SIST EN 1999-1-5:2007
(Main)Eurocode 9 - Design of aluminium structures - Part 1-5: Shell structures
Eurocode 9 - Design of aluminium structures - Part 1-5: Shell structures
(1)P EN 1999-1-5 applies to the structural design of aluminium structures, stiffened and unstiffened, that have the form of a shell of revolution or of a round panel in monocoque structures.
(2) The relevant parts of EN 1999 should be followed for specific application rules for structural design.
(3) Supplementary information for certain types of shells are given in EN 1993-1-6 and the relevant application parts which include:
- Part 3-1 for towers and masts;
- Part 3-2 for chimneys;
- Part 4-1 for silos;
- Part 4-2 for tanks;
- Part 4-3 for pipelines.
(4) The provisions in EN 1999-1-5 apply to axisymmetric shells (cylinders, cones, spheres) and associated circular or annular plates and beam section rings and stringer stiffeners where they form part of the complete structure.
(5) Single shell panels (cylindrical, conical or spherical) are not explicitly covered by EN 1999-1-5. However, the provisions can be applicable if the appropriate boundary conditions are duly taken into account.
Eurocode 9 - Bemessung und Konstruktion von Aluminiumtragwerken - Teil 1-5: Schalen
1.1.1 Anwendungsbereich von EN 1999
(1)P EN 1999 gilt für den Entwurf, die Berechnung und die Bemessung von Bauwerken und Tragwerken aus Aluminium. Sie entspricht den Grundsätzen und Anforderungen an die Sicherheit und Gebrauchs¬tauglichkeit von Tragwerken sowie den Grundlagen für ihre Bemessung und Nachweise, die in EN 1990 Grundlagen der Tragwerksplanung enthalten sind.
(2)P EN 1999 behandelt ausschließlich Anforderungen an die Tragfähigkeit, die Gebrauchstauglichkeit, die Dauerhaftigkeit und den Feuerwiderstand von Tragwerken aus Aluminium. Andere Anforderungen, wie z. B. Wärmeschutz oder Schallschutz, werden nicht behandelt.
(3) EN 1999 gilt in Verbindung mit folgenden Regelwerken:
EN 1990, Grundlagen der Tragwerksplanung
EN 1991, Einwirkungen auf Tragwerke
Europäische Normen für Bauprodukte, die für Aluminiumtragwerke Verwendung finden:
EN 1090 1, Ausführung von Stahltragwerken und Aluminiumtragwerken Teil 1: Allgemeine Liefer¬bedingungen )
EN 1090 3, Ausführung von Stahltragwerken und Aluminiumtragwerken Teil 3: Technische Regeln für die Ausführung von Aluminiumtragwerken 5)
(4) EN 1999 ist in fünf Teile gegliedert:
EN 1999 1 1, Bemessung und Konstruktion von Aluminiumtragwerken: Allgemeine Bemessungsregeln
EN 1999 1 2, Bemessung und Konstruktion von Aluminiumtragwerken: Tragwerksbemessung für den Brandfall
EN 1999 1 3, Bemessung und Konstruktion von Aluminiumtragwerken: Ermüdungsbeanspruchte Tragwerke
EN 1999 1 4, Bemessung und Konstruktion von Aluminiumtragwerken: Kaltgeformte Profiltafeln
EN 1999 1 5, Bemessung und Konstruktion von Aluminiumtragwerken: Schalen
Eurocode 9 - Calcul des structures en aluminium - Partie 1-5 : Coques
Evrokod 9 - Projektiranje konstrukcij iz aluminijevih zlitin - 1-5. del: Lupinaste konstrukcije
EN 1999 se uporablja na področju projektiranja zgradb in gradbeništva ter gradbenih objektov iz aluminija. Je v skladu z načeli in zahtevami za varnost in uporabnost objektov, osnovo njihovega projektiranja in preverjanja, ki so podani v EN 1990 – Osnove projektiranja. EN 1999 se ukvarja samo z zahtevami glede odpornosti, uporabnosti, trajnosti in požarne odpornosti aluminijevih konstrukcij. Drugih zahtev, npr. glede toplotne ali zvočne izolacije, ne obravnava. EN 1999 je namenjen uporabi v povezavi z: - EN 1990 Osnove projektiranja, - EN 1991 Vplivi na konstrukcije, – evropski standardi za gradbene izdelke, ki se nanašajo na aluminijeve konstrukcije, - EN 1090-1 Izvedba jeklenih in aluminijastih konstrukcij, – prvi del: Zahteve za ugotavljanje skladnosti sestavnih delov konstrukcij, – EN 1090-3 Izvedba jeklenih in aluminijevih konstrukcij, – tretji del: Tehnične zahteve za aluminijaste konstrukcije EN 1999 je razdeljen v pet delov: EN 1999-1-1 Projektiranje konstrukcij iz aluminijevih zlitin: Splošna pravila za konstrukcije. EN 1999-1-2 Projektiranje konstrukcij iz aluminijevih zlitin: Projektiranje požarnovarnih konstrukcij. EN 1999-1-3 Projektiranje konstrukcij iz aluminijevih zlitin: Konstrukcije občutljive na utrujenost. EN 1999-1-4 Projektiranje konstrukcij iz aluminijevih zlitin: Hladno oblikovane konstrukcijske pločevine. EN 1999-1-5 Projektiranje konstrukcij iz aluminijevih zlitin: Lupinaste konstrukcije.
General Information
Relations
Standards Content (Sample)
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Evrokod 9 - Projektiranje konstrukcij iz aluminijevih zlitin - 1-5. del: Lupinaste konstrukcijeEurocode 9 - Bemessung und Konstruktion von Aluminiumtragwerken - Teil 1-5: SchalenEurocode 9 - Calcul des structures en aluminium - Partie 1-5 : CoquesEurocode 9 - Design of aluminium structures - Part 1-5: Shell structures91.080.10Kovinske konstrukcijeMetal structures91.010.30Technical aspectsICS:Ta slovenski standard je istoveten z:EN 1999-1-5:2007SIST EN 1999-1-5:2007en,fr,de01-maj-2007SIST EN 1999-1-5:2007SLOVENSKI
STANDARDSIST ENV 1999-2:2002SIST ENV 1999-1-1:20021DGRPHãþD
EUROPEAN STANDARDNORME EUROPÉENNEEUROPÄISCHE NORMEN 1999-1-5February 2007ICS 13.220.50; 91.010.30; 91.080.10Supersedes ENV 1999-1-1:1998, ENV 1999-1-2:1998,ENV 1999-2:1998
English VersionEurocode 9 - Design of aluminium structures - Part 1-5: ShellstructuresEurocode 9 - Calcul des structures en aluminium - Partie 1-5 : CoquesEurocode 9 - Bemessung und Konstruktion vonAluminiumtragwerken - Teil 1-5: SchalenThis European Standard was approved by CEN on 11 October 2006.CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this EuropeanStandard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such nationalstandards may be obtained on application to the CEN Management Centre or to any CEN member.This European Standard exists in three official versions (English, French, German). A version in any other language made by translationunder the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as theofficial versions.CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATIONCOMITÉ EUROPÉEN DE NORMALISATIONEUROPÄISCHES KOMITEE FÜR NORMUNGManagement Centre: rue de Stassart, 36
B-1050 Brussels© 2007 CENAll rights of exploitation in any form and by any means reservedworldwide for CEN national Members.Ref. No. EN 1999-1-5:2007: ESIST EN 1999-1-5:2007
2 Content Page Foreword.5 National Annex for EN 1999-1-5.7 1 General.8 1.1 Scope.8 1.1.1 Scope of EN 1999.8 1.1.2 Scope of EN 1999-1-5.8 1.2 Normative references.9 1.3 Terms and definitions.10 1.3.1 Structural forms and geometry.10 1.3.2 Special definitions for buckling calculations.11 1.4 Symbols.12 1.5 Sign conventions.15 1.6 Coordinate systems.15 2 Basis of design.17 2.1 General.17 2.2 Consequence class and execution class.17 3 Materials and geometry.17 3.1 Material properties.17 3.2 Design values of geometrical data.17 3.3 Geometrical tolerances and geometrical imperfections.18 4 Durability.18 5 Structural analysis.18 5.1 Geometry.18 5.2 Boundary conditions.19 5.3 Actions and environmental influences.19 5.4 Stress resultants and stresses.20 5.5 Types of analysis.20 6 Ultimate limit state.21 6.1 Resistance of cross section.21 6.1.1 Design values of stresses.21 6.1.2 Design values of resistance.22 6.1.3 Stress limitation.22 6.1.4 Design by numerical analysis.22 6.2 Buckling resistance.23 6.2.1 General.23 6.2.2 Buckling-relevant geometrical tolerances.24 6.2.3 Shell in compression and shear.25 6.2.4 Effect of welding.27 6.2.5 Design by numerical analysis.30 7 Serviceability limit states.31 7.1 General.31 7.2 Deflections.31 Annex A [normative] - Expressions for shell buckling analysis.32 A.1 Unstiffened cylindrical shells of constant wall thickness.32 A.1.1 Notations and boundary conditions.32 A.1.2 Meridional (axial) compression.32 A.1.2.1 Critical meridional buckling stresses.32 SIST EN 1999-1-5:2007
3 A.1.2.2 Meridional buckling parameter.33 A.1.3 Circumferential (hoop) compression.34 A.1.3.1 Critical circumferential buckling stresses.34 A.1.3.2 Circumferential buckling parameter.35 A.1.4 Shear.37 A.1.4.1 Critical shear buckling stresses.37 A.1.4.2 Shear buckling parameters.38 A.1.5 Meridional (axial) compression with coexistent internal pressure.38 A.1.5.1 Pressurised critical meridional buckling stress.38 A.1.5.2 Pressurised meridional buckling parameters.38 A.1.6 Combinations of meridional (axial) compression, circumferential (hoop) compression and shear 39 A.2 Unstiffened cylindrical shells of stepwise wall thickness.40 A.2.1 General.40 A.2.1.1 Notations and boundary conditions.40 A.2.1.2 Geometry and joint offsets.41 A.2.2 Meridional (axial) compression.41 A.2.3 Circumferential (hoop) compression.41 A.2.3.1 Critical circumferential buckling stresses.41 A.2.3.2 Buckling strength verification for circumferential compression.44 A.2.4 Shear.44 A.2.4.1 Critical shear buckling stress.44 A.2.4.2 Buckling strength verification for shear.45 A.3 Unstiffened lap jointed cylindrical shells.45 A.3.1 General.45 A.3.1.1 Definitions.45 A.3.1.2 Geometry and stress resultants.45 A.3.2 Meridional (axial) compression.45 A.3.3 Circumferential (hoop) compression.45 A.3.4 Shear.46 A.4 Unstiffened conical shells.46 A.4.1 General.46 A.4.1.1 Notation.46 A.4.1.2 Boundary conditions.46 A.4.1.3 Geometry.47 A.4.2 Design buckling stresses.47 A.4.2.1 Equivalent cylinder.47 A.4.3 Buckling strength verification.47 A.4.3.1 Meridional compression.47 A.4.3.2 Circumferential (hoop) compression.48 A.4.3.3 Shear and uniform torsion.48 A.5 Stiffened cylindrical shells of constant wall thickness.48 A.5.1 General.48 A.5.2 Isotropic walls with meridional stiffeners.48 A.5.2.1 General.48 A.5.2.2
Meridional (axial) compression.49 A.5.2.3 Circumferential (hoop) compression.49 A.5.2.4
Shear.49 A.5.3 Isotropic walls with circumferential stiffeners.50 A.5.4 Circumferentially corrugated walls with meridional stiffeners.50 A.5.4.1 General.50 A.5.4.2 Axial compression.51 A.5.4.3 Stiffened wall treated as carrying axial compression only in the stiffeners.52 A.5.4.4 Circumferential (hoop) compression.53 SIST EN 1999-1-5:2007
4 A.5.5 Axially corrugated walls with ring stiffeners.53 A.5.5.1 General.53 A.5.5.2 Axial compression.54 A.5.5.3 Circumferential (hoop) compression.54 A.5.6 Stiffened wall treated as an orthotropic shell.54 A.5.6.1 General.54 A.5.6.2 Axial compression.55 A.5.6.3 Circumferential (hoop) compression.56 A.5.6.4 Shear.56 A.5.7 Equivalent orthotropic properties of corrugated sheeting.57 A.6 Unstiffened spherical shells under uniform circumferential compression.58 A.6.1 Notations and boundary conditions.58 A.6.2 Critical buckling stresses.59 A.6.3 Circumferential buckling parameter.59 Annex B [informative] - Expressions for buckling analysis of toriconical and torispherical shells.60 B.1 General.60 B.2 Notations and boundary conditions.60 B.3 External pressure.61 B.3.1 Critical external pressure.61 B.3.2 Uniform squash limit external pressure.62 B.3.3 External pressure buckling parameter.63 B.4 Internal pressure.63 B.4.1 Critical internal pressure.63 B.4.2 Uniform squash limit internal pressure.64 B.4.3 Internal pressure buckling parameter.65
5 Foreword This European Standard (EN 1999-1-5:2007) has been prepared by Technical Committee CEN/TC250 « Structural Eurocodes », the secretariat of which is held by BSI.
This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by August 2007, and conflicting national standards shall be withdrawn at the latest by March 2010. This European Standard supersedes ENV 1999-1-1:1998, ENV 1999-1-2:1998 and ENV 1999-2:1998. CEN/TC 250 is responsible for all Structural Eurocodes. According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard:
Austria, Bulgaria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italia, Latvia, Lithuania, Luxemburg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and the United Kingdom
Background of the Eurocode programme In 1975, the Commission of the European Community decided on an action programme in the field of construction, based on article 95 of the Treaty. The objective of the programme was the elimination of technical obstacles to trade and the harmonisation of technical specifications. Within this action programme, the Commission took the initiative to establish a set of harmonised technical rules for the design of construction works, which, in a first stage, would serve as an alternative to the national rules in force in the Member States and, ultimately, would replace them.
For fifteen years, the Commission, with the help of a Steering Committee with Representatives of Member States, conducted the development of the Eurocodes programme, which led to the first generation of European codes in the 1980s.
In 1989, the Commission and the Member States of the EU and EFTA decided, on the basis of an agreement1 between the Commission and CEN, to transfer the preparation and the publication of the Eurocodes to the CEN through a series of Mandates, in order to provide them with a future status of European Standard (EN). This links de facto the Eurocodes with the provisions of all the Council’s Directives and/or Commission’s Decisions dealing with European standards (e.g. the Council Directive 89/106/EEC on construction products - CPD - and Council Directives 93/37/EEC, 92/50/EEC and 89/440/EEC on public works and services and equivalent EFTA Directives initiated in pursuit of setting up the internal market). The Structural Eurocode programme comprises the following standards generally consisting of a number of Parts: EN 1990 Eurocode 0: Basis of Structural Design
EN 1991 Eurocode 1: Actions on structures EN 1992 Eurocode 2: Design of concrete structures EN 1993 Eurocode 3: Design of steel structures EN 1994 Eurocode 4: Design of composite steel and concrete structures EN 1995 Eurocode 5: Design of timber structures EN 1996 Eurocode 6: Design of masonry structures EN 1997 Eurocode 7: Geotechnical design EN 1998 Eurocode 8: Design of structures for earthquake resistance EN 1999 Eurocode 9: Design of aluminium structures
1 Agreement between the Commission of the European Communities and the European Committee for Standardisation (CEN) concerning the work on EUROCODES for the design of building and civil engineering works (BC/CEN/03/89). SIST EN 1999-1-5:2007
6 Eurocode standards recognise the responsibility of regulatory authorities in each Member State and have safeguarded their right to determine values related to regulatory safety matters at national level where these continue to vary from State to State. Status and field of application of Eurocodes
The Member States of the EU and EFTA recognise that Eurocodes serve as reference documents for the following purposes: - as a means to prove compliance of building and civil engineering works with the essential requirements of Council Directive 89/106/EEC, particularly Essential Requirement No.1 – Mechanical resistance and stability, and Essential Requirement No 2 – Safety in case of fire - as a basis for specifying contracts for the execution of construction works and related engineering services
- as a framework for drawing up harmonised technical specifications for construction products (En’s and ETA’s)
The Eurocodes, as far as they concern the construction works themselves, have a direct relationship with the Interpretative Documents2 referred to in Article 12 of the CPD, although they are of a different nature from harmonised product standards3. Therefore, technical aspects arising from the Eurocodes work need to be adequately considered by CEN Technical Committees and/or EOTA Working Groups working on product standards with a view to achieving full compatibility of these technical specifications with the Eurocodes.
The Eurocode standards provide common structural design rules for everyday use for the design of whole structures and component products of both a traditional and an innovative nature. Unusual forms of construc-tion or design conditions are not specifically covered and additional expert consideration will be required by the designer in such cases.
National standards implementing Eurocodes
The National Standards implementing Eurocodes will comprise the full text of the Eurocode (including any annexes), as published by CEN, which may be preceded by a National title page and National foreword, and may be followed by a National annex [informative].
The National Annex (informative) may only contain information on those parameters which are left open in the Eurocode for national choice, known as Nationally Determined Parameters, to be used for the design of buildings and civil engineering works to be constructed in the country concerned, i.e. : –
values for partial factors and/or classes where alternatives are given in the Eurocode; –
values to be used where a symbol only is given in the Eurocode; –
geographical and climatic data specific to the Member State, e.g. snow map; –
the procedure to be used where alternative procedures are given in the Eurocode; –
references to non-contradictory complementary information to assist the user to apply the Eurocode.
Links between Eurocodes and harmonised technical specifications (EN’s and ETA’s) for products
There is a need for consistency between the harmonised technical specifications for construction products and the technical rules for works4. Furthermore, all the information accompanying the CE Marking of the construction products, which refer to Eurocodes, shall clearly mention which Nationally Determined Para-meters have been taken into account.
2 According to Art. 3.3 of the CPD, the essential requirements (ERs) shall be given concrete form in interpretative documents for the creation of the necessary links between the essential requirements and the mandates for harmonised ENs and ETAGs/ETAs. 3 According to Art. 12 of the CPD the interpretative documents shall : a) give concrete form to the essential requirements by harmonising the terminology and the technical bases and indicating classes or levels for each requirement where necessary ; b) indicate methods of correlating these classes or levels of requirement with the technical specifications, e.g. methods of calculation and of proof, technical rules for project design, etc. ; c) serve as a reference for the establishment of harmonised standards and guidelines for European technical approvals. The Eurocodes, de facto, play a similar role in the field of the ER 1 and a part of ER 2. 4 see Art.3.3 and Art.12 of the CPD, as well as clauses 4.2, 4.3.1, 4.3.2 and 5.2 of ID 1.
National Annex for EN 1999-1-5
This European Standard gives alternative procedures, values and recommendations for classes with notes indicating where national choices may have to be made. Therefore the National Standard implementing EN 1999-1-5 should have a National Annex containing all Nationally Determined Parameters to be used for the design of aluminium shell structures to be constructed in the relevant country.
National choice is allowed in EN 1999-1-5 through clauses: – 2.1 (3) – 2.1 (4)
8 1 General 1.1 Scope 1.1.1 Scope of EN 1999
(1)P EN 1999 applies to the design of buildings and civil engineering and structural works in aluminium. It complies with the principles and requirements for the safety and serviceability of structures, the basis of their design and verification that are given in EN 1990 – Basis of structural design.
(2)P EN 1999 is only concerned with requirements for resistance, serviceability, durability and fire resis-tance of aluminium structures. Other requirements, e.g. concerning thermal or sound insulation, are not considered.
(3) EN 1999 is intended to be used in conjunction with: – EN 1990 Basis of structural design – EN 1991 Actions on structures – European Standards for construction products relevant for aluminium structures – EN 1090-1 Execution of steel structures and aluminium structures – Part 1: Requirements for conformity assessment of structural components5 – EN 1090-3 Execution of steel structures and aluminium structures – Part 3: Technical requirements for aluminium structures5
(4) EN 1999 is subdivided in five parts: EN 1999-1-1 Design of Aluminium Structures: General structural rules. EN 1999-1-2 Design of Aluminium Structures: Structural fire design. EN 1999-1-3 Design of Aluminium Structures: Structures susceptible to fatigue. EN 1999-1-4 Design of Aluminium Structures: Cold-formed structural sheeting. EN 1999-1-5 Design of Aluminium Structures: Shell structures.
1.1.2 Scope of EN 1999-1-5
(1)P EN 1999-1-5 applies to the structural design of aluminium structures, stiffened and unstiffened, that have the form of a shell of revolution or of a round panel in monocoque structures.
(2) The relevant parts of EN 1999 should be followed for specific application rules for structural design.
(3) Supplementary information for certain types of shells are given in EN 1993-1-6 and the relevant application parts which include: -
Part 3-1 for towers and masts;
-
Part 3-2 for chimneys;
-
Part 4-1 for silos;
-
Part 4-2 for tanks;
-
Part 4-3 for pipelines.
(4) The provisions in EN 1999-1-5 apply to axisymmetric shells (cylinders, cones, spheres) and associated circular or annular plates and beam section rings and stringer stiffeners where they form part of the complete structure.
5 To be published SIST EN 1999-1-5:2007
9 (5) Single shell panels (cylindrical, conical or spherical) are not explicitly covered by EN 1999-1-5. However, the provisions can be applicable if the appropriate boundary conditions are duly taken into account.
(6) Types of shell walls covered in EN 1999-1-5 can be, see Figure 1.1:
- shell wall constructed from flat rolled sheet, termed ‘isotropic’;
- shell wall with lap joints formed by connecting adjacent plates with overlapping sections, termed ‘lap-jointed; - shell wall with stiffeners attached to the outside, termed ‘externally stiffened’ irrespective of the spacing of the stiffeners; - shell wall with the corrugations running up the meridian, termed ‘axially corrugated’; - shell wall constructed from corrugated sheets with the corrugations running around the shell circum-ference, termed ‘circumferentially corrugated’.
Elevation
Plan Isotropic (unstiffened) lap-jointed externally
stiffened axially
corrugated circumferentially corrugated Figure 1.1 - Illustration of cylindrical shell forms (7) The provisions of EN 1999-1-5 are intended to be applied within the temperature range defined in EN 1999-1-1. The maximum temperature is restricted so that the influence of creep can be neglected. For structures subject to elevated temperatures associated with fire see EN 1999-1-2.
(8) EN 1999-1-5 does not cover the aspects of leakage.
1.2 Normative references (1) EN 1999-1-5 incorporates by dated or undated reference, provisions from other publications. These normative references are cited at the appropriate places in the text and the publications are listed hereafter. For dated references, subsequent amendments to or revisions of any of these publications apply to this European Standard only if incorporated in it by amendment or revision. For undated references the latest edition of the publication referred to applies (including amendments). EN 1090-1 Execution of steel structures and aluminium structures – Part 1: Requirements for conformity assessment of structural components5 EN 1090-3 Execution of steel structures and aluminium structures – Part 3: Technical requirements for aluminium structures5
10 EN 1990 Basis of structural design EN 1991 Actions on structures – All parts
EN 1993-1-6 Design of steel structures - Part 1-6: Shell structures EN 1993-3-2 Design of steel structures - Part 3-2: Chimneys EN 1993-4-1 Design of steel structures - Part 4-1: Silos EN 1993-4-2 Design of steel structures - Part 4-2: Tanks EN 1993-4-3 Design of steel structures - Part 4-3: Pipelines
EN 1999-1-1 Design of aluminium structures - Part 1-1: General rules EN 1999-1-2 Design of aluminium structures - Part 1-2: Structural fire design EN 1999-1-3 Design of aluminium structures - Part 1-3: Structures susceptible to fatigue EN 1999-1-4 Design of aluminium structures - Part 1-4: Cold-formed structural sheeting 1.3 Terms and definitions (1) Supplementary to EN 1999-1-1, for the purposes of this part, the following definitions apply:
1.3.1 Structural forms and geometry 1.3.1.1
shell A thin-walled body shaped as a curved surface with the thickness measured normal to the surface being small compared to the dimensions in the other directions. A shell carries its loads mainly by membrane forces. The middle surface may have finite radius of curvature at each point or infinite curvature in one direction, e.g. cylindrical shell. In EN 1999-1-5, a shell is a structure or a structural component formed from curved sheets or extrusions.
1.3.1.2
shell of revolution A shell composed of a number of parts, each of which is a complete axisymmetric shell. 1.3.1.3
complete axisymmetric shell A shell whose form is defined by a meridional generator line rotated around a single axis through 2π radians. The shell can be of any length.
1.3.1.4
shell segment A part of shell of revolution in the form of a defined shell geometry with a constant wall thickness: a cylinder, conical frustum, spherical frustum, annular plate or other form.
1.3.1.5
shell panel An incomplete axisymmetric shell: the shell form is defined by a rotation of the generator about the axis through less than 2π radians.
1.3.1.6
middle surface The surface that lies midway between the inside and outside surfaces of the shell at every point. If the shell is stiffened on only one surface, the reference middle surface is still taken as the middle surface of the curved shell plate. The middle surface is the reference surface for analysis, and can be discontinuous at changes of thickness or shell junctions, leading to eccentricities that are important to the shell response.
11 1.3.1.7
junction The point at which two or more shell segments meet: it can include a stiffener or not: the point of attachment of a ring stiffener to the shell may be treated as a junction.
1.3.1.8
stringer stiffener A local stiffening member that follows the meridian of the shell, representing a generator of the shell of revolution. It is provided to increase the stability, or to assist with the introduction of local loads. It is not intended to provide a primary resistance for bending due to transverse loads.
1.3.1.9
rib A local member that provides a primary load carrying path for bending down the meridian of the shell, representing a generator of the shell of revolution. It is used to transfer or distribute transverse loads by bending. 1.3.1.10
ring stiffener A local stiffening member that passes around the circumference of the shell of revolution at a given point on the meridian. It is assumed to have no stiffness in the meridional plane of the shell. It is provided to increase the stability or to introduce axisymmetric local loads acting in the plane of the ring by a state of axisymmetric normal forces. It is not intended to provide primary resistance for bending.
1.3.1.11
base ring.
A structural member that passes around the circumference of the shell of revolution at the base and provides means of attachment of the shell to a foundation or other element. It is needed to ensure that the assumed boundary conditions are achieved in practice.
1.3.2 Special definitions for buckling calculations
1.3.2.1
critical buckling load The smallest bifurcation or limit load determined assuming the idealised conditions of elastic material behaviour, perfect geometry, perfect load application, perfect support, material isotropy and absence of residual stresses (LBA analysis).
1.3.2.2
critical buckling stress The nominal membrane stress associated with the elastic critical buckling load.
1.3.2.3
characteristic buckling stress The nominal membrane stress associated with buckling in the presence of inelastic material behaviour and of geometrical and structural imperfections.
1.3.2.4
design buckling stress The design value of the buckling stress, obtained by dividing the characteristic buckling stress by the partial factor for resistance. 1.3.2.5
key value of the stress The value of stress in a non-uniform stress field that is used to characterise the stress magnitude in the buck-ling limit state assessment.
12 1.3.2.6
tolerance class The class of requirements to geometrical tolerances for work execution.
NOTE Geometrical tolerances for work execution are built up from fabrication of components and execution of the components at site.
1.4 Symbols
(1)
In addition to the symbols defined in EN 1999-1-1, the following are used.
(2)
Coordinate system (see Figure 1.2):
r
radial coordinate, normal to the axis of revolution;
x
meridional coordinate;
z axial coordinate;
θ
circumferential coordinate;
νφ
meridional slope: angle between axis of revolution and normal to the meridian of the shell:
(3) Pressures:
pn
normal to the shell;
px
meridional surface loading parallel to the shell;
pθ
circumferential surface loading parallel to the shell;
(4) Line forces:
Pn load per unit circumference normal to the shell;
Px load per unit circumference acting in the meridional direction;
Pθ
load per unit circumference acting circumferentially on the shell;
(5) Membrane stress resultants (see Figure 1.3a):
nx meridional membrane stress resultant;
nθ circumferential membrane stress resultant;
nxθ membrane shear stress resultant;
(6) Bending stress resultants (see Figure 1.3b):
mx meridional bending moment per unit width;
mθ
circumferential bending moment per unit width;
mxθ twisting shear moment per unit width;
qxn transverse shear force associated with meridional bending;
qθn transverse shear force associated with circumferential bending;
(7) Stresses:
σx
meridional stress;
σθ
circumferential stress;
σeq von Mises equivalent stress (can be negative in cyclic loading conditions);
τ,ντxθ in-plane shear stress;
τxn,ντθnνmeridional, circumferential transverse shear stresses associated with bending;
(8)
Displacements:
u meridional displacement;
v circumferential displacement;
w displacement normal to the shell surface,
βφ
meridional rotation (see 5.3.3);
13 (9)
Shell dimensions:
d
internal diameter of shell;
L total length of shell;
l length of shell segment;
lg gauge length for measurement of imperfections;
lg,θ gauge length for measurement of imperfections in circumferential direction;
lg,w gauge length for measurement of imperfections across welds;
lR limited length of shell for buckling strength assessment;
r
radius of the middle surface, normal to the axis of revolution;
t thickness of shell wall;
tmax maximum thickness of shell wall at a joint;
tmin minimum thickness of shell wall at a joint;
tave average thickness of shell wall at a joint;
β apex half angle of cone; θnxσθσxτxθσxσθτxθθpnφpθpxz Surface pressures
Coordinates
Membrane stresses vwuτθnτθnθnx
Directions
Displacements
Transverse shear
stresses θν= circumferential n = normal x = meridional
Figure 1.2 - Symbols in shells of revolutions nynxnxynxynxynxnxynymxymxymymymxmxymxmxy a) Membrane stress resultants b) Bending stress resultants Figure 1.3 - Stress resultants in the shell wall (In this figure x is meridional and y is circumferential) SIST EN 1999-1-5:2007
14 (10) Tolerances (see 6.2.2):
e
eccentricity between the middle surfaces of joined plates;
Ue
non-intended eccentricity tolerance parameter;
Ur
out-of-roundness tolerance parameter;
U0
initial dent tolerance parameter;
∆w0 tolerance normal to the shell surface;
(11) Properties of materials:
feq
von Mises equivalent strength;
fu
characteristic value of ultimate tensile strength;
fo characteristic value of 0,2 % proof strength;
(12) Parameters in strength assessment:
C coefficient in buckling strength assessment;
Cφ sheeting stretching stiffness in the axial direction;
Cθ sheeting stretching stiffness in the circumferential direction;
Cφθ sheeting stretching stiffness in membrane shear;
Dφ sheeting flexural rigidity in the axial direction;
Dθ sheeting flexural rigidity in the circumferential direction;
Dφθ sheeting twisting flexural rigidity in twisting;
R calculated resistance (used with subscripts to identify the basis);
Rpl plastic reference resistance (defined as a load factor on design loads);
Rcr
elastic critical buckling load (defined as a load factor on design loads);
k calibration factor for nonlinear analyses;
k(…) power of interaction expressions in buckling strength interaction expressions;
µ alloy hardening parameter in buckling curves for shells;
a(…) imperfection reduction factor in buckling strength assessment;
ν∆ range of parameter when alternating or cyclic actions are involved;
(13) Design stresses and stress resultants νσx,Ed design values of the buckling-relevant meridional membrane stress (positive when compression);
νσθ,Ed design values of the buckling-relevant circumferential membrane (hoop) stress (positive when compression);
ντνEd design values of the buckling-relevant shear membrane stress;
nx,Ed design values of the buckling-relevant meridional membrane stress resultant (positive when compression);
nθ,Ed design values of the buckling-relevant circumferential membrane (hoop) stress resultant (positive when compression);
nxθ,Ed
design values of the buckling-relevant shear membrane stress resultant. (14)
Critical buckling stresses and stress resistances: νσx,cr
meridional critical buckling stress;
νσθ,cr
circumferential critical buckling stress;
ντcr
shear critical buckling stress;
νσx,Rd
meridional design buckling stress resistance;
νσθ,Rd
circumferential design buckling stress resistance;
ντRd
shear design buckling stress resistance.
(15) Further symbols are defined where they first occur. SIST EN 1999-1-5:2007
15 1.5 Sign conventions (1) In general the sign conventions are the following, except as noted in (2) − outward direction positive; − internal pressure positive; − outward displacement positive; − tensile stresses positive; − shear stresses as shown in Figure 1.2. (2) For simplicity, for buckling analysis, compressive stresses are treated as positive. For these cases both external pressures and internal pressures are treated as positive. 1.6 Coordinate systems (1) In general, the convention for the global shell structure axis system is in cylindrical coordinates (see Figure 1.4) as follows:
coordinate along the central axis of a shell of revolution
z radial coordinate
r circumferential coordinate
θ zφsθr(m)(c)(p) (p) = pole, (m) = shell meridian,
(c) = instantaneous centre of meridional curvature
Figure 1.4 - Coordinate systems for a circular shell (2) The convention for structural elements attached to the shell wall (see Figure 1.5) is different for meridional and circumferential members.
(3) The convention for meridional straight structural elements (see Figure 1.5(I)) attached to the shell wall is:
meridional coordinate for barrel, hopper and roof attachment
x strong bending axis (parallel to flanges: axis for meridional bending)
y weak bending axis (perpendicular to flanges) z (4)
The convention for circumferential curved structural elements (see Figure 1.5(II)) attached to a shell wall is:
circumferential coordinate axis (curved)
θ radial axis (axis for bending in the meridional plane)
r meridional axis (axis for circumferential bending)
z SIST EN 1999-1-5:2007
xyzθrz a) meridional stiffener b) circumferential stiffener Figure 1.5 -
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