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Universitatea Politehnica TimioaraFacultatea de Construcii
Departamentul de Construcii Metalice i Mecanica Construciilor
PL CI CURBE SUBIRI
- CURS 6 -
- -
Proiectarea structurilor din oel
Rezistena i stabilitatea PCS
. .
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EN 1993-1-6 FRAMEWORK APPROACH FORDESIGN CHECKING OF SHELLS
Contents1. Introduction
2. Basis of design and modelling
3. Materials and geometry
4. Ultimate limit states in steel shells. ress resu an s an s resses n s e s
6. Plastic limit state (LS1)
7. Cyclic plasticity limit state (LS2)
.
9. Fatigue limit state (LS4)
ANNEX A (normative) - Membrane theory stresses in shells
ANNEX B (normative) - Additional expressions for plastic collapse
resistances
-
bending stresses
ANNEX D (normative) - Expressions for buckling stress design
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EN 1993-1-6 DESIGN CHECKING OF SHELLS1. Introduction
Scope
- -
form of a shell of revolution.
This Standard is intended for use in conjunct ion with EN 1993-1-1, EN 1993-1-3,EN 1993-1-4 EN 1993-1- 9 and the relevant a lication arts of EN 1993 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.
Normative references
Definitions
Symbols Sign conventions
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EN 1993-1-6 DESIGN CHECKING OF SHELLS2. Basis of desi n and modellin
Shells shall be designed in acc. with EN1990 and, in particular, to
satisfy the following requirements:
Overall equil ibrium
Equil ibrium between actions and internal forces and moments
Limitation of cracks due to fatigue
Types of analysis:
Global analysis Membrane theory analysis
of the structureConditions of use:- the boundary conditions are appropriate-linear elastic material law
Linear elastic bifurcation analysis
Geometrically nonlinear elastic analysis
support reactions without causing bending
effects;
- the shell geometry varies smoothly in
- linear small deflection theory
(undeformed geometry)LBA- linear elastic material law
- linear small deflection theory
GNA-change in the geometry of the structure
- the elastic bucklin load of the erfectMNA Materially nonl inear analysis
Geometrically and materially nonl inear analysis
Geometricall nonlinear elastic anal sis with im erfections included
s ape w ou scon nu es ;
- the loads have a smooth distribution
(without locally concentrated or point loads).
- mper ec ons o a n s are gnore
- the basis of the critical buckling resistance
evaluation
structure-
strain incrementGMNA- gives the geometrically nonlinear plastic
limit load and the plastic strain incrementGNIA- where compression or shear stresses
Geometrically and materially nonlinear analysis with imperfectionsincluded
- elastic buckling loads of the "real"imperfect structure- gives the elasto-plastic buckling loads forthe "real" imperfect structure
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EN 1993-1-6 DESIGN CHECKING OF SHELLS2. Basis of desi n and modellin
Type of analysis Shell theory Material law Shell geometry
Membrane theory of shells membrane equilibrium not applicable perfect
Linear elastic shell analysis (LA) linear bending and linear perfect
Linear elastic bifurcation analysis (LBA) linear bending and
stretching
linear perfect
Geometrically non-linear elastic analysis non-linear linear perfect
(GNA)
Materially non-linear analysis (MNA) linear non-linear perfect
Geometrically and materially non-linear
anal sis GMNA
non-linear non-linear perfect
Geometrically non-linear elastic analysis
with imperfections (GNIA)
non-linear linear imperfect
Geometrically and materially non-linear non-linear non-linear imperfect
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EN 1993-1-6 DESIGN CHECKING OF SHELLS3. Materials and eometr
The rules in EN 1993-1-6 are not limited to steel shell structures
The standard is valid for isotro ic shells and shell se ments made
from any materials that may be represented as ideal elastic-plastic
For materials with no well defined yield point, 0.2% proof stress can
Where materials have a significant different stress strain curve, there
are alternative ways of representation of the material behaviour
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EN 1993-1-6 DESIGN CHECKING OF SHELLS3. Materials and eometr
The material properties apply to temperatures not exceeding 150 C
(otherwise see EN 13084-7, 2005)
Bauschinger effect
For austenitic steels (and aluminium alloys) at higher plastic strains,-
curve
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EN 1993-1-6 DESIGN CHECKING OF SHELLS3. Materials and eometr
Geometrical tolerances and imperfections
Relevant tolerances due to the re uirements of serviceabilit :
out-of-roundness (deviation from circularity)
eccentricities (deviations from a continuous middle surface in the
local dimples (local normal deviations from the nominal middle surface)
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EN 1993-1-6 DESIGN CHECKING OF SHELLS3. Materials and eometr
Geometrical tolerances and imperfections
Other forms of eometric im erfections:
deviations from nominal thickness
lack of evenness of supportsa er a mper ec ons:
residual stresses caused by roll ing, pressing, welding, straightening etc.
inhomo eneities and anisotro ies
Wear and corrosion Non-uniformities of loading
Residual stresses
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EN 1993-1-6 DESIGN CHECKING OF SHELLS4. Ultimate limit states in steel shells
LS1: Plastic l imit
Identifies the stren th of the structure when stabilit la s no
significant role.
Covers two condit ions:ens e rup ure or compress ve y e roug e u c ness
development of a plastic col lapse mechanism involving bending
The lastic limit load is also relevant to a bucklin stren th
assessment
Rpl - the plastic limit load
Rcr- the elastic critical load
e p ast c m t oa oes not represent t e rea strengt even or
stocky structures): strain hardening of material, stabilizing or
destabil izing effects due to change in geometry should be
considered
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EN 1993-1-6 DESIGN CHECKING OF SHELLS4. Ultimate limit states in steel shells
LS1: Plastic l imit
T es of anal sis:
MNA: often underestimates the strength very considerably
Membrane theory calculations:
If the stress state is entirely axisymmetric, it gives a close approximation
e s resses are s gn can y unsymme r ca , s cr er on o en
provides a very conservative estimate of the plastic l imit load
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EN 1993-1-6 DESIGN CHECKING OF SHELLS4. Ultimate limit states in steel shells
LS1: Plastic l imit
Linear elastic shell bending theory: This is commonly more conservative
than membrane theory calculation (is based on the first yield on the
surface)
Geometricall nonlinear calculation GMNA : roblems arise over
whether the structure displays geometric hardening or geometric
softening
plastic reference resistance
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EN 1993-1-6 DESIGN CHECKING OF SHELLS4. Ultimate limit states in steel shells
LS2: Cyclic plasticity
Re eated c cles of loadin and unloadin eventuall leadin to local
cracking by exhaustion of the energy absorption capacity of the
material
procedures set out in the standard are adopted
Methods of analysis:
express ons n nnex
elastic analysis (LA or GNA)
MNA or GMNA and find plastic strains
LS4: Fatigue
Repeated cycles of increasing and decreasing stress lead to the
Methods of analysis:
expressions in Annex C (using stress concentration factors)
elastic analysis (LA or GNA), using stress concentration factors
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EN 1993-1-6 DESIGN CHECKING OF SHELLS4. Ultimate limit states in steel shells
LS3: Buckling
Caused b loss of stabilit under com ressive membrane or shear
membrane stresses in the shell wall, leading to inability to sustain
any increase in the stress resultants, possibly causing catastrophic
Three approaches used in the assessment of buckling resistance:
GMNIA analysis
MNA/LBA analysis
Buckling stresses
construction
For this purpose, three fabrication quality classes are set out
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EN 1993-1-6 DESIGN CHECKING OF SHELLS4. Ultimate limit states in steel shells
Design concepts for the limit states design of shells
The limit state verification should be carried out usin one of the
following:
Stress design:
secondary
local
appropriaten genera , pr mary s ress s a es con ro ,
whereas secondary stress states affect LS2 and
LS3 and local stresses govern LS4.
Direct design by application of standard expressions:
the limit states may be represented by standard expressions that have
been derived from either membrane theory, plastic mechanism theory or
linear elastic analysis
The membrane theory (Annex A) - primary stresses needed for assessing
LS1 and LS3. The plastic design (Annex B) - plastic limit loads for assessing LS1
The linear elastic analysis (Annex C) - stresses of the primary plus
secondary stress type for assessing LS2 and LS4. An LS3 assessment
may be based on the membrane part of these expressions.
Design by global numerical analysis