Orynyak I.V., Radchenko S.A. IPS NASU Pisarenko’ Institute for Problems of Strength , Kyiv, Ukraine National Academy of Sciences of Ukraine STRESS STATE CALCULATION OF COMPLEX PIPING SYSTEMS AT STATIC AND DYNAMIC LOADINGS 1th Hungarian-Ukrainian Joint Conference on Safety-Reliability and Risk Engineering Plants and Components 11,12 April 2006, Miskolc, Hungary
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Orynyak I.V., Radchenko S.A. IPS NASU Pisarenko’ Institute for Problems of Strength, Kyiv, Ukraine National Academy of Sciences of Ukraine Pisarenko’ Institute.
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Orynyak I.V., Radchenko S.A.
IPS NASUIPS NASU
Pisarenko’ Institute for Problems of Strength , Kyiv, Ukraine National Academy of Sciences of Ukraine
Pisarenko’ Institute for Problems of Strength , Kyiv, Ukraine National Academy of Sciences of Ukraine
STRESS STATE CALCULATION OF COMPLEX PIPING SYSTEMS AT STATIC AND DYNAMIC LOADINGS
STRESS STATE CALCULATION OF COMPLEX PIPING SYSTEMS AT STATIC AND DYNAMIC LOADINGS
1th Hungarian-Ukrainian Joint Conference on
Safety-Reliability and Risk Engineering Plants and Components
11,12 April 2006, Miskolc, Hungary
IPS NASUIPS NASU
3D model of pipeline system of RBMK Chernobyl NPP3D model of pipeline system of RBMK Chernobyl NPP
Problem statementProblem statement
Calculation
designis executed according to currently standards
doesn’t require high accuracy
uses high safety factors
uses old design solution
fitness for service
requires high accuracy
requires determination of
local distribution of stress: for calculation of defects for application of systems of
monitoring for application of strength
criteria
IPS NASUIPS NASUProblems of calculation pipe bend
A
C
B
D
A
C
B
D
zKzK
1d
0d
B
O
R
BR
BtR2
- parameter of flexibility - parameter of flexibility
- parameter of curvature
EI
sMK
ds
d
bendpipeforf
pipesraightforK
1,
1
1. Pipe bend as BEAM element in a piping 1. Pipe bend as BEAM element in a piping
2. The local stress-displacement fields of a SHELL 2. The local stress-displacement fields of a SHELL
• Saint Venant’s task;
• Geometrical non-linearity - internal pressure;
• End-effect; -3
-2
-1
0
1
2
3
0 30 60 90 120 150 180
end-effect
Saint Venant'ssolution
z
x
k
2
IPS NASUIPS NASU
Software “InfoPipeMaster” - Software “InfoPipeMaster” - information and calculating programinformation and calculating program
1. Gathering and storage the information about pipeline:
2. Calculation of the stress strain state:
static calculation static calculation
computer portrait, schemas, drawings and photos;
databases Materials, Soils, Objects and Defects;
results of technical inspection;
results of calculation
3. Comparative analysis of the results of the inspections executed during the different period of time .
4. Preparation of reports about a condition of object according to results of observation
«Geometry» «Calculation results»«Loads»• object type
• dimensions
• schemas, photos, drawings
• object label
• coordinates
• pressure
• temperature
• distribution forces
• weight
• displacements and angles
• forces and moments
• stresses
«Defect location»
«Geometry» «Calculation results»«Loads»• defect type
• dimensions• defect label
• element number
• coordinates
• pressure
• axial force
• bending moments
• stress intensity factor
• reference stress
• safety factor
DB «Objects»
DB «Defects»
IPS NASUIPS NASU The features of calculation modules The features of calculation modules • Pipelines are considered as beam structure where characteristics of cross sections are determined from theory of shells
• The calculation method is based on a method of initial parameters
• The continuity of the solution at transition from dynamics to a statics is provided
• Analytical solution for pipe bend are used
• Large library of elements with taking into account environment influence
• Accounting nonlinear supports and soil characteristics
• Convenient system for building and editing
• Abilities for data export – import with other software
IPS NASUIPS NASU
Equilibrium equationsEquilibrium equations
000
B
K
dBdK yx
yzxy mQ
BK
dB
dK
00
zyz mQ
dBdK
0
zz q
dBdQ
0
y
допy q
BN
dB
dQ
00
xy
доп
qB
Q
dBdN
00
000 2
21EtBPR
EFBN
EIKK
dBdθ доп
zin
z
GIK
B
θ
dBd xy
200
EI
KK
BdB
d yout
y 00
The equations for displacementsThe equations for displacements
0
2
0 2GIBRKK
dBd x
кр
yz w
zy
Bu
dB
d
00
w
122
21
0
2
00 EIBRKK
EFsN
EhRP
TBdB
du zinдоп
Tyw
The equations for curved beamThe equations for curved beam
The equations for angles of cross-section center The equations for angles of cross-section center
IPS NASUIPS NASUAnalytical solution for axial displacementAnalytical solution for axial displacement
.sin
221
4sincossin
4sincos
2sin
2sincos
4sin5cos8cos8
4cos54sinsin9
2sin3cos2
2sincos22
cos12
sin2
21
cos1sincos
0
2
0
2
000
220
220
000
2
000
020
00
0
00
00
0
00
00
EtPR
TBBq
BqQNEFB
BqBq
BNBQ
BmtBPR
FBN
K
IK
EIBK
Buu
y
xyдоп
xy
допy
z
доп
inz
in
zyw
IPS NASUIPS NASU Static calculation. Pipe bend - SHELLStatic calculation. Pipe bend - SHELL
Flexibility factor for in-plane bending of 900 bend having rigid flanges
Flexibility factor for in-plane bending of 900 bend having rigid flanges
mmt 5.12mmR 125
0
2
4
6
8
10
12
200 250 300 350 400 450 500
Saint Venant's solutionour resultsexperimentADINAP
K
0B
IPS NASUIPS NASUThe calculation of multi-branched 3D piping
Pump station view
IPS NASUIPS NASUPump station calculation model
Table of element
Calculation results
displacements
angles
forcesmoment
s
geometry
IPS NASUIPS NASU Dynamic analysisDynamic analysis
1. Determination of own frequencies and forms of vibrations of the piping. 2. Calculation forced vibrations of system.3. Restoration of value of external force by the measured displacements of the piping.
Tasks:Tasks:
Problems:Problems:1. Choice of the optimal method of the solution of statically indefinite beam system. 2. Determination of a local flexibility of curved beam by dynamic loading.Solution methods:Solution methods:1. Dynamic stiffness method for a case of harmonious loading. 2. A method of dynamic analysis for a case of non-stationary loading.
Advantages:Advantages:1. Accurate analytical solutions are used. 2. The continuity of the solution at transition from dynamics to a statics is provided.