SIST EN 1993-4-1:2007/kFprA1:2014
(Amendment)Eurocode 3 - Design of steel structures - Part 4-1: Silos
Eurocode 3 - Design of steel structures - Part 4-1: Silos
- Corrugated silos with vertical stiffeners
- Axially stiffened silos with isotropic walls
- Hopper buckling and transition junctions
- Anchorage and wind pressure combinations
- Internal ties in rectangular silos
- Elephant’s foot buckling and restrictions on all silos
Eurocode 3 - Bemessung und Konstruktion von Stahlbauten - Teil 4-1: Silos
Eurocode 3 - Calcul des structures en acier - Partie 4-1: Silos
Evrokod 3: Projektiranje jeklenih konstrukcij - 4-1. del: Silosi
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN 1993-4-1:2007/kFprA1:2014
01-november-2014
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/FprA1
ICS:
65.040.20 3RVORSMDLQQDSUDYH]D Buildings and installations for
SUHGHODYRLQVNODGLãþHQMH processing and storage of
NPHWLMVNLKSULGHONRY agricultural produce
91.010.30 7HKQLþQLYLGLNL Technical aspects
91.080.10 Kovinske konstrukcije Metal structures
SIST EN 1993-4-1:2007/kFprA1:2014 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/kFprA1:2014
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SIST EN 1993-4-1:2007/kFprA1:2014
EUROPEAN STANDARD
FINAL DRAFT
EN 1993-4-1:2007
NORME EUROPÉENNE
EUROPÄISCHE NORM
FprA1
August 2014
ICS 65.040.20; 91.010.30; 91.080.10
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 Stahlbauten
Silos - Teil 4-1: Silos
This draft amendment is submitted to CEN members for unique acceptance procedure. It has been drawn up by the Technical Committee
CEN/TC 250.
This draft amendment A1, if approved, will modify the European Standard EN 1993-4-1:2007. If this draft becomes an amendment, 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.
This draft amendment was established by CEN 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, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United
Kingdom.
Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are aware and to
provide supporting documentation.
Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without notice and
shall not be referred to as a European Standard.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2014 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 1993-4-1:2007/FprA1:2014 E
worldwide for CEN national Members.
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SIST EN 1993-4-1:2007/kFprA1:2014
EN 1993-4-1:2007/FprA1:2014 (E)
Contents Page
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 .4
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 .8
13 Modification to 5.3.2.5, Buckling under external pressure, internal partial vacuum and
wind .9
14 Modification to 5.3.2.6, Membrane shear . 10
15 Modifications to 5.3.3.3, Buckling under axial compression . 10
16 Modifications to 5.3.4.1, General . 12
17 Modifications to 5.3.4.2,Plastic limit state . 12
18 Modification to 5.3.4.3.1, General . 13
19 Modifications to 5.3.4.3.3, Stiffened wall treated as an orthotropic shell . 13
20 Modifications to 5.3.4.3.4, Stiffened wall treated as carrying axial compression only in the
stiffeners . 14
21 Modification to 6.3.1,General . 18
22 Modifications to 6.3.2.5, Local flexure at the transition . 19
23 Modification to 6.3.2.7, Buckling in hoppers . 19
24 Modification to 6.4.1,Supporting structures . 20
25 Modification to 8.2.2,Uniformly supported transition junctions . 20
26 Modification to 8.3.4.3,Annular plate transition junction . 22
27 Modification to 8.5.3, Base ring . 22
28 Modification to 9.4.1,General . 22
29 Modification to 9.4.2, General bending from direct action of the stored material . 23
30 Modification to 9.5.1, Forces in internal ties due to solids pressure on them . 23
2
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SIST EN 1993-4-1:2007/kFprA1:2014
EN 1993-4-1:2007/FprA1:2014 (E)
Foreword
This document (EN 1993-4-1:2007/FprA1:2014) has been prepared by Technical Committee CEN/TC 250
“Structural Eurocodes”, the secretariat of which is held by BSI.
This document is currently submitted to the Unique Acceptance Procedure.
3
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SIST EN 1993-4-1:2007/kFprA1:2014
EN 1993-4-1:2007/FprA1:2014 (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".
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:
" 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.".
7 Modification to 2.9.2.2,Partial factors for resistances
Add two new Paragraphs (4) and (5) after Paragraph (3)P:
4
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SIST EN 1993-4-1:2007/kFprA1:2014
EN 1993-4-1:2007/FprA1:2014 (E)
"(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 (5):
"(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).
(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.
5
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SIST EN 1993-4-1:2007/kFprA1:2014
EN 1993-4-1:2007/FprA1:2014 (E)
(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 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 Figure 4.2 with:
"
Key
1 effective middle surface
Figure 4.2 — Corrugation profile and geometric parameters
".
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 (no Poisson
effects).".
Replace Paragraph (5) with the following paragraph and renumber accordingly all the following equations in
the subclause:
"(5) The equivalent membrane properties (stretching stiffnesses) may be taken as:
C = Et (4.2)
x x
C = Et (4.3)
y y
C = Gt (4.4)
xy xy
where:
6
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SIST EN 1993-4-1:2007/kFprA1:2014
EN 1993-4-1:2007/FprA1:2014 (E)
t is the equivalent thickness for the smeared membrane stiffness normal to the corrugations,
x
given by:
3
2t
t = (4.5)
x
2
3d
t is the equivalent thickness for the smeared membrane stiffness parallel to the
y
corrugations, given by:
2 2
π d
t = t 1+ (4.6)
y
2
4l
t is the equivalent thickness for the smeared membrane shear stiffness, given by:
xy
t
t = (4.7)".
xy
2 2
π d
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)
x x
D = EI (4.9)
y y
D = GI (4.10)
xy xy
where:
I is the equivalent second moment of area per unit width for the smeared bending stiffness
x
to the corrugations, given by:
3
t 1
(4.11)
I =
x
2
2 2
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 2 2
td π d
(4.12)
I = 1+
y
2
8
8l
I is the equivalent second moment of area per unit width for the smeared twisting stiffness:
xy
3 2 2
t π d
I = 1+
xy
2
12
4l
(4.13)
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.".
7
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EN 1993-4-1:2007/FprA1:2014 (E)
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
".
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
α = (5.15)".
0
0,88
1+ 2,2Ψ (∆ w / t)
ok
Replace Paragraph (7) with:
"(7) The plastic pressurised imperfection reduction factor α should be based on the largest local internal
pp
pressure p at the location of the point being assessed where the local thickness is t, and coexistent with the
g
local value of axial compression that may cause buckling:
8
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EN 1993-4-1:2007/FprA1:2014 (E)
2
2
p
1 s + 1,21λ
g
x
α = 1− 1− (5.18)
pp
2 3 / 2
( )
s s+ 1
1,12+ s
λ
x
with:
p
r
g
p = ⋅
g
σ t
x,Rcr
(5.19)
1 r
s=
400 t
(5.20)
f
2
y
λ =
x
σ
x,Rcr (5.21)
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 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 of β = 0,60 and η = 1,0 are recommended." with "The
0,95 5,4
values of β= 1− and η= are recommended.".
1+1,2(∆w / t) 1+ 4,6(∆w / t)
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
p + C p
nu w nw
C = (5.40a)
wc
p + p
nu nw
where:
9
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EN 1993-4-1:2007/FprA1:2014 (E)
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:
"
τ
xθ, Ed, max
= (5.55)".
o
dτ
xθ, Ed
dy
15 Modifications 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 silo shell n
x,Ed
N at every level, as:
should be determined from the total axial force in the wall and stiffeners
x,Ed
N
f v p r
x, Ed
n = − (5.58a)
x, Ed
1+ f 2π r f
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
N = d + v p r
sx,Ed s
1+ f 2π r
(5.58b)
d t
s
in which f=
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.
10
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EN 1993-4-1:2007/FprA1:2014 (E)
(4) The buckling effective length of the stiffener used in determining the reduction factor χ should be taken as
equal to:
1/ 4
EI
sy
L =π (5.58c)
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:
3
t
K= k E
s
d
s
(5.58d)
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:
1 24
K=
2 2 2 2 2
r
ft + 12r {f+φ cos φ(tanφ+ 2g) − 2[2g sin2φ− 2g(cos 2φ− cosφ)− sinφ(cosφ−1)]}
(5.58e)
d
s
φ=
r
(5.58f)
1
2
f= {(4g +1)(2φ+ sin2φ)+ 4g(1− cos2φ)− 2sin2φ}
4
(5.58g)
2 2 2
t sin φ−12r [(1− cosφ)(1+ 3cosφ)−φ sin2φ]
g=
2 2
( ) [ ( ) ]
t 2φ+ sin2φ −12r 2φ 2+ cos2φ − 3sin2φ
(5.58h)
11
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EN 1993-4-1:2007/FprA1:2014 (E)
(8) Where the solids flow pattern, the pressure in the solid, the properties of the granular 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 5.3.2.4.
xR,k
(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, considering only
sR,k
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
(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):
12
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EN 1993-4-1:2007/FprA1:2014 (E)
"(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.".
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 recommended.".
dx dx
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 (Method a) in
x,Rcr
5.3.4.3.1) should be evaluated at each appropriate level in the silo. The critical buckling stress resultant n
x,Rcr
may be evaluated for any chosen circumferential mode (wave number) j and any prospective height of the
13
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EN 1993-4-1:2007/FprA1:2014 (E)
buckle by minimising the following expression with respect to both j and . The values of may take any
i i i
value up to the total height of the wall, but may take any smaller values. The minimisation to find the critical
value of n may be made by any appropriate minimisation (optimisation) procedure.
x,Rcr
1 A
2
n = A+
x,Rcr 1
2 2
A
jω
3
(5.65)
Where no ring stiffeners are present, the values of A , I and I should be taken as zero, but d should be
r r tr r
taken as non-zero to avoid division by zero. Where no stringer stiffeners are present, the values of A , I
s s
and I should be taken as zero, but d should be taken as non-zero to avoid division by zero.
ts s
It may be helpful to draw a contour plot of n against j and as this may provide a faster means of
x,Rcr i
optimising Formula (5.65) than simple trial and error.".
Replace Paragraph (5) with:
"(5) The design buckling resistance n per unit circumference for the orthotropic shell (Method a) in
x,Rd
5.3.4.3.1) should be determined as the lesser of:
n =α n /γ
x,Rd x x,Rcr M1
(5.69)
and
n = Af /(dγ )
x,0Rd eff y s M
(5.70)
where:
α is the elastic buckling imperfection reduction factor;
x
γ is the partial factor given in 2.9.2;
M1
d is the distance between the stringer stiffeners;
s
A is the effective cross-sectional area of the stringer stiffener.
eff
NOTE: The National Annex may choose the value of α . The value α = 0,80 is recommended.".
x x
20 Modifications to 5.3.4.3.4, Stiffened wall treated as carrying axial compression
only in the stiffeners
Replace Paragraphs (2)
...
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