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1 1 Eurocode 3 Background Design rules Elliptical tubes Introduction Cross-section Member L. Gardner Recent developments in steel structures: Introduction to Eurocode 3 & Elliptical hollow sections Dr Leroy Gardner Imperial College London South Africa, 2009 2 Eurocode 3 Background Design rules Elliptical tubes Introduction Cross-section Member L. Gardner Introduction to Eurocode 3
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Page 1: gardner

1

1

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Recent developments in steel structures:

Introduction to Eurocode 3 & Elliptical hollow sections

Dr Leroy GardnerImperial College London

South Africa, 2009

2

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Introduction to Eurocode 3

Page 2: gardner

2

3

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

• Introduction

• Load combinations

• Frame stability

• Key design rules

Outline:

Overview

4

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

• EN 1990 – Basis of structural design

• EN 1991 – Actions of structures

Scope of Eurocodes

The first 2 codes are material independent:

• A total of 10 codes (comprising 58 documents)

Scope of structural Eurocodes:

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3

5

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

• EN 1992 – Design of concrete structures

• EN 1993 – Design of steel structures

• EN 1994 – Design of composite structures

• EN 1995 – Design of timber structures

• EN 1996 – Design of masonry structures

• EN 1997 – Geotechnical design

• EN 1998 – Design of structures for earthquakes

• EN 1999 – Design of aluminium structures

Scope of Eurocodes

Remaining 8 codes focus on materials:

6

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

• Codes are published by CEN in 3 languages:

• English

• French

• German

• All codes originally developed in English, and then ‘exactly’ translated

• Other participating counties will translate through National standards bodies

Eurocodes

Page 4: gardner

4

7

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

National Annexes

National Annexes:

• Every Eurocode will contain a National Annex

• National choice

• Non-Contradictory Complementary Information

• Majority of UK NAs now published

8

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

• All codes are published – 58 documents

• 48 have a UK National Annex

• Conflicting steel design standards (e.g. BS 5950) to be withdrawn in 2010

Present situation

Present situation of Eurocodes:

Page 5: gardner

5

9

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Efficiency of EC3 vs BS 5950

• The common design rules are similar and thus lead to similar results

• Where vertical loading governs, it has been estimated that structures designed to EC3 will be 6-8% lighter.

Comparing the results of design to Eurocode 3 and BS 5950:

10

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Computer aided analysis and design

Computer aided analysis and design:

• Greater codification of structural analysis• FE may be implemented through e.g. ‘the general method’• Semi-rigid joints in structural analysis• Beam-column formulations need to be automated

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6

11

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Buildings and bridges

• Philosophy in structural Eurocodes not to repeat material

• BS 5950 vs BS 5400

• Owing to commonality of rules, it will be easier to make the transition between the two disciplines using Eurocode.

12

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Loading and load combinations

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7

13

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

• EN 1990 – Basis of design

• Includes load combinations

• EN 1991 – Actions on structures

• Dead loads, imposed loads, wind loads etc

EN 1990 and EN 1991

EN 1990 and EN 1991:

14

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Load combinations

Equation 6.10:

∑∑1>i

i,ki,0i,Q1,k1,QPj,k1≥j

j,G Q"+"Q"+"P"+"G ψγγγγ

1.35 x Permanent actions

‘to be combined with’ Actions due to

prestressing

1.5 x Leading variable action

1.5 x combination factor x Other variable actions

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15

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Load combinations for a typical structure from Equation 6.10:

Load combinations – Eq. 6.10

EHF

Dead + Wind (uplift)

D + I + W(wind leading)

D + I + W(imposed leading)

Dead + Imposed

Combination WindImposedDead

1.35 1.5 1.0

1.0 1.5 1.0

1.35 1.5 0.75 1.0

1.5 1.01.35 1.05

For Eq. 6.10b, Dead load factor reduces to 1.25.

16

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Remarks on loading and load combinations:

Remarks on load combinations

• Presentation of load combinations unfamiliar

• Idea of leading variable actions and combination factors etc is new

• Other than format and notation, loading codes are similar to existing BS

• Four basic load combinations arise

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9

17

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Overview of Eurocode 3

18

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

EN 1993: Eurocode 3

Eurocode 3 contains six parts:

• EN 1993-1 Generic rules

• EN 1993-2 Bridges

• EN 1993-3 Towers, masts & chimneys

• EN 1993-4 Silos, tanks & pipelines

• EN 1993-5 Piling

• EN 1993-6 Crane supporting structures

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10

19

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

EN 1993-1

Eurocode 3: Part 1 has 12 sub-parts:

• EN 1993-1-1 General rules

• EN 1993-1-2 Fire

• EN 1993-1-3 Cold-formed thin gauge

• EN 1993-1-4 Stainless steel

• EN 1993-1-5 Plated elements

• EN 1993-1-6 Shells

20

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

EN 1993-1

• EN 1993-1-7 Plates transversely loaded

• EN 1993-1-8 Joints

• EN 1993-1-9 Fatigue

• EN 1993-1-10 Fracture toughness

• EN 1993-1-11 Cables

• EN 1993-1-12 High strength steels

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11

21

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Axes convention

Different axes convention:

ZYMinor axis

YXMajor axis

XAlong the member

Eurocode 3BS 5950

22

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Labelling convention

Labelling convention:

b

h d

tw

tf

r

y y

z

z

t

b

r

h y y

z

z

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12

23

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Subscripts

Extensive use of sub-scripts – generally helpful:

• ‘Ed’ means design effect (i.e. factored member force or moment)

• ‘Rd’ means design resistance

So,

• NEd is an axial force

• NRd is the resistance to axial force

Sometimes tedious e.g. Ac,eff,loc

24

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Structural analysis

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13

25

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Analysis types:

• First order elastic• Second order elastic• First order plastic• Second order plastic

Analysis types

26

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Second order effects

• if they increase the action effects significantly

• or modify significantly the structural behaviour

EN 1993-1-1 Clause 5.2.1(2) states that deformed geometry (second order effects) shall be considered:

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14

27

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

For elastic analysis:

where

αcr is the factor by which the design loading would have to be increased to cause elastic instability in a global mode (λcr in BS 5950-1)

FEd is the design loading on the structure

Fcr is the elastic critical buckling load for global instability based on initial elastic stiffness.

10FF

Ed

crcr ≥=α

Limits for ignoring deformed geometry

28

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

• Portals with shallow roof slopes

• Beam and column frames (each storey)

where

HEd horizontal reaction at bottom of the storey

VEd total vertical load at bottom of the storey

δH,Ed storey sway when loaded with horizontal loads (eg wind, equivalent horizontal forces)

h storey height

⎟⎟⎠

⎞⎜⎜⎝

δ⎟⎟⎠

⎞⎜⎜⎝

⎛=α

Ed,HEd

Edcr

hVH

Simple estimate for αcr

Simple estimate for αcr may be applied to:

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15

29

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Limits for treatment of second order effects depend on αcr: Ed

crcr F

F=α

Second order effects more accurately

Second order effects by approximate means

First order only

Achievement

Second order analysisαcr<3

First order analysis plus amplification or effective length method

10>αcr>3

First order analysisαcr>10

ActionLimits on αcr

Frame stability

30

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Global initial sway imperfections:

Global imperfections for frames

mh0 ααφ=φ

factorsreductionareand

200/1valuebasictheiswhere

mh

0

αα

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16

31

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Global imperfections and checks

Global imperfections:

•Much easier to apply as equivalent horizontal forces φNEd, where NEd is the design compressive force in the column

Checks:

• Check cross-sections, members and joints based on maximum forces and moments from analyses

32

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Cross-section classification

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17

33

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Cross-section classification

• Cross-sectional resistance and rotation capacity are limited by the effects of local buckling.

• Eurocode 3 (and BS 5950) account for the effects of local buckling through cross-section classification.

• The classifications from BS 5950 of plastic, compact, semi-compact and slender are replaced in Eurocode 3 with Class 1, Class 2, Class 3 and Class 4, respectively.

34

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Cross-section classification

Deformation

Moment

Mel

Mpl

Class 1

Class 2

Class 4

Class 3

Eurocode 3 defines four classes of cross-section:

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18

35

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Definition of compressed widths – flat widths:

Compressed widths c

c

(a) Outstand flanges (b) Internal compression parts

c

c

Rolled

Welded c

Rolled

Welded

yf/235=ε

Limits on slenderness e.g. c/t ≤ 9ε

36

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Class 4 cross-sections

• Contain slender plate elements

• Local buckling in elastic range

• Effective width concept

Class 4 cross-sections:

Channel in pure compression

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19

37

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Compression members

38

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Elastic buckling theory

Two bounds for perfect columns: Yielding and buckling

Afy

Non-dimensional slenderness

Material yielding (squashing)

Euler (critical) buckling Ncr

NEd

NEd

Lcr

Load

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20

39

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Imperfections

Geometric imperfections

Residual stresses

40

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Residual stresses

Welding

Hot-rolling

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21

41

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Buckling curves

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.5 1 1.5 2 2.5

Curve a0 Curve a Curve b Curve c Curve d

Curve a0

Red

uctio

n fa

ctor

χ

Non-dimensional slenderness λ

42

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Cross-section resistance

sections4ClassforfA

N

ectionss3or21,ClassforAf

N

0M

yeffRd,c

0M

yRd,c

γ=

γ=

• Cross-section resistance in compression Nc,Rd depends on cross-section classification:

γM0 is specified as 1.0 in EN 1993

This value will also be adopted in the UK

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22

43

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Compression buckling resistance Nb,Rd:

1M

yRd,b

fAN

γ

χ=

1M

yeffRd,b

fAN

γ

χ=

Column buckling

for Class 1, 2 and 3

for (symmetric) Class 4

Reduction factor

44

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Member buckling

Calculate non-dimensional slenderness λ

3and2,1ClassforN

fA

cr

y=λ

4ClassforN

fA

cr

yeff=λ

Ncr is the elastic critical buckling load for the relevant buckling mode based on the gross properties of the cross-section

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23

45

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Non-dimensional slenderness

The non-dimensional slenderness used in EC3 is derived from the geometric slenderness (l/r), normalised by λ1.

y

1

fEr/l

π=

λλ

λ1 is the slenderness at which the elastic buckling stress is equal to the yield stress

46

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Buckling reduction factor -Graphical approach

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.5 1 1.5 2 2.5

Curve a0 Curve a Curve b Curve c Curve d

Curve a0

Red

uctio

n fa

ctor

χ

Non-dimensional slenderness λ

0.63

≈0.88

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24

47

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

• Calculate reduction factor, χ

1)(

15.022 ≤

λ−ϕ+ϕ=χ

))2.0(1(5.0 2λ+−λα+=ϕ

Column buckling

Imperfection factor α

Plateau length

48

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Imperfection factor α

0.760.490.340.210.13Imperfection factor α

dcbaa0Buckling curve

Imperfection factors α for 5 buckling curves:

Buckling curves are chosen from a selection table depending on type of section and axis of buckling

Page 25: gardner

25

49

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Column buckling design procedure

Design procedure for column buckling:

1. Determine design axial load NEd

2. Select section and determine geometry

3. Classify cross-section (if Class 1-3, no account need be made for local buckling)

4. Determine effective (buckling) length Lcr

5. Calculate Ncr and Afy

50

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Column buckling design procedure

6. Non-dimensional slenderness

7. Determine imperfection factor α

8. Calculate buckling reduction factor χ

9. Design buckling resistance

10. Check

cr

y

NfA

1M

yRd,b

fAN

γ

χ=

0.1NN

Rd,b

Ed ≤

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26

51

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Beams

52

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Non-dimensional slenderness

Beam behaviour analogous to yielding/buckling of columns.

M

Wyfy

Material yielding (in-plane bending)

Elastic member buckling Mcr

Lcr

MEd MEd

Non-dimensional slenderness LTλFully laterally restrained beams fail by in-plane bending

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27

53

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

In-plane bending

• Class 1 & 2 cross-sections:

0M

yplplRd,c

fWMM

γ==

0M

yelelRd,c

fWMM

γ==

• Class 3 cross-sections:

54

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

In-plane bending

• Class 4 cross-sections:

0M

yeffRd,c

fWM

γ=

Page 28: gardner

28

55

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Shear resistance Vpl,Rd

The usual approach is to use the plastic shear resistance Vpl,Rd

The plastic shear resistance is essentially defined as the yield strength in shear multiplied by a shear area Av:

0M

yvRd,pl

)3/f(AV

γ=

≈ 0.6 fy

56

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Shear buckling

The resistance of the web to shear buckling should also be checked, though this is unlikely to affect cross-sections of standard hot-rolled proportions.

Shear buckling need not be considered provided:

0.1;f

235where

websdunstiffene for 72th

y

w

w

=η=ε

ηε

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57

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Lateral torsional buckling

Lateral torsional buckling

Lateral torsional buckling is the member buckling mode associated with slender beams loaded about their major axis, without continuous lateral restraint.

If continuous lateral restraint is provided to the beam, then lateral torsional buckling will be prevented and failure will occur in another mode, generally in-plane bending (and/or shear).

58

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Lateral torsional buckling

Can be discounted when:

• Minor axis bending

• CHS, SHS, circular or square bar

• Fully laterally restrained beams

• < 0.2 (or 0.4 in some cases)LTλ

Page 30: gardner

30

59

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Lateral torsional buckling

Eurocode 3 design approach for lateral torsional buckling is analogous to the column buckling treatment.

The design buckling resistance Mb,Rd of a laterally unrestrained beam (or segment of beam) should be taken as:

1M

yyLTRd,b

fWM

γχ=

Reduction factor for LTB

60

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

LTB curves

4 buckling curves for LTB (a, b, c and d)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.5 1 1.5 2 2.5

Curve a

Curve b

Curve c

Curve d

Red

uctio

n fa

ctor

χLT

Non-dimensional slenderness LTλ0.2

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31

61

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

cr

yyLT M

fW=λ

Non-dimensional slenderness

• Buckling curves as for compression (except curve a0)

• Wy depends on section classification• Mcr is the elastic critical LTB moment

• Calculate lateral torsional buckling slenderness:

62

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Mcr under uniform moment

G is the shear modulusIT is the torsion constantIw is the warping constantIz is the minor axis second moment of areaLcr is the buckling length of the beam

5.0

z2

T2

cr

z

w2

cr

z2

0,cr EIGIL

II

LEIM ⎥

⎤⎢⎣

π+

π=

Under uniform moment the elastic critical lateral torsional buckling moment Mcr is:

Page 32: gardner

32

63

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Mcr under non-uniform moment

Numerical solutions have been calculated for a number of other loading conditions. For uniform doubly-symmetric cross-sections, loaded through the shear centre at the level of the centroidal axis, and with the standard conditions of restraint described, Mcr may be calculated by:

5.0

z2

T2

cr

z

w2

cr

z2

1cr EIGIL

II

LEICM ⎥

⎤⎢⎣

⎡π

=

64

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

For hot-rolled doubly symmetric I and H sections without destabilising loads, may be conservatively simplified to:

LTλ

LTofassessmentSimplified λ

1

z

1z

1LT 9.0

C19.0

C1

λλ

=λ=λ

y1zz f

E;i/L π=λ=λ

As a further simplification, C1 may also be conservatively taken = 1.0.

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33

65

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Design procedure for LTB

Design procedure for LTB:

1. Determine BMD and SFD from design loads

2. Select section and determine geometry

3. Classify cross-section (Class 1, 2, 3 or 4)

4. Determine effective (buckling) length Lcr –depends on boundary conditions and load level

5. Calculate Mcr and Wyfy

66

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Design procedure for LTB

6. Non-dimensional slenderness

7. Determine imperfection factor αLT

8. Calculate buckling reduction factor χLT

9. Design buckling resistance

10. Check for each unrestrained portion

cr

yyLT M

fW=λ

1M

yyLTRd,b

fWM

γχ=

0.1MM

Rd,b

Ed ≤

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34

67

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Sources of further information

68

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Sources of further information

• http://www.eurocodes.co.uk/

• http://www.steel-sci.org/publications/

• http://www.access-steel.com/

• http://www.steel-ncci.co.uk/

Page 35: gardner

35

69

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Observations on UK implementation:

Implementation in UK

• Existing British Standards withdrawn in 2010

• Public projects must be designed to Eurocodes from 2010

• ICE training courses running since 2005

• Demand for EC courses growing; demand for BS courses reducing

• Many participants now engaged in EC designs

• Design guidance and software

70

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Conclusions:

Conclusions

• Advanced design codes

• Greater in scope

• Biggest change since limit states

• Unfamiliar format

• Guidance material and training emerging

• Basis for other National design codes

Page 36: gardner

36

71

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Elliptical hollow sections (EHS)

72

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Overview

• Introduction/ strategy

• Structural investigations

• Design rules

• Conclusions

Outline contents:

Page 37: gardner

37

73

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Introduction

74

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

• Full-scale structural testing

• Non-linear numerical modelling

• Theoretical investigations

• Development of structural design rules

• Eurocode, BS, AISI

Stages of developments:

Strategy

Page 38: gardner

38

75

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

• Local buckling and section classification• Cross-section compression resistance

• Cross-section bending resistance

• Shear resistance

• Combined bending and shear

• Flexural buckling of columns

• Concrete-filled EHS

Structural scenarios addressed:

Areas examined

76

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

SHS CHSAxial loading

EHSRHSBending

Axial + bending

Elliptical hollow sections

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39

77

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Elliptical hollow sections

a

a

b b

z

y

Elliptical hollow sections (EHS):

• Combine merits of RHS and CHS

• Elegant appearance (CHS)

• Differing rigidities about principal axes (RHS)

78

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. GardnerHeathrow Airport, UK Jarrold store, UK

Applications

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40

79

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. GardnerMadrid Airport, Spain Society Bridge,

Scotland

Applications

80

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Cross-section classification

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81

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Compression (and minor axis bending):

Elastic critical buckling

b

b

a a

z

y)1(3r

tE2

maxcr

ν−=σ

1az

by 22

=⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛

)1(3ba

tE

22cr

ν−⎟⎟⎠

⎞⎜⎜⎝

⎛=σ

rmax

rmax is the maximum local radius of curvature

82

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

a

a

b b

Major axis bending:

Elastic critical buckling

rmax

Maximum compression

Compression

Tension

z

y

Buckling initiates

For a/b < 1.15, buckling initiates at extreme fibre

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83

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Material testing and geometric measurements:

Testing

Tensile coupons Geometric measurements

84

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Compression tests:

Testing

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43

85

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

• Nonlinear FE package ABAQUS

• Stage 1: Validation against tests– Measured material properties– Measured geometry– Measured geometric imperfection

FE modelling

86

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

• Stage 1: Validation against tests– Full loading history and failure models

well predicted

• Stage 2: Parametric studies (>800 FE results in total)– Cross-section slenderness– Member slenderness– Aspect ratios (for all tests, a/b = 2)

FE modelling

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87

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

0

600

1200

1800

0 6 12 18 24

End shortening δ (mm)

Load

N (k

N)

FE

Test

FE validation

88

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Compression

De/tε2

F u/F

y

De = 2rmax = 2a2/b, ε = (235/fy)0.5

0.0

0.5

1.0

1.5

2.0

0 30 60 90 120 150 180 210 240 270

2a

2b

EHSCHSFE

Class 1-3 Class 4

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89

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Minor axis bending tests:

Testing

90

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Minor axis bending – M/Mel

De/tε2

Mu/M

el

De = 2rmax = 2a2/b, ε = (235/fy)0.5

0.0

0.5

1.0

1.5

2.0

2.5

0 20 40 60 80 100 120 140 160 180 200 220 240 260

EHSCHSFE

2a

2b

Class 4Class 1-3

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46

91

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Minor axis bending – M/Mpl

De/tε2

Mu/M

pl

De = 2rmax = 2a2/b, ε = (235/fy)0.5

0.00.20.40.60.81.01.21.41.61.82.0

0 20 40 60 80 100 120 140 160 180 200 220 240 260

2a

2bClass 1-2 Class 3-4

EHSCHSFE

92

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Minor axis bending – Rotation capacity

De/tε2

Rot

atio

n ca

paci

ty

De = 2rmax = 2a2/b, ε = (235/fy)0.5

0369

1215182124273033

0 20 40 60 80 100 120 140 160 180 200 220 240 260

2a

2b

EHSCHSFE

Class 1 Class 2-4

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93

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Radii of curvature:

Major axis bending

2b

2a

0.125a2/b0.22a

0.4a2/b 0.42a

0.65a2/b

a2/b

94

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Summary of proposed measures of slenderness:

Slenderness parameters

Corresponding point on cross-sectionEquivalent diameterLoading

2a

2bAxial compression De = 2a2/b

2a

2bMinor axis bending (z-z) De = 2a2/b

2b

2aMajor axis bending (y-y)

De = 0.8a2/b a/b > 1.36

2b

2a

De = 2b2/a a/b ≤ 1.36

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95

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Summary of proposed slenderness limits:

Slenderness limits

90ε2Not applicableDe/tAxial compression

De/tMajor axis bending (y-y)

140ε270ε250ε2

De/tMinor axis bending (z-y)

Class 3Class 2Class 1

Proposed slenderness limits

Diameter ratio

Type of compression

loading

96

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Shear resistance

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97

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Shear tests

• A total of 24 three-point bending tests performed. Constant aspect ratio = 2.0.

• 12 minor axis tests, 12 major axis tests

• Three variations in cross-section slenderness (thickness)

• Four variations in span length (to investigate moment-shear interaction)

98

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Shear tests

• A total of 24 three-point bending tests performed

L/2 L/2

F

Moment gradient

Uniform shear

Uniform shear

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50

99

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Plastic shear resistance

• Design plastic shear resistance Vpl,Rd

0M

yvRd,pl

3/fAV

γ=

where Av= Shear areafy = Material yield strengthγM0= 1.0

100

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Plastic shear resistance

z

y

θ

r

π=

τ=∴

πτ

=

τ×××=

θ×τ××θ××= ∫π

A2VA

A2V

tr4V

)sin()tdr(2V

0v

0

0

00

Shear area for circular hollow sections: Av=2A/π

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101

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Plastic shear resistance

b b

a

a

z

y

For shear along z-z

a a

b

b

z

y

For shear along y-y

Av = (4b-2t)t Av = (4a-2t)t

102

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Design guidance

0.0

0.5

1.0

1.5

0.00 0.25 0.50 0.75 1.00 1.25

Vu/Vpl,Rd

Mu/M

pl,R

dor

Mu/M

el,R

d

Shear along y-yShear along z-z

Proposed shear-moment interaction

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103

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Design guidance

• For VEd < 50% Vpl,Rd

– Full bending resistance (Mel,Rd or Mpl,Rd)

• For VEd > 50% Vpl,Rd

– Reduced bending resistance

fyr = (1-ρ)fy

where ρ = (2VEd/Vpl,Rd – 1)1/2

104

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Column buckling

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53

105

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Column Tests

• A total of 24 column tests performed, constant aspect ratio = 2.0

• 12 minor axis tests, 12 major axis tests

• Three variations in cross-section slenderness (thickness)

• Four variations in column length

106

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Knife edgeLoad cell

LVDT

Strain gauge

CL

Hydraulic jack

Testing

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107

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Load-deflection response

0

200

400

600

800

1000

0 20 40 60 80 100 120

2nd order rigid plastic

2nd order elastic

Lateral deflection at mid-height ω (mm)

Load

N (k

N)

Elastic buckling

Plastic yielding

108

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

0

250

500

750

0 15 30 45 60

Lateral deflection at mid-height ω (mm)

Load

N (k

N)

Test

FE

FE validation

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109

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

0.0

0.5

1.0

1.5

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8

Member slenderness λ

Buckling about z-z

Buckling about y-y

Nu/

Ny

or N

u/N

eff

z

y

EC3 – curve ‘a’

Column buckling curve

110

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Conclusions:

Conclusions

• New and rare addition to hot-rolled range

• Significant testing and FE modelling programmes

• Design rules developed for primary structural configurations

• Development of comprehensive design rules ongoing

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111

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

Recent developments in steel structures:

Introduction to Eurocode 3 & Elliptical hollow sections

Dr Leroy GardnerImperial College London

South Africa, 2009

112

Eurocode 3

Background

Design rules

Elliptical tubes

Introduction

Cross-section

Member

L. Gardner

ReferencesReferences:

Gardner, L. & Nethercot, D. A. (2005). Designers’Guide to EN 1993-1-1: Eurocode 3: Design of Steel Structures. Thomas Telford Publishing.

Trahair, N. S., Bradford, M. A., Nethercot, D. A. & Gardner, L. (2008). The behaviour and design of steel structures to EC3. Fourth Edition. Taylor & Francis.

Gardner, L. and Chan, T. M. (2007). Cross-section classification of elliptical hollow sections. Steel and Composite Structures. 7(3), 185-200.


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