
1-1
1-1
1-1
1-1
3-1
1-1
1-1
1-1
1-1
1-1
2-1
1-1
1-1
1-1
1-1
26
15.01.2008
Dimensions
hxb
t
mm
mm
A
G
cm2
kg/m
ly
cm4
200 x 100 17.5
20.0
200 x 120 6.3
8.0
10.0
12.5
16.0
17.5
20.0
220 x 120 6.3
8.0
10.0
12.5
16.0
20.0
250 x 150 6.3
8.0
10.0
12.5
16.0
17.5
20.0
260 x 140 6.3
8.0
10.0
12.5
16.0
17.5
20.0
260 x 180 6.3
8.0
10.0
12.5
16.0
17.5
20.0
300 x 200 8.0
10.0
12.5
16.0
17.5
20.0
400 x 200 8.0
10.0
12.5
16.0
450 x 250 10.0
12.5
16.0
500 x 300 10.0
12.5
16.0
20.0
89.46
99.71
38.31
47.95
58.93
72.07
89.41
96.46
107.7
40.83
51.15
62.93
77.07
95.81
115.7
48.39
60.75
74.93
92.07
115.0
124.5
139.7
48.39
60.75
74.93
92.07
115.0
124.5
139.7
53.43
67.15
82.93
102.1
127.8
138.5
155.7
76.75
94.93
117.1
147.0
159.5
179.7
92.75
114.9
142.1
179.0
134.9
167.1
211.0
154.9
192.1
243.0
299.7
70.23
78.27
30.07
37.64
46.26
56.58
70.19
75.72
84.55
32.05
40.16
49.40
60.50
75.21
90.83
37.98
47.69
58.82
72.28
90.29
97.70
109.7
37.98
47.69
58.82
72.28
90.29
97.70
109.7
41.94
52.72
65.10
80.13
100.3
108.7
122.2
60.25
74.52
91.90
115.4
125.2
141.1
72.81
90.22
111.5
140.5
105.9
131.2
165.6
121.6
150.8
190.8
235.3
3 870
4 140
2 065
2 529
3 026
3 576
4 221
4 455
4 791
2 610
3 203
3 844
4 560
5 413
6 185
4 143
5 111
6 174
7 387
8 879
9 448
10 306
4 355
5 373
6 490
7 767
9 337
9 936
10 838
5 166
6 390
7 741
9 299
11 245
11 998
13 147
9 717
11 819
14 273
17 390
18 616
20 518
19 562
23 914
29 063
35 738
36 895
45 026
55 705
53 762
65 813
81 783
98 777
14:39 Uhr
Bending strong and weak axis
Wel.y
iy
lz Wel.z
cm3
cm
cm4 cm3
387.0
414.0
206.5
252.9
302.6
357.6
422.1
445.5
479.1
237.3
291.2
349.4
414.5
492.1
562.3
331.4
408.9
493.9
590.9
710.4
755.9
824.5
335.0
413.3
499.3
597.4
718.3
764.3
833.7
397.4
491.5
595.5
715.3
865.0
922.9
1 011
647.8
788.0
951.5
1 159
1 241
1 368
978.1
1 196
1 453
1 787
1 640
2 001
2 476
2 150
2 633
3 271
3 951
6.58
6.44
7.34
7.26
7.17
7.04
6.87
6.80
6.67
8.00
7.91
7.82
7.69
7.52
7.31
9.25
9.17
9.08
8.96
8.79
8.71
8.59
9.49
9.40
9.31
9.18
9.01
8.93
8.81
9.83
9.75
9.66
9.54
9.38
9.31
9.19
11.3
11.2
11.0
10.9
10.8
10.7
14.5
14.4
14.3
14.1
16.5
16.4
16.2
18.6
18.5
18.3
18.2
1 194
1 254
929.0
1 128
1 337
1 562
1 813
1 900
2 019
1 010
1 229
1 459
1 707
1 988
2 222
1 874
2 298
2 755
3 265
3 873
4 098
4 427
1 660
2 032
2 432
2 876
3 400
3 592
3 872
2 929
3 608
4 351
5 196
6 231
6 624
7 215
5 184
6 278
7 537
9 109
9 717
10 647
6 660
8 084
9 738
11 824
14 819
17 973
22 041
24 439
29 780
36 768
44 078
238.8
250.8
154.8
188.1
222.9
260.4
302.2
316.7
336.5
168.4
204.8
243.1
284.5
331.3
370.3
249.9
306.4
367.3
435.4
516.4
546.4
590.3
237.2
290.3
347.4
410.9
485.8
513.2
553.1
325.4
400.9
483.4
577.3
692.3
736.0
801.6
518.4
627.8
753.7
910.9
971.7
1 065
666.0
808.4
973.8
1 182
1 185
1 438
1 763
1 629
1 985
2 451
2 939
Seite 27
iz
cm
3.65
3.55
4.92
4.85
4.76
4.66
4.50
4.44
4.33
4.98
4.90
4.81
4.71
4.55
4.38
6.22
6.15
6.06
5.96
5.80
5.74
5.63
5.86
5.78
5.70
5.59
5.44
5.37
5.26
7.40
7.33
7.24
7.13
6.98
6.92
6.81
8.22
8.13
8.02
7.87
7.81
7.70
8.47
8.39
8.28
8.13
10.5
10.4
10.2
12.6
12.5
12.3
12.1
lT
cm4
fy = 35.5 kN/cm2
Npl
Mpl.y Mpl.z
kN
kNm kNm
3 137 3 176
3 350 3 540
2 028 1 360
2 495 1 702
3 001 2 092
3 569 2 559
4 247 3 174
4 496 3 424
4 856 3 824
2 315 1 449
2 850 1 816
3 431 2 234
4 087 2 736
4 873 3 401
5 589 4 108
4 054 1 718
5 021 2 157
6 090 2 660
7 326 3 269
8 868 4 083
9 463 4 418
10 368 4 960
3 803 1 718
4 704 2 157
5 698 2 660
6 841 3 269
8 257 4 083
8 800 4 418
9 619 4 960
5 810 1 897
7 221 2 384
8 798 2 944
10 643 3 624
12 993 4 537
13 918 4 915
15 351 5 528
10 562 2 725
12 908 3 370
15 677 4 156
19 252 5 219
20 677 5 661
22 912 6 380
15 735 3 293
19 259 4 080
23 438 5 044
28 871 6 355
33 284 4 790
40 719 5 931
50 545 7 491
52 450 5 500
64 389 6 819
80 329 8 627
97 447 10 640
185.5
202.3
89.71
111.0
134.5
161.6
195.2
208.2
227.9
103.8
128.6
156.1
188.0
228.1
267.5
142.9
177.7
216.8
262.7
321.6
344.9
381.3
145.9
181.5
221.4
268.3
328.4
352.2
389.4
168.6
210.1
256.9
312.2
383.8
412.5
457.6
276.7
339.2
413.7
511.4
550.9
613.6
427.1
525.4
643.7
800.7
710.0
872.4
1 090
921.1
1 134
1 422
1 734
109.1
117.6
62.81
77.44
93.42
111.6
133.7
142.0
154.4
67.90
83.80
101.2
121.1
145.5
168.6
100.3
124.4
151.2
182.5
221.9
237.4
261.1
94.80
117.5
142.7
172.0
208.8
223.2
245.2
130.9
162.9
198.8
240.9
295.0
316.5
350.1
209.1
255.9
311.3
383.4
412.3
457.9
263.7
323.4
394.5
487.9
472.4
578.9
720.3
648.1
796.5
995.3
1 210
Class
S 355
1-1
1-1
2-1
1-1
1-1
1-1
1-1
1-1
1-1
3-1
1-1
1-1
1-1
1-1
1-1
4-1
2-1
1-1
1-1
1-1
1-1
1-1
4-1
2-1
1-1
1-1
1-1
1-1
1-1
4-1
2-1
1-1
1-1
1-1
1-1
1-1
3-1
1-1
1-1
1-1
1-1
1-1
4-1
4-1
2-1
1-1
4-1
3-1
1-1
4-1
4-1
2-1
1-1
.
27
Umschlag_2007_engl
15.01.2008
14:43 Uhr
Seite 28
VA L L O U R E C & M A N N E S M A N N T U B E S
VA L LO U R E C & M A N N E S M A N N T U B E S
Vallourec Group
V & M 3 B 0 0 11 - 8 G B
V & M DEUTSCHLAND GmbH
Theodorstraße 90
40472 Düsseldorf · Germany
Phone +49 (2 11) 9 60-35 80
Fax +49 (2 11) 9 60-23 73
E-Mail: info.service@vmtubes.de
www.vmtubes.com/msh
according to Eurocode 3,
DIN EN 1993-1-1: 2005
and
DIN EN 1993-1-8: 2005

Design-support for MSH sections

Transcription

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