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eLibrary > BS EN 1993-4-1:2026 Eurocode 3. Design of steel structures - Silos >

BS EN 1993-4-1:2026 Eurocode 3. Design of steel structures - Silos, 2026

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European foreword
0 Introduction
1 Scope [Go to Page]
1.1 Scope of EN 1993-4-1
1.2 Assumptions
Figure 1.1 — Terminology used in silo structures
2 Normative references
3 Terms, definitions, symbols, sign conventions and units [Go to Page]
3.1 Terms and definitions
3.2 Symbols used in this document [Go to Page]
3.2.1 Latin upper-case letters
3.2.2 Latin lower-case letters
3.2.3 Greek letters
3.2.4 Subscripts
3.3 Sign conventions [Go to Page]
3.3.1 Conventions for global silo structure axis system for circular silos
Figure 3.1 — Global coordinate system and loadings on a circular silo [Go to Page]
3.3.2 Conventions for global silo structure axis system for rectangular silos
Figure 3.2 — Global coordinate system and loadings on a rectangular silo [Go to Page]
3.3.3 Conventions for structural element axes in both circular and rectangular silos
Figure 3.3 — Local coordinate systems for walls and meridional stiffeners on a shell
Figure 3.4 — Local coordinate systems for walls and meridional stiffeners on a box
Figure 3.5 — Local coordinate system for circumferential ring stiffeners on a shell for directions of bending [Go to Page]
3.3.4 Conventions for stress resultants for circular silos and rectangular silos
Figure 3.6 — Stress resultants in the shell silo wall
4 Basis of design [Go to Page]
4.1 Basic requirements
4.2 Units
4.3 Silo classifications [Go to Page]
4.3.1 Consequence Classification for silos
4.3.2 Structural Complexity Classification for silos
Figure 4.1 — Dimensions used to define Structural Complexity Classes
Table 4.1 (NDP) — Descriptions and quantified limits for parameter w for Structural Complexity Classes for silos [Go to Page]
4.3.3 Silo Group Categorization
Table 4.2 (NDP) — Silo Group (SG) defined by the Structural Complexity Class (SCC), and Consequence Class (CC) [Go to Page]
4.4 Verification by the partial factor method [Go to Page]
4.4.1 Partial factors for actions on silos
4.4.2 Partial factors for resistances
Table 4.3 — Partial factors for resistance
Table 4.4 (NDP) — Numerical values for partial factors for resistance for silo structures [Go to Page]
4.5 Actions and environmental effects [Go to Page]
4.5.1 General
4.5.2 Wind action
4.5.3 Combination of particulate solids pressures with other actions
4.6 Geometrical data
4.7 Modelling of the silo for determining action effects
4.8 Design assisted by testing
4.9 Action effects for limit state verifications
4.10 Durability
4.11 Fire resistance
5 Properties of materials [Go to Page]
5.1 General
Table 5.1 — Temperature dependent reduction factor kT
Table 5.2 — Temperature dependent reduction factor kT,E [Go to Page]
5.2 Structural steels
5.3 Stainless steels
5.4 Special alloy steels
5.5 Toughness requirements
6 Basis for structural analysis [Go to Page]
6.1 Ultimate limit states [Go to Page]
6.1.1 Basis
6.1.2 Required checks
6.1.3 High cycle fatigue and cyclic plasticity (low cycle fatigue)
6.1.4 Allowance for corrosion and abrasion
6.1.5 Allowance for temperature effects
6.2 Serviceability limit states
6.3 Analysis of the structure of a shell silo [Go to Page]
6.3.1 Modelling of the structural shell
6.3.2 Methods of analysis [Go to Page]
6.3.2.1 General
6.3.2.2 Silo Group 3
6.3.2.3 Silo Group 2
Figure 6.1 — Vertical deformation compatibility between ring girder and shell [Go to Page]
6.3.2.4 Silo Group 1
6.3.2.5 Silo Group 0
6.3.3 Geometric imperfections
6.4 Analysis of the box structure of a plate assembly silo [Go to Page]
6.4.1 Modelling of the structural box formed by an assembly of plates
6.4.2 Geometric imperfections
6.4.3 Methods of analysis
6.5 Analysis treatment of corrugated sheeting
Figure 6.2 — Corrugation profile and geometric parameters
Figure 6.3 — Corrugated sheeting and silo wall orientations
7 Ultimate limit state design of cylindrical shell walls [Go to Page]
7.1 Basis [Go to Page]
7.1.1 General
7.1.2 Silo wall design
7.2 Distinctions between cylindrical shell forms
Figure 7.1 — Illustrations of cylindrical shell forms [Go to Page]
7.3 Resistance of isotropic welded or bolted cylindrical walls [Go to Page]
7.3.1 General
7.3.2 Evaluation of design stress resultants
7.3.3 Plastic limit state
7.4 Resistance of isotropic cylindrical walls under axial compression [Go to Page]
7.4.1 Elastic buckling under uniform axial compression
Table 7.1 — Fabrication tolerance quality classes [Go to Page]
7.4.2 Elastic buckling under non-uniform axial compression
Figure 7.2 — Representation of local distribution of axial membrane stress resultant around the circumference [Go to Page]
7.4.3 Elastic axial compression buckling above a horizontal lap joint
7.4.4 Simple treatment of buckling resistance above a discrete support
7.4.5 Buckling resistance under axial compression evaluation
7.5 Resistance of isotropic cylindrical walls under external pressure, internal partial vacuum and wind [Go to Page]
7.5.1 Buckling of the cylindrical wall
Figure 7.3 — Notation for stepped wall with different heights of strakes
Table 7.2 — Values of external pressure buckling parameter Cb [Go to Page]
7.5.2 Upper edge restraint by an eaves ring
7.5.3 Secondary ring stiffeners
7.5.4 Resistance of isotropic cylindrical walls under membrane shear
7.6 Interactions between axial compression, circumferential compression and membrane shear in isotropic walls
7.7 Isotropic walls under cyclic loads [Go to Page]
7.7.1 Fatigue, LS4
7.7.2 Cyclic plasticity, LS2
7.8 Resistance of isotropic walls with vertical stiffeners [Go to Page]
7.8.1 General
7.8.2 Plastic limit state
7.8.3 Buckling under axial compression
7.8.4 Buckling under external pressure, partial vacuum or wind
7.8.5 Buckling under membrane shear
7.9 Resistance of horizontally corrugated cylindrical walls [Go to Page]
7.9.1 General
Figure 7.4 — Common arrangements for cold-formed vertical stiffeners on horizontally corrugated shells [Go to Page]
7.9.2 Tolerance requirements
7.9.3 Plastic limit state
Figure 7.5 — Typical bolt arrangement for a panel of a corrugated silo [Go to Page]
7.9.4 Buckling under axial compression [Go to Page]
7.9.4.1 General
7.9.4.2 Unstiffened corrugated wall
7.9.4.3 Stiffened corrugated cylindrical walls treated as carrying axial compression only in the stiffeners
Figure 7.6 — Evaluation of restraint stiffness against stiffener column buckling using a curved wall treatment
Figure 7.7 — Cold-formed stiffeners with edge stiffened flanges: buckling curve b (as in EN 1993-1-3)
Figure 7.8 —Stiffeners with unstiffened flanges: buckling curve c (as in EN 1993-1-1) [Go to Page]
7.9.4.4 Stiffened corrugated cylindrical wall treated as an orthotropic shell
7.9.4.5 Local, distortional and flexural torsional buckling of stiffeners
7.9.5 Buckling of corrugated cylindrical shells under external pressure, partial vacuum or wind
7.9.6 Buckling of corrugated cylindrical shells under membrane shear
7.10 Vertically corrugated cylindrical walls with ring stiffeners [Go to Page]
7.10.1 General
7.10.2 Plastic limit state
7.10.3 Buckling under axial compression
7.10.4 Buckling under external pressure, partial vacuum or wind
7.10.5 Membrane shear
7.11 Detailing for openings in cylindrical walls [Go to Page]
7.11.1 General
7.11.2 Rectangular openings
Figure 7.9 — Typical stiffening arrangements for openings in silo walls
8 Support conditions for cylindrical walls [Go to Page]
8.1 Shell with its base fully supported
8.2 Isotropic shell supported by a skirt
8.3 Isotropic cylindrical shell wall with engaged columns
Figure 8.1 — Different arrangements for support of silo with hopper [Go to Page]
8.4 Framework support beneath an isotropic walled silo
Figure 8.2 — Simple tour support framework
Figure 8.3 — Standard eight support framework
Figure 8.4 — Alternative eight support framework [Go to Page]
8.5 Discretely supported isotropic cylindrical shell without a ring girder
8.6 Discretely supported isotropic cylindrical shell with a ring girder
8.7 Discretely supported isotropic cylindrical shell with an intermediate ring [Go to Page]
8.7.1 Intermediate ring at the ideal height
Figure 8.5 — Discretely supported silo with intermediate ring [Go to Page]
8.7.2 Intermediate ring placed below the ideal height
8.8 Discretely supported isotropic silo with columns beneath the hopper
8.9 Local support details and ribs for load introduction in isotropic cylindrical walls [Go to Page]
8.9.1 Local supports beneath the wall of an isotropic cylinder
Figure 8.6 — Typical details of supports [Go to Page]
8.9.2 Local ribs for load introduction into isotropic cylindrical walls
Figure 8.7 — Typical details of loading rib attachments [Go to Page]
8.10 Anchorage at the base of an isotropic walled silo
8.11 Isotropic walled cylindrical shells with vertical stiffeners with the base fully supported
8.12 Corrugated stiffened cylindrical shells with the base fully supported
9 Ultimate limit state design of isotropic conical hoppers [Go to Page]
9.1 Basis [Go to Page]
9.1.1 General
9.1.2 Distinctions between hopper shell forms
9.2 Isotropic hopper wall design
9.3 Resistance of isotropic conical hoppers [Go to Page]
9.3.1 General
Figure 9.1 — Hopper shell segment [Go to Page]
9.3.2 Isotropic unstiffened welded or bolted hoppers [Go to Page]
9.3.2.1 General
9.3.2.2 Plastic mechanism or rupture in the hopper body
9.3.2.3 Rupture at the transition junction
Figure 9.2 — Hopper transition joint: potential for rupture [Go to Page]
9.3.2.4 Plastic mechanism at thickness changes or at the transition
Figure 9.3 — Plastic collapse of conical hopper [Go to Page]
9.3.2.5 Local flexure in the hopper below the transition
Figure 9.4 — Notation for the top of a conical hopper [Go to Page]
9.3.2.6 Hoppers that are part of a silo resting on discrete supports beneath the cylindrical wall
9.3.2.7 Buckling in shell hoppers
9.4 Considerations for special hopper structures [Go to Page]
9.4.1 Supporting structures
9.4.2 Hoppers supported on a structural framework
9.4.3 Column supported hopper
9.4.4 Unsymmetrical hopper
Figure 9.5 — Unsymmetrical hopper with engaged columns in cylinder [Go to Page]
9.4.5 Stiffened conical hoppers
9.4.6 Multi-segment conical hoppers
10 Ultimate limit state design of transition junctions and base rings in circular silos [Go to Page]
10.1 Basis [Go to Page]
10.1.1 General
10.1.2 Transition ring and ring girder design
10.1.3 Distinctions between transition junction forms
10.1.4 Modelling of isotropic transition junctions
Figure 10.1 — Example ring forms [Go to Page]
10.1.5 Limitations on ring placement
10.2 Analysis of the transition junction [Go to Page]
10.2.1 General
Figure 10.2 — Example showing membrane stresses developed in an annular plate ring and adjacent shell when the ring is eccentric [Go to Page]
10.2.2 Uniformly supported isotropic transition junctions
Figure 10.3 — Effective section of the cylinder / hopper / ring transition
Figure 10.4 — Notation for simple annular plate transition junction
Figure 10.5 — Transition junction without added ring
Figure 10.6 — Local pressures and membrane stress resultant loadings on the transition ring [Go to Page]
10.2.3 Isotropic transition junction ring girder above discrete supports
Figure 10.7 — Eccentricities of vertical loads at a ring girder [Go to Page]
10.3 Structural resistances for isotropic junctions [Go to Page]
10.3.1 General
10.3.2 Resistance to plastic limit state [Go to Page]
10.3.2.1 General
10.3.2.2 Plastic resistance based on elastic evaluation
10.3.2.3 Plastic resistance based on plastic evaluation
10.3.3 Resistance to in-plane buckling
10.3.4 Resistance to out-of-plane buckling and local shell buckling near the junction [Go to Page]
10.3.4.1 General
10.3.4.2 Local shell buckling near the junction
10.3.4.3 Annular plate transition junction
10.3.4.4 T section transition junction
10.4 Limit state verifications for isotropic transition junctions [Go to Page]
10.4.1 Uniformly supported transition junctions
10.4.2 Transition junction ring girder
10.5 Considerations concerning support arrangements for the junction [Go to Page]
10.5.1 Skirt supported junctions
10.5.2 Column supported junctions and ring girders
10.5.3 Base ring
11 Ultimate limit state design of circular conical roof structures [Go to Page]
11.1 Basis
11.2 Distinctions between roof structural forms [Go to Page]
11.2.1 Descriptors for roofs
11.3 Resistance of circular conical isotropic roofs on silos [Go to Page]
11.3.1 Shell or unsupported roofs
11.3.2 Framed or supported roofs
11.3.3 Profiled sheeting roofs
11.3.4 Eaves junction (roof to shell junction)
12 Ultimate limit state design of rectangular and polygonal silos [Go to Page]
12.1 Basis
12.2 Classification of polygonal structural forms [Go to Page]
12.2.1 Unstiffened silos
12.2.2 Stiffened silo
12.2.3 Silos with ties
Figure 12.1 — Plan view of tied rectangular box and multiple cells
Figure 12.2 — Typical details of wall panel and tie connections [Go to Page]
12.3 Resistance of unstiffened vertical walls
12.4 Resistance of silo walls composed of stiffened or corrugated plates [Go to Page]
12.4.1 General
Figure 12.3 — Typical vertical section through a corrugated rectangular silo wall
Figure 12.4 — Shear response of corrugated wall [Go to Page]
12.4.2 General bending from direct action of the stored material
Figure 12.5 — Bending neutral axis under combined horizontal pressure and frictional traction (vertical section) [Go to Page]
12.4.3 Membrane stresses from diaphragm action
Figure 12.6 — Membrane forces induced in walls by particulate solids pressures or wind loading [Go to Page]
12.4.4 Local bending action from the stored material and/or equipment
Figure 12.7 — Possible causes of local bending in corrugated plates [Go to Page]
12.5 Silos with internal ties [Go to Page]
12.5.1 Forces in internal ties due to particulate solids pressure on them
Figure 12.8 — Evaluation of factor β for internal ties
Figure 12.9 — Corner ties for which β = 0,7 [Go to Page]
12.5.2 Modelling and principles of calculation of ties
Figure 12.10 — Sections through a silo with internal ties
Figure 12.11 — Forces and deformation in a flexible tie fixed on horizontal elastic supports
Figure 12.12 — Tie tension forces acting on the structural walls [Go to Page]
12.5.3 Load cases for silos with internal ties
12.5.4 Vertical stiffeners on silos with internal ties
12.6 Strength of pyramidal hoppers
Figure 12.13 — Unsymmetrical hopper with inclined ribs [Go to Page]
12.7 Vertical stiffeners on box walls
12.8 Support requirements for plate assemblies
13 Serviceability requirements [Go to Page]
13.1 General
13.2 Deflections of stiffened and unstiffened isotropic cylindrical shell walls
13.3 Deflections of stiffened and unstiffened corrugated cylindrical shell walls
13.4 Conical hoppers [Go to Page]
13.4.1 Basis
13.4.2 Vibration
13.5 Rectangular and polygonal silos [Go to Page]
13.5.1 Basis
13.5.2 Deflections
Annex A (informative) Simplified rules for isotropic walled circular silos in Silo Group 1
A.1 Use of this Annex
A.2 Scope and field of application
A.3 Action combinations for Silo Group 1
A.4 Action effect assessment
A.5 Ultimate limit state assessment
A.5.1 General
A.5.2 Isotropic welded or bolted cylindrical walls
A.5.2.1 Plastic limit state
A.5.2.2 Axial compression
A.5.2.3 External pressure, internal partial vacuum and wind
A.5.3 Conical welded or bolted hoppers
Figure A.1 — Hopper global equilibrium
A.5.4 Transition junction
Figure A.2 — Notation for a simple transition junction
Annex B (informative) Simplified rules for transition junction ring girders in circular silos with horizontally corrugated wall and vertical stiffeners
B.1 Use of this annex
B.2 Scope and field of application
Figure B.1 — Illustration of fully supported vertical stiffeners
B.3 Evaluation of the circumferential force in the transition ring
Figure B.2 — Vertical forces acting at the level of the transition
B.4 Evaluation of the circumferential force in the transition ring
B.4.1 Geometry of the transition ring
Figure B.3 — Examples of transition ring sections
B.4.2 Determination of the circumferential force in the ring
Figure B.4 — Forces acting on the transition ring
B.5 Determination of the buckling resistance of the transition ring
Annex C (informative) Formulae for membrane stress resultants in conical hoppers
C.1 Use of this annex
C.2 Scope and field of application
C.3 General hopper theory pressures (as per EN 1991-4)
C.4 Uniform normal pressure po with frictional traction μpo
C.5 Linearly varying normal pressure from p1 at apex to p2 at transition with frictional traction μp
C.6 “Radial stress field” normal pressure pattern with triangular switch stress below the transition
Bibliography [Go to Page]

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