EUROCODES Background 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"
EUROCODES Background and Applications
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
1
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
2
ENVENV-EUROCODE 9 (1998) “ALUMINIUM STRUCTURAL DESIGN” DESIGN”
GENERAL INFORMATION ON EN 1999
Part 1.1 “General rules” rules” Part 1.2 “Fire design” design”
Federico M. Mazzolani (Chairman of TC 250250-SC9)
Part 1.3 “Structures susceptible to fatigue” fatigue”
Department of Structural Analysis and Design Faculty of Engineering University of Naples “Federico II” II”
EUROCODES Background and Applications
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
3
ENEN-EUROCODE 9 (2006) “ALUMINIUM STRUCTURAL DESIGN” DESIGN”
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
4
EUROCODE 9 – Part 1-1: General structural rules CONTENTS of Part 11-1
1) EN 19991999-1-1 GENERAL STRUCTURAL RULES
1) General
2) EN 19991999-1-2 STRUCTURAL FIRE DESIGN
2) Basis design
3) EN 19991999-1-3 ADDITIONAL RULES FOR STRUCTURES
3) Materials
SUSCEPTIBLE TO FATIGUE
4) Durability, corrosion and execution
4) EN 19991999-1-4 SUPPLIMENTARY RULES FOR COLDCOLD-
5) Structural analysis
FORMED SHEETING
6) Ultimate limit states for members
5) EN 19991999-1-5 SUPPLIMENTARY RULES FOR SHELL
7) Serviceability limit states
STRUCTURES
8) Ultimate limit states for connections
EUROCODES Background and Applications
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
ANNEXES to Part 11-1
EUROCODES Background and Applications
5
A) Execution classes
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
6
EUROCODE 9 – Part 1-2: Structural fire design
B) Equivalent T-stub in tension C) Materials selection D) Corrosion and surface protection E) Analytical models for stressstress-strain relationship F) Behaviour of crosscross-sections beyond elastic limit G) Rotation capacity H) Plastic hinge method for continuous beams I ) Lateral torsional buckling of beams and torsional or torsionaltorsional-flexural buckling of compressed members
CONTENTS of Part 11-2 1) General 2) Basis design 3) Material properties 4) Structural fire design 5) Structural analysis
J ) Properties of crosscross-sections K ) Shear lag effects in member design
Annex A : Properties of aluminium alloys not listed in EN 19991999-1-1
L ) Classification of joints
Annex B : Heat transfer to external structural aluminium members
M ) Adhesive bonded connections
EUROCODES Background and Applications
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
7
EUROCODE 9 – Part 1-3 : Additional rules for structures susceptible to fatigue
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
ANNEXES to Part 11-3
8
A) Bases of design B) Guidance on assessment by fracture mechanics C) Testing for fatigue design
CONTENTS of Part 1-3
1) General
D) Stress analysis
2) Basis design E) Adhesive bonds
3) Materials,constituent products and connecting devices 4) Durability
F) Low cycle fatigue range
5) Structural analysis
G) Influence of RR-ratio
6) Ultimate limit states of fatigue
H) Fatigue strength improvement of welds
7) Quality requirements
I ) Castings
8) Ultimate limit states for connections J ) Alternative tables for structural details
EUROCODES Background and Applications
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
9
EUROCODE 9 – Part 11-4 : Supplementary rules for coldcold-formed sheeting 1) General
CONTENTS of Part 11-4
2) Basis design
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
CONTENTS of Part 11-5
3) Materials
1) General
4) Durability
2) Basis design
5) Structural analysis
3) Materials and geometry
6) Ultimate limit states
4) Ultimate limit states
7) Serviceability limit states
5) Modelling for analysis
8) Connection with mechanical fasteners
6) Plastic limit state (LS 1)
9) Design assisted by testing
7) Cyclic plasticity limit state (LS 2)
Annex A : Testing procedures
8) Bucking limit state (LS 3)
Annex B : Durability of fasteners
Annex A : Expressions for bucking design
Annax C : Bibliography
EUROCODES Background and Applications
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
11
EN 1090 : Execution of steel and aluminium structures Part 3 : Technical rules for execution of aluminium structures
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
12
Annexes to EN 1090 – 3 ; Part 3 : Technical rules for execution of aluminium structures A) Welding procedure test for fillet welds
1.
Scope
2.
Normative references
3.
Terms and definitions
4.
Specifications and documentation
C) Project specification list D) Final inspection of fabricated aluminium components
B) Requirements on geometical tolerances which are not normally critical for the integrity of the structure
5.
Constituent materials and products
6.
Fabrication
7.
Welding
8.
Mechanical fastening and adhesive bonding
F) Proposed frame fpr quality plan
9.
Erection
G) Requirements for execution classes
10. Protective treatment
10
EUROCODE 9 – Part 11-5 : Supplementary rules for shell structures
E) Procedure test for determination of slip factor
H) Fastening of cold formed members and sheeting
11. Geometric tolerances 12. Inspection , testing and corrections
I ) Guidance for the determination of execution classes and structural classes
EUROCODES Background and Applications
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
13
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
14
INNOVATIVE ISSUES in EC 9 part 1.1
1. Classification of crosscross-sections 2. Extent of heat affected zones (HAZ) 3. Generalized formulation for ULS for axially loaded members 4. Generalized formulation for ULS for members in bending 5. Bucking curves approach for columns 6. Local bucking approach 7. Evaluation of rotation capacity 8. Plastic design approach 9. Classification of connections 10. T-stub model for end plate bolted connections
EUROCODES Background and Applications
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
15
Background of EC 9
AUTHORS OF CHAPTERS :
Federico M.MAZZOLANI Gunther VALTINAT Frans SOETENS Torsten HOGLUND Bruno ATZORI Magnus LANGSETH
The ECCS Recommendations (1978)
GENERAL INFORMATION ON EN 1999 (Federico Mazzolani)
Brussels, 18-20 February 2008 – Dissemination of information workshop
16
DESIGN CRITERIA F. Mazzolani University of Naples "Federico II"
DESIGN CRITERIA FOR ALUMINIUM ALLOY STRUCTURES Federico M. Mazzolani (Chairman of TC 250250-SC9)
DESIGN CRITERIA FOR ALUMINIUM STRUCTURES IN CIVIL ENGINEERING How can aluminium and its alloy satisfy
the requirements of civil engineering structures? In which applications can they compete
with other structural materials, like steel?
Department of Structural Analysis and Design Faculty of Engineering University of Naples “Federico II” II”
FIRST APPLICATIONS
HISTORICAL BACKGROUND Birth of aluminium :
1807 – isolation of AL element (Sir Humphry Davy – U.K.) 1827 – first aluminium nugget (Whoeler – Germany) 1854 – first electrolytic reduction (Henry Sainte Claire – France) 1886 – industrial electrolytic process (Paul Luis Touissant Héroult – France and Charles Martin Hall – USA)
Dirigible structures (details)
Eagles of the Napoleon III’ III’s insigna (1851(1851-1870)
Dirigible structures: Schwartz (1897) Zeppeling (1900)
Armaments and equipment for the First World War (1915(1915-1918)
Dirigible structures (details)
Navy structures
Presence of aluminium in different surroundings
Aircraft structures
Railway structures
Railway structures
Railway structures
Reservoirs for Railway
Reservoirs for Railway
Cladding
Windows
The Empire State Building in New York was the first building using anodised aluminium for windows
Aluminium sheets installed more than a century ago for cladding the dome of the San Gioacchino church in Rome
Decoration
The 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 collectors and Atomium fans. The remaining 30 tonnes of aluminium will be recycled.
The statue of Eros in Piccadilly Circus London (only recently cleaned and renovated)
Symbolic works
Markets for Extrusions
Markets for Roller roducts
Housing structures
Foilstock 13%
5%
22%
12%
15%
Stockists Packaging (rigid)
Building 18%
Building
11%
18%
51%
Engineering Transport Consumer durables
19%
Transport Engineering Others
16%
Per-capita use by world areas (in kg)
Markets for Ricycled Aluminium
40 35 30 13%
7%
Building
6%
Transport Engineering Others
1980
25
1990
20
2000
15 10
74%
5 0 Europe
USA
Japan
Different markets for aluminium products
BASIC PREREQUISITES OF ALUALU-ALLOYS
[t] 1.60E+06 1.40E+06
1.20E+06
1.00E+06
8.00E+05
6.00E+05
4.00E+05
2.00E+05 THE GROWTH OF ALUMINIUM ALLOYS IN BUILDINGS
0.00E+00 1960 1965 1970 1975 1980 1985 1990 1995 2000
Wide family of constructional materials,covering the range of mechanical properties of mild steels Corrosion resistance makes normally not necessary to provide protection protection coating Weigth reduction (respect to steel is 1 to 3) gives many advantages in transportation and erection Low elastic modulus increases the sensitivity to deformability and instability problems The material itself is not prone to brittle fracture Fabrication process by extrusion allows individually tailored shapes shapes to be designed Either bolting,riveting and welding techniques are available as connection solution
BASIC CONDITIONS FOR COMPETITION WITH STEEL
First pre-requisite:
First pre-requisite:
Corrosion resistance
Corrosion resistance ( C ) Second pre-requisite:
Lightness ( L ) Third pre-requisite:
Functionality of sections due to extrusion ( F )
Details of steel bolted connections
Steel detail
Second pre-requisite:
Second prepre-requisite:
Ligthness
Ligthness
Second prepre-requisite:
Second prepre-requisite:
Ligthness
Ligthness
Aluminium detail
steel hot rolled sections
aluminium extruded sections
extrusion process
1.Billets in parking
2. Heating (480° (480°C)
4. Transfer to extrusion
5. Extrusion
3. Cutting
6. Termal treatment
Phases of the extrusion process
Third prepre-requisite: Functionality of sections due to extrusion
“The geometrical properties of crosscross-section are improved by designing a shape which simultaneously gives the minimum weight and the highest structural efficiency” efficiency”
Third prepre-requisite: Functionality of sections due to extrusion
Sections for electrical towers
Third prepre-requisite: Functionality of sections due to extrusion
Third prepre-requisite: Functionality of sections due to extrusion
“The connecting systems among different component are simplified,thus improving joint details” details”
2
1
3
4
2
2
2
4
3 1
1 Sections for crane structures
Third prepre-requisite: Functionality of sections due to extrusion
Sections used in the building for agriculture
Building for agriculture
Third prepre-requisite: Functionality of sections due to extrusion
Industrial building
Third prepre-requisite: Functionality of sections due to extrusion
Section of the upper chord
Section for innovative floor structure
Welded connections
FIELDS OF STRUCTURAL APPLICATIONS
Bolted connections
x x x x x x x x x x x
C S to r a g e v e sse ls L a m p c o lu m n s P r o file d r o o f a n d w a ll c la d d in g S u p p o r t fo r r a ilw a y o v e r h e a d e le c tr ific a tio n E n c lo s u r e s tr u c tu r e s fo r sew ag e w ork s S o u n d b a r rie rs V e h ic le r e str a in t syste m s S e w a g e p la n t b r id g e s* S ilo s* T r a ffic s ig n a l g a n tr ie s * T r a ffic s ig n a l p o le s *
x x x x x x
x
x x x x x x x x x x x x x x x x x
C +F D om es over sew ag e ta n k s* M a r in a la n d in g sta g e s R o o f a c c e ss sta g in g D a m lo g s C u r ta in w a llin g O v e r c la d d in g su p p o r t syste m s P e d e str ia n p a r a p e ts C h ic k e n h o u se str u c tu r e s W o o d d ryin g k iln s S p a c e stru c tu re s (d o m e s, e tc .)* E x h ib itio n sta n d s* S w im m in g p o o l r o o fs * C a n o p ie s B u s sh e lte r s G r e e n h o u se s/G la ss h ou ses*
C +L L ig h tin g c o n tr o l to w e r s F la g p o le s A ir c r a ft a c c e s s b r id g e s T r a n sm issio n to w e r s B r id g e in sp e c tio n g a n trie s O ffs h o r e s tr u c tu r e s (liv in g q u a r te r s, b r id g e s)* T a n k flo ta tio n covers
C +F+L G r a tin g p la n k s H e lid e c k s*
x x x x x x x x x x
x x x x x x x
x x x x x x
F P r e fa b r ic a te d b a lc o n ie s* C o n v e yo r b e lt str u c tu r e s M o n o r a ils R obot su p p ort str u c tu r e s S h u tte r in g fo r m w ork T u n n e l sh u tte r in g
x x x x x x x x x x x
L C ran e boom s L o r r y m o u n te d c r a n e s P it p r o p s B r id g e s* M o b ile b r id g e in sp e c tio n g a n trie s S c a ffo ld in g s y s te m s L adders C h e r r y p ic k e rs T e le s c o p ic p la tfo r m s M a s ts fo r te n ts
F+L A ccess ram p s S u p p o r t fo r s h u tte r in g T r a c k w a ys (te m p o r a r y) E le v a to r s fo r b u ild in g m a te r ia ls S c a ffo ld p la n k s T re n c h su p p o rts G r a v e d ig g in g su p p o rts L o a d in g r a m p s L a n d in g m a ts fo r a ir c r a ft A ccess g an g w ays S h u tte r in g su p p o r t beam s M ilita r y b r id g e s* R a d io m a sts S h u tte r in g T e le sc o p ic c o n v e yo r b e lt str u c tu r e s G r a n d sta n d str u c tu r e s (tem p o ra ry) B u ild in g m a in te n a n c e g a n tr ie s F a b ric str u c tu r e fr a m e s
T a b le 1 .1 : T h e m a in s tr u c tu r a l a p p lic a tio n s o f a lu m in iu m a llo y s in s tr u c tu r a l e n g in e e r in g
Technical references
FIELDS OF APPLICATION IN CIVIL ENGINEERING Long span roof systems (reticular (reticular schemes of plane and space structures) structures) , where live load is small compared to dead load Structures located in corrosive or humid environments (swimming pool roofs,river bridges,hydraulic plants,offplants,off-shore superstructures) superstructures) Structures with moving parts,so that the lightness means economy during service (moving (moving bridges on rivers or channels,rotating crane bridges on circular pools in sewage plants) plants) Special purpose structures for which maintenance operations are particularly difficult (masts,lighting (masts,lighting towers,motorway sign portals) portals) Structures situated in inaccessible places far from the fabrication shop,so the transport economy and ease erection are extremelly important (electrical (electrical transmission towers,stair cases,provisional bridges) bridges)
Competition between steel and aluminium
Reference from literature
Charles Dickens (1812(1812-1870) 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”.
THANK YOU VERY MUCH FOR YOUR KIND ATTENTION
Reference from literature
Jules Verne (1844(1844-1896),the father of modern science fiction, wrote “From Earth to the Moon” Moon”: “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”.
FIELDS OF APPLICATION F. Mazzolani University of Naples "Federico II"
ALUMINIUM STRUCTURES IN THE FIELD OF CIVIL ENGINEERING :
ALUMINIUM ALLOY STRUCTURES: FIELDS OF APPLICATION Federico M. Mazzolani (Chairman of TC 250250-SC9)
BUILDINGS SPECIAL STRUCTURES BRIDGES REFURBISHMENT ENVELOPS ( FACADES )
Department of Structural Analysis and Design Faculty of Engineering University of Naples “Federico II” II”
ALUMINIUM PREFABRICATED STRUCTURES BUILDINGS : -prefabricated structures -plane structures -reticular space structures -domes
“Trelement” Trelement” building system (Germany)
‘50
Prefabricated clubclub-house (France) France) ALUMINIUM PREFABRICATED STRUCTURES
Prefabricated rural building (Italy) ALUMINIUM PREFABRICATED STRUCTURES
ALUMINIUM PREFABRICATED STRUCTURES
Prefabricated - aluminium house (Tokyo, 2000)
ALUMINIUM PREFABRICATED STRUCTURES
ALUMINIUM PREFABRICATED STRUCTURES
Provisional Exhibition Hall (Udine, Italy,2002) Italy,2002)
ALUMINIUM PREFABRICATED STRUCTURES (EDENBLUE SYSTEM)
Provisional Exhibition Hall (London, England, England, 2002)
ALUMINIUM PREFABRICATED STRUCTURES (EDENBLUE SYSTEM)
ALUMINIUM PREFABRICATED STRUCTURES (EDENBLUE SYSTEM)
ALUMINIUM PREFABRICATED STRUCTURES (EDENBLUE SYSTEM)
ALUMINIUM PLANE STRUCTURES
ALUMINIUMALUMINIUM-TIMBER STRUCTURE FOR INTERNAL MEZANINE
ALUMINIUM PLANE STRUCTURES
Rolling mill roof (Krenzlingen, Krenzlingen, CH )
ALUMINIUM PLANE STRUCTURES
Hangar (Hatfield, England)
ALUMINIUM PLANE STRUCTURES
Sporthall (Gand, Belgium)
ALUMINIUM PLANE STRUCTURES
Warehouse (Antwerp, Belgium)
ALUMINIUM PLANE STRUCTURES
ALUMINIUM PLANE STRUCTURES
Melsbroek airport (Brussels, Belgium)
ALUMINIUM PLANE STRUCTURES
Lecheria la Gran Via inSincelejo City (Colombia)
Roof of the tribune of the football stadium in Guayaquil (Equador) (Equador)
ALUMINIUM PLANE STRUCTURES
ALUMINIUM PLANE STRUCTURES
Urban Ricreation Center“ Center“Compensar” Compensar” (CUR) in Bogotà Bogotà (Colombia)
SwimmingSwimming-pool roof in Bogotà Bogotà (Colombia)
ALUMINIUM PLANE STRUCTURES
ALUMINIUM PLANE STRUCTURES
Aluminium Center in Utrecht(Holland)
Universidad del Norte in Barranquilla (Colombia)
“The Aluminium Forest” Forest”: 368 tubolar columns
ALUMINIUM PLANE STRUCTURES
Aluminium Center Micha de Haas
in Utrecht(Holland)
2.36 m
Number of nodes 13 724 Number of bolts 550 000 Number of bars 56 820 (total length 300 km)
ALUMINIUM RETICULAR SPACE STRUCTURES
14 m
Weigth 16 kg/mq
Erection phases of the Interamerican Exhibition Center of San Paulo (Brazil ,1969) (Brazil,1969)
Mash 60x60 ;erection ;erection time 27 hours
Covered area 67 600 mq
THE INTERAMERICAN EXHIBITION CENTRE ( SAN PAOLO, BRASIL)
THE INTERAMERICAN EXHIBITION CENTRE OF SAN PAOLO (BRASIL)
The International Congress center of Rio de Janeiro (Brazil)
THE INTERAMERICAN EXHIBITION CENTRE OF SAN PAOLO (BRASIL)
Industrial buildings (Brazil)
ALUMINIUM RETICULAR SPACE STRUCTURES
Guaymaral Country Club Bogotà Bogotà (Colombia)
Library “Luis Angelo Arango” Arango” Bogotà Bogotà (Colombia)
ALUMINIUM RETICULAR SPACE STRUCTURES
ALUMINIUM RETICULAR SPACE STRUCTURES
Hatogrande Country Club Bogotà Bogotà (Colombia)
Mall in Bogotà Bogotà (Colombia)
ALUMINIUM RETICULAR SPACE STRUCTURES
ALUMINIUM RETICULAR SPACE STRUCTURES
Traffic Office in Zapaquirà Zapaquirà (Colombia)
Swimming pool in Zerrezuela (Colombia)
ALUMINIUM RETICULAR SPACE STRUCTURES
ALUMINIUM RETICULAR SPACE STRUCTURES
Colegio Agustiniano in Bogotà Bogotà (Colombia) Centro Comercial “Salitre Plaza” Plaza”in Bogotà Bogotà
ALUMINIUM RETICULAR SPACE STRUCTURES
ALUMINIUM RETICULAR SPACE STRUCTURES
Empresas Publicas de Medellin
Building in Cali (Colombia)
ALUMINIUM RETICULAR SPACE STRUCTURES
ALUMINIUM RETICULAR SPACE STRUCTURES
THE PALASPORT OF QUITO (EQUADOR)
The Memorial Pyramid in La Baie (Quebec, Canada)
ALUMINIUM RETICULAR SPACE STRUCTURES
Shanghai Pudong Natatorium
THE MEMORIAL OF LA BAY (QUEBEC)
A 42,000 sq. ft. double layer grid vault roof
Shanghai Opera House
ALUMINIUM RETICULAR SPACE STRUCTURES IN ITALY
Conference Centre, Glasgow
Incenerator, Incenerator, London
Lords cricket ground, London Millenion Stadium, Walles
The structure of the Congress Center of Alghero
A proposal for the roof of the Olimpic Stadium in Rome (1990)
THE GEOGEO-SYSTEM (ITALY)
FULL SCALE TEST
“MERCATI TRAIANEI” TRAIANEI” MUSEUM (ROME)
“MERCATI TRAIANEI” TRAIANEI” MUSEUM (ROME)
Before restoration
After restoration
“MERCATI TRAIANEI” TRAIANEI” MUSEUM (ROME) “MERCATI TRAIANEI” TRAIANEI” MUSEUM (ROME)
Plane reticular space structure
“MERCATI TRAIANEI” TRAIANEI” MUSEUM (ROME)
Reticular geodetic dome
Reticular cylindrical vaults
“MERCATI TRAIANEI” TRAIANEI” MUSEUM (ROME)
Reticular geodetic dome
“MERCATI TRAIANEI” TRAIANEI” MUSEUM (ROME)
ALUMINIUM DOMES
ThreeThree-directional reticulated arches
ALUMINIUM DOMES
ALUMINIUM DOMES
Diameter 61 m
Diameter 110 m Weigth 24 kg/mq kg/mq
Dome of Discovery built in London for the Festival of Britain (1951)
ALUMINIUM DOMES
The geodetic dome of Guayaquil (Equador)
The Palasport of Paris (1959)
ALUMINIUM DOMES
Scientific Station at the South Pole
ALUMINIUM DOMES
ALUMINIUM DOMES
Industrial plants
The Conservatex system (USA): erection phases
ALUMINIUM DOMES
Epcot Center (Florida)
The TEMTEM-COR system (USA)
ALUMINIUM DOMES
Baylor University Ferrell Events Center (Waco, Texas)
The TEMTEM-COR system (USA)
The Conservatex system (USA): applications
housing
ALUMINIUM DOMES
Bell County Arena (Temple, Texas)
The TEMTEM-COR system (USA)
ALUMINIUM DOMES
University of Connecticut
The TEMTEM-COR system (USA)
ALUMINIUM DOMES
Spruce Goose Dome: Dome: erection phases
The “Spruce Goose” Goose” is the world’ world’s largest clearclear-span aluminium dome 415 feet in diameter (Long Beach, California)
ALUMINIUM GEODETIC DOMES FOR COAL STORAGE
The “Spruce Goose Dome” Dome” (Long Beach,California)
ALUMINIUM GEODETIC DOMES FOR COAL STORAGE
ALUMINIUM GEODETIC DOMES FOR COAL STORAGE
The “TEMTEM-COR” COR” dome in Taiwan
ENEL - CIVITAVECCHIA
The collapse of the “Geometrica” dome in Taiwan
The “Geometrica” Geometrica” dome in Taiwan
ALUMINIUM SPECIAL STRUCTURES
Motorway signs Electrical towers Lighting towers Antenna towers Hydraulic struct. Off-shore struct. Helydecks
ALUMINIUM SPECIAL STRUCTURES
Electrical transmission towers and typical extruded crosscross-sections
ALUMINIUM SPECIAL STRUCTURES
Motorway sign supports
ALUMINIUM SPECIAL STRUCTURES
Lighting towers
ALUMINIUM SPECIAL STRUCTURES
Aluminium towers in Naples (Italy) Italy)
100 years aluminium price THE TOWER FOR PARABOLIC ANTENNAS OF THE ELECTRICAL DEPARTMENT IN NAPLES
The Enel Tower: fabrication phases The Enel Tower: fabrication phases
The Enel Tower: Tower: fabrication phases
ENEL aluminium tower in Naples : erection phases
“INFORMATION “ TOWER “TIME EVULUTION” EVULUTION” TOWER
“MEMORY” MEMORY” TOWER
The Enel Tower : details
THE TOWERS OF TECCHIO’ TECCHIO’s SQUARE IN NAPLES
ALUMINIUM HYDRAULIC STRUCTURES
Reservoir: erection phases
Pipeline
The “Information” Information” Tower (Naples)
ALUMINIUM HYDRAULIC STRUCTURES
ALUMINIUM HYDRAULIC STRUCTURES
Sewage plant (Po Sangone, Sangone, Turin) Turin)
ALUMINIUM OFFOFF-SHORE STRUCTURES
bridges
ALUMINIUM OFFOFF-SHORE STRUCTURES
Helideck
Phases of fabrication
Helidecks
Helidecks
ALUMINIUM MOTORWAY BRIDGES
Motorway bridges Composite bridges Moving bridges Foot bridges Military bridges Marina bridges Floating bridges Bridge refurbishment Structural restoration
ALUMINIUM BRIDGES
Arvida bridge in Quebe (Canada , 1950 – L = 150 m)
Motorway bridge (France)
Motorway bridge (The Netherlands)
Moving Bridge at the Aberdeen Harbour
Motorway bridges
Composite aluminium – concrete bridges : sections, test and theory
Moving bridges over the Göta channel (Sweden)
Bascule bridge (1967): the first road bridge in aluminium ; 4m wide and 8,1 m span.
HandHand-pushed bridge Continuous bridge with swing span
Moving foot bridges
Foot bridges
Moving foot bridge in Oldersum (Germany)
Foot bridge in HemHem-Lenglet (France)
Foot bridges
Amsterdam (NL)
Villepinte (F)
The Gold Creek Footbridge -Valdez, Alaska (USA)
Foot bridges
Foot bridge in Jonquié Jonquiére (Quebec, Canada)
A cablecable-stayed foot bridge, designed for the City of Science in Naples (Italy)
Foot bridges
ALUMINIUM BRIDGES
Military bridges
A cablecable-stayed foot bridge, designed for the City of Science in Naples (Italy)
U.K. bridges
Swedish military bridge Kb 71
German military bridge (Dornier): erection phases
old cross-section
Joint
new cross-section FSW
Friction Stir Welding, FSW
FSW
Backing bar
MIG
FSW
MIG
FSW
MIG FSW
Tool shoulder Welding pin with special profile
friction stir weld
Weld
Length 20 m with a theoretical span of 19 m Bridge depth is 0,71 m
Marina applications
Marina applications
Marina applications
Marina applications
Floating road in Holland (2003)
Floating bridge with aluminium deck Sweden ( 1989 )
“The new Waterway”
DECK REPARATION Paving
250 mm
6 mm Acrydur, Acrydur, or
Weight
Grooves and tongues (no welds)
50 mm
40 mm poured asphalt Aluminium deck : 50 - 70 kg/m2
Span 1,0 m
: 600 - 700 kg/m2
Concrete deck
Large deck profiles 100 mm
300 mm
Span 2,8 m
Extruded decks
DECK REPARATION
Old bridge cut in parts and lifted away
100 kN
0 ?
-1
?
?
Deflection [mm]
?
-2
? ?
-3 Test
-4 ?
-5
? ?
-7
Theory
?
-6 c
L
Test on extruded decks
Deck
Modell
New bridge with aluminium deck
Deck reparation
STRUCTURAL RESTORATION OF SUSPENSION BRIDGES BY MEANS OF ALUMINIUM ALLOYS before
Substitution of r.c. deck with aluminium deck
after
THE MONTEMERLE BRIDGE
L= 80 + 80 m THE MONTEMERLE BRIDGE ON THE SOANE RIVER (FRANCE)
ON THE SOANE RIVER (FRANCE)
THE TREVOUX BRIDGE ON THE SAONE RIVER (FRANCE)
THE MONTEMERLE BRIDGE ON THE SOANE RIVER (FRANCE)
THE TREVOUX BRIDGE ON THE SAONE RIVER (FRANCE)
L= 80 + 80 m
L= 80 + 80 m
THE TREVOUX BRIDGE ON THE SAONE RIVER (FRANCE)
THE GROSLÈ GROSLÈE BRIDGE ON THE RÔNE RIVER (FRANCE)
THE TREVOUX BRIDGE ON THE SAONE RIVER (FRANCE)
L= 175 m
THE GROSLÈ GROSLÈE BRIDGE ON THE RÔNE RIVER (FRANCE)
THE GROSLÈ GROSLÈE BRIDGE ON THE RÔNE RIVER (FRANCE)
THE GROSLÈ GROSLÈE BRIDGE ON THE RÔNE RIVER (FRANCE)
STRUCTURAL RESTORATION OF THE “REAL FERDINANDO” FERDINANDO” BRIDGE : the first iron suspension bridge in Italy
THE “REAL FERDINANDO” FERDINANDO” BRIDGE ON THE GARIGLIANO RIVER (ITALY)
THE “REAL FERDINANDO” FERDINANDO” BRIDGE ON THE GARIGLIANO RIVER (ITALY)
Designer : Luigi Giura
Design data (geometry (geometry)) The “Maria Cristina” Cristina” Bridge on the Calore river (1835)
The “Real Ferdinando “Bridge on the Garigliano river (1832)
THE “REAL FERDINANDO” FERDINANDO” BRIDGE ON THE GARIGLIANO RIVER (ITALY)
Design data (loads (loads and stresses) stresses)
THE “REAL FERDINANDO” FERDINANDO” BRIDGE ON THE GARIGLIANO RIVER (ITALY)
Erection data (1828 – 1832)
Dead load : 260 kg/mq Live load : 240 kg/mq Maximum axial force in chains : 500 t Maximum stress in iron chains : 15 kg/mmq kg/mmq Strength of stone : 600 kg/cmq kg/cmq
THE “REAL FERDINANDO” FERDINANDO” BRIDGE ON THE GARIGLIANO RIVER (ITALY)
L = 85 m Distance between suspension chains 5,83 m Vertical ties every 1.37 m Two longitudinal iron beams with rectangular crosscrosssection Transversal wooden beams every 1,73 m Two couples of piers made of calcar stone Chain ancorage at 24 m from piers and 6 m depth Chains made of pinned iron plated elements
Work period : four years Iron : 70 000 kg Cost : 75 000 ducats Loading test : 2 groups of lancers 16 artillery carriages Proof engineer : king Ferdinand II (!)
Before 1944
Special device for connecting the chains to the piers
THE” THE”REAL FERDINANDO” FERDINANDO” BRIDGE ON THE GARIGLIANO RIVER (ITALY)
THE “REAL FERDINANDO” FERDINANDO” BRIDGE
THE “REAL FERDINANDO” FERDINANDO” BRIDGE
The piers
1944 - 1990
The top of the pier
The chain
THE “REAL FERDINANDO” FERDINANDO” BRIDGE
THE “REAL FERDINANDO” FERDINANDO” BRIDGE
The design
of restoration
The sphinx
THE “REAL FERDINANDO” FERDINANDO” BRIDGE
THE “REAL FERDINANDO” FERDINANDO” BRIDGE
Basis criteria for the structural restoration design
Results of the numerical analysis
The structural scheme gives a good performance under uniformelly distributed vertical loads only Due to the “mechanism” mechanism” feature of the structural scheme , it is too flexible under non symmetrical loading conditions The lack of bracing systems makes it unable to resist horizontal actions (wind , earthquake) earthquake) without large deflections The design live load (240 kg/mq) is too low even for pedestrian use
Conservation of the original shape : consolidation of piers ; keep the same shape of chains (two groups per sides) sides) ; keep the same spanning among the vertical ties , corresponding to the mash of the rails ; keep the same structural scheme of the deck.
Increase the flexural stiffness both vertical and horizontal: horizontal:
main longitudinal Vierendeel beams , whose mash corresponds to the vertical ties ; rigid transversal beams ; horizontal cross bracings with a mash of 5.83x(3x1,37) m.
Use of modern technologies and materials :
high strength steel for cables ; use of aluminium alloys instead of steel for deck.
THE NEW “REAL FERDINANDO” FERDINANDO” BRIDGE
THE NEW “REAL FERDINANDO” FERDINANDO” BRIDGE
The structures of the deck
THE NEW “REAL FERDINANDO” FERDINANDO” BRIDGE
Lateral supports and horizontal bracings
THE NEW “REAL FERDINANDO” FERDINANDO” BRIDGE
NON STRUCTURAL APPLICATIONS: FACADES AND ENVELOPS
1998 : the first aluminium bridge in Italy
ARCHITECTURAL COMPETITION
Sustainable Mediterranean architecture with aluminium facades
SELFRIDGES MALL IN BIRMINGHAM (Jan Kaplicky) Kaplicky) : Envelop made of 15 000 aluminium disquettes
ARCHITECTURAL
ARCHITECTURAL
COMPETITION
COMPETITION
before
after
THANK YOU VERY MUCH FOR YOUR KIND ATTENTION
The winner The Touring Hotel ( Italy )
STRENGTH AND STABILITY (PART 1.1) T. Höglund Torsten Höglund HB
EUROCODES
Design values of loads and resistances
EUROCODES
Design of aluminium members
Background and Applications
Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
1
Brussels, 18-20 February 2008 – Dissemination of information workshop
2
Design values of loads are given in Eurocode 0 and 1. Eurodode 9 gives the design values of resistance at the ultimate limit state, e.g.
M Rd =
Design of aluminium members according to EN 1999-1-1 Torsten Höglund Royal Institute of Technology Stockholm
M Rk
γM
=
Wel f o
(class 3 cross section)
γ M1
M Rd
design value of bending moment resistance
M Rk
characteristic value of bending moment resistance
f o = Rp0.2 γ M1 = 1,1
characteristic value of 0,2 % proof strength
Wel
section modulus
partial factor for general yielding
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.
EUROCODES
EUROCODES
Design values of loads and resistances
Background and Applications
Material properties
Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
3
Brussels, 18-20 February 2008 – Dissemination of information workshop
4
In a section with reduced strength due to welding (heat affected zone, HAZ)
M Rd =
Wel ρ u,haz f u
(in a section with HAZ across the section)
γ M2
M Rd
design value of bending moment resistance
fu
characteristic value of ultimate strength
γ M2 = 1,25 partial factor for failure ρ u, haz
reduction factor for the ultimate strength in HAZ
Part of Table 3.2 b.
EUROCODES Background and Applications
EUROCODES
Design of aluminium profiles
Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
5
Cross section class 3, 2 and 1
Brussels, 18-20 February 2008 – Dissemination of information workshop
6
m
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).
Local buckling behaviour / cross section class 4 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/t where b is the width and t is the thickness of the cross section part. 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.
m
f0,2
Collapse load
(4)
>
3
2
100 a Non uniform stresses
Reduction of weld length With positive root penetration: a = 1,2 a or a + 2 mm or a = a + apen (verified by testing)
Design of joints
EUROCODES Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
Design of joints
EUROCODES Background and Applications
33
Forces acting on a fillet weld
Brussels, 18-20 February 2008 – Dissemination of information workshop
34
Design strength fillet weld •
Stresses Æ comparison stress σc:
σ C = σ 2 + 3(τ 2 + τ
•
Throat section
2
)
Design stresses:
σC ≤
fw
γ Mw
Stresses σ , τ and τ , acting on the throat section of a fillet weld
Design of joints
EUROCODES Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
Design strength HAZ •
Tensile force perpendicular to failure plane
•
HAZ butt welds
σ≤ σ≤
fa,HAZ
γ Mw fa,HAZ ⋅ t e γ Mw ⋅ t
Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
(Partial penetration butt welds)
te = effective throat thickness fa,HAZ = Characteristic strength HAZ
36
HAZ fillet welds σ≤ σ≤
(Full penetration butt welds)
Design of joints
EUROCODES 35
fa,HAZ
γ Mw
fa,HAZ ⋅ te g1 γ Mw ⋅ t t
(Toe of the weld, full cross-section) (At the fusion boundary)
g1
For shear forces and combined tensile / shear forces similar rules apply
Design of joints
EUROCODES Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
Design of joints
EUROCODES Background and Applications
37
Design of connections with combined welds
Brussels, 18-20 February 2008 – Dissemination of information workshop
38
Bolted and riveted connections Positioning of holes
Two approaches Direction of load transfer
1. Welds designed for stresses in parent metal of the different parts of the joint Æ Linear Elastic Approach 2.
Loads acting on joint are distributed to the welds that are most suited to carry them Æ Plastic Approach
End distance e1: min. 1,2 d Edge distance e2: max. 4 t + 40 mm Æ corrosion environment 12 t + 150 mm Æ no corrosion Spacing p1: min. 2,2 d Spacing p2: min. 2,4 d
Design of joints
EUROCODES Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
max. 14 t or 200 mm
Design of joints
EUROCODES Background and Applications
39
Brussels, 18-20 February 2008 – Dissemination of information workshop
40
Categories of bolted connections
Design resistance of bolts
Shear connections • Category A: Bearing type
•
• •
– –
Fv ,Rd =
Shear resistance Bearing resistance
Category B: Slip-resistant at serviceability limit state –
Fv ,Rd =
Add. check at ult. limit state: shear and bearing
Category C: Slip-resistant at ultimate limit state –
•
Add. check: shear and bearing
–
•
Tension resistance
Category E: Preloaded high strength bolts –
Design of joints
EUROCODES Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
Distribution of forces between fasteners
γ Mb
0,5fub A
γ Mb
Strength grades lower than 10.9 Strength grade 10.9, stainless steel bolts, aluminium bolts
2,5αfu dt
γ Mb
α smallest of:
0,9fub As
γ Mb
EUROCODES Background and Applications
41
e1 p1 1 f ; − ; ub or 1,0 3d0 3d0 4 fu
Tension resistance
Ft ,Rd =
Tension resistance
0,6fub A
Bearing resistance
Fb,Rd =
Tension connections • Category D: non-preloaded bolts
•
Shear resistance per shear plane:
Design of joints
Brussels, 18-20 February 2008 – Dissemination of information workshop
Deductions for fastener holes
p
For compression members: no deductions for fastener holes
42
Design of joints
EUROCODES Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
Background and Applications
High strength bolts in slipresistant connections Preloaded bolts Surface treatments
Design of joints
EUROCODES 43
Brussels, 18-20 February 2008 – Dissemination of information workshop
44
Design of adhesive lap joints
force transfer by friction between clamped surfaces friction grip or slip-resistant connections
Design slip resistance: Fs,Rd =
nmµ
γ Ms
Fp,cd
Fp,cd = 0,7fub As
n = number of friction surfaces m = factor; m = 1,0 for nominal clearance holes µ = slip factor; µ = 0,27 up to 0,40 ÆΣt γMs = 1,25 for ultimate limit state 1,10 for serviceability limit state
Controlled tightening
EUROCODES Background and Applications
Design of joints
Brussels, 18-20 February 2008 – Dissemination of information workshop
Design of joints
EUROCODES Background and Applications
45
Strength of adhesive joints
Brussels, 18-20 February 2008 – Dissemination of information workshop
46
Adhesive bonded joints •
Design guidance applicable for: – – –
•
Shear forces Appropriate adhesives Specified surface preparation
Structural application: characteristic shear strength values fvADH:
Adhesive types
fvADH [N/mm2]
1-component epoxy
35
2-component epoxy
25
Higher values are allowed when demonstrated by tests
2-component acrylic 20
•
EUROCODES Background and Applications
Design of joints
Brussels, 18-20 February 2008 – Dissemination of information workshop
Design shear stress: σ =
EUROCODES Background and Applications
47
fv , ADH
γ M ,adh
where:
γ M ,adh = 3,0
Final remarks
Brussels, 18-20 February 2008 – Dissemination of information workshop
Hybrid connections
Final remarks
•
Different fasteners combined such as bolts and welds
•
Research resulted in up-to-date design rules
Unequal stiffness of different fasteners:
•
Design rules available for structural connections - welds
•
– –
•
Only higher stiffness fastener is acting Only design strength of stiffest fastener is taken into account
- bolts and rivets
- adhesives When fasteners act at the same time: design strengths may be summarised
•
EC9 important design tool for aluminium structures
48
COLD-FORMED STRUCTURES (PART 1.4) R. Landolfo University of Naples "Federico II"
EUROCODES Background and Applications
EUROCODES
Cold-Formed Structures (Part 1.4)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Cold-Formed Structures (Part 1.4)
Background and Applications
1
Brussels, 18-20 February 2008 – Dissemination of information workshop
2
BACKGROUND The European code for the design of aluminium structures, Eurocode 9, 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
Cold-Formed (CF) Structures Eurocode 9 - Part 1.4 Prof. Raffaele Landolfo University of Naples “Federico II”
EUROCODES Background and Applications
EUROCODES
Cold-Formed Structures (Part 1.4)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODE 9 – PART 1.4: CONTENT
Cold-Formed Structures (Part 1.4)
Background and Applications
3
EN 1999-1-4 2006 November
Brussels, 18-20 February 2008 – Dissemination of information workshop
4
BACKGROUND BASIC TYPES OF THIN-WALLED ELEMENTS
1 INTRODUCTION
The following basic types of thin-walled elements are identified in the classification process:
2 BASIS OF DESIGN 3 MATERIALS
• flat outstand element; • flat internal element; • curved internal element.
4 DURABILITY 5 STRUCTURAL ANALYSIS 6 ULTIMATE LIMIT STATES 7 SERVICEABILITY LIMIT STATES
These elements can be:
8 JOINT WITH MECHANICAL FASTENERS 9 DESIGN ASSISTED BY TESTING ANNEX A – TESTING PROCEDURES
- unreinforced, or - reinforced
ANNEX B – DURABILITY OF FASTENERS
by longitudinal stiffening ribs or edge lips or bulbs
EUROCODES Background and Applications
EUROCODES
Cold-Formed Structures (Part 1.4)
Brussels, 18-20 February 2008 – Dissemination of information workshop
BACKGROUND
Brussels, 18-20 February 2008 – Dissemination of information workshop
6
BACKGROUND SLENDERNESS OF UNREINFORCED FLAT ELEMENTS
BASIC TYPES OF THIN-WALLED ELEMENTS Unreinforced elements
Cold-Formed Structures (Part 1.4)
Background and Applications
5
Reinforced 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 where: b d t g
outstand element internal element
is is is is
or
the the the the
β = g d/t
width of an element; depth of a web element; element thickness; stress gradient coefficient, given by the expressions
EUROCODES
EUROCODES
Cold-Formed Structures (Part 1.4)
Background and Applications
Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
7
BACKGROUND
Cold-Formed Structures (Part 1.4)
Brussels, 18-20 February 2008 – Dissemination of information workshop
8
BACKGROUND
SLENDERNESS OF UNREINFORCED FLAT ELEMENTS
SLENDERNESS OF UNREINFORCED FLAT ELEMENTS Relationship defining the stress gradient coefficient (g):
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 where: b d t g
is is is is
Where ψ is the ratio of the stresses at the edges of the plate under consideration related to the maximum compressive stress.
β = g d/t
or
the the the the
g = 0.70 + 0.30 ψ g = 0.80 / (1 + ψ)
width of an element; depth of a web element; element thickness; stress gradient coefficient, given by the expressions
stress gradient coefficient vs. ψ coefficient
EUROCODES Background and Applications
EUROCODES
Cold-Formed Structures (Part 1.4)
Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
9
BACKGROUND
Cold-Formed Structures (Part 1.4)
Brussels, 18-20 February 2008 – Dissemination of information workshop
10
BACKGROUND
SLENDERNESS OF UNREINFORCED FLAT ELEMENTS In 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
Elements in beams
Element classification as a function of: - β value - Member type -beam -strut
class 1
β1 < β ≤ β2
class 2
β2 < β ≤ β3
class 3
β2 < β ≤ β3
class 3
β3 < β
class 4
β3 < β
class 4
EUROCODES Background and Applications
class 1 or 2
f0: 0.2% proof strength in MPa
Coupled Local and Distortional buckling
EUROCODES
Cold-Formed Structures (Part 1.4)
Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
11
BACKGROUND Element classification as a function of: - β value - Member type -beam -strut
β ≤ β2
Limit parameters β 1, β 2 and β3 as function of: - Element type -Outstand -Internal - Alloy type -Buckling class (Class A, Class B) -Welded -Unwelded
ε = 250 / f 0 Distortional buckling
Elements in struts
β ≤ β1
Cold-Formed Structures (Part 1.4)
Brussels, 18-20 February 2008 – Dissemination of information workshop
12
SECTION PROPERTIES Elements in beams
Elements in struts
β ≤ β1
class 1
β ≤ β2
β1 < β ≤ β2
class 2
β2 < β ≤ β3
class 3
β2 < β ≤ β3
class 3
β3 < β
class 4
β3 < β
class 4
class 1 or 2
INFLUENCE 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.
Limit parameters β 1, β 2 and β3 as function of: - Element type -Outstand -Internal - Alloy type -Buckling class (Class A, Class B) -Welded -Unwelded
ε = 250 / f 0
f0: 0.2% proof strength in MPa
Notional widths of plane cross section parts bp allowing for corner radii
EUROCODES Background and Applications
EUROCODES
Cold-Formed Structures (Part 1.4)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Cold-Formed Structures (Part 1.4)
Background and Applications
13
Brussels, 18-20 February 2008 – Dissemination of information workshop
SECTION PROPERTIES
14
SECTION PROPERTIES
INFLUENCE OF ROUNDED CORNERS
INFLUENCE OF ROUNDED CORNERS According to the code provisions, the influence of rounded corners with internal radius r ≤ 10 t And r ≤ 0.15 bp on section properties might be neglected, and the cross-section might be assumed to consist of plane elements with sharp corners
Notional widths of plane cross section parts bp allowing for corner radii Approximate allowance for rounded corners
EUROCODES Background and Applications
EUROCODES
Cold-Formed Structures (Part 1.4)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Cold-Formed Structures (Part 1.4)
Background and Applications
15
Brussels, 18-20 February 2008 – Dissemination of information workshop
16
SECTION PROPERTIES
SECTION PROPERTIES
INFLUENCE OF ROUNDED CORNERS
GEOMETRICAL PROPORTIONS
According to the code provisions, the influence of rounded corners with internal radius r ≤ 10 t And r ≤ 0.15 bp on section properties might be neglected, and the cross-section might be assumed to consist of plane elements with sharp corners
The provisions of Eurocode 9 – Part 1.4 may be applied only to crosssections 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
Approximate allowance for rounded corners
EUROCODES Background and Applications
EUROCODES
Cold-Formed Structures (Part 1.4)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Cold-Formed Structures (Part 1.4)
Background and Applications
17
Brussels, 18-20 February 2008 – Dissemination of information workshop
18
LOCAL AND DISTORTIONAL BUCKLING
LOCAL AND DISTORTIONAL BUCKLING
GENERAL
GENERAL 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:
The effect of local buckling on each compression element of the cross-section shall be conventionally accounted by replacing the nonuniform 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).
ρ = 1.0 if
ω ρ= 1 λp
⎛ ω2 ⎜1 − ⎜ λp ⎝
λ p ≤ λlim ⎞ ⎟ if λ p ≤ λlim ⎟ ⎠
where λ p is the normalised plate slenderness: Actual normal stress distribution
Effective width
Reduced stress Effective thickness
λp =
λlim
f 0.2 b p = σ cr t
12 (1 − ν 2 ) f 0.2 π2 E kσ
≅ 1.052
bp t
f 0 .2 E kσ
which takes into account stress distribution and boundary conditions by means of the buckling factor kσ and: are numerical coefficients ω1 and ω2 is the limit value of the normalised slenderness which corresponds to ρ=1
EUROCODES Background and Applications
EUROCODES
Cold-Formed Structures (Part 1.4)
Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
19
Cold-Formed Structures (Part 1.4)
Brussels, 18-20 February 2008 – Dissemination of information workshop
LOCAL AND DISTORTIONAL BUCKLING
20
LOCAL AND DISTORTIONAL BUCKLING
GENERAL Parameters ω1, ω2 andλlim -Heat treated -Not heat treated -Welded σ -Unwelded
are given as function of Alloy type
LOCAL AND DISTORTIONAL BUCKLING - EUROCODE 9 PART 1.1 Part 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.
1
A heat-treated, B heat-treated, welded ; non heat-trated, 0.8
C non heat-treated,
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.
0.6
0.4
Landolfo and Mazzolani’s buckling curves
λlim
ω1
ω2
A
1.00
0.22
0.673
B
0.88
0.22
0.440
C
0.76
0.19
0.380
curve
0.2
LOCAL AND DISTORTIONAL BUCKLING - EUROCODE 9 PART 1.4
0 0
0.5
1
1.5
2
2.5
λ
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. p
SHELL STRUCTURES (PART 1.5) A. Mandara University of Naples "Federico II"
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
1
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
2
Aluminium shells – applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures A. Mandara Department of Civil Engineering Second 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
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
3
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
4
The EN1999-1-5 Annexes The EN1999-1-5 General part
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
EUROCODES Background and Applications
5
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
6
Shell configurations allowed for in EN1999-1-5 The prEN1993-1-6
r
β
β t
t
r1
x, u
r2
θ, v
w
r
φ w
θ
r
t
h
L
Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
l
EUROCODES
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
7
Types of shell analysis in EN1999-1-5
EUROCODES Background and Applications
EUROCODES Background and Applications
9
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
10
Parametric analysis: Shell geometrical data and material features
Background activity - Main investigated aspects
• shell plastic buckling • • • • •
8
Specific issues for aluminium alloy shells in EN1999-1-5
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
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;
EUROCODES Background and Applications
The ABAQUS model
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
11
12
Buckling response of axially loaded cylinders Carichi Assiali [KN]
Imperfection model
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
6000
R/t = 200 f 02 = 200 N/mmq Tipo Incastrato Imperfezione Asimmetrica
Pcr,th = 5293.38 KN 5000
4000 W0/t =0.01
3000
2000
1000 W0/t =3 ABAQUS 0 0
2
4
6
8
10
12
Carichi Assiali [KN]
Abbassam enti Assiali [m m ]
6000
R/t = 200 f 02 = 200 N/mmq Tipo Incastrato Imperfezione Assial-Simmetrica
Pcr,th = 5293.38 KN 5000
W0/t =0.01 4000
3000
2000
w = ∑ w0e
−k1 x ( x− xo )2
( x − xo ) ⎤ −k1 y ( y− yo )2 ( y − yo ) ⎤ ⎡ ⎡ e cos⎢k2 xπ cos ⎢k2 yπ L ⎥⎦ R ⎥⎦ ⎣ ⎣
1000
W0/t =3
ABAQUS 0 0
10
20
30
40
50
60
70
80
Abbassam enti Assiali [m m ]
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Background and Applications
13
Brussels, 18-20 February 2008 – Dissemination of information workshop
1,4
Cylinders under axial load Imperfection Sensitivity Curves
Pu /Pcr,th
Diagramma Carichi-Spostamenti Radiali 0.07
1,2
Pcr,th = 0.058 N/m m q
0.06
14
Imperfection sensitivity curves (axially loaded cylinders)
Deflected shapes at buckling (cylinders under uniform external pressure) Carichi Superficiali [N/mmq]
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
EUROCODES
Brussels, 18-20 February 2008 – Dissemination of information workshop
CLASS A
0.05
CLASS B
CLASS C
0.04
1,0
0.03 ABAQUS 0.02
R/t = 200 L/R=2 f 02 = 100 N/mmq W 0 = 0.1 mm Tipo Appoggiato
0.01
0,8
0 0
5
10
15
20
25
30
35
40
Spoatam enti Radiali [m m ]
0,6
Carichi Superficiali [N/mmq]
Diagramma Carichi-Spostamenti Radiali 0.07
Pcr,th = 0.058 N/m m q
0.06
0,4
R/t = 200 R = 1000 mm t = 5 mm 2 f02 = 200 N/mm P cr,th = 5293.38 KN
0.05
0.04
0,2
0.03 ABAQUS
σ cr,th = 168.49 N/mm 2
0.02
R/t = 100 L/R=2 f 02 = 100 N/mmq W 0 = 0,75 mm Tipo Appoggiato
0.01
0
10
20
30
40
50
60
0,0
Spoatam enti Radiali [m m ]
EUROCODES Background and Applications
W0/t
0,0
0
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
0,2
EUROCODES Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
15
0,4
0,6
0,8
1,0
1,2
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
16
Imperfection sensitivity curves (cylinders under torsion)
Imperfection sensitivity curves (cylinders under external pressure) 1,0
1,0
Cylinders under external pressure Imperfection sensitivity curve
Pu /Pcr,th
0,8
Pu /Pcr,th 0,8
n=8 L = 1000 mm R= 1000 mm t= 10 mm R/t = 100 L/R=1 f02 = 100 N/mm2 n = 9
n=9
0,6
0,6
Pcr,th = 0.620 N/mm2
Class A
0,4
Class B
Class B
R/t = 200 L/R = 2 f02=200 N/mm2
Cylinders under torsion Imperfection sensitivity curve
0,2
t = 5 mm
τcr,th = 49.358 N/mm
W0/t
Pcr,th = 0.610 N/mm2
Class C
Longitudinal Imperfection Helical Imperfection
0,4
Class C
L = 1000 mm R= 1000 mm t= 10 mm R/t = 100 L/R=1 n=8 f02 = 100 N/mm2
0,2
Class A
2
W0/t
0,0
0,0 0,0
0,2
EUROCODES Background and Applications
0,4
0,6
0,8
1,0
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
0,0
0,2
EUROCODES Background and Applications
17
0,4
0,6
0,8
1,0
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
18
Semi-probabilistic interpretation of buckling data (axially loaded cylinders) - Weibull’s law
Semi-probabilistic interpretation of buckling data (axially loaded cylinders) - Weibull’s law 1.00
1.00
P(x)
P(x) = 1− e−(αx)
0.80
0.60
f02 = 200 N/mm
0.20
0.00 0.00
p (x) =
0.20
dP
C
C
A f02 = 200 N/mm2
0.60
Class A Class B Class C Weibull Curve A Weibull Curve B Weibull Curve C 5% Percentile Value
A
0.40
0.20
B
B
x 0.40
(x ) dx
0.80
2
Class A Class B Class C Weibull Curve A Weibull Curve B Weibull Curve C 5% Percentile Value
0.40
Cylinders under axial load Weak hardening alloys - R/t = 200-
P(x)
Cylinders under axial load Weak hardening alloys β - R/t = 100-
=
0.60
1 αβ
1 / α
x
(1
0.80 / α −1
)
e
−
(x
1.00 /β
)1 / α
x 0.00 0.00
p (x) =
0.20
dP
0.40
(x ) dx
=
0.60
1 αβ
1 / α
x
(1
0.80 / α −1
)
e
−
(x
1.00 /β
)1 / α
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
EUROCODES Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
19
Brussels, 18-20 February 2008 – Dissemination of information workshop
• shell plastic buckling • • • • •
20
Shell buckling – EC3 formulation
Background activity - Main investigated aspects
χ = 1 ⇔ λ ≤ λ0
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;
⎛ λ − λ0 χ = 1 − β ⎜⎜ ⎝ λ p − λ0
χ =
⎞ ⎟ ⎟ ⎠
η
⇔ λ0 < λ ≤ λ p
α ⇔ λp ≤ λ λ2
• 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)
Background and Applications
σ xRc
λp =
• imperfection sensitivity analysis of welded cylinders; • definition of simplified design procedures;
EUROCODES
f yk
λ =
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
EUROCODES Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
21
α 1− β
Brussels, 18-20 February 2008 – Dissemination of information workshop
Shell buckling – fabrication tolerance classes in EC3
22
Expressions of buckling factors according to EC3
t
r
A xial (meridional) load inward Δwox
λ0
Δwox
t gx
≤ U 0 m ax ⇔
gx
U
o m ax gx
EUROCODES Background and Applications
= 4
w o U 0 m ax ≤ t t
Dimple tolerance parameter
Rt
Gauge length
gx
Fabrication tolerance Description quality class Class A Excellent Class B High Class C Normal
Background and Applications
0.80 0.60
Minimum Value Medium Value Maximum Value 5%Percentile Value Experimental Value
Axial (meridional) load αx
Q 40 25 16
αx =
(
0.62
1 + 1.91 1 / Q r / t
)
1.44
αθ or ατ 0,75 0,65 0,50
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara) 24
Cylinders under external pressure Strong hardening alloys Quality class A EC3 Curve
0.8
L/R=2 R/T=200 L/R=2 R/T=100 L/R=2 R/T=50 L/R=1 R/T=200 L/R=1 R/T=100 L/R=1 R/T=50
Modified EC3 Curve
0.6 0.4
Cylinders under axial load Weak hardening alloys Quality Class C
0.00 0.00
χ
1.0
0.40 0.20
Excellent High Normal
External pressure (αθ) and torsion (shear) (ατ )
Comparison of EC3 buckling curves with simulation data 1.2
1.00
1.00
Brussels, 18-20 February 2008 – Dissemination of information workshop
Comparison of EC3 buckling curves with simulation data
EC3 Curve
0.60
1.00
EUROCODES 23
χ
0.60
η
Class A Class B Class C
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
1.20
β
Fabrication tolerance Description quality class
gx
w0
0.20
External pressure and torsion (shear) 0.40
L/R=4 R/T=200 L/R=4 R/T=100 L/R=4 R/T=50
Modified EC3 Curve
0.2
λ
λ 0.0
0.50
1.00
1.50
2.00
0.0
1.0
2.0
3.0
4.0
5.0
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
25
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Comparison of EC3 buckling curves with simulation data 1.2
χ
χ x = αχ
L/R=2 R/T=200 Imp. 1
Cylinders under torsion Weak hardening alloys Quality class C
1.0
L/R=2 R/T=200 Imp. 2
χ perf =
L/R=2 R/T=100 Imp. 1
0.8
L/R=2 R/T=50 Imp. 1
Alloy
f yk
λ=
1
σ xRc
φ + φ 2 − λ2
Axial (meridional) load α0 λ0 0.2 0.35 0.1 0.2
L/R=2 R/T=50 Imp. 2
Weak hardening alloys Strong hardening alloys
L/R=4 R/T=200 Imp. 2
0.4
perf
φ = 0 . 5 [1 + α 0 (λ − λ 0 ) + λ 2 ]
L/R=2 R/T=100 Imp. 2
0.6
26
Shell buckling - proposal for pr1999-1-5
External pressure λ0 α0 0.3 0.55 0.2 0.7
Shear (torsion) λ0 α0 0.5 0.3 0.4 0.4
L/R=4 R/T=100 Imp. 2 L/R=4 R/T=50 Imp. 2
0.2
EC3 Curve
λ
0.0 0.0
0.5
EUROCODES Background and Applications
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Fabrication tolerance D escription quality class Class A Excellent C lass B H igh Class C N orm al
EUROCODES Background and Applications
27
1.20
Minimum Value
χ
(
1 + 1 . 91 1 / Q r / t
)
1 .44
α θ or α τ
0,75 1 0,65 α θ , τ = 1 + 0, 2 1 − α ref λ − λ 0 / α 2ref 0,50
(
)(
)
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara) 28
Cylinders under external pressure Weak hardening alloys Quality class A
1.00
Medium Value Maximum Value
0.80
αx =
0 . 62
Buckling curves - proposal for EC9
1.20 1.00
40 25 16
External pressure (α θ ) and torsion (α τ ) α ref
αx
Brussels, 18-20 February 2008 – Dissemination of information workshop
Buckling curves - proposal for EC9
χ
A xial (m eridional) load Q
0.80
5% Percentile Value
0.60
0.60
L/R=2 R/T=200 L/R=2 R/T=100 L/R=2 R/T=50 L/R=1 R/T=200 L/R=1 R/T=100 L/R=1 R/T=50 L/R=4 R/T=200 L/R=4 R/T=100 L/R=4 R/T=50
0.40
0.40 Cylinders under axial load Weak hardening alloys Quality Class A
0.20
0.20
λ
λ 0.00 0.00
EUROCODES Background and Applications
0.50
1.00
1.50
2.00
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
0.00 0.00
EUROCODES Background and Applications
29
1.00 0.80 0.60
4.00
5.00
6.00
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
• shell plastic buckling
L/R=2 R/T=200 L/R=2 R/T=200 L/R=2 R/T=100 L/R=2 R/T=100 L/R=2 R/T=50 L/R=2 R/T=50 L/R=4 R/T=200 L/R=4 R/T=100 L/R=4 R/T=50
• • • • •
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;
0.40 0.20
λ 0.00 0.00
3.00
Background activity - Main investigated aspects
1.20 Cylinders under torsion Weak hardening alloys Quality class B
2.00
Brussels, 18-20 February 2008 – Dissemination of information workshop
Buckling curves - proposal for EC9
χ
1.00
1.00
2.00
3.00
4.00
5.00
• effect of welding effect (HAZ zones) • imperfection sensitivity analysis of welded cylinders; • definition of simplified design procedures;
30
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
EUROCODES Background and Applications
Brussels, 18-20 February 2008 – Dissemination of information workshop
31
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Exploitation of plastic buckling features (axially loaded cylinders)
32
Exploitation of plastic buckling features (axially loaded cylinders) 1,2
1,2 Pu /Pcr,th
Pu /Pcr,th A
1,0
B
C
A
1,0
B
C
Imperfection 1
Imperfection 1 0,8
0,8 2 0,6 0,4
σcr,th = 197.40 N/mm 0,2
0,0
0,4
σcr,th = 85.76 N/mm
2
0,2
clamped ends hinged ends
w0*/t
w0/t
4 2
w0/t
0,0
w0*/t
0,2
EUROCODES Background and Applications
0,4
0,6
0,8
1,0
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
0,2
Background and Applications
33
0,4
0,6
0,8
1,0
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
34
Exploitation of plastic buckling features (axially loaded cylinders) – Imperfection limit w0*/t 0.10
0.30 w0*/t
0,0
EUROCODES
Exploitation of plastic buckling features (axially loaded cylinders) – Imperfection limit w0*/t 0.27
3
R/t = 200 f 0.2 = 100 N/mm2 P cr,th = 2694.32 kN
4
clamped ends hinged ends
0,0
2 0,6
3
R/t = 50 f 0.2 = 200 N/mm2 P cr,th = 24806.01 kN
w0*/t
HINGED ENDS
CLAMPED ENDS
0.08
0.24 0.21 0.18
f 0.2 = 100 N/mm
0.15 0.12
f 0.2 = 200 N/mm
0.06
2
f 0.2 = 200 N/mm
2
2
f 0.2 = 100 N/mm
2
0.04
0.09
0.02
0.06 0.03
f 0.2 = 300 N/mm
f 0.2 = 300 N/mm
2
0.00
0.00 0
EUROCODES Background and Applications
50
100
150
200
250
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Description
Class A-plus
Excellent
Background and Applications
Class A Class B Class C
Very high High Normal
Fabrication tolerance quality class Class A-plus Class A Class B Class C
Q Description Clamped Hinged ends ends Excellent 60 50 Very high 40 High 25 Normal 16
150
200
250
300
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
1.20
Hinged ends 1 ⎛ t R⎞ + 0.02 ⎜5 ⎟ ⎜ f 0.2 ⎝ R t ⎟⎠ 0,006 0,01 0,016
36
χ
Minimum Value Medium Value Maximum Value 5% Percentile Value
EC3
1.00 0.80 0.60
Proposed EC9 Curve
Hinged ends
0.40
αx αx =
100
Exploitation of plastic buckling features (axially loaded cylinders) - Class A-plus buckling curves
Value of U0,.max (f0.2 in N/mm2) Clamped ends 1 ⎛ t R⎞ + 0.01 ⎜ 2.25 ⎟ ⎜ f 0.2 ⎝ R t ⎟⎠
50
EUROCODES 35
Exploitation of plastic buckling features (axially loaded cylinders) Definition of quality Class A-plus in prEN-1999-1-5 Fabrication tolerance quality class
0
300
Brussels, 18-20 February 2008 – Dissemination of information workshop
2
R/t
R/t
1 1.44
⎛ 1 0.6 E ⎞ λ − λx ,0 ) ⎟ 1 + 2.60 ⎜ ⎜ Q f 0,2 ( x ⎟ ⎝ ⎠
0.20 0.00 0.00
Cylinders under axial load Strong hardening alloys Quality Class A-plus
0.50
λ 1.00
1.50
2.00
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
37
38
Shell buckling – summary of EC9 formulation
Unstiffened shells
Shell buckling – summary of EC9 formulation
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Load cases • axial compression • external pressure • torsion Stiffened shells Axial (meridional) load λx,0 μx 0.2 0.35 0.1 0.2
Material buckling class A (Weak hardening alloys) B (Strong hardening alloys)
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
39
External pressure
Shear (torsion)
λθ,0 0.3 0.2
λτ,0 0.5 0.4
μθ 0.55 0.7
μτ 0.3 0.4
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Shell buckling – fabrication tolerance classes according to EC9
40
Background activity - Main investigated aspects
• shell plastic buckling • • • • •
Class 4 Class 3 Class 2 Class 1
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 Fabrication tolerance quality class Class 1 Class 2 Class 3 Class 4
Axial (meridional) load
16 25 40 50-60
Background and Applications
αref
αx
Q
EUROCODES
External pressure (αθ) and torsion (ατ)
αx =
(
0.62
1 + 1.91 1 / Q r / t
)
1.44
0,50 0,65 0,75 -
• imperfection sensitivity analysis of stiffened cylinders; • validation of EN1993-1-6 procedures and harmonization with EN1999 rules;
αθ or ατ α θ, τ =
(
1 + 0, 2 1 − αref
• effect of welding effect (HAZ zones)
1
) ( λ − λ0 ) / α2ref
• imperfection sensitivity analysis of welded cylinders; • definition of simplified design procedures;
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
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
EUROCODES Background and Applications
41
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Interaction between load cases ENV1993-1-6 formulation
42
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
43
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
44
Interaction between load case ENV 1993-1-6 – Interaction domains
Interaction between load case ENV 1993-1-6 – Interaction domains
Axial compression and External pressure
Axial compression and Torsion
τcr/τu
Pcr/Pu
σcr/σu
σcr/σu
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
45
Interaction between load case ENV 1993-1-6 – Interaction domains
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
46
Interaction between load cases prEN1993-1-6 formulation and proposal for prEN1999-1-5
External pressure and Torsion
τcr/τu
Pcr/Pu prEN1993-1-6
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
47
prEN1999-1-5
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
48
Interaction between load cases EN 1999-1-5 – Interaction domains
Interaction between load cases EN 1999-1-5 – Interaction domains
Axial compression and External pressure
Axial compression and Torsion
Pcr/Pu EC3 Class A
τcr/τu EC3
Class B
Class A
Class C
Class B
Class A
Class C
Class B
Class A
Class C
Class B
Proposal Class A
Class C
Proposal Class B
Proposal Class A
Proposal Class C
Proposal Class B Proposal Class C
σcr/σu
σcr/σu
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
49
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Interaction between load cases EN 1999-1-5 – Interaction domains
50
Interaction buckling check according to EC9
External pressure and Torsion
τcr/τu EC3 Class A Class B Class C Proposal Class A Proposal Class B Proposal Class C
Pcr/Pu
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
51
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Stiffener section
• shell plastic buckling • • • • •
52
Parametric analysis – Stiffened shells
Background activity - Main investigated aspects
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;
Shell geometry
Circular R/t=50
Square
Stiffener size
[mm]
[mm]
[mm]
[mm]
radius
5
10
25
50
side
5
10
25
50
5x20
10x20
25x20
50x20
5x10
10x10
25x10
50x10
5x5
10x5
25x5
50x5
R/t=100 Rectangular
sides
R/t=200
• 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;
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
53
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
54
Stiffened shells – Proposal for EN19991-5
Background activity - Main investigated aspects
Axial load
• 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;
n xRc
External pressure
EA s ⎞ ⎛ A ⎞ 1.2 1 ⎛ 1+ A + 2 = αx 5 EA ω2 ⎜⎝ Cθ d s ⎟⎠ ⎜⎝ 1 A3 ⎟⎠ 1+ Cφ d s
p nRc = α θ
with α x = 0.80
A2 ⎞ 1 ⎛ ⎜ A1 + ⎟ A3 ⎠ rj2 ⎝
with α θ = 0.50
[
]
A 1 = j 4 ω 4 C 44 + 2ω 2 (C 45 + C 66 ) + C 55 + C 22 + 2j 2 C 25 A 2 = 2ω (C 12 + C 33 )(C 22 + j C 25 )(C 12 + j ω C 14 ) 2
2
2
2
− (ω 2 C 11 + C 33 )(C 22 + j 2 C 25 ) 2 − ω 2 (C 22 + C 25 + ω 2 C 33 )(C 12 + j 2 ω 2 C 14 ) 2 A 3 = (ω 2 C11 + C 33 )(C 22 + C 25 + ω 2 C 33 ) − ω 2 (C 12 + C 33 ) 2
where
C 11 = C φ + EA s /d s
C 22 = C θ + EA r /d r C 33 = C φθ
C 12 = ν C φ C θ
C 25 = −e r EA r /(rd r )
C 14 = e s EA s /(rd s )
[
]
C 44 = D φ + EI s d s /r C 45 = ν D φ D θ /r ω=
πr jl i
2
2
C 55 = [D θ + EI r d r ]/r 2
[
]
C 66 = D φθ + 0,5(GI ts /d s + GI tr /d r /r 2
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
55
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Stiffened shells – Proposal for EN19991-5
56
Stiffened shells – Proposal for prEN19991-5
Equivalent orthotropic properties of corrugated sheeting (from prEN1999-1-6)
2t 3 Cφ = E ⋅ t x = E ⋅ 2 3d ⎛ π2d2 ⎞ ⎟ C θ = E ⋅ t y = E ⋅ t ⎜⎜ 1 + 4l 2 ⎟⎠ ⎝ G ⋅t C θϕ = G ⋅ t xy = ⎛ π2d2 ⎞ ⎜⎜ 1 + ⎟ 4l 2 ⎟⎠ ⎝ 3 Et 1 Dφ = E ⋅ I x = 12 1 - ν 2 ⎛ π2d2 ⎜⎜ 1 + 4l 2 ⎝ D ϕ = E ⋅ I y = 0,13Etd 2
(
D θϕ = G ⋅ I xy =
EUROCODES Background and Applications
)
G ⋅t3 12
⎛ π2d2 ⎜⎜ 1 + 4l 2 ⎝
Axial load 1,2 χ
Strong hardening alloys Quality class A
1,0 L/R=2; R/t=50
0,8 L/R=2; R/t=100
0,6
Q* = 1.3Q
χ x = αχ perf 0,4
⎞ ⎟⎟ ⎠
χ perf =
L/R=2; R/t=200
Q* = Q
1
φ + φ 2 − λ2
φ = 0.5[1 + α 0 (λ − λ0 ) + λ2 ]
0,2
λ
0,0 0,0
⎞ ⎟⎟ ⎠
0,2
0,4
0,6
0,8
1,0
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
57
Brussels, 18-20 February 2008 – Dissemination of information workshop
58
Stiffened shells – EC9 formulation
External pressure
General buckling curve formulation
1,2 χ
χ x = αχ perf χ perf =
1
φ + φ −λ
χ perf =
2
φ = 0.5[1 + α 0 (λ − λ0 ) + λ2 ]
0,8
χ x = αχ
Strong hardening alloys Quality class C 2
1,4
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Stiffened shells – Proposal for prEN19991-5
1,0
1,2
λ x = n0, xRk / nxRc
L/R=2; R/t=50
0,6
L/R=2; R/t=100
0,4
L/R=2; R/t=200
perf
1
φ + φ 2 − λ2
φ = 0 . 5 [1 + α 0 (λ − λ 0 ) + λ 2 ]
0,2 λ 0,0 0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
4,5
5,0
λθ = p0,nRk / pnRc
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Background activity - Main investigated aspects
• 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;
EUROCODES Background and Applications
59
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
60
Effect of welding (HAZ zones): definition of simplified design procedures
Rolling
Welding
MIG 0 < t ≤ 6mm 6 < t ≤ 12mm 12 < t ≤ 25mm t > 25mm
• effect of welding effect (HAZ zones) • imperfection sensitivity analysis of welded cylinders; • definition of simplified design procedures;
0 < t ≤ 6mm
bhaz = 20 mm bhaz = 30 mm bhaz = 35 mm bhaz = 40 mm
TIG bhaz = 30 mm
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
61
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
Effect of welding – Parametric analysis
62
Effect of welding – Imperfection sensitivity curves, axial compression 1,4
Pu /Pcr,th
Class 3
Class 2
Class 1
1,2
Unwelded
1,0
α = 0.86
0,8
Welded
0,6
α = 0.72
0,4
α = 0.80
α = 0.72
α = 0.71
α = 0.67
2 R/t = 50; f 0.2 = 200 N/mm ; ρo,haz=0,53
0,2
w0/t 0,0 0,0
EUROCODES Background and Applications
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
Brussels, 18-20 February 2008 – Dissemination of information workshop
EUROCODES Background and Applications
63
Class 2
• • • • •
Unwelded α = 0.76
0,8
α = 0.68 α = 0.56
0,6
α = 0.67
Welded
0,4
α = 0.61
0,2 w0/t
EUROCODES Background and Applications
0,3
0,4
0,5
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
ρi ,w = ωo + (1 − ωo )
λ i − λ i ,0 λ i ,w − λ i ,0
65
ρi,w 1,0
ρ o,haz
ω0 = ω (ρ0,haz) λi,0 = λi,0 (λi,w,0) 0
0
λ i,0
λ i,w
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;
• imperfection sensitivity analysis of welded cylinders; • definition of simplified design procedures;
0,6
Brussels, 18-20 February 2008 – Dissemination of information workshop
Effect of welding according to EC9
EN 1999 - Eurocode 9: Design of aluminium structures Part 1.5 - Shell structures (A. Mandara)
• effect of welding effect (HAZ zones)
0,0 0,2
0,6
• imperfection sensitivity analysis of stiffened cylinders; • validation of EN1993-1-6 procedures and harmonization with EN1999 rules;
R/t = 100; f 0.2 = 200 N/mm ; ρ0,haz = 0,53
0,1
0,5
• stiffened shells
α = 0.54 2
0,0
0,4
• shell plastic buckling
Class 1
1,2 1,0
0,3
Background activity - Main investigated aspects
1,4 Class 3
0,2
Brussels, 18-20 February 2008 – Dissemination of information workshop
Effect of welding – Imperfection sensitivity curves, axial compression Pu /Pcr,th
0,1
λ i,w,0
λi
64
