Orynyak I.V., Radchenko S.A. IPS 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 NASU 3D model of pipeline system of RBMK Chernobyl NPP Problem statement Calculation design is 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 NASU Problems of calculation pipe bend - parameter of flexibility - parameter of curvature 1. Pipe bend as BEAM element in a piping 2. The local stress-displacement fields of a SHELL Saint Venant’s task; Geometrical non-linearity - internal pressure; End-effect;

IPS NASU Software “InfoPipeMaster” - information and calculating program 1.Gathering and storage the information about pipeline: 2. Calculation of the stress strain state: 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 dynamic analysis calculation of defects

IPS NASU Databases structure «Object location» «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 NASU 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 NASU Equilibrium equations The equations for displacements The equations for curved beam The equations for angles of cross-section center

IPS NASU Analytical solution for axial displacement

IPS NASU Static calculation. Pipe bend - SHELL r R O  B O1O1 t  x y z vu w Equilibrium equations: Physical equations:

IPS NASU - strains - curvatures Geometric equations: Solution methods Complete - 8-th orderSimplified - 4-th order - semianalytical - analytical

Stress distribution on outside surface for in-plane bending of 90 0 bend having rigid flanges Example: bend radius ; inside radius ; thickness. Circumferential stress factor Longitudinal stress factor

IPS NASU Flexibility factor for in-plane bending of 90 0 bend having rigid flanges

IPS NASU The calculation of multi-branched 3D piping Pump station view

IPS NASU Pump station calculation model Table of element Calculation results displacements angles forces moments geometry

IPS NASU Dynamic 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: 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: 1. Dynamic stiffness method for a case of harmonious loading. 2. A method of dynamic analysis for a case of non-stationary loading. Advantages: 1. Accurate analytical solutions are used. 2. The continuity of the solution at transition from dynamics to a statics is provided.

IPS NASU Harmonious vibrations. Dynamic stiffness method 1. Straight beam. - the equations of movement at cross vibrations: inertial member - frequency of vibrations x y dx X0X0 X1X1 stiffness matrix

IPS NASU - the constraint equation : 2. Curved beam. The transition matrix Harmonious vibrations. Dynamic stiffness method

IPS NASU acceleration Non-stationary vibrations. Method of dynamic analysis - the equations of movement at cross vibrations: - the constraint equation :

IPS NASU Examples – dynamic stiffness method Е = 2∙106 МPа; G = 8∙105 МPа;  = 0.3;  = 8000 kg/m3; l = 5 m; R = 0.1 m; h = m. 1. The diagram of the bending moment in a middle point of articulate beam The restoration of value of exciting force by known displacement 1 1. The diagram of the bending moment in a middle point of articulate beam

IPS NASU 1. The frequency of vibrations is lower than first own frequency Examples – method of dynamic analysis

IPS NASU 2. The frequency of vibrations is higher than first own frequency Examples – method of dynamic analysis

IPS NASU The determination of dynamic flexibility of pipe bend The determination of dynamic flexibility of pipe bend - flexibility factor by harmonious vibrations - flexibility factor by non-stationary vibrations

IPS NASU Example L. Salley and J. Pan. A study of the modal characteristics of curved pipes // Applied Acoustics. – – V.63. – pp Е = 2.07∙106 МPа;  = 0.3;  = 8000 kg/m3; R = m; h = m; В = m; l=0.2 m; l l R h B

IPS NASU The calculation of defects cracks corrosion defects of form

IPS NASU Pressure calculation model altitude of the pipeline operating pressure

IPS NASU Strength analysis of defects dangerous zone conditionally dangerous zone safety zone defect state

IPS NASU Application of software “InfoPipeMaster” Chernobyl NPP Zaporozhye NPP South-Ukrainian NPP Ammoniac pipeline «Togliatti-Odessa» System oil pipelines JSC«Ukrtransnafta» System gas pipelines DE«Ukrtransgas»