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eLibrary > BS EN 1993-1-6:2025 Eurocode 3. Design of steel structures - Strength and stability of shell structures >

BS EN 1993-1-6:2025 Eurocode 3. Design of steel structures - Strength and stability of shell structures, 2025

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BS EN 1993-1-6:2025 Eurocode 3. Design of steel structures - Strength and stability of shell structures, 2025

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European foreword
0 Introduction
1 Scope [Go to Page]
1.1 Scope of EN 1993-1-6
1.2 Assumptions
2 Normative references
3 Terms, definitions and symbols [Go to Page]
3.1 Terms and definitions [Go to Page]
3.1.1 Structural forms and geometry
3.1.2 Limit states
3.1.3 Actions
3.1.4 Stress resultants and stresses in a shell
3.1.5 Types of analysis and their use
3.1.6 Stress categories used in stress design
3.1.7 Special definitions for buckling calculations
3.2 Symbols [Go to Page]
3.2.1 Coordinate system
Figure 3.1 — Coordinate system for a shell of revolution [Go to Page]
3.2.2 Shell dimensions
3.2.3 Distributed surface loads and pressures
3.2.4 Line forces
3.2.5 Membrane stress resultants
3.2.6 Bending stress resultants
3.2.7 Stresses
3.2.8 Displacements relative to the shell middle surface
Figure 3.2 — Symbols in a shell of revolution
Figure 3.3 — Membrane and bending stress resultants in a cylindrical shell [Go to Page]
3.2.9 Tolerances
3.2.10 Properties of materials
3.2.11 Parameters in resistance assessment
3.2.12 Subscripts
3.3 Sign conventions
4 Basis of design [Go to Page]
4.1 General rules [Go to Page]
4.1.1 Basic requirements
4.1.2 Specific requirements
4.2 Types of analysis [Go to Page]
4.2.1 General
4.2.2 Global analysis
4.2.3 Membrane theory analysis
4.2.4 Semi-membrane theory analysis
4.2.5 Linear elastic shell analysis (LA)
4.2.6 Linear elastic bifurcation analysis (LBA)
4.2.7 Geometrically nonlinear elastic analysis (GNA)
4.2.8 Materially nonlinear analysis (MNA)
4.2.9 Geometrically and materially nonlinear analysis (GMNA)
4.2.10 Geometrically nonlinear elastic analysis with imperfections explicitly included (GNIA)
4.2.11 Geometrically and materially nonlinear analysis with imperfections explicitly included (GMNIA)
4.3 Shell boundary conditions
4.4 Verification by the partial factor method
Table 4.1 — Partial factors for resistance
Table 4.2 (NDP) — Numerical values for partial factors for resistance for shell structures outside the scope of EN 1993-3, EN 1993-4-1 and EN 1993-4-2
5 Materials and geometry [Go to Page]
5.1 Material properties
5.2 Design values of geometrical data
5.3 Geometrical tolerances and geometrical imperfections
6 Structural analysis [Go to Page]
6.1 Types of design [Go to Page]
6.1.1 Stress design [Go to Page]
6.1.1.1 General
6.1.1.2 Primary stresses
6.1.1.3 Secondary stresses
6.1.1.4 Local stresses
6.1.2 Design using standard formulae
6.1.3 Design by computational analysis
6.2 Stress resultants and stresses in shells [Go to Page]
6.2.1 Stress resultants in the shell
6.2.2 Modelling of the shell for analysis [Go to Page]
6.2.2.1 Geometry
6.2.2.2 Boundary conditions
Table 6.1 — Boundary conditions for shell segments [Go to Page]
6.2.2.3 Actions and environmental influences
6.2.3 Types of analysis
Table 6.2 — Types of shell analysis [Go to Page]
6.3 Ultimate limit states to be considered [Go to Page]
6.3.1 LS1: Plastic failure
6.3.2 LS2: Cyclic plasticity
6.3.3 LS3: Buckling
6.3.4 LS4: Fatigue
6.4 Concepts for the limit state verifications [Go to Page]
6.4.1 General
7 Plastic failure Limit State (LS1) [Go to Page]
7.1 Design values of actions
7.2 Stress design [Go to Page]
7.2.1 Design values of stresses
7.2.2 Design values of resistance
Figure 7.1 — Joint efficiency of lap joints (LS1) [Go to Page]
7.2.3 Stress limitation
7.3 Design by computational MNA or GMNA analysis
7.4 Design using standard formulae
8 Cyclic plasticity Limit State (LS2) [Go to Page]
8.1 Design values of actions
8.2 Stress design [Go to Page]
8.2.1 Design values of stress range
8.2.2 Design values of resistance
8.2.3 Stress range limitation
8.3 Design by computational GMNA analysis [Go to Page]
8.3.1 Design values of total accumulated plastic strain
8.3.2 Total accumulated plastic strain limitation
8.4 Design using standard formulae
9 Buckling Limit State (LS3) [Go to Page]
9.1 Design values of actions
9.2 Special definitions and symbols
9.3 Buckling-relevant boundary conditions
Figure 9.1 — Schematic examples of simple boundary conditions for LS3
Figure 9.2 — Schematic examples of ring boundary conditions for LS3
Figure 9.3 — Schematic examples of multi-segment shells [Go to Page]
9.4 Buckling-relevant geometrical tolerances [Go to Page]
9.4.1 General
Figure 9.4 — Consistent choice of imperfection amplitude, using as an example
Table 9.1 — Required tolerance dependent on the shell stress state [Go to Page]
9.4.2 Assessment of the dominant membrane stress at any location
9.4.3 Out-of-roundness tolerance
Figure 9.5 — Measurement of diameters for assessment of out-of-roundness
Table 9.2 — Values for out-of-roundness tolerance parameter Ur,max [Go to Page]
9.4.4 Unintended eccentricity tolerance
Figure 9.6 — Unintended eccentricity and intended offset at a joint
Table 9.3 — Values for unintended eccentricity tolerances [Go to Page]
9.4.5 Dimple tolerances
Table 9.4 — Values for dimple tolerance parameters U0x,max and U0θ,ref
Figure 9.7 — Measurement of depths δ0 of initial dimples on the meridian
Figure 9.8 — Measurement of depths δ0 of initial dimples on the circumference [Go to Page]
9.4.6 Interface flatness tolerance
9.5 Stress design [Go to Page]
9.5.1 Design values of stresses
9.5.2 Design resistance (buckling strength)
9.5.3 Stress limitation (buckling strength verification)
9.6 Design using reference resistances [Go to Page]
9.6.1 Principle
9.6.2 Design value of actions
9.6.3 Design value of resistance
9.6.4 Buckling strength verification
9.7 Design by computational analysis using LBA and MNA analyses [Go to Page]
9.7.1 Design value of actions
9.7.2 Design value of resistance [Go to Page]
9.7.2.1 General
9.7.2.2 Reference elastic critical buckling resistance LBA
9.7.2.3 Reference plastic resistance MNA
Figure 9.9 — Definition of plastic reference plastic resistance Rpl and reference elastic critical buckling resistance Rcr derived from MNA and LBA analyses respectively [Go to Page]
9.7.2.4 Elastic-plastic resistance assessment
9.7.3 Buckling strength verification
9.8 Design by computational analysis using GMNIA analysis [Go to Page]
9.8.1 Design values of actions
9.8.2 Design value of resistance
Figure 9.10 — Definition of buckling resistance from a GMNIA analysis
Table 9.5 — Values for the dimple imperfection amplitude parameter Un [Go to Page]
9.8.3 Buckling strength verification
10 Fatigue Limit State (LS4) [Go to Page]
10.1 Design values of actions
10.2 Stress design [Go to Page]
10.2.1 General
10.2.2 Stress calculation methods
Table 10.1 — Values for the stress concentration factor kf,imp to compensate for unintended eccentricities not accounted for in the analysis [Go to Page]
10.2.3 Multiaxial stress fields
10.2.4 Design values of resistance (fatigue strength)
10.2.5 Fatigue verification
Annex A (informative) Membrane theory stresses in unstiffened shells
A.1 Use of this Annex
A.2 Scope and field of application
A.3 General
A.3.1 Action affects and resistances
A.3.2 Notation
A.3.3 Boundary conditions
A.3.4 Sign convention
A.4 Cylindrical shells
Table A.1 — Loads inducing axial (meridional) membrane stresses
Table A.2 — Loads inducing circumferential membrane stresses
Table A.3 — Loads inducing membrane shear stresses
A.5 Conical shells
Table A.4 — Loads inducing axial (meridional) membrane stresses
Table A.5 — Loads inducing circumferential membrane stresses
Table A.6 — Loads inducing membrane shear stresses
A.6 Spherical shells
Table A.7 — Loads inducing membrane stresses
Annex B (informative) Formulae for plastic reference resistances of unstiffened shells and circular plates
B.1 Use of this Annex
B.2 Scope and field of application
B.3 General
B.3.1 Resistances
B.3.2 Notation
B.3.3 Boundary conditions
B.4 Uniform unstiffened cylindrical shells
B.4.1 Radial ring line load
Figure B.1 — Radial ring line load on a cylinder
B.4.2 Radial outward ring line load and axial tension
Figure B.2 — Radial ring line load with axial tension on a cylinder
B.4.3 Radial ring line load, internal pressure and axial load
Figure B.3 — Radial ring line load with internal pressure and axial load on a cylinder
Table B.1 — Determination of the length measure ℓm
B.5 Cylindrical shells with local ring stiffeners
B.5.1 Radial line ring load alone
Figure B.4 — Radial line ring load on a ring stiffener attached to a cylinder
B.5.2 Radial line ring load with axial load
Figure B.5 — Radial line ring load on a ring stiffener attached to a cylinder with axial load
B.5.3 Radial line ring load, internal pressure and axial load
Figure B.6 — Radial line ring load on a ring stiffener attached to a cylinder with axial load and internal pressure
Table B.2 — Parameters in the plastic resistance evaluation
B.6 Junctions between conical and cylindrical shells
B.6.1 Meridional forces alone (simplified)
Figure B.7 — Cone-cylinder junction under only meridional forces
B.6.2 Internal pressure and meridional forces
Figure B.8 — Cone-cylinder junction with internal pressure and meridional forces
Table B.3 — Equivalent thickness evaluation
Table B.4 — Parameters for plastic resistance evaluation
B.7 Circular plates with axisymmetric boundary conditions
B.7.1 Uniform transverse pressure with simply supported boundary
Figure B.9 — Simply supported circular plate under uniform transverse pressure
B.7.2 Central circular patch of transverse pressure with simply supported boundary
Figure B.10 — Simply supported circular plate under central circular patch of transverse pressure
B.7.3 Uniform transverse pressure with clamped boundary
Figure B.11 — Clamped supported circular plate under uniform transverse pressure
B.7.4 Central circular patch of transverse pressure with clamped boundary
Figure B.12 — Clamped supported circular plate under central circular patch of transverse pressure
Annex C (informative) Formulae for linear elastic membrane and bending stresses in unstiffened cylindrical shells and circular plates
C.1 Use of this Annex
C.2 Scope and field of application
C.3 General
C.3.1 Action effects
C.3.2 Notation
C.3.3 Boundary conditions
C.4 Clamped base cylindrical shells
C.4.1 Uniform internal pressure
Figure C.1 — Clamped cylinder under uniform internal pressure
Table C.1 — Maximum stress values
C.4.2 Axial loading
Figure C.2 — Clamped cylinder under axial load
Table C.2 — Maximum stress values
C.4.3 Uniform internal pressure with axial loading
Figure C.3 — Clamped cylinder under axial load with internal pressure
Table C.3 — Maximum stress values
C.4.4 Hydrostatic internal pressure
Figure C.4 — Clamped cylinder under hydrostatic internal pressure
Table C.4 — Maximum stress notation
Table C.5 — Maximum stress values for different lengths ℓp
C.4.5 Radial outward base displacement
Figure C.5 — Clamped cylinder with radial outward base displacement
Table C.6 — Maximum stress values
C.4.6 Uniform temperature rise
Figure C.6 — Clamped cylinder with uniform temperature rise
Table C.7 — Maximum stress values
C.5 Pinned base cylindrical shells
C.5.1 Uniform internal pressure
Figure C.7 — Pinned cylinder under uniform internal pressure
Table C.8 — Maximum stress values
C.5.2 Axial loading
Figure C.8 — Pinned cylinder under axial load
Table C.9 — Maximum stress values
C.5.3 Uniform internal pressure with axial loading
Figure C.9 — Pinned cylinder under axial load with internal pressure
Table C.10 — Maximum stress values for different axial to internal pressure ratios
C.5.4 Hydrostatic internal pressure
Figure C.10 — Pinned cylinder under hydrostatic internal pressure
Table C.11 — Maximum stress notation
Table C.12 — Maximum stress values for different lengths ℓp
C.5.5 Radial outward base displacement
Figure C.11 — Pinned cylinder with radial outward base displacement
Table C.13 — Maximum stress values
C.5.6 Uniform temperature rise
Figure C.12 — Pinned cylinder under uniform temperature rise T
Table C.14 — Maximum stress values
C.5.7 Boundary rotation
Figure C.13 — Pinned cylinder with base rotation βϕ
Table C.15 — Maximum stress values
C.6 Internal conditions in cylindrical shells
C.6.1 Step change of internal pressure
Figure C.14 — Abrupt step change in internal pressure
Table C.16 — Maximum stress values
C.6.2 Hydrostatic internal pressure termination
Figure C.15 — Termination of a hydrostatic internal pressure
Table C.17 — Maximum stress notation
Table C.18 — Maximum stress values
C.6.3 Step change of thickness
Figure C.16 — Step change of thickness under uniform internal pressure
Table C.19 — Maximum stress notation
Table C.20 — Maximum stress values for different changes in thickness
C.7 Local ring stiffener on a cylindrical shell
C.7.1 Radial force only on the ring
Figure C.17 — Ring attached to uniform thickness cylinder with radial load alone
C.7.2 Axial loading
Figure C.18 — Ring attached to uniform thickness cylinder under axial load
C.7.3 Uniform internal pressure
Figure C.19 — Ring attached to uniform thickness cylinder under uniform internal pressure
Table C.21 — Maximum stress notation
Table C.22 — Maximum stress values for different values of κ
C.8 Circular plates with simply supported boundary conditions
C.8.1 Uniform transverse load
Figure C.20 — Circular plate with simply supported edges under uniform transverse pressure
C.8.2 Local circular distributed load
Figure C.21 — Circular plate with simply supported edges under local transverse pressure
C.9 Circular plates with clamped boundary conditions
C.9.1 Uniform load
Figure C.22 — Circular plate with clamped edges under uniform transverse pressure
Table C.23 — Maximum stress values
C.9.2 Plate with fixed boundary: local distributed load
Figure C.23 — Circular plate with clamped edges under local transverse pressure
Table C.24 — Maximum bending and von Mises stress values
Annex D (normative) Formulae to determine the buckling resistance of unstiffened shells when using stress design
D.1 Use of this annex
D.2 Scope and field of application
D.3 Cylindrical shells of constant wall thickness: basic load cases
D.3.1 Notation and boundary conditions
Figure D.1 — Cylinder geometry, membrane stresses and stress resultants
D.3.2 Dimensionless lengths
D.3.3 Axial (meridional) compression
D.3.3.1 Length domains
D.3.3.2 Critical axial buckling stresses
D.3.3.3 Axial compression buckling capacity parameters
Table D.1 — Values of axial compression fabrication quality parameter Qx
D.3.3.4 Stainless steel cylinders under axial compression
Table D.2 — Values of the capacity parameters χxh, , μx0 and μxh for cylindrical shells made of austenitic, austenitic-ferritic and ferritic steels
Table D.3 — Formulae for the capacity parameters βx, ηx0 and ηxp for cylindrical shells made of austenitic, austenitic-ferritic and ferritic steels
D.3.4 Circumferential (hoop) compression
D.3.4.1 Length domains
Table D.4 — External pressure buckling factors for medium-length cylinders Cθ
Table D.5 — External pressure buckling factors for short cylinders Cθs
D.3.4.2 Critical circumferential buckling stresses
D.3.4.3 Circumferential buckling capacity parameters
Table D.6 — Values of circumferential compression fabrication quality parameter Qθ
D.3.5 Shear (torsion)
D.3.5.1 Length domains
D.3.5.2 Critical shear buckling stresses
D.3.5.3 Shear buckling capacity parameters
Table D.7 — Values of shear fabrication quality parameter Qτ
D.4 Cylindrical shells of constant wall thickness: combined cases
D.4.1 Axial (meridional) compression with coexistent internal pressure
D.4.1.1 Pressurised critical axial buckling stress
D.4.1.2 Pressurised axial buckling capacity parameters
D.4.2 External pressure under a wind pressure distribution
D.4.2.1 Critical circumferential buckling pressure under wind
Figure D.2 — Wind pressure distribution
D.4.3 Combinations of axial (meridional) compression, circumferential (hoop) compression and shear
Figure D.3 — Examples of interaction-relevant groups of membrane stress components
D.5 Cylindrical shells of stepwise variable wall thickness
D.5.1 General
D.5.1.1 Notation and boundary conditions
D.5.1.2 Geometry and joint offsets
Figure D.4 — Intended offset e0 in a butt-jointed shell
D.5.2 Axial (meridional) compression
D.5.3 Circumferential (hoop) compression
D.5.3.1 Critical circumferential buckling pressure and stresses
Figure D.5 — Stepped cylinder notation
D.5.3.2 Critical circumferential buckling pressure under wind
D.5.3.3 Buckling strength verification for circumferential compression in a stepped wall
D.5.3.4 Stiffening rings to resist buckling under external pressure and wind
D.5.3.4.1 General
D.5.3.4.2 Stiffness requirement for the top ring
Table D.8 — Simple values of the minimum flexural stiffness of a top ring
D.5.3.4.3 Bending moments in the top ring
D.5.4 Shear
D.5.4.1 Critical shear buckling stresses
D.5.4.2 Buckling strength verification for shear
D.6 Lap jointed cylindrical shells
D.6.1 General
D.6.1.1 Definitions
D.6.1.1.1 Circumferential lap joint
D.6.1.1.2 Meridional lap joint
D.6.1.2 Geometry and stress resultants
Figure D.6 — Lap jointed shell
D.6.2 Axial (meridional) compression
D.6.3 Circumferential (hoop) compression
D.6.4 Shear
D.7 Complete and truncated conical shells
D.7.1 General
D.7.1.1 Notation
Figure D.7 — Cone geometry, membrane stresses and stress resultants
D.7.1.2 Boundary conditions
D.7.1.3 Geometry
D.7.2 Design buckling stresses
D.7.2.1 Equivalent cylinder
D.7.2.2 Meridional compression
D.7.2.3 Circumferential (hoop) compression
D.7.2.4 Uniform external pressure
D.7.2.5 Shear
D.7.2.6 Uniform torsion
D.7.3 Buckling strength verification
D.7.3.1 Meridional compression
D.7.3.2 Circumferential (hoop) compression and uniform external pressure
D.7.3.3 Shear and uniform torsion
Annex E (normative) Formulae to determine the buckling resistance of unstiffened shells when using reference resistance design
E.1 Use of this annex
E.2 Scope and field of application
E.3 Cylindrical shells under uniform global bending
E.3.1 General
E.3.1.1 Notation
Figure E.1 — Cylinder under uniform global bending
E.3.1.2 Boundary conditions
E.3.1.3 Loading conditions
E.3.1.4 Length characterisation
E.3.2 Buckling resistance under uniform global bending
E.3.2.1 Reference plastic resistance
E.3.2.2 Reference elastic critical buckling resistance
E.3.2.3 Length domains
E.3.2.4 Buckling capacity parameters
Table E.1 — Values of fabrication quality parameter Qb
E.3.2.5 Characteristic buckling resistance
E.3.3 Buckling resistance under uniform global bending with axial compression
E.3.3.1 General
E.3.3.2 Interaction verification
E.4 Spherical dome shells
E.4.1 General
E.4.1.1 Scope
E.4.1.2 Notation
Figure E.2 — Spherical shell geometry
E.4.1.3 Support and boundary conditions
Figure E.3 — Illustrations of different support conditions
E.4.1.4 Loading conditions
Figure E.4 — Spherical dome subjected to uniform external pressure
E.4.2 Tolerances for spherical shells
E.4.3 Buckling design for uniform external pressure
E.4.3.1 Limitation on buckling calculations
E.4.3.2 Reference elastic critical buckling resistance
E.4.3.3 Reference plastic resistance
E.4.3.4 Buckling capacity parameters for simple conditions
Table E.2 — Values of dome fabrication quality parameter Qs
E.4.3.5 Characteristic buckling resistance
E.4.4 Buckling strength verification for uniform external pressure
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