eurocodes 1999.pdf · brussels, 18-20 february 2008 – dissemination of information workshop 1...

EUROCODESBackground and Applications

“Dissemination of information for training” workshop 18-20 February 2008 Brussels

EN 1999 Eurocode 9: Design of aluminium structures Organised by European Commission: DG Enterprise and Industry, Joint Research Centre with the support of CEN/TC250, CEN Management Centre and Member States

Wednesday, February 20 – Palais des Académies EN 1999 - Eurocode 9: Design of aluminium structures Marie-Thérèse room

9:00-9:15 General information on EN 1999 F. Mazzolani University of Naples "Federico II"

9:15-10:00 Design criteria F. Mazzolani University of Naples "Federico II"

10:00-10:30 Fields of application F. Mazzolani University of Naples "Federico II"

10:30-11:00 Coffee

11:00-11:45 Selection of structural alloys R. Gitter GDA/AluConsult

11:45-13.00 Strength and stability (Part 1.1) T. Höglund Torsten Höglund HB

13:00-14:00 Lunch

14:00-14:45 Connections(Part 1.1) F. Soetens TNO

14:45-15:30 Fatigue (Part 1.3) D. Kosteas Technische Universität München

15:30-16:00 Coffee

16:00-16:45 Cold-formed structures (Part 1.4) R. Landolfo University of Naples "Federico II"

16:45-17:30 Shell structures (Part 1.5) A. Mandara

17:30-18:00 Discussion and close University of Naples "Federico II" All workshop material will be available at http://eurocodes.jrc.ec.europa.eu

GENERAL INFORMATION ON EN 1999

F. Mazzolani University of Naples "Federico II"

Brussels, 18-20 February 2008 – Dissemination of information workshop 1


GENERAL INFORMATIONGENERAL INFORMATIONON EN 1999ON EN 1999

Federico M. MazzolaniFederico M. Mazzolani((ChairmanChairman of TC 250of TC 250--SC9)SC9)

Department of Structural Analysis and DesignDepartment of Structural Analysis and DesignFaculty of EngineeringFaculty of Engineering

University of Naples University of Naples ““Federico IIFederico II””

GENERAL INFORMATION ON EN 1999(Federico Mazzolani)




ENVENV--EUROCODE 9 (1998)EUROCODE 9 (1998)““ALUMINIUM STRUCTURAL DESIGNALUMINIUM STRUCTURAL DESIGN””

Part 1.1Part 1.1 ““General rulesGeneral rules””

Part 1.2Part 1.2 ““Fire designFire design””

Part 1.3Part 1.3 ““Structures susceptible to fatigueStructures susceptible to fatigue””




11)) ENEN 19991999--11--11 GENERAL STRUCTURAL RULESGENERAL STRUCTURAL RULES

2) EN 19992) EN 1999--11--22 STRUCTURALSTRUCTURAL FIRE DESIGNFIRE DESIGN

3) EN 19993) EN 1999--11--33 ADDITIONALADDITIONAL RULES FOR STRUCTURES RULES FOR STRUCTURES

SUSCEPTIBLE TO FATIGUESUSCEPTIBLE TO FATIGUE

4) EN 19994) EN 1999--11--44 SUPPLIMENTARYSUPPLIMENTARY RULES FOR COLDRULES FOR COLD--

FORMED SHEETINGFORMED SHEETING

5) EN 19995) EN 1999--11--55 SUPPLIMENTARYSUPPLIMENTARY RULES FOR SHELL RULES FOR SHELL

STRUCTURESSTRUCTURES

ENEN--EUROCODE 9 (2006)EUROCODE 9 (2006)““ALUMINIUM STRUCTURAL DESIGNALUMINIUM STRUCTURAL DESIGN””




11)) GeneralGeneral

2)2) Basis designBasis design

3)3) MaterialsMaterials

4)4) Durability, corrosion and executionDurability, corrosion and execution

5)5) Structural analysisStructural analysis

6)6) Ultimate limit states for membersUltimate limit states for members

7)7) Serviceability limit statesServiceability limit states

8)8) Ultimate limit states for connectionsUltimate limit states for connections

CONTENTS of Part 1CONTENTS of Part 1--11

EUROCODE 9 – Part 1-1: General structural rules




AA)) Execution classesExecution classes

BB)) EquivalentEquivalent TT--stubstub inin tensiontension

C)C) MaterialsMaterials selectionselection

D)D) CorrosionCorrosion andand surfacesurface protectionprotection

E)E) AnalyticalAnalytical modelsmodels forfor stressstress--strainstrain relationshiprelationship

F)F) BehaviourBehaviour ofof crosscross--sectionssections beyondbeyond elasticelastic limitlimit

G)G) RotationRotation capacitycapacity

H)H) PlasticPlastic hingehinge methodmethod forfor continuouscontinuous beamsbeams

I ) I ) Lateral torsional buckling of beams and Lateral torsional buckling of beams and torsionaltorsional oror

torsionaltorsional--flexuralflexural bucklingbuckling ofof compressedcompressed membersmembers

J ) J ) PropertiesProperties ofof crosscross--sectionssections

K ) K ) ShearShear laglag effectseffects inin membermember designdesign

L ) L ) Classification of jointsClassification of joints

M ) M ) Adhesive bonded connectionsAdhesive bonded connections

ANNEXESANNEXEStoto Part 1Part 1--11




11)) GeneralGeneral


3)3) Material propertiesMaterial properties

4)4) Structural fire designStructural fire design

5)5) StructuralStructural analysisanalysis

AnnexAnnex AA : Properties of aluminium alloys not listed in EN 1999: Properties of aluminium alloys not listed in EN 1999--11--11

AnnexAnnex BB : Heat transfer to external structural aluminium members: Heat transfer to external structural aluminium members


EUROCODE 9 – Part 1-2: Structural fire design




11)) GeneralGeneral


3)3) Materials,constituent products and connecting devicesMaterials,constituent products and connecting devices

4)4) DurabilityDurability


6)6) Ultimate limit states of fatigueUltimate limit states of fatigue

7)7) Quality requirementsQuality requirements

8)8) Ultimate limit states for connectionsUltimate limit states for connections

CONTENTS of CONTENTS of PartPart 11--33

EUROCODE 9 – Part 1-3 : Additional rules for structures susceptible to fatigue




ANNEXESANNEXEStoto Part 1Part 1--33

AA)) Bases of designBases of design

BB)) GuidanceGuidance onon assessmentassessment byby fracturefracture mechanicsmechanics

C)C) TestingTesting forfor fatiguefatigue designdesign

D)D) StressStress analysisanalysis

E)E) AdhesiveAdhesive bondsbonds

F)F) LowLow cyclecycle fatiguefatigue rangerange

G)G) InfluenceInfluence of Rof R--ratioratio

H)H) Fatigue strength improvement of weldsFatigue strength improvement of welds

I ) I ) CastingsCastings

J ) J ) Alternative tables Alternative tables forfor structuralstructural detailsdetails




11)) GeneralGeneral


3)3) MaterialsMaterials

4)4) DurabilityDurability


6)6) Ultimate limit states Ultimate limit states

7)7) Serviceability limit statesServiceability limit states

8)8) Connection with mechanical fastenersConnection with mechanical fasteners

9)9) Design assisted by testingDesign assisted by testing

AnnexAnnex AA : Testing procedures: Testing procedures

AnnexAnnex BB : Durability of fasteners: Durability of fasteners

AnnaxAnnax CC : Bibliography: Bibliography


EUROCODE 9 EUROCODE 9 –– Part 1Part 1--4 : Supplementary rules for cold4 : Supplementary rules for cold--formed sheetingformed sheetingBrussels, 18-20 February 2008 – Dissemination of information workshop 10



11)) GeneralGeneral


3)3) Materials and geometryMaterials and geometry

4)4) Ultimate limit statesUltimate limit states

5)5) Modelling for analysisModelling for analysis

6)6) Plastic limit state (LS 1)Plastic limit state (LS 1)

7)7) Cyclic plasticity limit state (LS 2)Cyclic plasticity limit state (LS 2)

8)8) Bucking limit state (LS Bucking limit state (LS 3)3)

AnnexAnnex AA : Expressions for bucking design: Expressions for bucking design


EUROCODE 9 EUROCODE 9 –– Part 1Part 1--5 : Supplementary rules for shell structures5 : Supplementary rules for shell structures




PartPart 3 : 3 : TechnicalTechnical rules for execution of rules for execution of aluminiumaluminium structuresstructures1.1. ScopeScope

2.2. Normative referencesNormative references

3.3. Terms and definitionsTerms and definitions

4.4. Specifications and documentationSpecifications and documentation

5.5. Constituent materials and productsConstituent materials and products

6.6. FabricationFabrication

7.7. WeldingWelding

8.8. Mechanical fastening and adhesive bondingMechanical fastening and adhesive bonding

9.9. ErectionErection

10.10. Protective treatmentProtective treatment

11.11. Geometric tolerancesGeometric tolerances

12.12. Inspection , testing and correctionsInspection , testing and corrections

EN 1090 : Execution of steel and aluminium structuresBrussels, 18-20 February 2008 – Dissemination of information workshop 12



Annexes to Annexes to ENEN 10901090 –– 33 ;; PartPart 3 : 3 : Technical rules for execution of Technical rules for execution of aluminiumaluminium structuresstructures

AA)) Welding procedure test for fillet weldsWelding procedure test for fillet welds

BB)) RequirementsRequirements onon geometicalgeometical tolerancestolerances whichwhich areare notnot normallynormally criticalcritical forfor

thethe integrityintegrity of the of the structurestructure

C)C) ProjectProject specificationspecification listlist

D)D) FinalFinal inspectioninspection ofof fabricatedfabricated aluminiumaluminium componentscomponents

E)E) Procedure test Procedure test forfor determinationdetermination of slip of slip factorfactor

F)F) ProposedProposed frameframe fprfpr qualityquality planplan

G)G) Requirements for execution Requirements for execution classesclasses

H)H) FasteningFastening ofof coldcold formedformed membersmembers andand sheetingsheeting

I ) I ) Guidance for the determination of execution Guidance for the determination of execution classesclasses andand structuralstructural classesclasses




INNOVATIVE ISSUES in EC 9 part 1.1INNOVATIVE ISSUES in EC 9 part 1.1

1.1. ClassificationClassification ofof crosscross--sectionssections2.2. Extent of heat affected zones (HAZ)Extent of heat affected zones (HAZ)3.3. Generalized formulation for ULS Generalized formulation for ULS forfor axiallyaxially loadedloaded membersmembers4.4. GeneralizedGeneralized formulationformulation forfor ULSULS forfor membersmembers inin bendingbending5.5. BuckingBucking curvescurves approachapproach forfor columnscolumns6.6. LocalLocal buckingbucking approachapproach7.7. Evaluation of rotation Evaluation of rotation capacitycapacity8.8. Plastic design Plastic design approachapproach9.9. ClassificationClassification ofof connectionsconnections10.10. TT--stubstub modelmodel forfor endend plateplate boltedbolted connectionsconnections




The ECCS RecommendationsThe ECCS Recommendations(1978)(1978)




AUTHORS OF CHAPTERSAUTHORS OF CHAPTERS ::

Federico M.MAZZOLANIFederico M.MAZZOLANIGuntherGunther VALTINATVALTINATFransFrans SOETENSSOETENSTorstenTorsten HOGLUNDHOGLUNDBruno ATZORIBruno ATZORIMagnusMagnus LANGSETHLANGSETH

Background of EC 9Background of EC 9Brussels, 18-20 February 2008 – Dissemination of information workshop 16



DESIGN CRITERIA


DESIGN CRITERIA FOR DESIGN CRITERIA FOR ALUMINIUM ALLOY ALUMINIUM ALLOY

STRUCTURESSTRUCTURES




How can aluminium and its alloy satisfythe requirements of civil engineering structures?

In which applications can they compete with other structural materials, like steel?

DESIGN CRITERIA FOR ALUMINIUM DESIGN CRITERIA FOR ALUMINIUM STRUCTURES IN CIVIL ENGINEERINGSTRUCTURES IN CIVIL ENGINEERING

HISTORICAL BACKGROUNDHISTORICAL BACKGROUNDBirth of aluminium :Birth of aluminium :

18071807 –– isolation of AL element isolation of AL element (Sir(Sir HumphryHumphry DavyDavy –– U.K.)U.K.)

18271827 –– first aluminium nugget first aluminium nugget ((WhoelerWhoeler –– Germany)Germany)

18541854 –– first electrolytic reduction first electrolytic reduction (Henry Sainte Claire (Henry Sainte Claire –– France)France)

18861886 –– industrial electrolytic process industrial electrolytic process (Paul Luis (Paul Luis TouissantTouissant HHééroultroult –– France and France and Charles Martin Hall Charles Martin Hall –– USA)USA)

FIRST APPLICATIONSFIRST APPLICATIONSEagles of the Napoleon Eagles of the Napoleon IIIIII’’ss insignainsigna(1851(1851--1870)1870)

Dirigible structures:Dirigible structures:Schwartz (1897)Schwartz (1897)ZeppelingZeppeling (1900)(1900)

Armaments and equipment for the First Armaments and equipment for the First World War (1915World War (1915--1918)1918)

Dirigible structures Dirigible structures ((details)details)

Dirigible structures (details)Dirigible structures (details)

Presence of Presence of aluminiumaluminium in different surroundings in different surroundings

Navy structuresNavy structures

Aircraft structuresAircraft structures Railway structuresRailway structures

Railway structuresRailway structures

Railway structuresRailway structures

Reservoirs for RailwayReservoirs for Railway Reservoirs for RailwayReservoirs for Railway

AluminiumAluminium sheetssheetsinstalled more than a century ago for claddinginstalled more than a century ago for claddingthe dome of the San the dome of the San GioacchinoGioacchino churchchurch inin RomeRome

CladdingCladding

The Empire State Buildingin New York was the firstbuilding using anodisedaluminium for windows

WindowsWindows

The statue of Eros in Piccadilly Circus LondonThe statue of Eros in Piccadilly Circus London

(only recently cleaned and renovated)(only recently cleaned and renovated)

DecorationDecorationThe Atomium was built for the Universal Exhibition of Brussels in 1958,nevertheless aged over the years.The Atomium is a structure that is half way between sculpture and architecture,symbolising a crystal molecule of steel by the scale of its atoms,magnified 165 billion times. The aluminium cladding - initially conceived to last six months –has served its purpose for almost 50 years and is ready for a new life. Now the Atomium is undergoing renovation:the original aluminium skin will serve for new purposes.A thousand aluminium triangular panels are available for sale with a certificate of authenticity for collectorsand Atomium fans. The remaining 30 tonnes of aluminium will be recycled.

Symbolic worksSymbolic works

Housing structuresHousing structures Markets for Roller roducts

22%

18%19%

11%

12%

13% 5%FoilstockStockistsPackaging (rigid)BuildingEngineeringTransportConsumer durables

Markets for Extrusions

51%

16%

18%

15%BuildingTransportEngineeringOthers

Markets for Ricycled Aluminium

6%

74%

13% 7%BuildingTransportEngineeringOthers

Per-capita use by world areas (in kg)

0

5

10

15

20

25

30

35

40

Europe USA Japan

198019902000

Different markets for aluminium productsDifferent markets for aluminium products

0.00E+00

2.00E+05

4.00E+05

6.00E+05

8.00E+05

1.00E+06

1.20E+06

1.40E+06

1.60E+06

1960 1965 1970 1975 1980 1985 1990 1995 2000

[t]

THE GROWTH OF ALUMINIUM ALLOYS IN BUILDINGSTHE GROWTH OF ALUMINIUM ALLOYS IN BUILDINGS

BASIC PREREQUISITES OF ALUBASIC PREREQUISITES OF ALU--ALLOYSALLOYS

Wide family of constructional Wide family of constructional materials,coveringmaterials,covering the range of mechanical the range of mechanical properties of mild steelsproperties of mild steelsCorrosion resistance makes normally not necessary to provide proCorrosion resistance makes normally not necessary to provide protectiontectioncoatingcoatingWeigthWeigth reduction (respect to steel is 1 to 3) reduction (respect to steel is 1 to 3) givesgives many advantages in many advantages in transportation and erectiontransportation and erectionLow elastic modulus increases the sensitivity toLow elastic modulus increases the sensitivity todeformabilitydeformability and instability problemsand instability problemsThe material itself is not prone to brittle fractureThe material itself is not prone to brittle fractureFabrication process by extrusion allows individually tailored shFabrication process by extrusion allows individually tailored shapes to be apes to be designeddesignedEitherEither bolting,rivetingbolting,riveting and welding techniques are available as connection and welding techniques are available as connection solutionsolution

BASIC CONDITIONSBASIC CONDITIONSFOR COMPETITION WITH STEELFOR COMPETITION WITH STEEL

First preFirst pre--requisite:requisite:Corrosion resistance ( C )Corrosion resistance ( C )

Second preSecond pre--requisite:requisite:Lightness ( L )Lightness ( L )

Third preThird pre--requisite:requisite:Functionality of sections Functionality of sections

due to extrusion ( F )due to extrusion ( F )

First preFirst pre--requisite:requisite:Corrosion resistanceCorrosion resistance

Details of steel Details of steel boltedboltedconnectionsconnections

Steel detailSteel detail Aluminium detailAluminium detail

Second preSecond pre--requisite:requisite:LigthnessLigthness




steel hot rolled sectionssteel hot rolled sections aluminiumaluminium extruded sectionsextruded sections

extrusion processextrusion process

6.6. TermalTermal treatmenttreatment5. Extrusion5. Extrusion4. Transfer to extrusion4. Transfer to extrusion

1.Billets in parking1.Billets in parking 3. Cutting3. Cutting2. Heating (4802. Heating (480°°C)C)

Phases of the extrusion processPhases of the extrusion process

““The geometrical properties of crossThe geometrical properties of cross--section are improvedsection are improvedby designing a shape which simultaneously gives the by designing a shape which simultaneously gives the minimum weight and the highest structural efficiencyminimum weight and the highest structural efficiency””

Third preThird pre--requisite:requisite:Functionality of sections due to extrusionFunctionality of sections due to extrusion


Sections for electrical towersSections for electrical towers


Sections for crane structuresSections for crane structures

11

11

443322

33

2222

22

11

44

““The connecting systems among differentThe connecting systems among differentcomponent are simplified,thus improving joint detailscomponent are simplified,thus improving joint details””


Building for agricultureBuilding for agriculture


Sections used in the building for agricultureSections used in the building for agriculture


Industrial buildingIndustrial building


Section of the upper chordSection of the upper chord Section for innovative floor structureSection for innovative floor structure

Bolted connectionsBolted connections Welded connectionsWelded connections

C + L L i g h t i n g c o n t r o l t o w e r s F l a g p o l e s A i r c r a f t a c c e s s b r i d g e s T r a n s m i s s i o n t o w e r s B r i d g e i n s p e c t i o n g a n t r i e s O f f s h o r e s t r u c t u r e s ( l i v i n g q u a r t e r s , b r i d g e s ) * T a n k f l o t a t i o n c o v e r s

CS t o r a g e v e s s e l s L a m p c o l u m n s P r o f i l e d r o o f a n d w a l l c l a d d i n g

S u p p o r t f o r r a i l w a y o v e r h e a d e l e c t r i f i c a t i o n

E n c l o s u r e s t r u c t u r e s f o r s e w a g e w o r k s

S o u n d b a r r i e r s V e h i c l e r e s t r a i n t s y s t e m s

S e w a g e p l a n t b r i d g e s * S i l o s * T r a f f i c s i g n a l g a n t r i e s * T r a f f i c s i g n a l p o l e s *

LC r a n e b o o m s L o r r y m o u n t e d c r a n e s P i t p r o p s B r i d g e s * M o b i l e b r i d g e i n s p e c t i o n g a n t r i e s S c a f f o l d i n g s y s t e m s L a d d e r s C h e r r y p i c k e r s T e l e s c o p i c p l a t f o r m s M a s t s f o r t e n t s

C + F + L G r a t i n g p l a n k s H e l i d e c k s *

C + F D o m e s o v e r s e w a g e t a n k s *

M a r i n a l a n d i n g s t a g e s R o o f a c c e s s s t a g i n g D a m l o g s C u r t a i n w a l l i n g O v e r c l a d d i n g s u p p o r t s y s t e m s

P e d e s t r i a n p a r a p e t s C h i c k e n h o u s e s t r u c t u r e s

W o o d d r y i n g k i l n s S p a c e s t r u c t u r e s ( d o m e s , e t c . ) *

E x h i b i t i o n s t a n d s * S w i m m i n g p o o l r o o f s * C a n o p i e s B u s s h e l t e r s G r e e n h o u s e s / G l a s s h o u s e s *

FP r e f a b r i c a t e d b a l c o n i e s * C o n v e y o r b e l t s t r u c t u r e s M o n o r a i l s R o b o t s u p p o r t s t r u c t u r e s S h u t t e r i n g f o r m w o r kT u n n e l s h u t t e r i n g

F + L A c c e s s r a m p s S u p p o r t f o r s h u t t e r i n g T r a c k w a y s ( t e m p o r a r y )E l e v a t o r s f o r b u i l d i n g m a t e r i a l s S c a f f o l d p l a n k s T r e n c h s u p p o r t s G r a v e d i g g i n g s u p p o r t s L o a d i n g r a m p s L a n d i n g m a t s f o r a i r c r a f t A c c e s s g a n g w a y s S h u t t e r i n g s u p p o r t b e a m s M i l i t a r y b r i d g e s * R a d i o m a s t s S h u t t e r i n g T e l e s c o p i c c o n v e y o r b e l t s t r u c t u r e s G r a n d s t a n d s t r u c t u r e s ( t e m p o r a r y ) B u i l d i n g m a i n t e n a n c e g a n t r i e s F a b r i c s t r u c t u r e f r a m e s

T a b l e 1 . 1 : T h e m a i n s t r u c t u r a l a p p l i c a t i o n s o f a l u m i n i u m a l l o y s i n s t r u c t u r a l e n g i n e e r i n g

FIE

LD

S O

F ST

RU

CT

UR

AL

FIE

LD

S O

F ST

RU

CT

UR

AL

APP

LIC

AT

ION

SA

PPL

ICA

TIO

NS

FIELDS OF APPLICATION IN CIVIL ENGINEERINGFIELDS OF APPLICATION IN CIVIL ENGINEERINGLong span roof systems (Long span roof systems (reticular schemes of plane and space reticular schemes of plane and space structuresstructures) , where live load is small compared to dead load) , where live load is small compared to dead loadStructures located in corrosive or humid environmentsStructures located in corrosive or humid environments((swimming pool roofs,river bridges,hydraulic plants,offswimming pool roofs,river bridges,hydraulic plants,off--shoreshoresuperstructuressuperstructures))Structures with moving parts,so that the lightness means Structures with moving parts,so that the lightness means economy during service (economy during service (moving bridges on rivers or moving bridges on rivers or channels,rotating crane bridges on circular pools in sewage channels,rotating crane bridges on circular pools in sewage plantsplants))Special purpose structures for which maintenance operations Special purpose structures for which maintenance operations are particularly difficult (are particularly difficult (masts,lighting towers,motorway sign masts,lighting towers,motorway sign portalsportals))Structures situated in inaccessible places far from the Structures situated in inaccessible places far from the fabrication shop,so the transport economy and ease erection are fabrication shop,so the transport economy and ease erection are extremellyextremelly important (important (electrical transmission towers,stair electrical transmission towers,stair cases,provisional bridgescases,provisional bridges))

Technical referencesTechnical references Competition between steel and aluminiumCompetition between steel and aluminium

Reference from literatureReference from literature

Charles Dickens (1812Charles Dickens (1812--1870) wrote :1870) wrote :“Within the course of the last two years … a treasure has been divined, unearthed and brought to light ... what do you think of a metal as white as silver, as unalterable as gold, as easily melted as copper, as tough as iron, which is malleable, ductile, and with the singular quality of being lighter that glass? Such a metal does exist and that in considerable quantities on the surface of the globe. The advantages to be derived from a metal endowed with such qualities are easy to be understood. Its future place as a raw material in all sorts of industrial applications is undoubted, and we may expect soon to see it, in some shape or other, in the hands of the civilised world at large”.

Jules Verne (1844Jules Verne (1844--1896),the father of modern science 1896),the father of modern science fiction, wrote fiction, wrote ““From Earth to the From Earth to the MoonMoon””::

“This valuable metal possesses the whiteness of silver, the indestructibility of gold, the tenacity of iron, the fusibility of copper, the lightness of glass. It is easily wrought, is very widely distributed, forming the base of most of the rocks, is three times lighter than iron, and seems to have been created for the express purpose of furnishing us with the material for our projectile”.

Reference from literatureReference from literature

THANK YOUVERY MUCH FOR

YOUR KIND ATTENTION

FIELDS OF APPLICATION


ALUMINIUMALUMINIUM ALLOY STRUCTURES:ALLOY STRUCTURES:FIELDSFIELDS OFOF APPLICATIONAPPLICATION




BUILDINGSBUILDINGSSPECIAL STRUCTURESSPECIAL STRUCTURESBRIDGESBRIDGESREFURBISHMENTREFURBISHMENTENVELOPSENVELOPS ( FACADES )( FACADES )

ALUMINIUM STRUCTURES IN THE ALUMINIUM STRUCTURES IN THE FIELD OF CIVIL FIELD OF CIVIL ENGINEERING :ENGINEERING :

BUILDINGS :

-prefabricated structures-plane structures-reticular space structures-domes

ALUMINIUM PREFABRICATED STRUCTURESALUMINIUM PREFABRICATED STRUCTURES

ALUMINIUM PREFABRICATED STRUCTURES

““TrelementTrelement”” building system building system (Germany)(Germany)

PrefabricatedPrefabricated clubclub--househouse((FranceFrance))

‘50


PrefabricatedPrefabricated ruralrural buildingbuilding(Italy)(Italy)


PrefabricatedPrefabricated -- aluminium house (Tokyo, 2000)aluminium house (Tokyo, 2000)


Provisional Exhibition Hall (Udine, Provisional Exhibition Hall (Udine, ItalyItaly,2002),2002)

Provisional Exhibition Hall Provisional Exhibition Hall

(London,(London, EnglandEngland, 2002), 2002)

ALUMINIUM PREFABRICATED STRUCTURESALUMINIUM PREFABRICATED STRUCTURES ALUMINIUM PREFABRICATED STRUCTURES (EDENBLUE SYSTEM)ALUMINIUM PREFABRICATED STRUCTURES (EDENBLUE SYSTEM)

ALUMINIUM PREFABRICATED STRUCTURES (EDENBLUE SYSTEM)ALUMINIUM PREFABRICATED STRUCTURES (EDENBLUE SYSTEM) ALUMINIUM PREFABRICATED STRUCTURES (EDENBLUE SYSTEM)ALUMINIUM PREFABRICATED STRUCTURES (EDENBLUE SYSTEM)

ALUMINIUMALUMINIUM PREFABRICATED STRUCTURES (EDENBLUE SYSTEM) ALUMINIUMALUMINIUM--TIMBER STRUCTURE FOR INTERNAL MEZANINETIMBER STRUCTURE FOR INTERNAL MEZANINE

ALUMINIUM PLANE STRUCTURESALUMINIUM PLANE STRUCTURES

Rolling mill roof Rolling mill roof ((KrenzlingenKrenzlingen, CH ), CH )



HangarHangar(Hatfield, England)(Hatfield, England)

SporthallSporthall(Gand, Belgium)(Gand, Belgium)


WarehouseWarehouse(Antwerp, Belgium)(Antwerp, Belgium)


Melsbroek airport Melsbroek airport

(Brussels, Belgium)(Brussels, Belgium)


Roof of the tribune of the football stadium in Guayaquil (EquadoRoof of the tribune of the football stadium in Guayaquil (Equador)r)

ALUMINIUM PLANE STRUCTURESALUMINIUM PLANE STRUCTURES ALUMINIUM PLANE STRUCTURESALUMINIUM PLANE STRUCTURES

LecheriaLecheria la Gran Via la Gran Via inSincelejoinSincelejo City (Colombia)City (Colombia)

SwimmingSwimming--poolpool roofroof inin BogotBogotàà (Colombia)(Colombia)


UrbanUrban RicreationRicreation CenterCenter““CompensarCompensar”” (CUR)(CUR)inin BogotBogotàà (Colombia)(Colombia)


UniversidadUniversidad deldel NorteNorteinin BarranquillaBarranquilla

(Colombia)(Colombia)


AluminiumAluminium Center in Utrecht(Holland)Center in Utrecht(Holland)

““TheThe AluminiumAluminium ForestForest””::368368 tubolartubolar columnscolumns


AluminiumAluminium CenterCenter

in Utrecht(Holland)in Utrecht(Holland) MichaMicha dede HaasHaas


ALUMINIUM RETICULAR SPACE STRUCTURESALUMINIUM RETICULAR SPACE STRUCTURES

Erection phases of the Interamerican Exhibition CenterErection phases of the Interamerican Exhibition Centerof San Paulo (of San Paulo (BrazilBrazil,1969),1969)

MashMash 60x60 ;60x60 ;erectionerection time 27 time 27 hourshours CoveredCovered area 67 600 mq area 67 600 mq

WeigthWeigth 16 kg/mq 16 kg/mq

NumberNumber ofof nodesnodes 13 72413 724NumberNumber ofof boltsbolts 550 000550 000NumberNumber ofof barsbars 56 820 (total 56 820 (total lengthlength 300 km) 300 km)

2.36 m14 m

THE INTERAMERICAN EXHIBITION CENTRE ( SAN PAOLO, BRASIL)THE INTERAMERICAN EXHIBITION CENTRE ( SAN PAOLO, BRASIL)

THE INTERAMERICAN EXHIBITION CENTRE OF THE INTERAMERICAN EXHIBITION CENTRE OF SAN PAOLO (BRASIL)SAN PAOLO (BRASIL)

THE INTERAMERICAN EXHIBITION CENTRE OFTHE INTERAMERICAN EXHIBITION CENTRE OFSAN PAOLO (BRASIL)SAN PAOLO (BRASIL)

The International Congress center of Rio de Janeiro (Brazil)The International Congress center of Rio de Janeiro (Brazil) Industrial buildings (Brazil)Industrial buildings (Brazil)


LibraryLibrary ““LuisLuis AngeloAngelo ArangoArango””

BogotBogotàà (Colombia)(Colombia)


GuaymaralGuaymaral Country ClubCountry ClubBogotBogotàà (Colombia)(Colombia)


MallMall inin BogotBogotàà(Colombia)(Colombia)


HatograndeHatogrande Country ClubCountry ClubBogotBogotàà (Colombia)(Colombia)


TrafficTraffic OfficeOfficeinin ZapaquirZapaquiràà



SwimmingSwimming poolpoolinin ZerrezuelaZerrezuela



ColegioColegio AgustinianoAgustinianoinin BogotBogotàà (Colombia)(Colombia)


CentroCentro ComercialComercial ““SalitreSalitre PlazaPlaza””inin BogotBogotàà


EmpresasEmpresas PublicasPublicas dede MedellinMedellin


Building in Cali (Colombia)Building in Cali (Colombia)


THE PALASPORT OF QUITO (EQUADOR)THE PALASPORT OF QUITO (EQUADOR)

The Memorial PyramidThe Memorial Pyramidin La Baie (Quebec, Canada)in La Baie (Quebec, Canada)


THE MEMORIAL OF THE MEMORIAL OF LA BAY (QUEBEC)LA BAY (QUEBEC)

Shanghai Shanghai PudongPudong NatatoriumNatatorium

A 42,000 sq. ft. double layer grid vault roofA 42,000 sq. ft. double layer grid vault roof

Shanghai Opera HouseShanghai Opera House

Conference Centre, GlasgowConference Centre, Glasgow

Lords cricket ground, LondonLords cricket ground, London

InceneratorIncenerator, London, London

MillenionMillenion Stadium,Stadium, WallesWalles

ALUMINIUM RETICULAR SPACE STRUCTURES ALUMINIUM RETICULAR SPACE STRUCTURES IN ITALYIN ITALY

The structure of the Congress Center of AlgheroThe structure of the Congress Center of AlgheroA proposal for the roof of the Olimpic Stadium in A proposal for the roof of the Olimpic Stadium in RomeRome (1990)(1990)

FULL SCALE TESTFULL SCALE TEST

THE GEOTHE GEO--SYSTEM (ITALY)SYSTEM (ITALY)

““MERCATI TRAIANEIMERCATI TRAIANEI”” MUSEUM (ROME)MUSEUM (ROME)““MERCATI TRAIANEIMERCATI TRAIANEI”” MUSEUM (ROME)MUSEUM (ROME)

Before restorationBefore restoration

After restorationAfter restoration

““MERCATI TRAIANEIMERCATI TRAIANEI”” MUSEUM (ROME)MUSEUM (ROME)

Plane reticular space structurePlane reticular space structure


Reticular cylindrical vaultsReticular cylindrical vaults


Reticular geodetic domeReticular geodetic dome


Reticular geodetic dome

““MERCATI TRAIANEIMERCATI TRAIANEI”” MUSEUM (ROME)MUSEUM (ROME) ALUMINIUM DOMESALUMINIUM DOMES

ALUMINIUM DOMESALUMINIUM DOMES

Dome of Discovery built in Dome of Discovery built in LondonLondon forfor the Festival of the Festival of

BritainBritain (1951)(1951)

ThreeThree--directionaldirectionalreticulated archesreticulated arches

Diameter 110 m Diameter 110 m

WeigthWeigth 24 kg/24 kg/mqmq

The Palasport of Paris (1959)The Palasport of Paris (1959)

Diameter 61 mDiameter 61 m


The geodetic dome of Guayaquil (Equador)The geodetic dome of Guayaquil (Equador)


Scientific Station at the South PoleScientific Station at the South Pole


TheThe ConservatexConservatex system (USA):system (USA):

erection phaseserection phases


TheThe ConservatexConservatex systemsystem(USA):(USA): applicationsapplications housing

Industrial plants


Epcot Center (Florida)

The TEMThe TEM--COR system (USA)COR system (USA)

ALUMINIUM DOMESALUMINIUM DOMESBell County Arena (Temple, Texas)



Baylor University Ferrell Events Center (Waco, Texas)Baylor University Ferrell Events Center (Waco, Texas)



University of ConnecticutUniversity of Connecticut



Spruce Goose DomeSpruce Goose Dome:: erectionerection phasesphases

TheThe ““Spruce GooseSpruce Goose”” is the worldis the world’’s largest clears largest clear--span aluminium span aluminium dome 415 feet in diameter (Long Beach, California)dome 415 feet in diameter (Long Beach, California)


TheThe ““SpruceSpruce GooseGoose DomeDome”” (Long Beach,California)(Long Beach,California)

ALUMINIUM GEODETIC DOMES FOR COAL STORAGEALUMINIUM GEODETIC DOMES FOR COAL STORAGEALUMINIUM GEODETIC DOMES FOR COAL STORAGEALUMINIUM GEODETIC DOMES FOR COAL STORAGE

ENELENEL -- CIVITAVECCHIACIVITAVECCHIA

ALUMINIUM GEODETIC DOMES FOR COAL STORAGEALUMINIUM GEODETIC DOMES FOR COAL STORAGE

TheThe ““TEMTEM--CORCOR”” dome in Taiwandome in Taiwan

TheThe ““GeometricaGeometrica”” dome in Taiwandome in Taiwan

The collapse of the “Geometrica” dome in Taiwan

ALUMINIUM SPECIAL STRUCTURES ALUMINIUM SPECIAL STRUCTURES

Motorway signsElectrical towersLighting towersAntenna towersHydraulic struct.Off-shore struct.Helydecks

ALUMINIUM SPECIAL STRUCTURESALUMINIUM SPECIAL STRUCTURES

Motorway sign supportsMotorway sign supports

Electrical transmission towers and typical extruded crossElectrical transmission towers and typical extruded cross--sectionssections


Lighting towersLighting towers


Aluminium towers in Aluminium towers in NaplesNaples ((ItalyItaly))


THE TOWER FORTHE TOWER FORPARABOLIC ANTENNASPARABOLIC ANTENNASOF THE ELECTRICALOF THE ELECTRICAL

DEPARTMENT IN NAPLESDEPARTMENT IN NAPLES

100100 yearsyears aluminiumaluminium priceprice

The Enel Tower:The Enel Tower: fabricationfabrication phasesphases

The Enel Tower:The Enel Tower:

fabricationfabrication phasesphases

TheThe EnelEnel TowerTower::fabricationfabrication phasesphases ENELENEL aluminiumaluminium towertower inin NaplesNaples :: erectionerection phasesphases

The Enel TowerThe Enel Tower :: detailsdetails THE TOWERS OF THE TOWERS OF TECCHIOTECCHIO’’s SQUARE IN NAPLESs SQUARE IN NAPLES

““MEMORYMEMORY”” TOWERTOWER

““INFORMATIONINFORMATION ““ TOWERTOWER

““TIME EVULUTIONTIME EVULUTION”” TOWERTOWER

TheThe ““InformationInformation”” Tower (Naples)Tower (Naples)Reservoir:Reservoir: erection phaseserection phases PipelinePipeline

ALUMINIUM HYDRAULIC STRUCTURESALUMINIUM HYDRAULIC STRUCTURES


SewageSewage plantplant (Po(Po SangoneSangone,, TurinTurin))


HelideckHelideckbridges

ALUMINIUM OFFALUMINIUM OFF--SHORE STRUCTURESSHORE STRUCTURES

Phases of fabricationPhases of fabrication

ALUMINIUM OFFALUMINIUM OFF--SHORE STRUCTURESSHORE STRUCTURES

Helidecks HelidecksHelidecks

ALUMINIUM BRIDGESALUMINIUM BRIDGES

Motorway bridgesComposite bridgesMoving bridgesFoot bridgesMilitary bridgesMarina bridgesFloating bridgesBridge refurbishmentStructural restoration

ArvidaArvida bridge in bridge in QuebeQuebe (Canada , 1950 (Canada , 1950 –– L = 150 m)L = 150 m)

ALUMINIUM MOTORWAY BRIDGESALUMINIUM MOTORWAY BRIDGES

Motorway bridge (France)Motorway bridge (France) Motorway bridge (The Netherlands)Motorway bridge (The Netherlands)

Motorway bridgesMotorway bridges

Composite aluminium Composite aluminium –– concrete bridgesconcrete bridges : sections, test and theory: sections, test and theory

MovingMoving Bridge at the Aberdeen Bridge at the Aberdeen HarbourHarbour

Bascule bridge Bascule bridge (1967):(1967):the first road bridge in aluminium

; 4m wide and 8,1 m span.

HandHand--pushed bridgepushed bridge

Moving bridges over the Moving bridges over the GGöötata channel (Sweden)channel (Sweden)

Continuous bridge with swing spanContinuous bridge with swing span

MovingMoving footfoot bridgesbridges

Moving foot bridge in Oldersum (Germany)Moving foot bridge in Oldersum (Germany)

Foot bridgesFoot bridges

Foot bridge in HemFoot bridge in Hem--Lenglet (France)Lenglet (France)


Amsterdam (NL)

Villepinte (F) The Gold Creek Footbridge The Gold Creek Footbridge --Valdez, Alaska (USA)Valdez, Alaska (USA)

Foot bridge in JonquiFoot bridge in Jonquiéére (Quebec, Canada)re (Quebec, Canada)


A cableA cable--stayed foot bridge, stayed foot bridge, designed for the City of Science designed for the City of Science

in Naples (Italy)in Naples (Italy)

Foot bridges

A cableA cable--stayed foot bridge, stayed foot bridge, designeddesigned for the City of Science in Naples (Italy)for the City of Science in Naples (Italy)

ALUMINIUM BRIDGESALUMINIUM BRIDGES

Military bridgesbridges

U.K. bridgesU.K. bridges

GermanGerman militarymilitary bridge (Dornier):bridge (Dornier): erection phaseserection phases Swedish military bridge Kb 71Swedish military bridge Kb 71

Friction StirWelding, FSW

FSW FSW

FSW

FSW FSW

MIG MIG

MIG

Toolshoulder

Joint

Welding pin withspecial profile WeldBacking

bar

new cross-section

old cross-section

friction stir weldfriction stir weld

Length 20 m with a theoretical span of 19 m Length 20 m with a theoretical span of 19 m Bridge depth is 0,71 mBridge depth is 0,71 m

Marina applicationsMarina applications MarinaMarinaapplicationsapplications

Marina applicationsMarina applications Marina applicationsMarina applications

Floating bridge with aluminium deckFloating bridge with aluminium deckSweden ( 1989 )Sweden ( 1989 )

Floating road in Holland (2003)

“The new Waterway”

DECK REPARATIONDECK REPARATION

Extruded decksExtruded decks

PavingPaving6 mm 6 mm AcrydurAcrydur, or, or

40 mm poured asphalt40 mm poured asphalt

WeightWeightAluminium deck : 50 Aluminium deck : 50 -- 70 kg/m70 kg/m22

Concrete deckConcrete deck : 600 : 600 -- 700 kg/m700 kg/m22

300 mm

100

mm

250 mm

50 m

m Grooves and tongues (no welds)Grooves and tongues (no welds)

Span 1,0 mSpan 1,0 m

Large deck profilesLarge deck profiles

Span 2,8 mSpan 2,8 m

Test on extruded decks

Modell

Deck

? ??

?

? ?

?

?

?

?

0

-1

-2

-3

-4

-5

-6

-7 cL

Def

lec t

ion

[mm

]

100 kN

Theory

Test

DECK REPARATIONDECK REPARATION

New bridge with aluminium deckNew bridge with aluminium deck

Old bridge cut in partsOld bridge cut in partsand lifted awayand lifted away

Deck reparationDeck reparation

Substitution of r.c. deck Substitution of r.c. deck withwith aluminium deckaluminium deck

before

after

STRUCTURAL RESTORATION OF STRUCTURAL RESTORATION OF SUSPENSION BRIDGES BY MEANS OF SUSPENSION BRIDGES BY MEANS OF

ALUMINIUM ALLOYSALUMINIUM ALLOYS

L= 80 + 80 m

ONON THE SOANE RIVER THE SOANE RIVER ((FRANCE)FRANCE)

THE MONTEMERLE BRIDGETHE MONTEMERLE BRIDGE

THE MONTEMERLE BRIDGE ON THE SOANE THE MONTEMERLE BRIDGE ON THE SOANE RIVER (FRANCE)RIVER (FRANCE)

THE MONTEMERLE BRIDGE ON THE SOANE RIVER THE MONTEMERLE BRIDGE ON THE SOANE RIVER (FRANCE)(FRANCE)

THE TREVOUX BRIDGE ON THE SAONE RIVER THE TREVOUX BRIDGE ON THE SAONE RIVER (FRANCE)(FRANCE)

L= 80 + 80 m

THE TREVOUX BRIDGE ON THE SAONE THE TREVOUX BRIDGE ON THE SAONE RIVER (FRANCE)RIVER (FRANCE)

L= 80 + 80 mL= 80 + 80 m



THE GROSLTHE GROSLÈÈE BRIDGE ON THE RÔNE E BRIDGE ON THE RÔNE RIVER (FRANCE)RIVER (FRANCE)

L= 175 m

THE GROSLTHE GROSLÈÈE BRIDGE ON THE E BRIDGE ON THE RÔNERÔNE RIVER (FRANCE)RIVER (FRANCE)



STRUCTURAL RESTORATION OF THE STRUCTURAL RESTORATION OF THE ““REAL FERDINANDOREAL FERDINANDO”” BRIDGE :BRIDGE :

the first iron suspension bridge in Italythe first iron suspension bridge in Italy

THETHE ““REAL FERDINANDOREAL FERDINANDO”” BRIDGEBRIDGEON THE GARIGLIANO RIVER (ITALY)ON THE GARIGLIANO RIVER (ITALY)

TheThe ““RealReal FerdinandoFerdinando ““BridgeBridgeon the Garigliano river (1832)on the Garigliano river (1832)

TheThe ““MariaMaria CristinaCristina”” BridgeBridgeon the Calore river (1835)on the Calore river (1835)

Designer : Luigi GiuraDesigner : Luigi Giura

Design data (Design data (geometrygeometry))

L = 85 mL = 85 mDistanceDistance betweenbetween suspensionsuspension chainschains 5,83 m5,83 mVerticalVertical tiesties everyevery 1.37 m1.37 mTwo longitudinal iron Two longitudinal iron beamsbeams withwith rectangularrectangular crosscross--sectionsectionTransversalTransversal woodenwooden beamsbeams everyevery 1,73 m1,73 mTwo couples of piers made of calcar Two couples of piers made of calcar stonestoneChain ancorage at 24 m from piers and 6 m Chain ancorage at 24 m from piers and 6 m depthdepthChainsChains mademade ofof pinnedpinned ironiron platedplated elementselements


Design data (Design data (loadsloads andand stressesstresses))

DeadDead loadload : 260 kg/mq: 260 kg/mqLive load : 240 kg/mqLive load : 240 kg/mqMaximum axial force in chains : 500 tMaximum axial force in chains : 500 tMaximum stress in Maximum stress in ironiron chainschains : 15 kg/: 15 kg/mmqmmqStrengthStrength ofof stonestone : 600 kg/: 600 kg/cmqcmq


Erection data (1828 Erection data (1828 –– 1832)1832)

WorkWork periodperiod :: fourfour yearsyearsIronIron : 70 000 kg: 70 000 kgCost : 75 000 Cost : 75 000 ducatsducatsLoadingLoading test : 2 test : 2 groupsgroups ofof lancerslancers

1616 artilleryartillery carriagescarriagesProofProof engineer : engineer : kingking FerdinandFerdinand II (!)II (!)



SpecialSpecial devicedeviceforfor connectingconnectingthethe chainschains toto thethe pierspiers

THETHE””REAL FERDINANDOREAL FERDINANDO”” BRIDGEBRIDGEON THE GARIGLIANO RIVER (ITALY)ON THE GARIGLIANO RIVER (ITALY)

BeforeBefore 19441944

THETHE ““REAL FERDINANDOREAL FERDINANDO”” BRIDGEBRIDGE

19441944 -- 19901990 TheThe pierspiers

The top of The top of thethe pierpier

TheThe chainchain


TheThe sphinxsphinx


The design of The design of restorationrestorationTHETHE ““REAL FERDINANDOREAL FERDINANDO”” BRIDGEBRIDGE

ResultsResults of the of the numericalnumerical analysisanalysis

TheThe structuralstructural schemescheme givesgives aa goodgood performance under performance under uniformellyuniformelly distributeddistributed verticalvertical loadsloads onlyonlyDueDue toto thethe ““mechanismmechanism”” featurefeature of the of the structuralstructuralschemescheme ,, itit isis tootoo flexibleflexible under non under non symmetricalsymmetricalloadingloading conditionsconditionsTheThe lacklack ofof bracingbracing systemssystems makesmakes itit unableunable toto resistresisthorizontalhorizontal actionsactions ((windwind ,, earthquakeearthquake)) withoutwithout largelargedeflectionsdeflectionsThe design live The design live loadload (240 kg/mq) (240 kg/mq) isis tootoo lowlow eveneven forforpedestrianpedestrian useuse

THETHE ““REAL FERDINANDOREAL FERDINANDO”” BRIDGEBRIDGEBasisBasis criteriacriteria forfor thethe structuralstructural restorationrestoration designdesign

ConservationConservation of the of the originaloriginal shapeshape ::consolidation of piers ; consolidation of piers ; keep the same shape of chains (two keep the same shape of chains (two groupsgroups perper sidessides) ;) ;keepkeep thethe samesame spanningspanning amongamong thethe verticalvertical tiesties ,,correspondingcorresponding toto thethe mashmash of the of the railsrails ;;keepkeep thethe samesame structuralstructural schemescheme of the deck.of the deck.

IncreaseIncrease thethe flexuralflexural stiffnessstiffness bothboth verticalvertical andand horizontalhorizontal::mainmain longitudinallongitudinal VierendeelVierendeel beamsbeams ,, whosewhose mashmash correspondscorrespondstoto thethe verticalvertical tiesties ;;rigidrigid transversaltransversal beamsbeams ;;horizontal cross bracings horizontal cross bracings withwith aa mashmash of 5.83x(3x1,37) m. of 5.83x(3x1,37) m.

UseUse ofof modernmodern technologiestechnologies andand materialsmaterials ::high strength steel for cables ; high strength steel for cables ; use of aluminium alloys instead of steel use of aluminium alloys instead of steel forfor deck.deck.


THETHE NEWNEW ““REALREAL FERDINANDOFERDINANDO”” BRIDGEBRIDGE

TheThe structuresstructures of the deckof the deck


LateralLateral supportssupportsandand horizontalhorizontal bracingsbracings

THE NEWTHE NEW ““REAL FERDINANDOREAL FERDINANDO”” BRIDGEBRIDGE

1998 : the first 1998 : the first aluminiumaluminium bridge in bridge in ItalyItaly


NON STRUCTURAL APPLICATIONS:NON STRUCTURAL APPLICATIONS:FACADES AND ENVELOPSFACADES AND ENVELOPS

SELFRIDGES MALL IN BIRMINGHAM (Jan SELFRIDGES MALL IN BIRMINGHAM (Jan KaplickyKaplicky) :) :Envelop made of 15 000 aluminium Envelop made of 15 000 aluminium disquettesdisquettes

ARCHITECTURALARCHITECTURALCOMPETITIONCOMPETITION

Sustainable MediterraneanSustainable Mediterraneanarchitecturearchitecture

with aluminium facadeswith aluminium facades

ARCHITECTURALARCHITECTURAL

COMPETITIONCOMPETITION

The winner The winner The Touring HotelThe Touring Hotel

( Italy )( Italy )

ARCHITECTURALARCHITECTURAL

COMPETITIONCOMPETITION

afterafter

beforebefore

THANK YOUTHANK YOUVERY MUCH FOR VERY MUCH FOR

YOUR KIND YOUR KIND ATTENTIONATTENTION

STRENGTH AND STABILITY (PART 1.1)

T. Höglund Torsten Höglund HB


EUROCODESBackground and Applications Design of aluminium members

Design of aluminium membersaccording to EN 1999-1-1

Torsten HöglundRoyal Institute of Technology

Stockholm



Design values of loads and resistances

Eurodode 9 gives the design values of resistance at the ultimate limit state, e.g.

M1

oel

M

RkRd γγ

fWMM == (class 3 cross section)

p0.2o Rf =partial factor for general yielding1,1M1 =γ

characteristic value of 0,2 % proof strength

elW section modulus

Design values of loads are given in Eurocode 0 and 1.

RkM characteristic value of bending moment resistanceRdM design value of bending moment resistance

For class 4 cross sections (slender sections, sections with large width/thickness ratio) Wel is replaced by Weff for the effective cross section. However, if the deflection at the serviceability limit state is decisive then a simplified method may be used; see page 17.


EUROCODESBackground and Applications Design values of loads and resistances

M2

uhazu,elRd γ

ρ fWM = (in a section with HAZ across the section)

ufpartial factor for failure25,1M2 =γ

characteristic value of ultimate strength

hazu,ρ reduction factor for the ultimate strength in HAZ

In a section with reduced strength due to welding (heat affected zone, HAZ)

RdM design value of bending moment resistance


EUROCODESBackground and Applications Material properties

Part of Table 3.2 b.


EUROCODESBackground and Applications Design of aluminium profiles

Except for massive sections and very stocky sections local buckling will occure in compressed parts at failure. However, the behaviour is different depending on the slenderness β = b/twhere b is the width and t is the thickness of the cross section part.

Local buckling behaviour / cross section class 4

Buckling load

Collapse load

f0,2m

(4) > 3

If β > β3 where β3 is roughly 6 for an outstand part and 22 for an internal part, then local buckling will occure before the compressive stress reach the 0,2 % proof stress fo. Such a section part is called slender and the cross section is referred to as Class 4 cross section.

For very slender sections there is a post-buckling strength allowed for by using an effective cross section.


EUROCODESBackground and Applications Cross section class 3, 2 and 1

If β for the most slender part of the cross section is β < β3 and β > β2 where β2 is roughly 4,5 (16), then the cross section belong to class 3, non slender section. Then buckling will occur for a stress equal to or somewhat larger than fo and some part of the cross section closer to the neutral axis (webs) may be larger than according to the theory of elasticity (linear stress distribution).

If βmax < β1 = 3 (11) then rotation capacity is large enough for redistribution of bending moment using plastic global analysis (class 1).

(2) 1 < < 2

m

m f0,2

(1) 1

f0,2m

(3) 2 < < 3

If β for the most slender part is less than β2then also parts of the cross section close to the neutral axis will reach fo (class 2).


EUROCODESBackground and Applications Local buckling - slenderness limits

Buckling Internal part Outstand partclass β1/ε β2/ε β3/ε β1/ε β2/ε β3/ε

A, without weld 11 16 22 3 4,5 6A, with weld 9 13 18 2,5 4 5B, without weld 13 16,5 18 3,5 4,5 5B, med weld 10 13,5 15 3 3,5 4

The above given limits β3 , β2 and β1 are valid for material buckling class A and fo = 250 N/mm2. For buckling class B and welded sections the limits are smaller.

o250 /f=ε

4321

Bending

Axial compression

Cross section classLoading

bf

b w

tw

t f mmbf = 70tf = 14bw = 90tw = 4

For the web of a beam in bending β = 0,4bw/tw

web

Example 1: Give cross section classoutstand

internal

webflangeflange

(Buckling class is defined later)


EUROCODESBackground and Applications Internal / outstand cross section part

For outstand cross section parts, b is the width of the flat part out-side the fillet. For internal parts b is the flat part between the fillets, except for cold-formed sections and rounded outside corners.


EUROCODESBackground and Applications Stress gradient

For cross section parts with stress gradient (ψ = σ2/σ1) thenβ = η bw/tw where

η = 0,70 + 0,30ψ if 1 > ψ > -1η = 0,80/(1- ψ) if ψ < -1

If the part is less highly stressed than the most severely stressed fibres in the section, a modified expression may be used for ε

)/()250( 21o zz/f ⋅=ε

1

2

z2

4321

Bending

Axial compression


mmbf = 140tf = 10bw = 180tw = 6

xx

Example 2: Give cross section class

b wt f

internal


EUROCODESBackground and Applications Axial force cross section resistance

For axial compression the cross section resistance (no flexural buckling) is the same for cross section class 1, 2 and 3

M1oRd /γAfN = where γM1 = 1,1 = partial factor for material

For class 4 cross section the cross section resistance is

M1oeffRd /γfAN = where Aeff = area of effective cross section

This effective cross section is build up of section with effective thickness teff for the cross section parts that belong to class 4.

tt ceff ρ= where ρc = reduction factor for local buckling 221

)/()/( εβεβρ

CCc −=

Buckling Internal part Outstand partclass C1 C2 C1 C2

A, without weld 32 220 10 24A, with weld 29 198 9 20B, without weld 29 198 9 20B, with weld 25 150 8 16


EUROCODESBackground and Applications Bending moment resistance

For bending moment the formulae for the resistance is depending on cross section class. For class 2 cross section the resistance is given by

M1oplplRd,2 /γfWMM == where Wpl = plastic section modulus

For class 1 cross section the resistance may be somewhat larger but Mpl is a good approximation.

M1oelel /γfWM = with Wel = elastic section modulus

The actual resistance if found by interpolation

plW A z= ⋅∑

For class 3 cross section the resistance is somewhere between Mpl and Mel where

eIW /el =

23

3elplelRd,3 )(

ββββ

−−

−+= MMMM

However, in most cases Mel could be used as a conservative approximation

M1oeffRd,4 /γfWM = where Weff = section modulus for effective cross section

For class 4 cross section the resistance is


EUROCODESBackground and Applications Effective cross section

The effective cross section is different for axial force and bending moment.

No effective cross section is needed for the combined loading axial force and bending moment. The combination is solved using interaction formulae.

y

te,w

te,f

tw

bw

bc

bf

t f

t f

te,w

tw

te,f

te,f

y

zte,f

tw

Effective section for y- axis bending

Effective section for z- axis bending

Effective section for axial compression


EUROCODESBackground and Applications Effective cross section for axial force

The effective cross section is based on the effective thickness of the cross section parts.

If the cross section is symmetric, then the effective cross section is also symmetric.

If the cross section is asymmetric, then there might be a shift in the neutral axis. For axially compressed extruded profiles this shift is ignored i.e. the axial force is taken as acting in the centre of the effective cross section. For cold-formed sections the shift should be allowed for by adding a bending moment ΔMEd = NEdeNwhere eN is the shift in neutral axis for gross and effective cross section.

In principle only the flat parts between fillets need to be reduced, however, for simplicity, the whole flange or web may be reduced.


EUROCODESBackground and Applications Effective cross section for bending moment

To find the effective cross section for bending moment is sometimes a tricky task and is not presented here in detail. Just a few comments:

• Local buckling may only occur on the compression side. For a member in bending, even if the cross section is symmetric, the effective section is asymmetric

• The neutral axis of the effective cross section is shifted closer to the tension side and the compressed part of the cross section is increased

• In principle an iteration procedure should be used, however, only two steps are necessary

E.g. for an I-section the first step is to calculate the effective thickness of the compression flange and calculate the neutral axis for that section. The second step is to calculate the effective thickness of the web based on this neutral axis. This is then the effective cross section.


EUROCODESBackground and Applications Effective cross section for bending moment

4321

flangewebBending

webflangeAxial compression


b w

t f

mmbf = 70tf = 14bw = 90tw = 4

From above we know the cross section class

221

)/()/( εβεβρ

CCc −= 220,32 21 == CC

514/70 ==β

Compression, web

22,1 3 == βε988,0

5,22220

5,2232

2 =−=cρ ρc is very close to one. Use gross cross section

M1oplRd,2 /γfWM =

M1oeffRd,4 /γfWM =

Compression and bending, flange

5,224/90 ==β

5,4,6 23 == ββ

23

3elplelRd,3 )(

ββββ

−−

−+= MMMMWhich formula to be used?


EUROCODESBackground and Applications Summary for members in bending

Web slenderness


EUROCODESBackground and Applications Serviceability limit state

The relatively low elastic modulus of aluminium (compared to steel) means that the deflection at the serviceability limit state is often decisive. Then conservative design at the ultimate limit state can often be accepted.

For class 1, 2 and 3 cross section the resistance according to the theory of elasticity could be used e.g.

el oRd

M1

W fMγ

=

corresponding to the horisontal line marked ”steel” on the previous slide. For class 4 cross section the resistance could be given by

el oRd c

M1

W fM ργ

= ⋅

where ρc is the reduction factor for local buckling for the cross section part with the largest value of β / β3. This might be rather conservative but no effective cross section need to be found.


EUROCODESBackground and Applications Buckling class

• Small residual stresses in extruded profiles mean that the buckling curves are not depending on the shape of the cross section (as for steel)

• Buckling curve depends on material and longitudinal welding

• Material buckling class A or B depends on the σ - ε –diagram for small strains (proportional limit - 0,2-proof stress ratio, fp/fo)

• Buckling class is given in Table 3.2 a and b


EUROCODESBackground and Applications Effective width - effective thickness


EUROCODESBackground and Applications Why effective thickness?

Simple calculations You only need to reduce the thickness, not to define start and stop of effective widths.

Within the HAZs the lesser of the reduction for local buckling and HAZ softening is used.

The effects of plate buckling on shear lag may be taken into account by first reducing the flange width to an effective width, then reducing the thickness to an effective thickness for local buckling basing the slenderness β on the effective width for shear lag. (National choice)

Easier to allow for combination of local buckling and HAZ

Easy to combine with shear lag where effective width is used

beff beff

b0 b0

CL

1 2

3

4


EUROCODESBackground and Applications Heat Affected Zone, HAZ

Reduction factor

ρo,haz for 0,2 % proof strength and ρo,haz for ultimate strength

0,800,71T67020

0,640,50T6

0,690,54T5

0,780,91T4

6082

Ultimate strength

ρu,haz

0,2 % p. strength

ρo,haz

Tem-per

Alloy

Example: Extruded profile, t < 5

5754

0,600,48T66082

0,630,53H14

0,560,30H16

0,640,37H143005

Ultimate strength

ρu,haz

0,2 % p. strength

ρo,haz

Tem-per

Alloy

Sheet, strip and plate, t < 5


EUROCODESBackground and Applications Width of heat affected zone

0 5 10 15 20 250

MIG

TIG, t<6

20

30

40

10

T1 < 60oC

t mm

bhaz mm

When 60oC < T1 < 120oCmultiply with

1 + (T1 - 60) / 120 6xxx alloy1 + (T1 - 60) / 80 7xxx alloy

T1 = interpass cooling temperature when multipass welds are laid

b haz


EUROCODESBackground and Applications Longitudinally welded section

For a longitudinally welded section the loss of strength in the heat affected zone HAZ should be allowed for. The cross section classification is made as for extruded sections, except that the limits β1, β2 and β3 are somewhat smaller.

tt hazo,haz ρ=

where ρo,haz is the reduction factor for the 0,2 % proof stress. If the cross section belong to class 4 the effective thickness is the lesser of ρc t and ρo,haz t within bhaz and ρc t besides HAZ.Question 1: If a welded section is symmetric and belong to class 3 is then the reduced cross section due to HAZ asymmetric?

2

1

Qu. noyes

Question 2: If a welded section is symmetric and belong to class 4 is then the reduced cross section usually asymmetric?

xx

Bending moment

min(ρo,haztw; ρctw)min(ρo,haztf; ρctf)

b2z + t w

z

tw

ρctw

teff = ρctf

b c

t f

bhaz

b haz

ρo,haztf

For the resistance a reduced thickness is used within the widths bhaz of the HAZs


EUROCODESBackground and Applications Member with transverse welds or welded attachments

For a member with a transverse cross weld the resistance is the lesser of

a) The strength in the sections beside the weld and the HAZ

b) The strength in the HAZc) The strength of the weld

The strength of the sections besides the welds and the HAZs is based on the 0,2 % proof strength fo whereas the strength in the HAZs is the ultimate strength ρu,hazfu and in the weld fw, but with larger partial factors γM2 = γMw = 1,25.

M1oRdo, /γAfN =

M2uhazu,Rdu, /γρ AfN =

MwwwRdw, /γAfN =

a)

b)c)

So ,for a member in tension the resistance is the lesser of


EUROCODESBackground and Applications Member with transverse welds or welded attachments

Question 1: Which is the lesser of the strength in HAZ and the weld for a tension member in EN-AW 6082-T6 with a but weld with Aw = A made of filler metal 5356 (γM2 = γMw)

2u,haz u u,haz 185 /f f N mmρ = =

2w /210 mmNf =

Table 3.2b

Table 8.8

Question 2: What is the difference for a member with an attachment?

Formula c) is not applicable

M1oRdo, /γAfN =

M2uhazu,Rdu, /γρ AfN =

MwwwRdw, /γAfN =

a)

b)c)


EUROCODESBackground and Applications Member with holes

M1oRdo, /γAfN =

M2netuRdu, /9,0 γAfN =a)

b)

For a member in tension the resistance is the lesser of

For a member with (bolt) holes the resistance is the lesser ofa) The strength in the sections beside the holesb) The strength in the section with the holes

bb 1

s s1

pp

p

d

21

3

3

21

Anet = min:t (b - 2d)t (b - 4d + 2s2/(4p))t (b1 + 2×0,65s1– 4d + 2s2/(4p))

line 1line 2line 3

The net area Anet shall be taken as the gross area less appropriate deductions for holes, see figure.

Note 0,9


EUROCODESBackground and Applications Flexural, torsion-flexural and lateral-torsional buckling

NN

SG N

My

N Mz

N

My

MyN MyN

Mz

SG N

My

(Flexural) buckling

Torsional buckling

Torsional-flexural buckling

Lateral-torsional buckling

Flexural buckling

Lateral-torsional buckling

Axial force

Bending moment

Axial force and bending moment


EUROCODESBackground and Applications Flexural buckling

4. Buckling class and reduction factor from formulae or diagram

cr

y

NN

=λ

2cr

2cr

πl

EIN =1. Critical load according to classic theory

oeffy fAN =

M1yRdb, /γκχNN =

2. Yield load

3. Slenderness parameter

6. Resistance

χ

00,10,20,30,40,50,60,70,80,9

1

χ

0 2,00,5 1,0 1,5 λ

12Class AClass B

5. Factor to allow for longitudinally or transverse welds

κ = 1 for members without welds


EUROCODESBackground and Applications Flexural buckling, members with longitudinal welds

λκ λλ )1(3,11 1,005,01011 1AA

AA −− ⎟

⎠⎞

⎜⎝⎛ +−⎟

⎠⎞

⎜⎝⎛ −−=

For members with longitudinal welds

)1( hazo,haz1 ρ−−= AAA

hazA

where

= area of HAZ

Buckling class A

1=κ 2,0≤λif

Buckling class B

λλκ λλ )1(4,1)5,0( 22,0)4(04,01 −− −+= 2,0>λif


EUROCODESBackground and Applications Members with transverse welds at the ends

If the welds are at the ends then κ = 1 in the formula for flexural buckling (1). However, then a check is also needed of the section resistance at the ends where κ = ωo.(2)

M1yRdb, /γχNN =

M1yoRd /γω NN =

M1o

M2uhazu,o /

/γ

γρω

ff

=

is the lesser of 1 and 2Rdb,N

and

where

(1)

(2)

Utilization grade

For members with cross welds the κ factor is depending on where the weld is placed along the member.


EUROCODESBackground and Applications Transverse welds at any section

If the weld is at a distance xs from one endthen the resistance at that section is found for κ = ωx (3). Furthermore the resistance for the member without weld should also be checked. (1)

If the weld is at the centre of the member then ωx = ωo. )/sin()1( crs

ox lxπχχ

ωω

−+=

M1yxRdb, /γχω NN =(3)

Utilization grade

Note that at the weld χhaz is based on ohaz ωλλ = (6.68a)

M1yRdb, /γχNN =

is the lesser of 1 and 3Rdb,N

and(1)


EUROCODESBackground and Applications Torsional and torsional-flexural buckling

00,10,20,30,40,50,60,70,80,9

1

χ

0 2,00,5 1,0 1,5λT

12

1 Cross section composed of radiating outstands, 2 General cross section

(1) For sections containing reinforced outstands such that mode 1 would be critical in terms of local buckling, the member should be regarded as "general" and Aeff determined allowing for either or both local buckling and HAZ material.

2) For sections such as angles, tees and cruciforms, composed entirely of radiating outstands, local and torsional buckling are closely related. When determining Aeff allowance should be made, where appropriate, for the presence of HAZ material but no reduction should be made for local buckling i.e. ρc = 1.

Formulae for critical load Ncr are given in Annex I of Eurocode 9 part 1-1.

N

fA

cr

oeff=λ


EUROCODESBackground and Applications Buckling length factor k

The buckling length should be taken as lcr = kL. The figure gives guidance for k.

End conditions1. Held in position and restrained in rotation at both ends2. Held in position at both ends and restrained in rotation at one end 3. Held in position at both ends, but not restrained in rotation4. Held in position at one end, and restrained in rotation at both ends5. Held in position and restrained in rotation at one end, and partially

restrained in rotation but not held in position at the other end6. Held in position and restrained in rotation at one end, but not held in

position or restrained at the other end


EUROCODESBackground and Applications Lateral-torsional buckling of beams

My

My

Fz

⎟⎟⎠

⎞⎜⎜⎝

⎛+= 2

w2

vcrππ

LEKGKEI

LM y

cr

oyel,LT M

fWαλ =

00,10,20,30,40,50,60,70,80,9

1

χLT

0 2,00,5 1,0 1,5λLT

12

1 Class 1 and 2 cross sections2 Class 3 and 4 cross sections

Critical moment

Slenderness parameter

Reduction factor χLT

Resistance

1oyel,LTLTb, / MfWM γαχ=


EUROCODESBackground and Applications Lateral-torsional buckling need not be checked

a) Bending takes place about the minor principal axis

b) Hollow sections with h/b < 2

c) Rotation is prevented

d) The compression flange is fully restrained against lateral movement throughout its length

e) The slenderness parameter between points of effective lateral restraint is less than 0,4.

c)h/b<2

b

h

b)a)

λLT < 0,4

e)d)

Lateral-torsional buckling need not be checked in any of the following circumstances

LTλ


EUROCODESBackground and Applications Bending and axial compression

1 Classification of cross-sections for members with combined bending and axial forces is made for the loading components separately. No classification is made for the combined state of stress.

2 A cross-section can belong to different classes for axial force, major axis bending and minor axis bending. The combined state of stress is accounted for in the interaction expressions. These interaction expressions can be used for all classes of cross-section. The influence of local buckling and yielding on the resistance for combined loading is accounted for by the resistances in the denominators and the exponents, which are functions of the slenderness of the cross-section.

3 Section check is included in the check of flexural and lateral-torsional buckling

major axis (y-axis) bending:

00,1Rdy,0

Edy,

Rdxy

Edyc

M

M +

N N ≤⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

ωωχ

ξ

minor axis (z-axis) bending:

00,1Rdz,0

Edz,

Rdxz

Ed ≤⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

M M

+ N

N zcc

ωωχ

ξη

All exponents may conservatively be given the value 0,8. Alternative expressions depend on shape factors αy or αz and reduction factors χy or χz.


EUROCODESBackground and Applications Comparison with Eurocode 3 for steel

Ec 3Ec 9

0 0

0,5

0,5

1,0

1,0

1,0

Klass 3

ψy =

λy = 0

λy = 1,23

y,Edy,Rd

MM

NEdNRd

λy = 0,62

Ec 3Ec 9

0 0,5 1,0

1,0Klass 2

0

0,5

1,0

λy = 0

λy = 0,62

λy = 1,23

ψy =

NEdNRd

y,Ed

y,Rd

MM

Major axis bending, constant bending moment

Cross section class 3 Cross section class 2


EUROCODESBackground and Applications Design section

Basic case

M2 < M1

Max(e + v) occur in the span if N is large and/or the slenderness of the member is large

Max(e + v) occur at the end if M1 is large and/or the slenderness of the member is small

N.v = second order bending moment


EUROCODESBackground and Applications Different end moments or transverse loads

cr

x πsin)1(

1

lxχχ

ω−+

=10 =ω

M1,EdMy,Rd

M2,EdMy,Rd

NEdNRd

NEdχNRd

NEdNRd

NEdχωxNRd

MEdMy,Rd

+max

x

Ed,1 Ed,2 Rd

Rd Ed

( ) 1cosπ(1/ 1)c

M M Nx =l M Nπ

χ−⎛ ⎞

⋅ ⋅⎜ ⎟ −⎝ ⎠

xω1

varies according to a sine curve and so also the first term K in the interaction formula

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛

Rd0

Ed,

Rd

Edyc

maxy,

y

xy MM

NN

ωωχ

ξ

is found for 0but ≥x

KB

00,1Rdy,0

Edy,

Rdxy

Edyc

M

M +

N N ≤⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

ωωχ

ξ

K + B 1≤

In principal all sections along the member need to be checked. However


EUROCODESBackground and Applications Equivalent moment

1// 1MRk

Ed,

1MRk

Ed ≤+γγχ y,

yyy

y MM

kN

N

ycr,

Edy

myyy

1NN

Ck

χ−=

Edmy

cr,y0,79 0, 21 0,36( 0,33) NC

Nψ ψ= + + −

Cross section class 3 and 4

yyycr,

Edy

myyy

1 CNN

Ck

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=

χ

Cross section class 1 and 2

( ) ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+−−+= yyC

wwC λλ 16,1211 2

myy

yyy 5,1yel,

ypl,y ≤=

WW

w

ψ M1M1For example for

In Eurocode 3 (steel) the method with equivalent constant bending moment is used. Then for different bending moment distribution different coefficient are needed. One example is given below.


EUROCODESBackground and Applications Member with transverse weld

M1o

M2uhazu,o /

/γ

γρω

ff

=

)/sin()1( crs

ox.haz lxπχχ

ωω−+

=

For members with transverse (local) weld two checks should be made

1. As if there were no weld 2. Check in the section with the weld

cr

y

NN

=λ χ ohaz ωλλ = hazχ

hazχχ =for00,1Rdy,0

Edy,

Rdx

Edyc

M

M +

N N ≤⎟⎟

⎠

⎞⎜⎜⎝

⎛

ωωχ

ξ

cr

x πsin)1(

1

lxχχ

ω−+

=

10 =ω


EUROCODESBackground and Applications Lateral-torsional buckling

00,1zc

Rdz,0

Edz,c

Rdy,LT xLT

Edy,

Rdxz

Edc

M

M + M

M+

N N ≤⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ξγη

ωωχωχ

Check for flexural buckling and

As for flexural buckling all exponents may conservatively be given the value 0,8. Alternative expressions depend on shape factors αy or αz and reduction factors χy or χz.

For class (1 and) 2 cross sections α = Wpl/Wel

For class 3 cross sections α = between Wpl/Wel and 1

For class 4 cross sections α = Weff/Wel

The shape factors are:


EUROCODESBackground and Applications Lateral-torsional buckling

1cc

RdLT,LT

Ed,

Rd

Ed ≤⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛γη

ωχωχ y,x

y

xz MM

NN

If there are no lateral bending moment Mz,Ed = 0 then

21butor1 022

0 ≤≤= ηααη yzwhereor8,0 0c zχηη =

where0c γγ = 56,11butor1 02

0 ≤≤= γαγ z

LTx,x and ωωmember and/or of the moment distribution along the member. If there are no cross welds and constant moment then both ω are = 1 else

are coefficients which allow for HAZ across the

ox

cr

π(1 )sinz zx

l

ωωχ χ

=+ −

ox,LT

LT LTcr

π(1 )sin xl

ωωχ χ

=+ −

NMy

NM y


EUROCODESBackground and Applications Design of frames

Three methods are possible:

a) “Equivalent buckling length method”

b) “Equivalent sway imperfection method”

c) ”Alternative method”

M I

(a) (c)(b)

+= h

l cr

I0I

L

h

qEd

x

HEd

(d)

=A

A

φ φ

L cr

(e)

L cr

A - A(g)

MIIMII

(f)

+

Rk

cr

NN

λ =

RkN RkN


EUROCODESBackground and Applications The equivalent column method

M I

(a) (c)(b)

+= h

l cr

I0I

L

h

qEd

x

HEd

The second order bending moment is allowed for by the critical buckling length.

(a) System and load(b) Equivalent column length(c) First order bending moment


EUROCODESBackground and Applications The equivalent sway method

(d)

=A

A

φ φL c

r

(e)

L cr

A - A(g)

MIIMII

(f)

+

(d) System, load and initial sway imperfection

(e) Initial local bow imperfection and buckling length for flexural buckling

(f) Second order moment including moment from sway imperfection

(g) Initial local bow and buckling length for lateral-torsional buckling


EUROCODESBackground and Applications Equivalent horizontal forces

2,0

eqv8

L

eNq dEd=gives

8 ,0

2eqv

dEdeNLq

=

The effect of initial sway imperfection and bow imperfection may be replaced by systems of equivalent horizontal forces introduced for each columns.

NEd

NEd

φ

NEd

NEd

φ NEd

φ NEd

NEd

NEd

NEd

NEd

e0,d

4NEde0d

L

4NEde0d

L

8NEde0d

L2L

Initial sway imperfection Initial bow imperfection


EUROCODESBackground and Applications Initial sway imperfection

Initial sway

2001

0 =φ

mh0 ααφφ ⋅⋅=

0,132but2

h ≤≤= hhαα ⎟

⎠⎞

⎜⎝⎛ +=

m115,0mα

h = height in m meters

m = number of column in a row including only those columns which carry a vertical load NEd > 50 % of the average value for the columns

φ

ΣF1

ΣF5

ΣF4

ΣF3

ΣF2

φ ΣF1

φ ΣF5

φ ΣF4

φ ΣF3

φ ΣF2

Equivalent horizontal forces


EUROCODESBackground and Applications Alternative method

h

Rk

cr

NN

λ =

RkN crN

χ 0,deIn principle


EUROCODESBackground and Applications Elastic or plastic global analysis

Elastic global analysis may be used in all cases.

Plastic global analysis

1. Plastic global analysis may be used only where the structure has sufficient rotation capacity at the actual location of the plastic hinge, whether this is in the members or in the joints. Where a plastic hinge occurs in a member, the member cross sections should be double symmetric or single symmetric with a plane of symmetry in the same plane as the rotation of the plastic hinge and it should satisfy the requirements for cross section class 1.

2. Where a plastic hinge occurs in a joint the joint should either have sufficient strength to ensure the hinge remains in the member or should be able to sustain the plastic resistance for a sufficient rotation.

3. Only certain alloys have the required ductility to allow sufficient rotation capacity.

4. Plastic global analysis should not be used for beams with transverse welds on the tension side of the member at the plastic hinge locations.

5. For plastic global analysis of beams recommendations are given in Annex H.

6. Plastic global analysis should only be used where the stability of members can be assured.


EUROCODESBackground and Applications Torsion

The beam is twisted around the shear centre

The deflection due to twisting may be larger than the deflection due to bending

Fη

Fz

Fξ

1. Divide the load in the direction of the principal axes

2. Calculate the deflection in those directions

3. Calculate the vertical deflection

The load also deflects laterally, in this case to the left because the lateral deflection due to twist is larger than due to bending.

Aluminium profiles are often asymmetric resulting in torsion. Example: Shear centre


EUROCODESBackground and Applications How to avoid torsion?

C = 1000

v

C = 3.5

vS.C.

c.

a. Add stiffeners

b. Change cross section so that the load acts through the shear centre

c. Use hollow sections

Cv = torsion stiffness (relative)


EUROCODESBackground and Applications St Venants torsion resistance

For members subjected to torsion for which distortional deformations and warping torsion may be disregarded (St Venants torsion) the design value of the torsional moment at each cross-section shall satisfy

)3/(where M1oplT,RdRdEd γfWTTT =≤

τ

τ

h t

V

VSt Venants torsion

Warping torsion

t1

t 2

δ t2

b2

b 1

D

Fillets increase torsion stiffness and strength considerably; see Annex J


EUROCODESBackground and Applications Warping torsion resistance

If the resultant force is acting through the shear centre there is no torsional moment due to that loading.

Formulae for the shear centre for some frequent cross-sections. see Annex J

For members subjected to torsion for which distortional deformations may be disregarded but not warping torsion (Vlasov torsion) the total torsional moment at any cross-section should be considered as the sum of two internal effects:

The following stresses due to torsion should be taken into account:- the shear stresses τt,Ed due to St. Venant torsion moment Tt,Ed

- the direct stresses σw,Ed due to the bimoment BEd and shear stresses τw,Ed due to warping torsion moment Tw,Ed.

Check the von Mises yield criterion

Cfffff

≤⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛ 2

1Mo

Ed

1Mo

Edz,

1Mo

Edx,2

1Mo

Edz,2

1Mo

Edx,

/3

//// γτ

γσ

γσ

γσ

γσ

2,1where =C


EUROCODESBackground and Applications Other structures covered in part 1-1

h0

a

Ach Ach

yy

h0a

yy

b

L/2

L/2

e0

NEd

NEd

z

z

b

Ach Ach

z

z

L

Un-stiffened and stiffened plates under in-plane loadings [2]

Built-up columns with lacings and battening [Eurocode 3]


EUROCODESBackground and Applications Plate girders

Bending

Shear

Patch loading

Corrugated web

h

w t w

b f t f c

MSd

K G

H Ea

V f

V f

V w

V w

+

(a) (b) (c)

Ed

h f

b c

b c =

bw

/2

t f

b w

t f,ef

h w

+ tension field

BS 8118 [4] Höglund [2, 8]

Rotated stress field

Höglund [5]

Others [6]

Lagerkvist [6j] Tryland [6l]

Höglund [5] Benson [6a] Ullman [12]

References


EUROCODESBackground and Applications Main references

[2] Höglund, T., Design of members. TALAT CD-ROM lecture 2301, (Training in Aluminium Application Technologies), European Aluminium Association. http://www.eaa.net/eaa/education/TALAT/general/cdrom.htm

[3] Mazzolani (ed), Valtinat, Höglund, Soetens, Atzori, Langseth, Aluminium Structural Design. CISM Courses and Lectures No. 443, SpringerWienNewYork 2003

[5] Höglund, T., Shear Buckling resistance of Steel and Aluminium Plate Girders. Thin-Walled Structures Vol. 29, Nos. 1-4, pp. 13-30, 1997

[1] Eurocode 9, EN 1999-1-1. Eurocode 9: Design of Aluminium Structures – Part 1-1: General rules. CEN (European Committee for Standardization) 2007.

[4] BS 8118 Structural use of aluminium, Part 1. Code of practice for designPart 2. Specification for material, workmanship and protection 1991


EUROCODESBackground and Applications [6] References on Shear Buckling and Patch Loading

[a] Benson, P.G.(1992). Shear buckling and overall web buckling of welded aluminium girders. Royal Institute of Technology, Division of Steel Structures, Stockholm, PhD thesis

[b] Brown, K.E.P.(1990). The post-buckling and collapse behaviour of aluminium girders. University of WalesCollege of Cardiff, PhD thesis.

[c] Burt, C.A.(1987). The ultimate strength of aluminium plate girders. University of Wales College of Cardiff, PhD.

[d] Edlund, S., Jansson, R. and Höglund, T.(2001). Shear buckling of Welded Aluminium Girders. 9th Nordic Steel Construction Conference, Helsinki.

[e] Evans, H.R. and Lee, A.Y.N.(1984). An appraisal, by comparison with experimental data, of new design procedures for aluminium plate girders. Proc. Inst. Civ. Eng. Structures & Buildings, Feb. 1984.

[f] Evans, H.R. and Hamoodi, M.J. (1987). The collapse of welded aluminium plate girders - an experimental study. Thin-Walled Structures 5.

[g] Evans, H.R. and Burt, C.(1990). Ultimate load determination for welded aluminium plate girders. Aluminium Structures: advances, design and construction. Elsevier Applied Science, London and New York.

[h] Höglund, T.(1972). Design of thin plate I girders in shear and bending with special reference to web buckling. Royal Inst of Technology, Dept. of Building Statics and Structural Engineering, Stockholm.

[i] Höglund, T.(1995). Shear buckling of Steel and Aluminium Plate Girders. Royal Inst of Technology, Dept. of Structural Engineering, Technical Report 1995:4, Stockholm

[j] Lagerqvist, O. (1994). Patch loading. Resistance of Steel Girders Subjected to Concentrated Forces. Ph.D. thesis, Luleå University of Technology, Division of Steel Structures, Luleå, Sweden.

[k] Rockey, K.C. and Evans, H.R.(1970). An experimental study of the ultimate load capacity of welded aluminium plate girders loaded in shear. Research Report, University of Wales College of Cardiff.

[l] Tryland, T. (1999). Aluminium and Steel Beams under Concentrated Loading. Dr.Ing. Thesis. Norwegian University of Science and Technology, Trondheim, Norway.


EUROCODESBackground and Applications References on beam columns

[7] Höglund, T., Approximativ metod för dimensionering av böjd och tryckt stång.Royal Inst. of Technology, Division of Building Statics and Structural Engineering, Bulletin 77, Stockholm 1968

[9] Edlund, S., Buckling of T-section Beam-Columns in Aluminium with or without Transverse Welds. Royal Inst. of Technology, Department of Structural Engineering, Stockholm 2000

[8] Höglund, T., Dimensionering av stålkonstruktioner. Extract from the handbook Bygg, Chapter K18. The Swedish Institute of Steel Construction, Stockholm 1994

English Translation in: Höglund, T., Steel structures, Design according to the Swedish Regulations for Steel Structures, BSK. Dept. of Steel Structures, Royal Inst. of Technology, Stockholm 1988


EUROCODESBackground and Applications References on local and overall buckling

[11] Hopperstad, O.S., Langseth, M. and Tryland, T., Ultimate strength of aluminium alloy outstands in compression: experiments and simplified analysis. Thin-walled Structures, 34, pp. 279-294, 1999

[10] Langseth, M. and Hopperstad, O.S., Local buckling of square thin-walled aluminium extrusions. Thin-walled Structures, 27, pp. 117-126, 1996

[12] Ullman, R., Shear Buckling of Aluminium Girders with Corrugated webs. Royal Inst. of Technology, Department of Structural Engineering, ISRN KTH/BKN/B-67-SE, Stockholm 2002


EUROCODESBackground and Applications Eurocode 9, strength and stability

Thank you for your attention !

CONNECTIONS(PART 1.1)

F. Soetens TNO


EUROCODESBackground and Applications Connections (Part 1.1)

Connections (Part 1.1)Eurocode 9: Design of aluminium structures

Prof.ir.F.Soetens

Eindhoven University of Technology, Eindhoven, TNO Built Environment and Geosciences, Delft, The Netherlands


EUROCODESBackground and Applications Connections (Part 1.1)

Contents1. Introduction

2. Joining Technology

3. Design of Joints• Welds• Bolts, rivets• Adhesives• Hybrid connections

4. Final remarks


EUROCODESBackground and Applications Introduction

Importance of Joining Technology

Design of aluminium structures requires knowledge of:

• Available joining techniques• Design of connections

To arrive at optimum performance at low costs.

Joining is a key technology in aluminium structural engineering



Types of joints• Primary structures

– Welded connections– Bolted connections– Riveted connections– Adhesive joints

• Special joints– Solid state welding– Joints with cast parts– Snap joints, rolled joints etc.

• Joints in Thin-walled Structures– Thread forming and self-drilling screws– Blind rivets– Cartridge fired pin– Spot welding



Advantage of welded connection• Saving work and material• Absence of drilling• Tight joints• No crevice corrosion• Joint preparation by extrusion



Requirements of joints• Structural requirements

– Strength– Stiffness– Deformation capacity

• Non-structural requirements– Economic aspects– Durability– Tightness– Aesthetics



Principles of design



Strength, stiffness and deformation capacity

• Strength:– Analytical determination– Determination by tests

• Stiffness:– Influence on entire structure– Influence on force distribution

in connections– Distribution of loads

• Deformation capacity:– Prevention of brittle fracture– Redistribution of stresses


EUROCODESBackground and Applications Joining technology

Welding• Gas welding• Metal arc welding• TIG• MIG• Electric resistance welding

– Spot welding– Seam welding

• Solid state welding– Ultrasonic welding– Electron beam welding– Friction welding



Principle of TIG welding



Principle of MIG welding



Friction stir welding



Screws, bolts and rivets• Aluminium

• Steel

• Thread inserts



Thread inserts

Ensat Heli-coil



Solid Rivets



Special jointsProfile to profile joints

Groove and tongue Hooked connection



Resistance spot weldingAdvantages• Fast, automatic• Small distortion• Excellent weld strength

Limitations• Only lap joints• Max. 3.2 mm thickness• Access to both sides required• Expensive equipment



Thread forming and selfdrillingscrews

Thread forming Self drilling and Self drilling andscrew thread forming thread forming



Adhesive bondingAdvantages• Microstructure unaffected• Joining of different materials• Joining of very thin parts• High fatigue strength• Good vibration damping

Disadvantages• Low strength• Pretreatment of surfaces• Ageing• Tolerance of process parameters



Structure of adhesive joint1. Strength parent material2. Adhesive strength oxide

layer3. Strength oxide layer4. Adhesive strength between

oxide layer and interface5. Adhesive strength between

interface and adhesive6. Cohesion strength of

adhesive



Failure of adhesive joints

Adhesion failure Cohesion failure Mixed failure



Properties of adhesives

180-190Silicone120-140Polyamide80-100Polyurethane80-100Methylacrylate80-120Phenolic adhesive60-90Two-component epoxy110-130One-component epoxyTemperature Range ºCAdhesive base



Design of adhesive metal joints


EUROCODESBackground and Applications Design of joints

Welded connections• Design of welded joints

– Strength of the welds– Strength of the HAZ

• Design guidance applicable for– Welding process MIG or TIG (up to t = 6 mm)– Approved welder and welding procedure– Prescribed combinations of parent and filler metal– Statically loaded structures

• Above conditions not fulfilled– Primary structures testing– Secondary structures or non loaded members γMw = 1,6



Heat-affected zone (HAZ)

• Heat-treatable alloysCondition T4 or higher HAZ softening(6xxx and 7xxx series)

• Non-heat treatable alloys TIG welding morein work-hardened cond. severe than MIG(3xxx and 5xxx series) welding



HAZ softening factor ρHAZ

0,600,60H14, H16, H183xxx

0,800,80H240,860,86H225xxx

0,600,80T60,700,90T47xxx

0,500,65T60,600,65T51,01,0T46xxx

ρHAZ (TIG) ρHAZ (MIG)ConditionAlloy series



Extent of HAZ (bHAZ)

-40t > 25 mm

-3512 < t ≤ 25 mm

-306 < t ≤ 12 mm

30200 < t ≤ 6 mm

TIGMIGbHAZ (mm)



Characteristic strength weld metal (fw)

• Lower than parent metal strength• Depending on filler metal used (appropriate 5xxx or 4xxx

series)

Parent metalFillermetal 7020

T66082 T6

6061 T6

6005 T6

6060 T5

5454 H24

5083 O

3003 H12

210190170150150--954043

260210190160160220240-5356

Characteristic strength values weld metal fw [N/mm2]



Design of butt welds• Strength members full penetration butt welds

• Throat thickness equal to thickness t

• Effective length equals total weld length when run-on and run-off plates are used



Design stresses• Normal stress, perpendicular

to weld axis

• Shear stress

• Normal + shear stress

Mw

wfγ

σ ≤

Mw

wfγ

τ 6,0≤

Mw

wfγ

τσ ≤+ 22 3



Design of fillet welds• Strength of fillet welds

– Throat section– Forces acting on throat section

• Throat section

– Effective throat thickness a– Effective length

Longitudinal fillet weldLength > 100 aNon uniform stresses

Reduction of

weld length



Effective throat thickness

With positive root penetration:a = 1,2 a or a + 2 mm or a = a + apen (verified by testing)



Forces acting on a fillet weld

Stresses σ , τ and τ , acting on the throat section of a fillet weld

Throat section



Design strength fillet weld

• Stresses comparison stress σc:

• Design stresses:

( )222 3 ττσσ ++=C

Mw

wC

fγ

σ ≤



Design strength HAZ• Tensile force perpendicular to failure plane

• HAZ butt welds

(Full penetration butt welds)

(Partial penetration butt welds)

te = effective throat thicknessfa,HAZ = Characteristic strength HAZ

Mw

HAZafγ

σ ,≤

ttf

Mw

eHAZa

⋅⋅

≤γ

σ ,



HAZ fillet welds(Toe of the weld, full cross-section)

(At the fusion boundary)

For shear forces and combined tensile / shear forces similar rules apply

Mw

HAZafγ

σ ,≤

tg

ttf

Mw

eHAZa 1,

⋅⋅

≤γ

σ

g1



Design of connections with combined welds

Two approaches

1. Welds designed for stresses in parent metal of the different parts of the joint Linear Elastic Approach

2. Loads acting on joint are distributed to the welds that are mostsuited to carry them Plastic Approach



Bolted and riveted connectionsPositioning of holes

Direction ofload transfer

End distance e1: min. 1,2 d

Edge distance e2: max. 4 t + 40 mm corrosion environment12 t + 150 mm no corrosion

Spacing p1: min. 2,2 dSpacing p2: min. 2,4 d

max. 14 t or 200 mm



Categories of bolted connectionsShear connections• Category A: Bearing type

– Shear resistance– Bearing resistance

• Category B: Slip-resistant at serviceability limit state– Add. check at ult. limit state: shear and bearing

• Category C: Slip-resistant at ultimate limit state– Add. check: shear and bearing

Tension connections• Category D: non-preloaded bolts

– Tension resistance• Category E: Preloaded high strength bolts

– Tension resistance



Design resistance of bolts• Shear resistance per shear plane:

Strength grades lower than 10.9

Strength grade 10.9, stainless steel bolts,aluminium bolts

• Bearing resistance

α smallest of:

• Tension resistance

Mb

ubRdv

AfFγ6,0

, =

Mb

ubRdv

AfFγ5,0

, =

Mb

uRdb

dtfFγα5,2

, =

Mb

subRdt

AfFγ9,0

, =

0,1or;41

3;

3 0

1

0

1

u

ub

ff

dp

de

−



Distribution of forces between fasteners

p



Deductions for fastener holes

For compression members: no deductions for fastener holes



High strength bolts in slip-resistant connections

Preloaded bolts force transfer by frictionSurface treatments between clamped surfaces

friction grip orslip-resistant connections

Design slip resistance:

cdpMs

Rds FnmF ,, γµ

=

subcdp AfF 7,0, =

n = number of friction surfacesm = factor; m = 1,0 for nominal clearance holesµ = slip factor; µ = 0,27 up to 0,40 ΣtγMs = 1,25 for ultimate limit state

1,10 for serviceability limit state

Controlled tightening



Design of adhesive lap joints



Strength of adhesive joints



Adhesive bonded joints• Design guidance applicable for:

– Shear forces– Appropriate adhesives– Specified surface preparation

• Structural application: characteristic shear strength values fvADH:

• Design shear stress: where:

202-component acrylic252-component epoxy351-component epoxyfvADH [N/mm2]Adhesive types

Higher values are allowed when demonstrated by tests

adhM

ADHvf

,

,

γσ = 0,3, =adhMγ



Hybrid connections• Different fasteners combined such as bolts and welds

• Unequal stiffness of different fasteners:– Only higher stiffness fastener is acting– Only design strength of stiffest fastener is taken into account

• When fasteners act at the same time: design strengths may be summarised


EUROCODESBackground and Applications Final remarks

Final remarks• Research resulted in up-to-date design rules

• Design rules available for structural connections- welds- bolts and rivets- adhesives

• EC9 important design tool for aluminium structures

COLD-FORMED STRUCTURES (PART 1.4)

R. Landolfo University of Naples "Federico II"


EUROCODESBackground and Applications Cold-Formed Structures (Part 1.4)

Cold-Formed (CF) StructuresEurocode 9 - Part 1.4

Prof. Raffaele Landolfo

University of Naples “Federico II”



BACKGROUNDThe European code for the design of aluminium structures, Eurocode9, provides in Part 1.1 (EN 1999-1-1) general rules for structures. In addition, Part 1.4 (EN 1993-1-4) provides supplementary rules for CF sheeting



EUROCODE 9 – PART 1.4: CONTENT

1 INTRODUCTION

2 BASIS OF DESIGN

3 MATERIALS

4 DURABILITY

5 STRUCTURAL ANALYSIS

6 ULTIMATE LIMIT STATES

7 SERVICEABILITY LIMIT STATES

8 JOINT WITH MECHANICAL FASTENERS

9 DESIGN ASSISTED BY TESTING

ANNEX A – TESTING PROCEDURES

ANNEX B – DURABILITY OF FASTENERS

EN 1999-1-4 2006 November



The following basic types of thin-walled elements are identified in the classification process:

• flat outstand element;• flat internal element;• curved internal element.

These elements can be:

- unreinforced, or- reinforced

by longitudinal stiffening ribs or edge lips or bulbs

BACKGROUNDBASIC TYPES OF THIN-WALLED ELEMENTS



BACKGROUNDBASIC TYPES OF THIN-WALLED ELEMENTS

outstand element

internal element

Unreinforced elements Reinforced elements



BACKGROUNDSLENDERNESS OF UNREINFORCED FLAT ELEMENTS

Eurocode 9 relates the classification of elements in a cross-section to the value of the slenderness parameter β, which is defined according to the type of elements as a function of the b/t ratio.

In the case of plane unreinforced elements, β is related to the stress gradient:

β = g b/t or β = g d/t

where:b is the width of an element;d is the depth of a web element;t is the element thickness;g is the stress gradient coefficient, given by the expressions




Eurocode 9 relates the classification of elements in a cross-section to the value of the slenderness parameter β, which is defined according to the type of elements as a function of the b/t ratio.

In the case of plane unreinforced elements, β is related to the stress gradient:

β = g b/t or β = g d/t

where:b is the width of an element;d is the depth of a web element;t is the element thickness;g is the stress gradient coefficient, given by the expressions




Relationship defining the stress gradient coefficient (g):

g = 0.70 + 0.30 ψg = 0.80 / (1 + ψ)

Where ψ is the ratio of the stresses at the edges of the plate under consideration related to the maximum compressive stress.

stress gradient coefficient

vs.

ψ coefficient



BACKGROUNDSLENDERNESS OF UNREINFORCED FLAT ELEMENTSIn the case of plane stiffened elements, more complex formulations are provided in order to take into account three possible buckling modes:a) mode 1: the stiffened element buckles as a unit, so that the

stiffener buckles with the same curvature as the element;b) mode 2: the sub-elements and the stiffener buckle as

individual elements with the junction between them remaining straight;

c) mode 3: this is a combination of modes 1 and 2, in which both sub-elements and whole element buckle.

Local buckling

Distortional buckling Coupled Local and Distortional buckling



BACKGROUND

class 4β3 < βclass 4β3 < β

class 3β2 < β ≤ β3class 3β2 < β ≤ β3

class 2β1 < β ≤ β2

class 1 or 2β ≤ β2class 1β ≤ β1

Elements in strutsElements in beamsElement classification as a function of:- β value- Member type-beam-strut

Limit parameters β1, β2and β3 as function of:- Element type-Outstand-Internal

- Alloy type-Buckling class(Class A, Class B)-Welded-Unwelded

0/250 f=ε f0: 0.2% proof strength in MPa



BACKGROUND

class 4β3 < βclass 4β3 < β

class 3β2 < β ≤ β3class 3β2 < β ≤ β3

class 2β1 < β ≤ β2

class 1 or 2β ≤ β2class 1β ≤ β1

Elements in strutsElements in beamsElement classification as a function of:- β value- Member type

-beam-strut

Limit parameters β1, β2and β3 as function of:- Element type

-Outstand-Internal

- Alloy type-Buckling class(Class A, Class B)-Welded-Unwelded

0/250 f=ε f0: 0.2% proof strength in MPa



SECTION PROPERTIESINFLUENCE OF ROUNDED CORNERS

As in the Eurocode 3, also Eurocode 9 – Part 1.4 takes into account the presence of rounded corners by referring to the notational flat width bp of each plane element, measured from the midpoints of adjacent corner elements.

Notional widths of plane cross section parts bp allowing for corner radii




Notional widths of plane cross section parts bpallowing for corner radii




According to the code provisions, the influence of rounded corners with internal radiusr ≤ 10 tAndr ≤ 0.15 bpon section properties might be neglected, and the cross-section might be assumed to consist of plane elements with sharp corners

Approximate allowance for rounded corners




According to the code provisions, the influence of rounded corners with internal radiusr ≤ 10 tAndr ≤ 0.15 bpon section properties might be neglected, and the cross-section might be assumed to consist of plane elements with sharp corners

Approximate allowance for rounded corners



SECTION PROPERTIESGEOMETRICAL PROPORTIONS

The provisions of Eurocode 9 – Part 1.4 may be applied only to cross-sections within the range of width-to-thickness ratios for which sufficient experience and verification by testing is available:

b/t ≤ 300 for compressed flanges

b/t ≤ E/f0 for webs

Cross-sections with larger width-to-thickness ratios may also be used, provided that their resistance at ultimate limit states and their behaviour at serviceability limit states are verified by testing



The effect of local buckling on each compression element of the cross-section shall be conventionally accounted by replacing the non-uniform distribution of stress, occurring in the post-buckling range, with a uniform distribution of the maximum stress (σmax) acting on a reduced portion of the element, having the same width (b) but a reduced thickness (effective thickness, teff).

Actual normal stress distribution Effective width Reduced stress Effective thickness

GENERAL

LOCAL AND DISTORTIONAL BUCKLINGBrussels, 18-20 February 2008 – Dissemination of information workshop 18


GENERAL

LOCAL AND DISTORTIONAL BUCKLING

The most suitable expression for evaluating the local buckling coefficient ρ which reduces the thickness (or, equivalently, the strength) of an aluminium compressed plate, is given by following relationship:

lim if 0.1 λλρ ≤= p

lim21 if 1 λλ

λω

λω

ρ ≤⎟⎟⎠

⎞⎜⎜⎝

⎛−= p

pp

which takes into account stress distribution and boundary conditions by means of the buckling factor kσand:ω1 and ω2 are numerical coefficients

is the limit value of the normalised slenderness which corresponds to ρ=1limλ

σσ

≅π

ν−=

σ=λ

kEf

tb

kEf

tbf pp

crp

2.02

2.02

2.0 052.1)1(12

pλwhere is the normalised plate slenderness:



GENERAL


0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1 σ

λ

A B C

heat-treated,

heat-treated, welded ; non heat-trated,

non heat-treated,

p

0.3800.190.76C

0.4400.220.88B

0.6730.221.00A

ω2ω1curve

Parameters ω1, ω2 and are given as function of Alloy type-Heat treated-Not heat treated-Welded-Unwelded

limλ

limλ

Landolfo and Mazzolani’s

buckling curves




LOCAL AND DISTORTIONAL BUCKLING - EUROCODE 9 PART 1.1Part 1.1 of Eurocode 9 uses the above-mentioned approach for class 4 compression elements.

For sake of simplicity, it modifies the formulations by explicitly introducing the β=b/t ratio and rounding the subsequent coefficients so as to obtain integers.

Part 1.1 of Eurocode 9 prescribes to use the same formulations also for stiffened elements and to apply the factor ρ to the area of the stiffener as well as to the basic plate thickness.

Part 1.4 of Eurocode 9 gives a more specific and detailed approach for CF thin-walled aluminium sheeting, although it is easily extensible to aluminium CF.

LOCAL AND DISTORTIONAL BUCKLING - EUROCODE 9 PART 1.4

SHELL STRUCTURES (PART 1.5)

A. Mandara University of Naples "Federico II"



EN 1999 - Eurocode 9: Design of aluminium structuresPart 1.5 - Shell structures (A. Mandara)

EN 1999 - Eurocode 9: Design of aluminiumstructures Part 1.5 - Shell structures

A. Mandara

Department of Civil EngineeringSecond University of Naples – School of Engineering

Real Casa dell’Annunziata – Via Roma, 29, Aversa (CE)

Eurocodes - Background and Applications“Dissemination of information for training” workshop

Brussels 18-20 February 2008



Aluminium shells – applications




The EN1999-1-5General part




The EN1999-1-5Annexes




The prEN1993-1-6




w θ, v

x, u

t

r

l

t

r1

hL

r2

r

β β

w

φ

θ

r

t

Shell configurations allowed for in EN1999-1-5





Types of shell analysis in EN1999-1-5Brussels, 18-20 February 2008 – Dissemination of information workshop 8


Specific issues for aluminium alloy shells in EN1999-1-5




• shell plastic buckling• imperfection sensitivity analysis of aluminium cylinders;• set-up of buckling curves for aluminium shells;• definition of imperfection classes for plastic buckling; • interaction between load cases;• introduction of additional shell configurations;

• stiffened shells• imperfection sensitivity analysis of stiffened cylinders;• validation of EN1993-1-6 procedures and harmonization with

EN1999 rules;• effect of welding effect (HAZ zones)

• imperfection sensitivity analysis of welded cylinders;• definition of simplified design procedures;

Background activity - Main investigated aspects




Parametric analysis:Shell geometrical data and material

features

The ABAQUS model




Imperfection model

⎥⎦⎤

⎢⎣⎡ −

⎥⎦⎤

⎢⎣⎡ −

= −−−−∑ Ryyke

Lxxkeww o

yyyko

xxxk oyox

)(cos)(cos 2)(

2)(

0

21

21 ππ




Buckling response of axially loaded cylinders

0

1000

2000

3000

4000

5000

6000

0 2 4 6 8 10 12

Abbassamenti Assiali [mm]

Car

ichi

Ass

iali

[KN

]

R/t = 200f02 = 200 N/mmqTipo IncastratoImperfezione Asimmetrica

ABAQUS

Pcr,th = 5293.38 KN

W0/t =0.01

W0/t =3

0

1000

2000

3000

4000

5000

6000

0 10 20 30 40 50 60 70 80

Abbassamenti Assiali [mm]

Car

ichi

Ass

iali

[KN

]

R/t = 200f02 = 200 N/mmqTipo IncastratoImperfezione Assial-Simmetrica

ABAQUS

Pcr,th = 5293.38 KN

W0/t =0.01

W0/t =3




Deflected shapes at buckling (cylinders under uniform external pressure)

Diagramma Carichi-Spostamenti Radiali

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 5 10 15 20 25 30 35 40

Spoatamenti Radiali [mm]

Car

ichi

Sup

erfic

iali

[N/m

mq]

R/t = 200 L/R=2f 02 = 100 N/mmq

W 0 = 0.1 mmTipo Appoggiato

ABAQUS

Pcr,th = 0.058 N/mmq

Diagramma Carichi-Spostamenti Radiali

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 10 20 30 40 50 60

Spoatamenti Radiali [mm]

Car

ichi

Sup

erfic

iali

[N/m

mq]

R/t = 100 L/R=2f02 = 100 N/mmqW 0 = 0,75 mm

Tipo Appoggiato

ABAQUS

Pcr,th = 0.058 N/mmq




Imperfection sensitivity curves (axially loaded cylinders)

Cylinders under axial load Imperfection Sensitivity Curves

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

0,0 0,2 0,4 0,6 0,8 1,0 1,2

W0/t

Pu /Pcr,th

R/t = 200 R = 1000 mm t = 5 mmf02 = 200 N/mm2

P cr,th = 5293.38 KNσ cr,th = 168.49 N/mm 2

CLASS A CLASS B CLASS C




Imperfection sensitivity curves (cylinders under external pressure)

Cylinders under external pressureImperfection sensitivity curve

0,0

0,2

0,4

0,6

0,8

1,0

0,0 0,2 0,4 0,6 0,8 1,0

W0/t

Pu /Pcr,th

L = 1000 mm R= 1000 mm t= 10 mmR/t = 100 L/R=1f02 = 100 N/mm2 n = 9 Pcr,th = 0.620 N/mm2

L = 1000 mm R= 1000 mm t= 10 mmR/t = 100 L/R=1f02 = 100 N/mm2 n=8Pcr,th = 0.610 N/mm2

n=8

Class A Class CClass B

n = 9




Imperfection sensitivity curves (cylinders under torsion)

Cylinders under torsionImperfection sensitivity curve

0,0

0,2

0,4

0,6

0,8

1,0

0,0 0,2 0,4 0,6 0,8 1,0

W0/t

Pu /Pcr,th

Longitudinal ImperfectionHelical Imperfection

R/t = 200 L/R = 2 t = 5 mmf02=200 N/mm2

τcr,th = 49.358 N/mm2

Class CClass BClass A




( )βα−−= xexP 1)(

( ) ( ) ( ) αβ−−αααβ

==/1/1/1

/11)( xex

dxxdPxp

Cylinders under axial loadWeak hardening alloys

- R/t = 100-

0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.20 0.40 0.60 0.80 1.00

x

P(x)

Class AClass BClass CWeibull Curve AWeibull Curve BWeibull Curve C5% Percentile Value

A

B

C

f02 = 200 N/mm2

Semi-probabilistic interpretation of buckling data(axially loaded cylinders) - Weibull’s law





- R/t = 200-

0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.20 0.40 0.60 0.80 1.00

x

P(x)

Class AClass BClass CWeibull Curve AWeibull Curve BWeibull Curve C5% Percentile Value

A

B

C

f02 = 200 N/mm2

( ) ( ) ( ) αβ−−αααβ

==/1/1/1

/11)( xex

dxxdPxp


Semi-probabilistic interpretation of buckling data(axially loaded cylinders) - Weibull’s law











Shell buckling – EC3 formulation

λλλαχ

λλλλλ

λλβχ

λλχη

≤⇔=

≤<⇔⎟⎟⎠

⎞⎜⎜⎝

⎛

−−

−=

≤⇔=

p

pp

2

00

0

0

1

1

βαλ

σλ

−=

=

1p

xRc

ykf




Shell buckling – fabrication tolerance classes in EC3

0 max00 max

gxo

gx

Uw wUt t

≤ ⇔ ≤


Fabrication tolerance quality

class

Description

Class A Excellent Class B High Class C Normal

r t

Δwox

inward

gx

Δwox

gx

t

Gauge length

m a x

4o

g x

U

R t=

Dimple tolerance parameter



Expressions of buckling factors according to EC3

Axial (meridional) load External pressure

and torsion (shear) λ 0 0.20 0.40

β 0.60 0.60

η 1.00 1.00

Axial (meridional) load

External pres-sure (αθ) and

torsion (shear) (ατ)

Fabrication tolerance quality class

Description

Q αx αθ or ατ Class A Excellent 40 0,75 Class B High 25 0,65 Class C Normal 16 ( ) 44.1

//191.11

62.0

trQx

+=α

0,50




Cylinders under axial load Weak hardening alloys

Quality Class C0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 0.50 1.00 1.50 2.00

λ

χ Minimum ValueMedium ValueMaximum Value5%Percentile ValueExperimental Value

EC3 Curve

Modified EC3 Curve

Comparison of EC3 buckling curves with simulation data




Cylinders under external pressureStrong hardening alloys

Quality class A

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 1.0 2.0 3.0 4.0 5.0

λ

χ L/R=2 R/T=200L/R=2 R/T=100L/R=2 R/T=50L/R=1 R/T=200L/R=1 R/T=100L/R=1 R/T=50L/R=4 R/T=200L/R=4 R/T=100L/R=4 R/T=50

EC3 Curve

Modified EC3 Curve





Cylinders under torsionWeak hardening alloys

Quality class C

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

λ

χ L/R=2 R/T=200 Imp. 1

L/R=2 R/T=200 Imp. 2

L/R=2 R/T=100 Imp. 1

L/R=2 R/T=100 Imp. 2

L/R=2 R/T=50 Imp. 1

L/R=2 R/T=50 Imp. 2

L/R=4 R/T=200 Imp. 2

L/R=4 R/T=100 Imp. 2

L/R=4 R/T=50 Imp. 2

EC3 Curve





Shell buckling - proposal for pr1999-1-5

( )[ ]200

22

15.0

1

λλλαφ

λφφχ

αχχ

+−+=

−+=

=

perf

perfx

xRc

ykfσ

λ =

Axial (meridional) load External pressure (α θ) and torsion (α τ) Fabrication tolerance

quality class

DescriptionQ αx α ref α θ or ατ

Class A Excellent 40 0,75 Class B High 25 0,65 Class C Normal 16 ( ) 44.1

//191.11

62.0

trQx

+=α

0,50 ( )( ), 20

11 0, 2 1 /ref ref

θ τα =+ − α λ − λ α

Alloy Axial (meridional) load External pressure Shear (torsion) λ0 α0 λ0 α0 λ0 α0

Weak hardening alloys 0.2 0.35 0.3 0.55 0.5 0.3 Strong hardening alloys 0.1 0.2 0.2 0.7 0.4 0.4





Quality Class A

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 0.50 1.00 1.50 2.00

λ

χ Minimum Value

Medium Value

Maximum Value

5% Percentile Value

Buckling curves - proposal for EC9




Cylinders under external pressureWeak hardening alloys

Quality class A

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 1.00 2.00 3.00 4.00 5.00 6.00

λ






Cylinders under torsion Weak hardening alloys

Quality class B

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 1.00 2.00 3.00 4.00 5.00

λ














0,0

0,2

0,4

0,6

0,8

1,0

1,2

0,0 0,2 0,4 0,6 0,8 1,0

w0/t

Pu /Pcr,th

R/t = 50 f 0.2 = 200 N/mm2

P cr,th = 24806.01 kNσcr,th = 197.40 N/mm2

clamped ends hinged ends

Imperfection 1

2

3

4

w0*/t

A B C


Exploitation of plastic buckling features(axially loaded cylinders)



0,0

0,2

0,4

0,6

0,8

1,0

1,2

0,0 0,2 0,4 0,6 0,8 1,0

w0/t

Pu /Pcr,th

R/t = 200 f 0.2 = 100 N/mm2

P cr,th = 2694.32 kNσcr,th = 85.76 N/mm 2

clamped ends hinged ends

Imperfection 1

234

w0*/t

A B C

Exploitation of plastic buckling features(axially loaded cylinders)




HINGED ENDS

0.00

0.03

0.06

0.09

0.12

0.15

0.18

0.21

0.24

0.27

0.30

0 50 100 150 200 250 300

R/t

w0*/t

f 0.2 = 100 N/mm2

f 0.2 = 200 N/mm2

f 0.2 = 300 N/mm2

Exploitation of plastic buckling features (axially loaded cylinders) – Imperfection limit w0*/t




CLAMPED ENDS

0.00

0.02

0.04

0.06

0.08

0.10

0 50 100 150 200 250 300

R/t

w0*/t

f 0.2 = 100 N/mm2f 0.2 = 200 N/mm2

f 0.2 = 300 N/mm2

Exploitation of plastic buckling features (axially loaded cylinders) – Imperfection limit w0*/t




Exploitation of plastic buckling features (axially loaded cylinders) Definition of quality Class A-plus in prEN-1999-1-5

Fabrication tolerance quality class Description Value of U0,.max (f0.2 in N/mm2)

Clamped ends Hinged ends

Class A-plus Excellent 0.2

1 2.25 0.01t Rf R t

⎛ ⎞+⎜ ⎟⎜ ⎟

⎝ ⎠

0.2

1 5 0.02t Rf R t

⎛ ⎞+⎜ ⎟⎜ ⎟

⎝ ⎠

Class A Very high 0,006 Class B High 0,01 Class C Normal 0,016

Q Fabrication tolerance quality class Description Clamped

ends Hinged

ends αx

Class A-plus Excellent 60 50 Class A Very high 40 Class B High 25 Class C Normal 16

( )1.44

,00,2

1

1 0.61 2.60x

x xE

Q f

α

λ λ

=⎛ ⎞

+ −⎜ ⎟⎜ ⎟⎝ ⎠




Cylinders under axial loadStrong hardening alloys

Quality Class A-plus

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 0.50 1.00 1.50 2.00

λ

χ Minimum ValueMedium ValueMaximum Value5% Percentile Value

EC3

Proposed EC9 Curve

Hinged ends

Exploitation of plastic buckling features (axially loaded cylinders) - Class A-plus buckling curves




Shell buckling – summary of EC9 formulation

Unstiffened shells

Stiffened shells

Load cases • axial compression• external pressure• torsion




Material buckling class Axial (meridional) load External pressure Shear (torsion)

λx,0 μx λθ,0 μθ λτ,0 μτ A (Weak hardening alloys) 0.2 0.35 0.3 0.55 0.5 0.3 B (Strong hardening alloys) 0.1 0.2 0.2 0.7 0.4 0.4


Shell buckling – summary of EC9 formulation



Shell buckling – fabrication tolerance classes according to EC9

Class 1Class 2Class 3Class 4

Axial (meridional) load External pressure (αθ) and torsion (ατ) Fabrication

tolerance quality

class Q αx αref αθ or ατ

Class 1 16 0,50 Class 2 25 0,65 Class 3 40 0,75 Class 4 50-60

( ) 44.1//191.11

62.0

trQx

+=α

- ( )( ), 2

0

11 0,2 1 /ref ref

θ τα =+ − α λ − λ α












Interaction between load cases

• interaction between load cases• axial compression – external pressure• axial compression – torsion• external pressure – torsion

• validation of EN1993-1-6 procedures• proposal for an alternative formulation




Interaction between load cases ENV1993-1-6 formulation




σcr/σu

Pcr/Pu

Axial compression and External pressure

Interaction between load case ENV 1993-1-6 – Interaction domains




σcr/σu

τcr/τu

Axial compression and Torsion





Pcr/Pu

τcr/τu

External pressure and Torsion





Interaction between load casesprEN1993-1-6 formulation and proposal for prEN1999-1-5

prEN1993-1-6 prEN1999-1-5




σcr/σu

Pcr/PuEC3Class AClass BClass CClass AClass BClass CProposal Class AProposal Class BProposal Class C

Axial compression and External pressure

Interaction between load casesEN 1999-1-5 – Interaction domains




σcr/σu

τcr/τuEC3Class AClass BClass CClass AClass BClass CProposal Class AProposal Class BProposal Class C

Axial compression and Torsion





Pcr/Pu

τcr/τu

EC3Class AClass BClass CProposal Class AProposal Class BProposal Class C

External pressure and Torsion





Interaction buckling check according to EC9












Parametric analysis – Stiffened shells

50x525x510x55x5

50x1025x1010x105x10

50x2025x2010x205x20

sides

R/t=50

R/t=100

R/t=200Rectangular

5025105sideSquare

5025105radiusCircular

[mm][mm][mm][mm]Stiffenersize

Shellgeometry

Stiffenersection












Stiffened shells – Proposal for EN19991-5Axial load

s 2xRc 12

θ s 3

EA A1.2 1n 1 A5 C d Aω1

0.80

x

s

x

EAC d

withφ

⎛ ⎞⎛ ⎞= α + +⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠+

α =

External pressure

2nRc 12

3

A1p AArj

0.50with

θ

θ

⎛ ⎞= α +⎜ ⎟

⎝ ⎠

α =

where

[ ]

i

2θφ45

2ssφ44

sss14

θφ12

ssφ11

jl

πrω

/rDDνC

/rdEIDC

)/(rdEAeC

CCνC

/dEACC

=

=

+=

=

=

+=

[ ][ ] 2

rtrstsφθ66

2rrθ55

rrr25

φθ33

rrθ22

/r/dGI/d0,5(GIDC

/rdEIDC

)/(rdEAeC

CC

/dEACC

++=

+=

−=

=

+=

[ ]

23312

233

225223311

23

214

221233

22522

2225

2223311

2

1422

12252

2233122

2

252

225566452

4444

1

)C(Cω)CωC)(CCC(ωA

)Cωj)(CCωC(Cω)Cj)(CCC(ω

)Cωj)(CCj)(CC(C2ωA

C2jCC)C(C2ωCωjA

+−+++=

+++−++−

+++=

+++++=




Equivalent orthotropic properties of corrugated sheeting (from prEN1999-1-6)

( )

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅=⋅=

=⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅=⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅=⋅=

⋅=⋅=

ϕ

ϕ

ϕ

2

223

xyθ

2y

2

222

3

xφ

2

22xyθ

2

22

yθ

2

3

xφ

4l

dπ1

12

tGIGD

0,13EtdIED

4l

dπ1

1

ν-112

EtIED

4l

dπ1

tGtGC

4l

dπ1tEtEC

3d

2tEtEC

Stiffened shells – Proposal for EN19991-5




0,0

0,2

0,4

0,6

0,8

1,0

1,2

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

λ

χ

L/R=2; R/t=50

L/R=2; R/t=100

L/R=2; R/t=200

Strong hardening alloysQuality class A

Q* = 1.3Q

Q* = Q

0, /x xRk xRcn nλ =

Axial load

Stiffened shells – Proposal for prEN19991-5


( )[ ]200

22

15.0

1

λλλαφ

λφφχ

αχχ

+−+=

−+=

=

perf

perfx



0,0

0,2

0,4

0,6

0,8

1,0

1,2

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0

λ

χ

L/R=2; R/t=50

L/R=2; R/t=100

L/R=2; R/t=200

Strong hardening alloysQuality class C

0, /nRk nRcp pθλ =

External pressure

Stiffened shells – Proposal for prEN19991-5


( )[ ]200

22

15.0

1

λλλαφ

λφφχ

αχχ

+−+=

−+=

=

perf

perfx



General buckling curve formulation

( )[ ]200

22

15.0

1

λλλαφ

λφφχ

αχχ

+−+=

−+=

=

perf

perfx

Stiffened shells – EC9 formulation












Rolling Welding

MIGMIGbhaz = 20 mmbhaz = 30 mmbhaz = 35 mmbhaz = 40 mm

TIGbhaz = 30 mm

0 t 6mm< ≤6 t 12mm< ≤

12 t 25mm< ≤t 25mm>

0 t 6mm< ≤


Effect of welding (HAZ zones):definition of simplified design procedures




Effect of welding – Parametric analysis



0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

0,0 0,1 0,2 0,3 0,4 0,5 0,6

w0/t

Pu /Pcr,th

α = 0.86α = 0.80

α = 0.72

α = 0.72 α = 0.71α = 0.67

Welded

Unwelded

R/t = 50; f 0.2 = 200 N/mm2; ρo,haz=0,53

Class 3 Class 2 Class 1

Effect of welding – Imperfection sensitivity curves, axial compression




0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

0,0 0,1 0,2 0,3 0,4 0,5 0,6

w0/t

Pu /Pcr,th

α = 0.61α = 0.67

α = 0.54

α = 0.56α = 0.68

α = 0.76

Welded

Unwelded

Class 3 Class 2 Class 1

R/t = 100; f 0.2 = 200 N/mm2; ρ0,haz = 0,53

Effect of welding – Imperfection sensitivity curves, axial compression












λ i,wλ i,0

ρo,haz

1,0

00

ρi,w

λi,w,0 λ i

,0,w o o

,w ,0(1 ) i i

ii i

λ − λρ = ω + − ω

λ − λ

ω0 = ω (ρ0,haz)

λi,0 = λi,0 (λi,w,0)


Effect of welding according to EC9

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