placi curbe - 6

8/13/2019 placi curbe - 6

1/15

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

. .


2/15

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


3/15

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


4/15

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


5/15

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


6/15

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


7/15


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


8/15


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)


9/15


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


10/15

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


11/15


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


12/15


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


13/15


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


14/15


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


15/15


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

placi curbe - 6

Documents

Transcript of placi curbe - 6