Concise Eurocode 3 v0 1

Concise

Eurocode 3 Design of steel structures

Prepared by

ec-team

www.eurocode.info

Contents

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ec-team www.eurocode.info

page 3

Introduction

Version 0.1

This Eurocode concise is a summery of the EN 1993 (Eurocode 3). It only describes the most important parts. It can not stand 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 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. ec-team copyright 2006


page 4

Material

Structural steel properties1: Modulus of elsticity E 210.000 N/mm2

Shear modulus G 81.000 N/mm2

Poissons ratio ν 0,3 -Thermal expansion coefficient α 12 x 10-6 °C-1

Density g 7850 kg/m3

Yield- and ultimate stresses in N/mm2 for structural steel according to EN 100252:

fy fu fy fuS 235 235 360 215 340S 275 355 430 255 410S 355 355 510 335 490S 275 N/NL 275 390 255 370S 355 N/NL 355 490 335 470S 420 N/NL 420 540 390 520S 460 N/NL 460 570 430 550S 275 M/ML 275 380 255 360S 355 M/ML 355 470 335 450S 420 M/ML 420 520 390 500S 460 M/ML 460 550 430 530S 460 Q/QL/QL1 460 570 440 550S 235 W 235 360 215 340S 355 W 355 510 335 490

0 < t ≤ 40 mm 40 < t ≤ 80 mmEN 10025

1 EN 1993-1-1, 3.2.6 2 EN 1993-1-1, 3


page 5

Determination of maximum permissible value of element thickness3:

TED Referance temperature oC

σED Stress acompanying the referance temperature MPa

ε Strain rate sec 1−

εcf Degree of cold forming %

Yield stress at a given thickness: fy t( ) fy.norm 0.25t

1mm⋅−

Temperatur allowance for strain rates: ∆Tε

1440 fy t( )−

550ln

ε

4 10 4−⋅ sec 1−⋅

⎛⎜⎝

⎞

⎠

1.5⋅

Temperatur allowance for cold forming: ∆Tε.cf 3− εcf⋅

TED [oC] 10 0 -10 -20 -30 -40 -50

S 235 JR 60 50 40 35 30 25 20S 235 J0 90 75 60 50 40 35 30S 235 J2 125 105 90 75 60 50 40S 355 JR 40 35 25 20 15 15 10S 355 J0 60 50 40 35 25 20 15S 355 J2 90 75 60 50 40 35 25

S 235 JR 90 75 65 55 45 40 35S 235 J0 125 105 90 75 65 55 45S 235 J2 170 145 125 105 90 75 65S 355 JR 65 55 45 40 30 25 25S 355 J0 95 80 65 55 45 40 30S 355 J2 135 110 95 80 65 55 45

S 235 JR 135 155 100 85 75 65 60S 235 J0 175 155 135 115 100 85 75S 235 J2 200 200 175 155 135 115 100S 355 JR 110 95 80 70 60 55 45S 355 J0 150 130 110 95 80 70 60S 355 J2 200 175 150 130 110 95 80

σEd=0,75 fy(t)

σEd=0,50 fy(t)

σEd=0,25 fy(t)

Permissible thickness t in mm

3 EN 1993-1-10, 2.3


page 6

Resistance of cross-sections

Partial factors:

γm0 1.00 cross-sections

γm1 1.00 members to instability assessed by member checks

γm2 1.25 cross sections in tension to fracture

Yiels criterion for elastic verification:

σx.Edfy

γM0

⎛⎜⎜⎜⎝

⎞

⎟

⎠

2σz.Ed

fyγM0

⎛⎜⎜⎜⎝

⎞

⎟

⎠

2

+σx.Ed

fyγM0

⎛⎜⎜⎜⎝

⎞

⎟

⎠

σz.Edfy

γM0

⎛⎜⎜⎜⎝

⎞

⎟

⎠

⋅− 3τEdfy

γM0

⎛⎜⎜⎜⎝

⎞

⎟

⎠

2

⋅+ 1≤

Conservative approximation for class 1, 2, and 3:

NEd

NRd

My.Ed

My.Rd+

Mz.Ed

Mz.Rd+ 1≤


page 7

Tension

Design criterion:

NEd Nt.Rd≤ ⇒ NEdA fy⋅

γM0≤

Plate with hole:

Nt.Rd MIN Npl.Rd Nu.Rd,( )

Npl.RdA fy⋅

γM0Nu.Rd

0.9 Anet⋅ fu⋅

γM2

Anet MAX A t d0⋅− t n d0⋅s2

4p∑−⎛⎜⎜⎝

⎞

⎠

⋅,⎡⎢⎢⎣

⎤⎥⎥⎦


page 8

Compression

Design criterion:

NEd Nc.Rd≤

Class 1, 2 and 3:

Nc.RdA fy⋅

γm0

Class 4:

Nc.RdAeff fy⋅

γm0


page 9

Bending moment

Design criterion:

MEd Mc.Rd≤

Binding about one axis:

Class 1 and 2: Mc.Rd Mpl.Rd Mpl.RdWpl fy⋅

γM0

Class 3: Mc.Rd Mel.Rd Mel.RdWel fy⋅

γM0

Class 4: Mc.RdWeff fy⋅

γM0

Binding about two axis:

My.Ed

Mpl.y.Rd

⎛⎜⎜⎝

⎞

⎠

α Mz.Ed

Mpl.z.Rd

⎛⎜⎜⎝

⎞

⎠

β

+ 1≤

α β

2 5

2 2

6 6


page 10

Shear

Design criterion:

VEd Vc.Rd≤

Plastic design:

Vc.Rd Vpl.Rd Vpl.Rd

AvFy

3

⎛⎜⎝

⎞

⎠⋅

γM0 Shear area Av:

rolled

A 2 b⋅ tf⋅− tw 2 r⋅+( ) tf⋅+ hw tw⋅≥

rolled

A 2 b⋅ tf⋅− tw r+( ) tf⋅+

rolled

0.9 A b tf⋅−( )⋅

welded

∑ hw tw⋅( )

welded

A ∑ hw tw⋅( )−

rolled

A h⋅

b h+

rolled

A b⋅

b h+

2 A⋅

π


page 11

Elastic design:

τEd 3 γM0⋅⋅

fy1≤

τEdVEd S⋅

I t⋅S y A⋅

Secound area of momentof the whole cross sectionI

I and H sections: τEdVEd

hw tw⋅

b tf⋅

hw tw⋅0.6≥


page 12

Torsion


page 13

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 Mpl.Rd Mpl.RdWpl fy⋅ 1 ρ−( )⋅

γM0

Class 3 Mc.Rd Mel.Rd Mel.RdWel fy⋅ 1 ρ−( )⋅

γM0

Class 4 Mc.RdWeff fy⋅ 1 ρ−( )⋅

γM0

ρ2 VEd⋅

Vpl.Rd1−

⎛⎜⎜⎝

⎞

⎠

2

Vpl.Rd

AvFy

3

⎛⎜⎝

⎞

⎠⋅

γM0Av: see "shear"


page 14

Bending and axial force

Design criterion:

MEd MN.Rd≤

Class 1 and 2:

Allowance for NEd only if:

y-y axis:NEd 0.25 Npl.Rd⋅≤ ⇒ NEd

0.25 A⋅ fy⋅

γm0≤

and:

NEd0.5 hw⋅ tw⋅ fy⋅

γM0≤

z-z axis:

NEdhw tw⋅ fy⋅

γM0≤

y-y axis:

MN.y.RdMpl.y.Rd 1 n−( )⋅

1 0.5 a⋅−2 Wpl.y⋅

A fy⋅ NEd γM0⋅−

γM0 A 2 b⋅ tf⋅+( )⋅⋅


page 15

z-z axis:

if:NEd γM0⋅

A fy⋅

A 2 b⋅ tf⋅−

A≤ ⇒ MN.z.Rd

Wpl.z fy⋅

γM0

else: MN.z.Rd Mpl.z.Rd 1n a−

1 a−⎛⎜⎝

⎞⎠

2−

⎡⎢⎣

⎤⎥⎦

⋅

⇓

MN.z.RdWpl.z fy⋅

γM01

NEd γM0⋅

A fy⋅

A 2 b⋅ tf⋅−

A−

1A 2 b⋅ tf⋅−

A−

⎛⎜⎜⎜⎜⎝

⎞

⎟⎟

⎠

2

−

⎡⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎦

⋅

Class 1 and 2:

y-y axis:

MN.y.RdMpl.y.Rd 1 n−( )⋅

1 0.5 aw⋅−2

Wpl.y

γM0


A 2 b t⋅⋅+⋅⋅

z-z axis:

MN.z.RdMpl.z.Rd 1 n−( )⋅

1 0.5 af⋅−2

Wpl.z

γM0


A 2 h t⋅⋅+⋅⋅


page 16

Binding about two axis:

My.Ed

Mpl.y.Rd

⎛⎜⎜⎝

⎞

⎠

α Mz.Ed

Mpl.z.Rd

⎛⎜⎜⎝

⎞

⎠

β

+ 1≤

α β

2 5

N Ed

A f y⋅γ M0⋅⋅ 1≥

2 2

6

1.66

1 1.13N Ed

A f y⋅γ M0⋅

⎛⎜⎜⎝

⎞

⎠

2

⋅−

6≤


page 17

Bending and axial force

Allowance for VEd only if:

VEd 0.5 Vpl.Rd⋅≤

Use the above calculations, but reduce the yield strength to:

fy.M.V.N fy 1 ρ−( )⋅ fy 12 VEd⋅

Vpl.Rd 1−

⎛⎜⎜⎝

⎞

⎠

2

−

⎡⎢⎢⎣

⎤⎥⎥⎦

⋅

Vpl.Rd

AvFy

3

⎛⎜⎝

⎞

⎠⋅

γM0


page 18

Buckling

Imperfection factor α 4

rolled

0,21 for h/b >1,2 0,34 for h/b ≤1,2

rolled

0,34 for h/b >1,2 0,49 for h/b ≤1,2

welded

0,34

welded

0,49

Factor k for determining the buckling length Lcr

4 For limitations and additional sections see table 6.2, EN 1993-1-1

0,21 for hot finished 0,49 for cold formed

0,49

0,34


page 19

Compression members

Design criterion:

NEd Nb.Rd≤

Class 1, 2 and 3:

Lcr k L⋅ Lcr Buckling length

k Buckling length factorε

235fy L Length of member

i Radius of gyrationλ1 π

E

fy⋅

α Imperfection factor

λLcr

i

1λ1

⋅

φ 0.5 1 α λ 0.2−( )⋅+ λ2

+⎡⎣ ⎤⎦⋅

χ1

φ φ2

λ2

−+

1.0≤

Nb.Rdχ A⋅ fy⋅

γM1

Class 4:Substiture λ ande Nb,Rd with:

λLcr

i

Aeff

A

λ1⋅

Nb.Rdχ Aeff⋅ fy⋅

γM1


page 20

Bending and axial compression


page 21

Bolts, rivets or pins


page 22

Bolts and rivets


page 23

slip resistant


page 24

Combined tension and shear


page 25

Pin connections


page 26

Welded connections


page 27

Fillet weld


page 28

butt weld


page 29

Structural joints


page 30

Basic components


page 31

Beam-to-column joints

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