SIST EN 1993-4-1:2007/A1:2017

SLOVENSKI STANDARD
SIST EN 1993-4-1:2007/A1:2017
01-september-2017
Evrokod 3: Projektiranje jeklenih konstrukcij - 4-1. del: Silosi
Eurocode 3 - Design of steel structures - Part 4-1: Silos
Eurocode 3 - Bemessung und Konstruktion von Stahlbauten - Teil 4-1: Silos
Eurocode 3 - Calcul des structures en acier - Partie 4-1: Silos
Ta slovenski standard je istoveten z: EN 1993-4-1:2007/A1:2017
ICS:
65.040.20 3RVORSMDLQQDSUDYH]D Buildings and installations for
SUHGHODYRLQVNODGLãþHQMH processing and storage of
NPHWLMVNLKSULGHONRY agricultural produce
91.010.30 7HKQLþQLYLGLNL Technical aspects
91.080.13 Jeklene konstrukcije Steel structures
SIST EN 1993-4-1:2007/A1:2017 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN 1993-4-1:2007/A1:2017

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SIST EN 1993-4-1:2007/A1:2017


EN 1993-4-1:2007/A1
EUROPEAN STANDARD

NORME EUROPÉENNE

June 2017
EUROPÄISCHE NORM
ICS 65.040.20; 91.010.30; 91.080.13
English Version

Eurocode 3 - Design of steel structures - Part 4-1: Silos
Eurocode 3 - Calcul des structures en acier - Partie 4-1 : Eurocode 3 - Bemessung und Konstruktion von
Silos Stahlbauten - Teil 4-1: Silos
This amendment A1 modifies the European Standard EN 1993-4-1:2007; it was approved by CEN on 3 March 2017.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for inclusion of
this amendment into the relevant national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.

This amendment exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the
same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.





EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2017 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 1993-4-1:2007/A1:2017 E
worldwide for CEN national Members.

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SIST EN 1993-4-1:2007/A1:2017
EN 1993-4-1:2007/A1:2017 (E)
Contents Page
European foreword . 3
1 Modification to the Foreword . 4
2 Modifications to 1.2, Normative references . 4
3 Modification to 1.6.1, Roman upper case letters . 4
4 Modification to 1.6.2, Roman lower case letters . 4
5 Modification to 2.7, Modelling of the silo for determining action effects . 4
6 Modification to 2.9.1, General . 4
7 Modification to 2.9.2.2, Partial factors for resistances . 5
8 Modification to 2.10, Durability . 5
9 Modification to 4.2.2.1, General . 5
10 Modification to 4.2.2.3, Consequence Class 2 . 5
11 Modifications to 4.4, Equivalent orthotropic properties of corrugated sheeting . 6
12 Modifications to 5.3.2.4, Buckling under axial compression. 9
13 Modification to 5.3.2.5, Buckling under external pressure, internal partial vacuum
and wind . 10
14 Modification to 5.3.2.6, Membrane shear . 10
15 Modification to 5.3.3.3, Buckling under axial compression. 10
16 Modifications to 5.3.4.1, General . 13
17 Modifications to 5.3.4.2,Plastic limit state . 13
18 Modification to 5.3.4.3.1, General . 14
19 Modifications to 5.3.4.3.3, Stiffened wall treated as an orthotropic shell . 14
20 Modification to 5.3.4.3.4, Stiffened wall treated as carrying axial compression only in
the stiffeners . 15
21 Modification to 6.3.1,General . 20
22 Modifications to 6.3.2.5, Local flexure at the transition . 20
23 Modification to 6.3.2.7, Buckling in hoppers . 20
24 Modification to 6.4.1,Supporting structures . 21
25 Modification to 8.2.2,Uniformly supported transition junctions . 21
26 Modification to 8.3.4.3,Annular plate transition junction . 24
27 Modification to 8.5.3, Base ring . 24
28 Modification to 9.4.1, General . 25
29 Modification to 9.4.2, General bending from direct action of the stored material . 25
30 Modification to 9.5.1, Forces in internal ties due to solids pressure on them . 26

2

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SIST EN 1993-4-1:2007/A1:2017
EN 1993-4-1:2007/A1:2017 (E)
European foreword
This document (EN 1993-4-1:2007/A1:2017) has been prepared by Technical Committee CEN/TC 250
“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 June 2018, and conflicting national standards shall be
withdrawn at the latest by June 2018.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent
rights.
This document has been prepared under a mandate given to CEN by the European Commission and the
European Free Trade Association.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
3

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SIST EN 1993-4-1:2007/A1:2017
EN 1993-4-1:2007/A1:2017 (E)
1 Modification to the Foreword
In the Section "National Annex for EN1993-4-1", replace the following entry:
"
− 6.3.2.7 (3)"
with:
"
− 6.3.2.7 (4)".
2 Modifications to 1.2, Normative references
In the entry dedicated to EN 1990, replace "EN 1990" with "EN 1990:2002" and replace the title of this
reference with "Eurocode – Basis of structural design".
In the entry dedicated to EN 1993, in the list, replace "Part 1.6:" with "Part 1.6:2007:".
3 Modification to 1.6.1, Roman upper case letters
Replace:
"R local radius at the crest or trough of a corrugation."
ϕ
with:
"r local radius at the crest or trough of a corrugation.".
ϕ
4 Modification to 1.6.2, Roman lower case letters
Replace:
"ℓ wavelength of a corrugation in corrugated sheeting;"
with:
"l wavelength of a corrugation in corrugated sheeting;".
5 Modification to 2.7, Modelling of the silo for determining action effects
Replace Paragraph (1)P with:
"(1)P The general requirements set out in EN 1990 shall be followed.".
6 Modification to 2.9.1, General
Replace Paragraph (1)P with:
"(1)P The general requirements set out in EN 1990 shall be satisfied.".
4

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SIST EN 1993-4-1:2007/A1:2017
EN 1993-4-1:2007/A1:2017 (E)
7 Modification to 2.9.2.2, Partial factors for resistances
Add two new Paragraphs (4) and (5) after Paragraph (3)P:
"(4) Where hot rolled steel sections are used as part of a silo structure, the relevant partial factors for
resistance should be taken from EN 1993-1-1.
(5) Where cold-formed steel sections are used as part of a silo structure, the relevant partial factors for
resistance should be taken from EN 1993-1-3.".
8 Modification to 2.10, Durability
Replace Paragraph (1) with:
"(1) The general requirements set out in 2.4 of EN 1990:2002 should be followed.".
9 Modification to 4.2.2.1, General
After Paragraph (2), add the following new Paragraphs (3) to (6):
"(3) Where the silo is subject to any form of unsymmetrical bulk solids loading (patch loads, eccentric
discharge, unsymmetrical filling etc.), the structural model should be designed to capture the
membrane shear transmission within the silo wall and between the wall and rings.
NOTE The shear transmission between parts of the wall and rings has special importance in construction
using bolts or other discrete connectors (e.g. between the wall and hopper, between the cylinder wall and vertical
stiffeners or support, and between different strakes of the cylinder).
(4) Where a ring girder is used to redistribute silo wall forces into discrete supports, and where bolts or
discrete connectors are used to join the structural elements, the shear transmission between the parts
of the ring due to shell bending and ring girder bending phenomena should be determined.
(5) The stiffness of the stored bulk solid in resisting wall deformations or in increasing the buckling
resistance of the shell structure should only be considered where a rational analysis is used and there is
clear evidence that the solid against the wall is not in motion at the specified location during discharge.
In such situations, the relevant information on the flow pattern, the pressure in the solid and the
properties of the specific stored bulk solid should be determined from EN 1991-4.
(6) Where a corrugated silo exhibits mass flow, the solid held stationary within the corrugations should
not be considered as stationary in (5).".
10 Modification to 4.2.2.3, Consequence Class 2
Delete the following Paragraphs (10) to (12):
"(10) Where the silo is subject to any form of unsymmetrical bulk solids loading (patch loads, eccentric
discharge, unsymmetrical filling etc.), the structural model should be designed to capture the
membrane shear transmission within the silo wall and between the wall and rings.
NOTE The shear transmission between parts of the wall and rings has special importance in construction
using bolts or other discrete connectors (e.g. between the wall and hopper, between different strakes of the
barrel).
5

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SIST EN 1993-4-1:2007/A1:2017
EN 1993-4-1:2007/A1:2017 (E)
(11) Where a ring girder is used to redistribute silo wall forces into discrete supports, and where bolts
or discrete connectors are used to join the structural elements, the shear transmission between the
parts of the ring due to shell bending and ring girder bending phenomena should be determined.
(12) Except where a rational analysis is used and there is clear evidence that the solid against the wall is
not in motion during discharge, the stiffness of the bulk solid in resisting wall deformations or in
increasing the buckling resistance of the structure should not be considered.".
11 Modifications to 4.4, Equivalent orthotropic properties of corrugated sheeting
Replace Figure 4.2 with:
"

Key
1 effective middle surface
Figure 4.2 — Corrugation profile and geometric parameters
".
Replace the notation lines in Paragraph (3) with:
"where:
d is the crest to crest dimension;
l is the wavelength of the corrugation;
r is the local radius at the crest or trough.".
ϕ
Replace Paragraph (4):
"(4) All properties may be treated as one-dimensional, giving no Poisson effects between different
directions."
with:
"(4) The equivalent properties of the sheeting in each of the two principal directions may be treated as
independent, so that strains in one direction do not produce stresses in the orthogonal direction (i.e. no
Poisson effects).".
6

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SIST EN 1993-4-1:2007/A1:2017
EN 1993-4-1:2007/A1:2017 (E)
Replace Paragraph (5) with the following paragraph:
"(5) The equivalent membrane properties (stretching stiffnesses) may be taken as:
(4.2)
C = Et
xx
C = Et (4.3)
yy
C =Gt (4.4)
xy xy
where:
t is the equivalent thickness for the smeared membrane stiffness normal to the
x
corrugations, given by:
3
(4.5)
2t
t =
x
2
3d
t is the equivalent thickness for the smeared membrane stiffness parallel to the
y
corrugations, given by:
22
(4.6)
 π d 
t t 1+
y  
2
4l
 
t is the equivalent thickness for the smeared membrane shear stiffness, given by:
xy
t
t =
xy
22
 π d 
(4.7)".
1+
 2 
4l
 

Replace Paragraph (6) with:
"(6) The equivalent bending properties (flexural stiffnesses) are defined in terms of the flexural rigidity
for moments causing bending stresses in that direction, and may be taken as:
D = EI (4.8)
xx
D = EI (4.9)
yy
D =GI (4.10)
xy xy
where:
I is the equivalent second moment of area per unit width for the smeared bending
x
stiffness perpendicular to the corrugations, given by:
7
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SIST EN 1993-4-1:2007/A1:2017
EN 1993-4-1:2007/A1:2017 (E)
3
(4.11)
t 1
I =
x
2 22
 
12 1−v π d
( )
1+
 
2
4l
 
I is the equivalent second moment of area per unit width for the smeared bending stiffness
y
parallel to the corrugations. For the corrugated profiles described in 4.4(2), it may be taken as:
2 22
(4.12)
td  π d 
I 1+
y  
2
88l
 
I is the equivalent second moment of area per unit width for the smeared twisting
xy
stiffness:
3 22
td π 
(4.13)
I 1+
xy  
2
12 4l
 

NOTE The convention for bending moments in plates relates to the direction in which the plate becomes
curved, so is contrary to the convention used for beams. Bending parallel to the corrugation engages the bending
stiffness of the corrugated profile, induces stresses parallel to the corrugation, and is the chief reason for using
corrugated construction.".
Replace Paragraph (7) with the following text and figure:
"(7) In circular silos, the corrugations are commonly arranged to run circumferentially. In this
arrangement, the directions x and y in the above expressions should be taken as the vertical x and
circumferential θ directions respectively, see Figure 4.3 a). In the less common arrangement in which
the corrugations run vertically, the directions x and y in the above expressions should be taken as the
circumferential θ and vertical x directions respectively, see Figure 4.3 b).


a) Corrugations running horizontally b) Corrugations running vertically
Figure 4.3 — Corrugated sheeting and silo wall orientations
".
8
=
=

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SIST EN 1993-4-1:2007/A1:2017
EN 1993-4-1:2007/A1:2017 (E)
Replace Paragraph (9) with the following text:
"(9) In rectangular silos, the corrugations are commonly arranged to run horizontally. In this
arrangement, the directions x and y in the above expressions should be taken as the vertical x and
horizontal y directions respectively, see Figure 4.3 a). In the less common arrangement where the
corrugations run vertically, the directions x and y in the above expressions should be interchanged on
the real structure and taken as the vertical y and horizontal x directions respectively, see Figure 4.3 b).".
12 Modifications to 5.3.2.4, Buckling under axial compression
In Paragraph (4), replace Formula (5.15) with:
"
0,83 (5.15)".
α =
0
0,88
1+Ψ2, 2 wt/
( )
ok

Replace Paragraph (7) with:
"(7) The plastic pressurised imperfection reduction factor α should be based on the largest local
pp
internal pressure p at the location of the point being assessed where the local thickness is t, and
g
coexistent with the local value of axial compression that may cause buckling:
22
(5.18)
p  

1 s +1, 21λ
g
x
α=1− 1−
  
pp 
2 3/2
λ 1,12+s ss+1
( )

x  

 
with:
p
r
g
(5.19)
p ⋅
g
σ t
x,Rcr
 1 r
(5.20)
s=
  
400 t
  
f
2 y (5.21)
λ =
x
σ
x,Rcr
where:
p is the largest design value of the local internal pressure (see EN 1991-4).
g
Different extremes of the material properties for a solid, defined in EN 1991-4, lead to different coupled
values of axial force and internal pressure. A consistent pair of values should be used each time when
applying Formulae (5.16) and (5.18).".
Add a new Paragraph (7a):
"(7a) The increase in buckling resistance of the shell structure due to the elastic stiffness of stationary
bulk solid may only be considered using a rational analysis, where there is clear evidence that the solid
against the wall is not in motion at the specified location during discharge and the relevant information
9
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SIST EN 1993-4-1:2007/A1:2017
EN 1993-4-1:2007/A1:2017 (E)
on the flow pattern, the pressure in the solid and the properties of the specific stored bulk solid are
determined from EN 1991-4.".
st
In Paragraph (9), in the 1 sentence, replace "lies in the range 0,3 < s < 1,0, the above" with "lies in the
range 0,3 < s < 0,8, the above".
In Paragraph (15), in the NOTE, replace "The values β = 0,60 and η = 1,0 are recommended." with "The
values of
0,95 5,4 and χ =1,0  are recommended.".
h
β 1− η=
1+1,2 wt/ 1+ 4,6 wt/
( ) ( )
ok ok
13 Modification to 5.3.2.5, Buckling under external pressure, internal partial
vacuum and wind
Replace Paragraph (9) with the following and the new Formula (5.40a):
"(9) Where the silo is isolated and subject to a combination of both wind loading and internal vacuum,
the value of C to be used in expression (5.38) should be modified to C , as given by:
w wc
(5.40a)
p +Cp
nu w nw
C =
wc
pp+
nu nw
where:
p is the design value of the uniform external pressure;
nu
p is the design value of the stagnation pressure of the wind;
nw
C is the wind pressure distribution coefficient given in Paragraph (8).".
w
14 Modification to 5.3.2.6, Membrane shear
In Paragraph (5), replace Formula (5.55) with:
"
(5.55)".
τ
xθ,Ed,max
 =
o
dτ
 
xθ,Ed
 
dy
 

15 Modification to 5.3.3.3, Buckling under axial compression
Replace Paragraphs (1) to (4) with:
"(1) The spacing of the stiffeners should not exceed the lesser of 24° and 1 000 mm.
(2) The axial compressive stress in the silo shell differs from that in the stiffeners due to the effect of
internal pressure acting on the silo shell alone. The axial stress resultant per unit circumference in the
10
=

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SIST EN 1993-4-1:2007/A1:2017
EN 1993-4-1:2007/A1:2017 (E)
silo shell n should be determined from the total axial force in the wall and stiffeners N at every
x,Ed x,Ed
level, as:
(5.58a)
N
f v pr
x,Ed
n −
x,Ed 
1+ f 2π rf

The axial force in each stiffener N should be determined from the total axial force in the wall and
sx,Ed
stiffeners N at each level, as:
x,Ed
N
1
x,Ed (5.58b)
N d +v pr
sx,Ed s
12+ frπ

dt
s
f=
in which
Α
s

where:
t is the local value of the shell wall thickness;
d is the circumferential distance between adjacent stiffeners;
s
A is the cross-sectional area of each stiffener;
s
ν is Poisson’s ratio (taken as 0,30);
p is the local value of the internal pressure (see EN 1991-4).
(3) Where the silo wall is not in contact with the stored solid, the buckling resistance of the stiffener to
axial compression should be calculated assuming a uniform compressive stress on the entire cross-
sectional area at any level.
(4) The buckling effective length of the stiffener used in determining the reduction factor χ should be
taken as equal to:
1/4
(5.58c)
EI

sy
L =π
e 
K

but not greater than the distance between adjacent ring stiffeners
where:
2
EI is the flexural rigidity of the stiffener for bending normal to the plane of the wall (Nmm );
sy
K is the stiffness offered by the shell wall (N/mm per mm of wall height) to restrain buckling
  normal to the wall.
(5) The stiffness of the shell wall K in restraining the effective length of the stiffener should be
determined assuming that the wall spans between adjacent vertical stiffeners on either side. Two
alternative methods may be used, as defined in Paragraphs (6) and (7).
(6) A simple assessment of the value of K may be made treating the shell wall as straight with simply
supported boundary conditions (see Figure 5.5). The value of K may then be estimated as:
11
=
=

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EN 1993-4-1:2007/A1:2017 (E)
3
 
t (5.58d)
K=kE
 
s
d
 s
where:
k is a stiffness coefficient.
s
NOTE The National Annex may choose the value of k . The value k = 0,5 is recommended.
s s
t is the local thickness of the shell wall at the location being assessed;
d is the circumferential separation of the vertical stiffeners.
s
(7) A more advanced assessment of the value of K may be made by treating the curved wall as an arch
spanning between adjacent stiffeners (Figure 5.6). The value of K may then be estimated using:

3
1 2Et


K=

2
22 2 2
r

ft +12r f+φφcos tanφ+−2g 2 2g sin2φ− 2g cos2φ− cosφ − sinφ cosφ−1
( ) ( ) ( )
{ }



(5.58e)
d
s
(5.58f)
φ=
r
1
2
(5.58g)
fg4+1(2φφ+ sin2 )+−4g(1 cos2φ)− 2sin2φ
( )
{ }
4
22 2
trsinφ−12  1− cosφ 1+−3cosφ φsin2φ
( )( )
(5.58h)
 
g=
22

tr2φφ+−sin2 12 2φ 2+ cos2φ − 3sin2φ
( ) ( )

(8) Where the flow pattern in the granular solid, the pressure in the solid, the properties of the solid,
and the relationship of the solid’s stiffness to the local pressure can all be reliably predicted using EN
1991-4, a rational analysis of the stiffness of stationary solid against the silo wall may be included in the
assessment of the stiffness of the shell wall K.
(9) The characteristic buckling resistance of the shell wall n should be calculated as defined in
x,Rk
5.3.2.4.
(10) Where a rolled section is used for the stiffener, the axial compression buckling resistance of the
stiffener N should be assessed as under concentric compression according to EN 1993-1-1,
s,b,Rk
considering only buckling normal to the shell wall.
(11) Where a cold-formed member is used for the stiffener, the axial compression buckling resistance
should assessed as under concentric compression according to EN 1993-1-3, considering only buckling
normal to the shell wall.
(12) The connectors between the stiffener and the silo shell should be at a vertical spacing not greater
than L /4, where L is determined using Paragraph (4).
e e
12
=

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EN 1993-4-1:2007/A1:2017 (E)
(13) Where the centroid of one segment of the stiffener is not co-linear with the centroid of the adjacent
segment, consideration should be given to the use of a longer sleeve and the connection should be
designed to transmit the bending moment arising from the eccentricity of the axial force transferred.
(14) There should be no cause introducing unintentional bending moments into the stiffener (e.g.
resulting from an eccentricity between the section centroidal axis and the centroid of the bolts used in
connections, such as sleeves, overlaps, etc.).
(15) The eccentricity of the stiffener centroid to the silo shell middle surface may be ignored.".
16 Modifications to 5.3.4.1, General
Replace Paragraph (1):
"(1) All calculations should be carried out with thicknesses exclusive of coatings and tolerances."
with:
"(1) All calculations should be carried out with thicknesses exclusive of coatings. Tolerances on
thickness should be adopted according to the requirements of EN 1993-1-3.".
Replace Paragraph (4):
"(4) Particular attention should be paid to ensure that the stiffeners are flexurally continuous with
respect to bending in the meridional plane normal to the wall, because the flexural continuity of the
stiffener is essential in developing resistance to buckling under wind or external pressure as well as
when the stored solids flow."
with:
"(4) Where the continuity of stiffeners is obtained by semi-rigid connections such as overlaps or
sleeves, etc., the rotational rigidity of the connections should be taken into account in the verification of
their resistance and stability under actions due to stored solids as well as under wind or external
pressure.".
17 Modifications to 5.3.4.2,Plastic limit state
Replace Paragraph (3):
"(3) The spacing between fasteners around the circumference should not exceed 3° of the
circumference."
with:
"(3) The spacing between fasteners around the circumference should not exceed the lesser of 500 mm
and 15° of the circumference, as shown in Figure 5.4.".
13

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SIST EN 1993-4-1:2007/A1:2017
EN 1993-4-1:2007/A1:2017 (E)
Replace Figure 5.4 with:
"

Figure 5.4 — Typical bolt arrangement for a panel of a corrugated silo
".
18 Modification to 5.3.4.3.1, General
In Paragraph (2), replace:
"b) buckling of the individual stiffeners (corrugated wall assumed to carry no axial force, but
providing restraint to the stiffeners) and following 5.3.4.3.4 if the horizontal distance
between stiffeners does not satisfy 5.3.4.3.3 (2)."
with:
"b) buckling of the individual stiffeners (corrugated wall assumed to carry no axial force, but
providing restraint to the stiffeners) and following 5.3.4.3.4.".
19 Modifications to 5.3.4.3.3, Stiffened wall treated as an orthotropic shell
In Paragraph (2), replace:
"NOTE The National Annex may choose the value of k . The value k = 7,4 is recommended."
dx dx
with the following paragraph:
"NOTE The National Annex may choose the value of k . The value k = 9,1 is
dx dx
recommended.".
Replace the top part of Paragraph (3) (including Equation (5.65) itself) with:
"(3) The critical buckling stress resultant n per unit circumference of the orthotropic shell
x,Rcr
(Method a) in 5.3.4.3.1) should be evaluated at each appropriate level in the silo. The critical buckling
stress resultant n may be evaluated for any chosen circumferential mode (wave number) j and any
x,Rcr
prospective height of the buckle ℓ by minimising the following expression with respect to both j and ℓ .
i i
The values of ℓ may take any value up to the total height of the wall, but may take any smaller values.
i
14

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SIST EN 1993-4-1:2007/A1:2017
EN 1993-4-1:2007/A1:2017 (E)
The minimisation to find the critical value of n may be made by any appropriate minimisation
x,Rcr
(optimisation) procedure.

1 A
(5.65)
2
nA+

x,Rcr 1
22
jAω
3
Where no ring stiffeners are present, the values of A , I and I should be taken as zero, but d should
r r tr r
be taken as non-zero to avoid division by zero. Where no stringer stiffeners are present, the values of
A , I and I should be taken as zero, but d should be taken as non-zero to avoid division by zero.
s s ts s
It may be helpful to draw a contour plot of n against j and ℓ as this may provide a faster means of
x,Rcr i
optimising Formula (5.65) than simple trial and error.".
Replace Paragraph (
...