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Boru tesisatlarında ısıl gerilme analizi

Boru tesisatlarında ısıl gerilme analizi

##### Dosyalar

##### Tarih

1997

##### Yazarlar

Avcı, Sema

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

##### Özet

Endüstriyel tüm sistemlerde borulama elemanlarından emilmesi gereken bir ısıl gerilme bulunmaktadır. İdeal verimle çalışan sistemi elde etme çabaları içinde bu ısıl gerilmenin giderilmesi önemli bir sorun oluşturmaktadır. Bu çalışmada bir boru- esnekliği probleminin matrissel formda nasıl çözüleceği verilmiştir. Ama asıl ilgilenilen konu çevresel şartların değişimi ile oluşan bu ısıl gerilmelerin nasıl giderileceğidir. Bu çalışmada kompansatörlerin bu amaca nasıl hizmet ettikleride anlatılmaktadır. Borulama sistemlerinde, ısıl genleşme analizi yaparken teoriyi iyi anlamak ve konuyu anlamayı kolaylaştırmak için, Bölüm 2 de temel bağıntı ve kavramak açıklanmıştır. Bu bölümde borulama problemlerinin matrissel formda nasıl çözüleceği gösterilmiştir. Matrissel çözüme gerek duyulmasının sebebi ise, çok karmaşık olan borulama sistemlerinde elle çözüm elde etmenin neredeyse olanaksız olmasıdır. Matrissel çözüm çözüm yöntemini bir sisteme sokma açısından bir kolaylıktır. Yapılan çalışmalar sonucu bunca karmaşık olan sistemlerin çözümünde sonlu elemanlar yönteminin kullanılmasının uygun olduğu görülmüştür. Bu çalışmada uygulamalar kısmında yer alan problemler sonlu elemanlar yöntemini kullanan ANSYS programı ile çözülmüştür. Ve basit sistemler için elle yapılan çözümler ile ANSYS ile yapılan çözümler karşılaştırılmıştır. Bölüm 3 de kompansatörlerin nasıl kullanılacağını, seçileceğim ve kompansatör kullanırken gereken yardımcı elemanlarının neler olduğu bu yardımcı elemanları seçerken dikkat edilmesi gereken unsurları anlatılır. Bölüm 4 uygulamalardan ibarettir. Buradaki örnekler,düz bir borunun incelenmesinden başlar,bir boru sisteminde Q parçasının anlamını açıklar ve sistemde yapılan konstrüksiyon değişiklikler ile sistemin nasıl iyileştirildiğini anlatır.

Piping systems form one of the most commonly used elements in today's industry and daily use. Pipes are used to carry various sorts of fluids or gases from one place to another with the basic principle of flow from a high pressure to a lower pressure environment. From nuclear energy field to plumbing at our homes, to the natural gas transporting miles long piping systems, they are used everywhere. All different kinds of materials and technology is used to make the piping systems convenient for the individual purpose, to reduce the cost and to provide the longest service life and the reliability possible. Of course, all these require extensive engineering study and research. No material or structure is perfectly rigid. Small or large, every configuration change shape or move under both internal and external loading conditions. Piping systems are no exclusion to this universal law. Under temperature variations, internal pressurization, weight of the structure itself or the material transported, external stressing and because of many other possible reasons, the pipes change their dimensions or their states of stressing. A piping system is a system that travels a distance between two specific points (usually stationary locations). This implies the distance between the start and the end of the pipe being a constant value. Considering the fact that the pipe will change its dimensions during its service, this change in dimension becomes an important issue to be determined since the pipe may elongate or contract more than the acceptable limits and induce extremely high compressive or tensile stresses at the connections (usually named as anchors or terminal points). These stresses may cause the cracking or failure of the pipe itseld or the destruction of the anchors or terminal points. This may not seem to be a considerable problem for a small piping system such as a pipe connecting the furnace in your home to your radiator. However, considering a nuclear plant using a piping system for transporting toxic waste, it sure would be fatal if these pipes cracked and all the toxic waste leaked through the pipes. Due to the above stated importance of the problem, extensive studies are made in the last century on the expansion and flexibility of piping systems. The basic aim of these studies were to determine the magnitude of the stresses or expansions created by expanding pipes, internal to the piping system, and the reactions they exert upon the terminal equipment or anchors, and decide whether or not they are tolerable. Theoretical, as well as experimental and numerical studies are made. Generally, deep theory is avoided due to the time such studies take and their inconvenience to the engineer in the field who is supposed to use them. Tabular and simplified geometry solutions are rather preferred. With the invent of fast computers, matrix form solutions became possible, thanks to the computation speed provided by the computers. This study focuses on the expansion and flexibility analysis of piping systems. Theoretical and practical solution methods are summarized and used in example problems to give the reader a better feel of the application. Deep theory is avoided wherever it is felt that doing so would disturb the focus of the study. Appropriate references are given under these circumstances. XVH Chapter 1 is the introduction of the study and its contents. The importance of the problem is emphasized and the possible uses of this study are mentioned. Chapter 2 includes a thorough explanation of piping expansion and flexiblity analysis. Tables that list the mechanical and thermo-mechanical properties of various engineering materials are given. Matrix methods to determine the flexibility of piping systems are explained. The transformations of coordinates to make displacement and stresses in different directions be compatible toeach other are given. The relations between the stresses and deflections at any point in the pipes are derived and presented. The formation of the Compliance and Stiffness matrices and the determination of their components using the normalization and the base point approaches are included. Looped and unlooped systems are both considered. Effects of non-uniform temperature distribution and internal pressurization are lsited. Individual components (such as an elbow or a straight portion of a pipe system) are treated individually and their compliances are derived. Expansion Stress Range and Stress Intensification concepts are introduced. Cold-drawing and its importance is explained. Finally, simplified methods for desk-top calculations are given. These include the simple conservative approach, the graphical and tabular approaches and many other simplified methods. Chapter 3 introduces the bellow joints, ball joints and swivel joints, these element are used either alone or within compensators to absorb the expansion a piping system undergoes. The theory and the studies for these elements are scarce because there is no standart geometry or material while there are many manufacturers which produce them. The best source of information related to these elements would be the individual manufacturers. Bellows are classified in two major groups: 1- That involve sliding - in which there is relative motion of parts 2- That involve flexing - in which there is no relative motion of parts The main purpose is to allow the motion to absorb the expansion while avoiding any leakage of the transported material. To achieve this, many lubricants and materials are developed specific for this industry. In addition, since there is cyclic loading of these elements, fatigue life considerations are made. Chapter 3 gives the sizing methodology for bellow joints to absorbaxial, lateral or angular expansions. This methodology is intended to be as simple as possible to allow the piping engineer do the calculations easily. Fatigue life calculation procedure is explained with an example. Buckling and bending are also mentioned. Chapter 4 is dedicated to compensators. Compensators absorb the expansions, contractions and vibrations that occur during the service life of a piping system and provide a continuous and efficient operation. They include bellow joints, ball joints and swivel joints which have very high flexibilities. They increase the total flexibility of a piping system and are most commonly used where high expansions or stress concentrations are expected in a pipe. The compensators are grouped under three major categories 1- Axial Compensators 2- Lateral Compensators 3- Angular Compensators By using axial compensators, the flow does not have to change its direction, which minimizes the losses within the pipe, therefore pressure is not lost. The structure is nor affected by lateral expansion and it can freely expand. The important point is that XIX the structure has to withstand the pressure thrust that is exerted by the material flowing inside the system. Axial compensators require very small assemblies and thus, the cost is low. Their drawback is their need for extra strong guides to keep the compensator in line which impose potential economical and technical risks. For a long pipeline, many axial compensators are needed which increase the total cost although they are relatively cheap elements individually. Lateral compensators can absorb both the axial and the lateral expansions. In a system where there are elbows that change the direction of the pipe, the use of lateral compensators reduce the cost appreciably. Their advantage is that they require less guiding as compared to axial compensators and expansion in two directions can be absorbed with a single lateral compensator. Their darwback is that they can be only used where there is a turn in the pipe. In addition, while expanding laterally, the lateral compensator contracts axially and can induce axial stresses on the pipe. Therefore, angular compensators should be used in long piping systems. Angular compensators require change in pipe direction for absorbing expansions. They are the most suitable elements to absorb expansions in two or three directions. Like the lateral compensators, they minimize the need for guides. One major advantage is that unless the pipe is extremely long, they do not require guiding. Any expansion in any direction can be absorbed, threfore they are crucial elements in complicated piping systems. Their drawback is the requirement for large spaces and the turns in the pipes. Chapter 4 focuses on different compensator applications. The bellow dynamics, service life, effects of the level of temperature, expansion, internal pressure, preset, stress frequency, pressure and thermal shock, corrosion and improper installation on the servicability of the compensators are studied. Guides, terminal fixtures (anchors and terminal equipment) and bellow mounts and their importance in piping flexibility is emphasized. Design, piping line planning, guiding, isolation and installation of axial, lateral and angular compensators are explained with individual examples. Finally, three examples including complete design processes are presented followed by rules of thumb of compensator selection. These examples are shown below, Example. 1 A pipe which is subjected to a change intemperature will change it's physical dimensions if it is free, if it is not, will be placed in condition of stree and will exert reactive forces and moments on the equipment at its ends. The basic problem is to determine the magnitude of these stresses in the piping system and reactions, it exerts upon the terminal equipment and decide whether or not are tolerable. First consider the which is fixed at two ends, X X L=lm Basic equation of unit expansion is: aAT=- (1) E Consider a steam pipe of, a =12.5 e -9 1/°C, E=2.1 e5 N/mm2 xx and taking temperature rise 220 °C, we get 12.5 1(T. 220 2.110s normal stress at both ends, as o = 577.5 N/mm2 Acting force, for pipi DN 150 (A=3206.3 mm2) is, F=oA= 1.851 638 N If one and is not fixed, thermel expansion is Ax=aAT =2.75 mm The results are, Example 2. L shapped construction which is fixed two ends c Hf 4*> c Using theory the following give equations are obtained Deformation at B Ay = - EI Fya 3 Mba2 Fh -^ + abAT EA (2) Ax = EI F,b3 Mbb' F a = ^ + aaAT EA (3) Force at B 3EI (4ab + a2)Ax+3b2Ay x ~ ab(a+b) b2 (4) XXI Moment at B 3EI (4ab + b2)Ay + 3a2Ax y ~ ab(a + b) a2 Mb=~c7 - ut (aAx + bAy) ab(a+b) (5) (6) and five unknows Ax, Ay, Fx, Fy, Mb are solved from these five equations for Ay and Ax where interia moment is, *(d;-df) 64 and using these parameters, Moment at A MA=a Fy-MB Moment at C Mc= b Fx-Mc M. d, (7) m (9) (10) (11) Numerical example, Pipe size DN 150, a=10 m, b=10 m Temperature rise AT=220 °C Material steel E=2.1 105 N/mm2, a -12.5 10"6 1/°C The results can be found from hand calculation and program. Some contents of program output are, SBEND TORSIONAL MOMENT 't I ? SBEND SP SDIR SDIR : Direct axial stress SBEND : Maximum bending stress ST : Shear stressdue to torsion SP : Hoop stress SIG 1 : Max. principal stress at outer surface SIG 3 : Min principal stress at outer surface SHEAR FORCE xxu ST : Max. equivalent stress intensity at outer surface SEQV : Max equivalent stress at outer surface deformations, forces and moments.

Piping systems form one of the most commonly used elements in today's industry and daily use. Pipes are used to carry various sorts of fluids or gases from one place to another with the basic principle of flow from a high pressure to a lower pressure environment. From nuclear energy field to plumbing at our homes, to the natural gas transporting miles long piping systems, they are used everywhere. All different kinds of materials and technology is used to make the piping systems convenient for the individual purpose, to reduce the cost and to provide the longest service life and the reliability possible. Of course, all these require extensive engineering study and research. No material or structure is perfectly rigid. Small or large, every configuration change shape or move under both internal and external loading conditions. Piping systems are no exclusion to this universal law. Under temperature variations, internal pressurization, weight of the structure itself or the material transported, external stressing and because of many other possible reasons, the pipes change their dimensions or their states of stressing. A piping system is a system that travels a distance between two specific points (usually stationary locations). This implies the distance between the start and the end of the pipe being a constant value. Considering the fact that the pipe will change its dimensions during its service, this change in dimension becomes an important issue to be determined since the pipe may elongate or contract more than the acceptable limits and induce extremely high compressive or tensile stresses at the connections (usually named as anchors or terminal points). These stresses may cause the cracking or failure of the pipe itseld or the destruction of the anchors or terminal points. This may not seem to be a considerable problem for a small piping system such as a pipe connecting the furnace in your home to your radiator. However, considering a nuclear plant using a piping system for transporting toxic waste, it sure would be fatal if these pipes cracked and all the toxic waste leaked through the pipes. Due to the above stated importance of the problem, extensive studies are made in the last century on the expansion and flexibility of piping systems. The basic aim of these studies were to determine the magnitude of the stresses or expansions created by expanding pipes, internal to the piping system, and the reactions they exert upon the terminal equipment or anchors, and decide whether or not they are tolerable. Theoretical, as well as experimental and numerical studies are made. Generally, deep theory is avoided due to the time such studies take and their inconvenience to the engineer in the field who is supposed to use them. Tabular and simplified geometry solutions are rather preferred. With the invent of fast computers, matrix form solutions became possible, thanks to the computation speed provided by the computers. This study focuses on the expansion and flexibility analysis of piping systems. Theoretical and practical solution methods are summarized and used in example problems to give the reader a better feel of the application. Deep theory is avoided wherever it is felt that doing so would disturb the focus of the study. Appropriate references are given under these circumstances. XVH Chapter 1 is the introduction of the study and its contents. The importance of the problem is emphasized and the possible uses of this study are mentioned. Chapter 2 includes a thorough explanation of piping expansion and flexiblity analysis. Tables that list the mechanical and thermo-mechanical properties of various engineering materials are given. Matrix methods to determine the flexibility of piping systems are explained. The transformations of coordinates to make displacement and stresses in different directions be compatible toeach other are given. The relations between the stresses and deflections at any point in the pipes are derived and presented. The formation of the Compliance and Stiffness matrices and the determination of their components using the normalization and the base point approaches are included. Looped and unlooped systems are both considered. Effects of non-uniform temperature distribution and internal pressurization are lsited. Individual components (such as an elbow or a straight portion of a pipe system) are treated individually and their compliances are derived. Expansion Stress Range and Stress Intensification concepts are introduced. Cold-drawing and its importance is explained. Finally, simplified methods for desk-top calculations are given. These include the simple conservative approach, the graphical and tabular approaches and many other simplified methods. Chapter 3 introduces the bellow joints, ball joints and swivel joints, these element are used either alone or within compensators to absorb the expansion a piping system undergoes. The theory and the studies for these elements are scarce because there is no standart geometry or material while there are many manufacturers which produce them. The best source of information related to these elements would be the individual manufacturers. Bellows are classified in two major groups: 1- That involve sliding - in which there is relative motion of parts 2- That involve flexing - in which there is no relative motion of parts The main purpose is to allow the motion to absorb the expansion while avoiding any leakage of the transported material. To achieve this, many lubricants and materials are developed specific for this industry. In addition, since there is cyclic loading of these elements, fatigue life considerations are made. Chapter 3 gives the sizing methodology for bellow joints to absorbaxial, lateral or angular expansions. This methodology is intended to be as simple as possible to allow the piping engineer do the calculations easily. Fatigue life calculation procedure is explained with an example. Buckling and bending are also mentioned. Chapter 4 is dedicated to compensators. Compensators absorb the expansions, contractions and vibrations that occur during the service life of a piping system and provide a continuous and efficient operation. They include bellow joints, ball joints and swivel joints which have very high flexibilities. They increase the total flexibility of a piping system and are most commonly used where high expansions or stress concentrations are expected in a pipe. The compensators are grouped under three major categories 1- Axial Compensators 2- Lateral Compensators 3- Angular Compensators By using axial compensators, the flow does not have to change its direction, which minimizes the losses within the pipe, therefore pressure is not lost. The structure is nor affected by lateral expansion and it can freely expand. The important point is that XIX the structure has to withstand the pressure thrust that is exerted by the material flowing inside the system. Axial compensators require very small assemblies and thus, the cost is low. Their drawback is their need for extra strong guides to keep the compensator in line which impose potential economical and technical risks. For a long pipeline, many axial compensators are needed which increase the total cost although they are relatively cheap elements individually. Lateral compensators can absorb both the axial and the lateral expansions. In a system where there are elbows that change the direction of the pipe, the use of lateral compensators reduce the cost appreciably. Their advantage is that they require less guiding as compared to axial compensators and expansion in two directions can be absorbed with a single lateral compensator. Their darwback is that they can be only used where there is a turn in the pipe. In addition, while expanding laterally, the lateral compensator contracts axially and can induce axial stresses on the pipe. Therefore, angular compensators should be used in long piping systems. Angular compensators require change in pipe direction for absorbing expansions. They are the most suitable elements to absorb expansions in two or three directions. Like the lateral compensators, they minimize the need for guides. One major advantage is that unless the pipe is extremely long, they do not require guiding. Any expansion in any direction can be absorbed, threfore they are crucial elements in complicated piping systems. Their drawback is the requirement for large spaces and the turns in the pipes. Chapter 4 focuses on different compensator applications. The bellow dynamics, service life, effects of the level of temperature, expansion, internal pressure, preset, stress frequency, pressure and thermal shock, corrosion and improper installation on the servicability of the compensators are studied. Guides, terminal fixtures (anchors and terminal equipment) and bellow mounts and their importance in piping flexibility is emphasized. Design, piping line planning, guiding, isolation and installation of axial, lateral and angular compensators are explained with individual examples. Finally, three examples including complete design processes are presented followed by rules of thumb of compensator selection. These examples are shown below, Example. 1 A pipe which is subjected to a change intemperature will change it's physical dimensions if it is free, if it is not, will be placed in condition of stree and will exert reactive forces and moments on the equipment at its ends. The basic problem is to determine the magnitude of these stresses in the piping system and reactions, it exerts upon the terminal equipment and decide whether or not are tolerable. First consider the which is fixed at two ends, X X L=lm Basic equation of unit expansion is: aAT=- (1) E Consider a steam pipe of, a =12.5 e -9 1/°C, E=2.1 e5 N/mm2 xx and taking temperature rise 220 °C, we get 12.5 1(T. 220 2.110s normal stress at both ends, as o = 577.5 N/mm2 Acting force, for pipi DN 150 (A=3206.3 mm2) is, F=oA= 1.851 638 N If one and is not fixed, thermel expansion is Ax=aAT =2.75 mm The results are, Example 2. L shapped construction which is fixed two ends c Hf 4*> c Using theory the following give equations are obtained Deformation at B Ay = - EI Fya 3 Mba2 Fh -^ + abAT EA (2) Ax = EI F,b3 Mbb' F a = ^ + aaAT EA (3) Force at B 3EI (4ab + a2)Ax+3b2Ay x ~ ab(a+b) b2 (4) XXI Moment at B 3EI (4ab + b2)Ay + 3a2Ax y ~ ab(a + b) a2 Mb=~c7 - ut (aAx + bAy) ab(a+b) (5) (6) and five unknows Ax, Ay, Fx, Fy, Mb are solved from these five equations for Ay and Ax where interia moment is, *(d;-df) 64 and using these parameters, Moment at A MA=a Fy-MB Moment at C Mc= b Fx-Mc M. d, (7) m (9) (10) (11) Numerical example, Pipe size DN 150, a=10 m, b=10 m Temperature rise AT=220 °C Material steel E=2.1 105 N/mm2, a -12.5 10"6 1/°C The results can be found from hand calculation and program. Some contents of program output are, SBEND TORSIONAL MOMENT 't I ? SBEND SP SDIR SDIR : Direct axial stress SBEND : Maximum bending stress ST : Shear stressdue to torsion SP : Hoop stress SIG 1 : Max. principal stress at outer surface SIG 3 : Min principal stress at outer surface SHEAR FORCE xxu ST : Max. equivalent stress intensity at outer surface SEQV : Max equivalent stress at outer surface deformations, forces and moments.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1997

##### Anahtar kelimeler

Boru hatları,
Boru tesisatları,
Termal gerilme,
Pipelines,
Piping,
Thermal stress