Concise Eurocode 3 Design of steel structures
Prepared by ec-team
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Contents
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Contents
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Introduction
Version 0.1 This Eurocode concise is a summery of the EN 1993 (Eurocode 3). It only describes the most most important parts. It can not stand alone. alone. Knowledge to the complete Eurocode is necessary when using the concise. This concise is an ideal tool for students, technicians and engineers as a reference to the Eurocode. This paper has been prepared by the ec-team who is also behind the website www.eurocode.info The purpose of the website – and this paper – is to increase the knowledge and understanding of the Eurocode program. As stated in “Guidance Paper L” the European Commission encourages encourages to “ the production of handbooks, design aids, software etc to facilitate the implementation of the EN Eurocodes ”. ”. The www.eurocode.info is a private funded project. The service and all material on the site are free of charge. This document may not be distributed in other ways than from www.eurocode.info. It may not be sold or made any commercial profit with it. ec-team do not warrant, guarantee, or take any representations regarding the use, or the results of use, of the written materials in terms of correctness, accuracy, correctness or otherwise. The format of this paper is A5. If printed it is recommended to print it on A5 paper.
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page 3
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Material
Structural steel properties 1: Modulus of elsticity Shear modulus Poissons ratio Thermal expansion coefficient Density
E G ν α
g
210.000 N/mm2 81.000 N/mm2 0,3 -6 -1 12 x 10 °C 7850 kg/m3
Yield- and ultimate stresses in N/mm 2 for structural steel according to EN 100252: EN 10025 S S S S S S S S S S S S S S
1 2
235 275 355 275 355 420 460 275 355 420 460 460 235 355
N/NL N/NL N/NL N/NL M/ML M/ML M/ML M/ML Q/QL/QL1 W W
0
≤
40 mm f u 360 430 510 390 490 540 570 380 470 520 550 570 360 510
40 < t f y 215 255 335 255 335 390 430 255 335 390 430 440 215 335
≤
80 mm f u 340 410 490 370 470 520 550 360 450 500 530 550 340 490
EN 1993-1-1, 3.2.6 EN 1993-1-1, 3
page 4
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Determination of maximum permissible value of element thickness 3: TED
Referance temperature
o
σED
Stress acompanying the referance temperature
MPa
ε
Strain rate
sec
εcf
Degree of cold forming
%
Yield stress at a given thickness:
C
−1
t f y.norm − 0.25 ⋅ 1mm
f y ( t)
1440 − fy ( t)
Temperatur allowance for strain rates:
∆T ε
Temperatur allowance for cold forming:
∆Tε.cf −3 ⋅ εcf
550
1.5 ε ⎛ ⎞ ⋅ ln ⎝ 4 ⋅ 10− 4 ⋅ sec− 1 ⎠
Permissible thickness t in mm o
TED [ C]
10
0
-10
-20
-30
-40
-50
=0,75 f y(t)
σEd
S 235 JR
60
50
40
35
30
25
20
S 235 J0
90
75
60
50
40
35
30
S 235 J2
125 105
90
75
60
50
40
S 355 JR
40
35
25
20
15
15
10
S 355 J0
60
50
40
35
25
20
15
S 355 J2
90
75
60
50
40
35
25
=0,50 f y(t)
σEd
S 235 JR
90
75
65
55
45
40
35
S 235 J0
125 105
90
75
65
55
45
S 235 J2
170 145 125 105
90
75
65
S 355 JR
65
55
45
40
30
25
25
S 355 J0
95
80
65
55
45
40
30
S 355 J2
135 110
95
80
65
55
45
=0,25 f y(t)
σEd
3
S 235 JR
135 155 100
75
65
60
S 235 J0
175 155 135 115 100
85
75
S 235 J2
200 200 175 155 135 115 100
S 355 JR
110
80
70
60
55
45
S 355 J0
150 130 110
95
80
70
60
S 355 J2
200 175 150 130 110
95
80
95
85
EN 1993-1-10, 2.3
page 5
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Resistance of cross-sections
Partial factors:
γ m0
1.00
cross-sections
γ m1
1.00
members to instability assessed by member checks
γ m2
1.25
cross sections in tension to fracture
Yiels criterion for elastic verification: 2
2
2
⎛ σx.Ed ⎞ ⎛ σz.Ed ⎞ ⎛ σx.Ed ⎞ ⎛ σz.Ed ⎞ ⎛ τEd ⎞ + − ⋅ + 3⋅ ≤1 f f f f f ⎜ y ⎟ ⎜ y ⎟ ⎜ y ⎟⎜ y ⎟ ⎜ y ⎟ ⎝ γ M0 ⎠ ⎝ γ M0 ⎠ ⎝ γ M0 ⎠ ⎝ γ M0 ⎠ ⎝ γ M0 ⎠ Conservative approximation for class 1, 2, and 3: NEd NRd
+
My.Ed My.Rd
+
Mz.Ed Mz.Rd
≤1
page 6
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Tension
Design criterion: NEd ≤ Nt.Rd
⇒
A ⋅ f y
NEd ≤ γ M0
Plate with hole: Nt.Rd
Npl.Rd
(
A ⋅ f y
γ M0
⎡
A net
)
MIN Npl.Rd , Nu.Rd
⋅ net ⋅ f u γ M2
0.9 A
Nu.Rd
⎛
MAX A − t ⋅ d0 , t ⋅ n ⋅ d0 −
⎣
⎝
∑
s
2
⎞⎤
4p
⎠⎦
page 7
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Compression
Design criterion: NEd ≤ Nc.Rd Class 1, 2 and 3: Nc.Rd
Class 4: Nc.Rd
A ⋅ f y
γ m0 A eff ⋅ f y
γ m0
page 8
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Bending moment
Design criterion: MEd ≤ Mc.Rd Binding about one axis: Class 1 and 2:
Mc.Rd
Class 3:
Mpl.Rd
Mc.Rd
Class 4:
Mel.Rd
Mpl.Rd
Mel.Rd
Wpl ⋅ f y
γ M0 Wel ⋅ f y
γ M0
Weff ⋅ f y
Mc.Rd
γ M0
Binding about two axis:
⎛
My.Ed
⎞
⎝ Mpl.y.Rd ⎠
α
+
⎛
Mz.Ed
⎞
⎝ Mpl.z.Rd ⎠
2
5
2
2
6
6
β
≤1
page 9
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Shear
Design criterion: VEd ≤ Vc.Rd A v ⋅
Plastic design: Vc.Rd Vpl.Rd
Vpl.Rd
⎛ Fy ⎞ ⎝ 3 ⎠
γ M0
Shear area A v:
rolled
rolled
rolled
welded
welded
(
)
A − 2 ⋅ b ⋅ tf + tw + 2 ⋅ r ⋅ tf ≥ hw ⋅ tw
(
)
A − 2 ⋅ b ⋅ tf + tw + r ⋅ tf
(
)
0.9 ⋅ A − b ⋅ tf
∑ ( hw ⋅ tw)
(
A − ∑ hw ⋅ tw
)
A ⋅ h rolled
b+h A ⋅ b
rolled
b+h
⋅ π
2 A
page 10
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Elastic design:
τEd⋅
3
⋅ γ M0
f y
τEd
≤1
VEd ⋅ S I⋅ t
S I
I and H sections:
τEd
y ⋅ A Secound area of moment of the whole cross section VEd
b ⋅ tf
hw ⋅ tw
hw ⋅ tw
≥ 0.6
page 11
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Torsion
page 12
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Bending and shear
Shear may be neglicted if 0.5⋅ VEd ≤ Vpl.Rd Design criterion: MEd ≤ Mc.Rd Binding about one axis: Class 1 and 2
Mc.Rd
Class 3
Mc.Rd
Class 4
ρ
⎛
Mc.Rd
⋅ Ed
2 V
⎝ Vpl.Rd
⎞
−1
⎠
Mpl.Rd
Mpl.Rd
Mel.Rd
Mel.Rd
Wpl ⋅ f y ⋅ ( 1 − ρ )
γ M0 Wel ⋅ f y ⋅ ( 1 − ρ )
γ M0
Weff ⋅ f y ⋅ ( 1 − ρ )
γ M0 A v ⋅
2
Vpl.Rd
⎛ Fy ⎞ ⎝ 3 ⎠
γ M0
A v : see "shear"
page 13
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Bending and axial force
Design criterion: MEd ≤ MN.Rd
Class 1 and 2:
Allowance for N Ed only if: y-y axis: NEd ≤
⋅ Npl.Rd ⇒
0.25
and:
NEd ≤
0.25 ⋅ A ⋅ f y
γ m0
⋅ hw ⋅ tw ⋅ f y
0.5
NEd ≤ z-z axis: NEd ≤
γ M0 hw ⋅ tw ⋅ f y
γ M0
y-y axis: MN.y.Rd
Mpl.y.Rd⋅ ( 1 − n) 1
− 0.5⋅ a
2
⋅ Wpl.y⋅
A ⋅ f y − NEd ⋅ γ M0
γ M0 ⋅ ( A + 2⋅ b ⋅ tf )
page 14
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if:
A ⋅ f y
≤
A − 2 ⋅ b ⋅ tf
⇒
A
MN.z.Rd
Wpl.z ⋅ f y
γ M0
⎡
else: MN.z.Rd
⇓ MN.z.Rd
2 n − a ⎞ ⎤ ⎛ Mpl.z.Rd ⋅ 1 − ⎣ ⎝ 1 − a ⎠ ⎦ 2⎤ ⎡ ⎛ N ⋅ γ 2 ⋅ b ⋅ t ⎞ A − Ed M0 f − ⎜ ⎥ Wpl.z ⋅ f y ⎢ A ⋅ f A y ⎜ ⎟ ⎥ ⋅ ⎢1 − ⎜ ⎟⎥ γ M0 ⎢ A − 2 ⋅ b ⋅ tf ⎜ 1− A ⎣ ⎝ ⎠ ⎦
Class 1 and 2: y-y axis: MN.y.Rd
Mpl.y.Rd⋅ ( 1 − n) 1
− 0.5⋅ aw
2
⋅
Wpl.y A ⋅ f y − NEd ⋅ γ M0
γ M0
⋅
A + 2 ⋅ b ⋅ t
z-z axis: MN.z.Rd
Mpl.z.Rd ⋅ ( 1 − n) 1
− 0.5⋅ af
2
⋅
Wpl.z A ⋅ f y − NEd ⋅ γ M0
γ M0
⋅
A + 2 ⋅ h ⋅ t
page 15
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Binding about two axis:
⎛
My.Ed
⎞
⎝ Mpl.y.Rd ⎠
α
+
⎛
Mz.Ed
⎞
⎝ Mpl.z.Rd ⎠
2
β
≤1
5
⋅
N Ed
⋅ γ M0 ≥ 1 A ⋅ f y
2
2 1.66
6 1
− 1.13⋅
⎛ N Ed A ⋅ f y
⎝
⎞
2
≤6
⋅ γ M0
⎠
page 16
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Bending and axial force
Allowance for V Ed only if: VEd ≤
⋅ pl.Rd
0.5 V
Use the above calculations, but reduce the yield strength to:
⎡
f y.M.V.N
f y ⋅ ( 1 − ρ ) A v ⋅
Vpl.Rd
⎛ Fy ⎞
⎛
⋅ Ed ⎞ f y ⋅ 1 − ⎣ ⎝ Vpl.Rd − 1 ⎠ 2 V
⎤
2
⎦
⎝ 3 ⎠
γ M0
page 17
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Buckling
Imperfection factor α
4
rolled
0,21 for h/b >1,2 0,34 for h/b ≤1,2
0,21 for hot finished 0,49 for cold formed
rolled
0,34 for h/b >1,2 0,49 for h/b ≤1,2
0,49
0,34
0,34
welded
welded
0,49
Factor k for determining the buckling length L cr
4
For limitations and additional sections see table 6.2, EN 1993-1-1
page 18
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Compression members
Design criterion: NEd ≤ Nb.Rd Class 1, 2 and 3: k⋅ L
Lcr
k
Buckling length factor
L
Length of member
E
i
Radius of gyration
f y
α
Imperfection factor
f y
λ1 π ⋅
φ
Buckling length
235
ε
λ
Lcr
Lcr i
⋅
⋅
1
λ1
0.5 1
+ α ⋅ ( λ − 0.2) + λ 1
χ φ+
2
2
≤ 1.0 2
φ −λ χ A ⋅ ⋅ f y
Nb.Rd
γ M1
Class 4: Substiture λ ande Nb,Rd with: A eff
λ
Lcr i
Nb.Rd
⋅
A
λ1 χ A ⋅ eff ⋅ f y γ M1 page 19
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Bending and axial compression
page 20
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Bolts, rivets or pins
page 21
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Bolts and rivets
page 22
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slip resistant
page 23
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Combined tension and shear
page 24
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Pin connections
page 25
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Welded connections
page 26
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Fillet weld
page 27
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butt weld
page 28
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Structural joints
page 29
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Basic components
page 30
