This document describes a study to more accurately estimate reaction moments in gimbal and hinged expansion joints. The study analyzed test results from 13 large expansion joints and identified additional forces not considered in current standards, such as friction and lateral pressure forces. An equation is proposed that adds these additional forces to the spring rate calculation to better estimate expansion joint reaction moments. The proposed equation is shown to more closely match test results than the standard equation.
IRJET - Analysis and Designing of Diaphragm Spring WashersIRJET Journal
This document analyzes and designs diaphragm spring washers through numerical analysis and finite element analysis (FEA). It analyzes four cases of diaphragm springs with different height to thickness (h/t) ratios of 0.4, 0.7, 1.04, and 1.4. The FEA results for deformation, stress, and strain are presented for each case. The maximum deformation, stress, and strain values increase as the h/t ratio increases from 0.4 to 1.04. The document concludes that the FEA results agree well with numerical results and can be used for similar applications in the future.
This document discusses issues with determining appropriate bolt torque and tension for flanged pipe connections. There are currently no clear guidelines in Australian Standard AS 2885 or other codes. The document recommends including an appendix to AS 2885 that provides a normative methodology for relating bolt torque to stress levels. It proposes defining acceptable bolt stress levels for various load cases and a procedure for tensioning bolts that involves determining the required preload, measuring bolt extension to validate friction coefficients, and uniformly applying the validated torque value.
Structural Analysis and Optimization of Buckling Strength through Stiffeners ...IRJET Journal
The document summarizes research on analyzing and optimizing the buckling strength of a vacuum chamber through stiffeners and thickness variation. A spherical pressure vessel is modeled in CATIA and analyzed in ANSYS. Various cases are considered: the original geometry, adding 1 stiffener, adding 1 stiffener with a saddle, increasing thickness to 18mm and 20mm, and adding 4 stiffeners with a saddle. Boundary conditions and loading are applied and buckling strength, hoop stress, and pre-stresses are analyzed. Results show stiffeners improve buckling strength more than thickness variation. Non-linear buckling analysis is proposed for future work. In conclusion, adding stiffeners prevents crack growth more effectively than changing
IRJET- Strength Behaviour of Hardened ConcreteIRJET Journal
The document discusses testing conducted on hardened concrete cylinders drilled from a dam in India to study their stress-strain behavior and determine elastic parameters. 10 concrete cylinder samples were tested for properties like unit weight, water absorption, ultrasonic pulse velocity, modulus of elasticity, Poisson's ratio, and crushing strength. The stress-strain curves of 2 samples tested under controlled strain conditions showed increased strain at failure compared to conventional testing. The results are presented in a table and figures showing typical stress-strain behaviors.
The document describes designing and optimizing the saddle support of a horizontal pressure vessel using finite element analysis. It discusses prior research on saddle support design and stresses. The problem aims to analyze how varying the number of gusset plates and gusset thickness impacts stresses on a saddle support designed for a given pressure vessel. Key parameters of the pressure vessel and saddle support are defined. The goal is to reduce stresses and material usage through optimization to lower costs.
FEA Based Validation of Weld Joint Used In Chassis of Light Commercial Vehicl...ijiert bestjournal
Generally automotive systems are subjected to dynam ic and static loads,due to hives driving and adverse conditions of the road surface,thus it causes cracks,noise,vibration and failure in an automobile,since in general the total effect of work for automobile system is lowered. Such effect is arising due to behaviour in types of loading,construction and condition of the work where the automobile system is and reducing it s strength. Therefore however most of the Light Commercial Vehicles (LCV) chassis are man ufactured by welding to reduce the weight of the chassis. Hence there is a more stress concentration occurs at a welded joint region. The fundamental task is to develop a model of welded joint to sustain various loads of LCV chassis. Effect of different design parameters,properties of material are observed with respect to the strength of the weld and location of stress concentrations are identified. During the design process model parameters are often alter ed to evaluate alternative welding joining choices,to reduce weight of the system to sustain varying loading conditions without failure.
IRJET - Analysis and Designing of Diaphragm Spring WashersIRJET Journal
This document analyzes and designs diaphragm spring washers through numerical analysis and finite element analysis (FEA). It analyzes four cases of diaphragm springs with different height to thickness (h/t) ratios of 0.4, 0.7, 1.04, and 1.4. The FEA results for deformation, stress, and strain are presented for each case. The maximum deformation, stress, and strain values increase as the h/t ratio increases from 0.4 to 1.04. The document concludes that the FEA results agree well with numerical results and can be used for similar applications in the future.
This document discusses issues with determining appropriate bolt torque and tension for flanged pipe connections. There are currently no clear guidelines in Australian Standard AS 2885 or other codes. The document recommends including an appendix to AS 2885 that provides a normative methodology for relating bolt torque to stress levels. It proposes defining acceptable bolt stress levels for various load cases and a procedure for tensioning bolts that involves determining the required preload, measuring bolt extension to validate friction coefficients, and uniformly applying the validated torque value.
Structural Analysis and Optimization of Buckling Strength through Stiffeners ...IRJET Journal
The document summarizes research on analyzing and optimizing the buckling strength of a vacuum chamber through stiffeners and thickness variation. A spherical pressure vessel is modeled in CATIA and analyzed in ANSYS. Various cases are considered: the original geometry, adding 1 stiffener, adding 1 stiffener with a saddle, increasing thickness to 18mm and 20mm, and adding 4 stiffeners with a saddle. Boundary conditions and loading are applied and buckling strength, hoop stress, and pre-stresses are analyzed. Results show stiffeners improve buckling strength more than thickness variation. Non-linear buckling analysis is proposed for future work. In conclusion, adding stiffeners prevents crack growth more effectively than changing
IRJET- Strength Behaviour of Hardened ConcreteIRJET Journal
The document discusses testing conducted on hardened concrete cylinders drilled from a dam in India to study their stress-strain behavior and determine elastic parameters. 10 concrete cylinder samples were tested for properties like unit weight, water absorption, ultrasonic pulse velocity, modulus of elasticity, Poisson's ratio, and crushing strength. The stress-strain curves of 2 samples tested under controlled strain conditions showed increased strain at failure compared to conventional testing. The results are presented in a table and figures showing typical stress-strain behaviors.
The document describes designing and optimizing the saddle support of a horizontal pressure vessel using finite element analysis. It discusses prior research on saddle support design and stresses. The problem aims to analyze how varying the number of gusset plates and gusset thickness impacts stresses on a saddle support designed for a given pressure vessel. Key parameters of the pressure vessel and saddle support are defined. The goal is to reduce stresses and material usage through optimization to lower costs.
FEA Based Validation of Weld Joint Used In Chassis of Light Commercial Vehicl...ijiert bestjournal
Generally automotive systems are subjected to dynam ic and static loads,due to hives driving and adverse conditions of the road surface,thus it causes cracks,noise,vibration and failure in an automobile,since in general the total effect of work for automobile system is lowered. Such effect is arising due to behaviour in types of loading,construction and condition of the work where the automobile system is and reducing it s strength. Therefore however most of the Light Commercial Vehicles (LCV) chassis are man ufactured by welding to reduce the weight of the chassis. Hence there is a more stress concentration occurs at a welded joint region. The fundamental task is to develop a model of welded joint to sustain various loads of LCV chassis. Effect of different design parameters,properties of material are observed with respect to the strength of the weld and location of stress concentrations are identified. During the design process model parameters are often alter ed to evaluate alternative welding joining choices,to reduce weight of the system to sustain varying loading conditions without failure.
Design and Analysis of Crankshaft for Internal Combustion Engineijtsrd
In this project design and analysis of the crankshaft for the combustion engine. These components have a large volume component with complex geometry and need huge investment. These will be converts reciprocating or linear motion of the piston into a rotary motion. In this project the product is modeled in a 3D model with all available constraint by using advanced cad software CATIA V5. this model will be converted to initial graphics exchange specification IGES format and imported to ANSYS workbench to perform static analysis. Finite element analysis FEA is performed to obtain the various stress and critical location of crankshaft under loads by using ANSYS software. This project helps to many researchers to select best material to production of crankshaft. Md. Hameed | Chova Deekshith | Gorge Bhanu Prasad | Chalamala Teja ""Design and Analysis of Crankshaft for Internal Combustion Engine"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-3 , April 2019, URL: https://www.ijtsrd.com/papers/ijtsrd23531.pdf
Paper URL: https://www.ijtsrd.com/engineering/mechanical-engineering/23531/design-and-analysis-of-crankshaft-for-internal-combustion-engine/md-hameed
Pins require very little service and total failure seldom occurs. Wear, pitting, and scoring are the usual troubles
encountered with pins. In this paper, going to apply induction hardening process on pins and its comparison will
be done with existing pins. Different hardening thickness or case depth will be applied and analysis will be done
to interpret the results. Case depth of 1mm, 2mm or 2.5mm will be taken in induction hardening process.
Caterpillar 320dl excavator model is taken for study. Material used for the pins is EN8 grade of steel. And
different material used for the pin for analysis purpose will be bronze alloy, Titanium. The main objective in this
project is to determine the appropriate induction hardening case depth to be used in manufacturing pins.ThreedHiympeenrsmioensh
m aondde Alsn osfy sp iwnisl lu bseed u sined e xtoc aavnaatloyrz ew tihlle bsetr ecsres astteadtu uss oinng t hCea ptiianVs.5 T shoef tmwaarxei,m mumes hdienfgo rwmiallt iboen ,d monaex iumsuinmg
stress point and dangerous areas are found by the stress analysis.
Finite Element Analysis of Connecting Rod for Two Wheeler and Optimization of...IRJET Journal
This document presents a finite element analysis of a connecting rod for a two-wheeler under static load conditions. A connecting rod from a Hero Splendor motorcycle was modeled in CREO and analyzed in ANSYS. Two materials, C70S6 steel and structural steel, were considered. For each material, the maximum and minimum von Mises stress, principal stress, elastic strain, shear stress, and total deformation under an applied load of 677N were determined. For C70S6 steel, the maximum total deformation was 0.01271 mm and minimum was 0.00164 mm. The maximum elastic strain was 1.960×10^-4 and minimum was 4.218×10^-6. For structural steel,
Here are the steps to model the structural steel support:
1. Add a structural steel material (e.g. A36)
2. Define steel sections (e.g. W8x10, W6x15)
3. Add steel elements between the pipe supports and ground
4. Specify the pipe support nodes as CNODEs for the steel elements
5. Run analysis
6. Check stresses in steel
7. Check effect on piping loads and stresses
This models the structural aspect of the supports and incorporates it into the full piping analysis. It allows evaluation of both the piping and support system.
behavior of reterofitted steel structures using cost effective retrofitting t...iit roorkee
This document summarizes research on retrofitting techniques for steel structures. It focuses on comparing the fatigue performance of a 120-year-old riveted steel bridge girder to a new equivalent welded girder. Finite element models are created to analyze stresses in the girders when uncracked, cracked, and retrofitted. Retrofitting involves adding plates with bolts to the bottom flange near the mid-span where cracking is most critical. Results show retrofitting normalizes the stress distribution and eliminates the effect of cracking, extending the design life of the old structure in a cost-effective way compared to replacement.
Given:
Stresses:
i) 350 N/mm2 for 85% of time
ii) 500 N/mm2 for 3% of time
iii) 400 N/mm2 for 12% of remaining time
Material: Plain carbon steel 50C
Using Miner's rule:
For stress i)
N1/Nf1 = 0.85
Where, N1 is no. of cycles component can withstand at stress 350 N/mm2
Nf1 is no. of cycles to failure at stress 350 N/mm2
Similarly, for other stresses:
N2/Nf2 = 0.03
N3/Nf3 = 0.12
Equ
The document discusses stress concentration and fatigue failure in machine elements. It defines stress concentration as the localization of high stresses due to irregularities or abrupt changes in cross-section. Stress concentration can be reduced by avoiding sharp changes in cross-section and providing fillets and chamfers. Fatigue failure occurs when fluctuating stresses cause cracks over numerous load cycles. The endurance limit is the maximum stress amplitude that causes failure after an infinite number of cycles. Factors like stress concentration, surface finish, size, and mean stress affect the endurance limit. Designs should minimize stress raisers and protect against corrosion to prevent fatigue failures.
The document discusses design considerations for machine elements subjected to fluctuating loads. It covers topics such as stress concentration, fatigue failure, endurance limit, factors affecting fatigue strength, and methods to reduce stress concentration and improve fatigue life. Stress concentration occurs due to discontinuities and can be reduced by avoiding abrupt changes in cross-section and providing fillets. Fatigue failure is caused by fluctuating stresses and depends on factors like the number of cycles and mean stress. The endurance limit is the maximum stress amplitude a material can withstand without failure under completely reversed loading. Surface finish, size, and mean stress affect the endurance limit.
FINITE ELEMENT ANALYSIS OF GAS FOIL BEARINGSIRJET Journal
The document discusses finite element analysis of gas foil bearings. Three different gas foil bearing models (GFB1, GFB2, GFB3) were created with varying parameters like journal diameter, foil thickness, number of bumps, etc. Finite element analysis was performed on the models in ANSYS to determine stiffness values. The bearing models were subjected to varying loads and temperatures. Deflection values increased linearly with increasing load. Stiffness decreased with increasing temperature difference between the bearing and ambient temperature. Plots of load-deflection and stiffness-temperature were obtained. The finite element analysis provided stiffness coefficients of the gas foil bearings at different operating conditions.
Design Optimization and Analysis of a Steam Turbine Rotor GroovesIOSR Journals
1. The document describes a finite element analysis performed to optimize the design of steam turbine rotor grooves.
2. The analysis evaluated different fillet radii ranging from 13 to 50 mm to determine the maximum principal stress and stress concentration factor.
3. The optimal design was found to have a fillet radius of 40 mm, which reduced the stress concentration factor to 1.152 and deformation to 0.066121 mm.
ESTIMATION OF CREEP PARAMETERS IN AN ISOTROPIC UNIFORM COMPOSITE CYLINDERijiert bestjournal
In applications such as pressure vessel for industr ial gases or a media transportation of high- pressurized fluids and piping of nuclear reactors,the cylinder has to operate under severe mechanical and thermal loads,causing significant c reep hence reduced service life (Gupta and Phatak,2001;Tachibana and Iyoku,2004;Hagihara a nd Miyazaki,2008). As an example,in the high temperature engineering test reactor,the temp erature reaches of the order of 900 oC (Tachibana and Iyoku,2004). The piping of reactor cooling system are subjected to high temperature and pressure and may be damaged due to high heat generated from the reactor core (Hagihara and Miyazaki,2008). A number of studies pertaining to creep behaviour of the cylinder assume the cylinder to be made of monolith ic material. However,under severe thermo mechanical loads cylinder made of monolithic materi als may not perform well. The weight reduction achieved in engineering components,resul ting from the use of aluminum/aluminum base alloys,is expected to save power and fuel due to a reduction in the payload of dynamic systems. However,the enhanced creep of aluminum an d its alloys may be a big hindrance in such applications. Aluminum matrix composites offer a unique combination of properties,unlike many monolithic materials like metals and alloys,w hich can be tailored by modifying the content of reinforcement.
Optimization in mechanical seal design for api 682 category i applications ij...Dr.Vikas Deulgaonkar
The paper covers development of mechanical seal design to optimize the adaptive part for API 682 category 1 applications. Under the guidelines of Forschungskuratorium Maschinenbau (FKM) the static strength is investigated using local stresses. Static structural load case is carried out on the adaptive parts with non-average element-nodal stresses. The new design performance is investigated using finite element analysis in terms of equivalent stress. Improved features in the design and their effects on manufacturing benefits, seal performance leading final product cost/weight optimization are discussed. Evaluation of centrifugally cast stainless steel raw material instead of forged wrought raw material is discussed.
IRJET- Minimisation of Maintenance Actions through Design Analysis of Hydraul...IRJET Journal
This document discusses the design analysis and optimization of a hydraulic cylinder for use in trailers. It aims to minimize maintenance needs through design improvements. The document presents a 3D model and finite element analysis of a two-stage hydraulic cylinder. The analysis examines stress distribution under working conditions. The design was optimized to improve reliability, functionality, safety, and reduce costs. Various failure modes of hydraulic cylinders are also briefly discussed, along with causes and troubleshooting methods. The goal is to design a hydraulic cylinder that requires fewer maintenance actions through an improved design informed by modeling and analysis.
IRJET- Minimisation of Maintenance Actions through Design Analysis of Hyd...IRJET Journal
This document discusses the design analysis and optimization of a hydraulic cylinder for use in trailers. It aims to minimize maintenance needs through design improvements. The document begins with an introduction on trailers and hydraulic cylinders. It then reviews previous literature on hydraulic cylinder design analysis using modeling software. This includes analyzing stresses on different materials, seal performance, and fatigue life. The document then discusses failures that can occur in hydraulic cylinders due to issues like seal leakage. It aims to optimize the design of a two-stage hydraulic cylinder through modeling and analysis to reduce failure risks and lower maintenance needs.
This document compares two finite element models of a heat exchanger tube-to-tubesheet joint subjected to transient thermal loading. Model I represents tubes as beam elements while Model II represents tubes as spring elements. Both models are analyzed at two time points on the thermal loading curve. Results show that maximum stresses and deformations calculated by the two models are similar, with Model II requiring 38% less computational time. Therefore, using spring elements to model tubes provides a feasible way to determine joint stresses within a reasonable solution time frame for transient thermal-structural analysis of heat exchanger tube-to-tubesheet joints.
EFFECT OF PARTICLE CONTENT IN ANALYSIS OF CREEP IN AN ISOTROPIC UNIFORM COMPO...ijiert bestjournal
The following paper discusses the effect of particl e content in analysis of creep in an isotropic uniform composite cylinder. The paper is a part of the series of papers published under the analysis of creep in an isotropic uniform composite cylinder.
EFFECT OF PARTICLE CONTENT IN ANALYSIS OF CREEP IN AN ISOTROPIC UNIFORM COMPO...ijiert bestjournal
The following paper discusses the effect of particl e content in analysis of creep in an isotropic uniform composite cylinder. The paper is a part of the series of papers published under the analysis of creep in an isotropic uniform composite cylinder.
This document discusses a finite element analysis of fatigue in a piston ring. It begins with an introduction to piston rings and their importance. It then describes conducting a finite element analysis to model the stresses on a piston ring under different loading conditions like gas pressure, thermal loading, and contact with the piston. The analysis identified fatigue-critical locations and calculated fatigue lives. Figures 1-8 show results of the modeling like stress distributions, deformed shapes, and comparisons of coating and uncoated rings. The conclusion is that fatigue remains an issue for piston rings and manufacturers are working to reduce weight while increasing power, further challenging fatigue life.
IRJET- Effect of Contaminated Oil on Temperature Variation of Tilting Pad...IRJET Journal
This document summarizes a study on the effect of contaminated oil on the temperature variation of tilting pad thrust bearings with bronze pads having a catenoidal surface profile. The study involved performing experiments on a test rig with 8 bronze pads under varying speeds, loads, and cooling flow rates. Temperature sensors were placed in a grid pattern over one of the pads to measure temperature changes at different locations. Results showed that adding contaminated powder to the lubricant caused fluid temperatures to increase more with higher thrust loads compared to using non-contaminated oil. The maximum temperature also shifted towards the trailing edge of the pad.
Design of Self Regulating Pressure Valve using Transient Finite Element AnalysisIRJET Journal
This document describes the design of a self-regulating pressure valve using finite element analysis. The valve aims to regulate pressure in a system by mechanically controlling fluid flow. It uses a spring-loaded restrictor plate that closes off flow as a critical pressure is reached. The analysis determines appropriate material, plate thickness, spring stiffness, and other dimensions to withstand loads from fluid pressure and flow. Finite element modeling and steady-state analysis are performed to test the design and ensure stresses remain below yield levels. The goal is to create a purely mechanical system with an automatic response to safely regulate pressure within a specified range.
The document summarizes a mechanical engineering project involving modeling and programming an expansion joint using Pro/E software. It describes modeling bellows, sleeves, and other expansion joint components in the software. Finite element analysis was performed on a bellows model to analyze stress and displacement under various pressures. C-programming and Pro/PROGRAM tools were used to automate design variations and iterations.
Design and Analysis of Crankshaft for Internal Combustion Engineijtsrd
In this project design and analysis of the crankshaft for the combustion engine. These components have a large volume component with complex geometry and need huge investment. These will be converts reciprocating or linear motion of the piston into a rotary motion. In this project the product is modeled in a 3D model with all available constraint by using advanced cad software CATIA V5. this model will be converted to initial graphics exchange specification IGES format and imported to ANSYS workbench to perform static analysis. Finite element analysis FEA is performed to obtain the various stress and critical location of crankshaft under loads by using ANSYS software. This project helps to many researchers to select best material to production of crankshaft. Md. Hameed | Chova Deekshith | Gorge Bhanu Prasad | Chalamala Teja ""Design and Analysis of Crankshaft for Internal Combustion Engine"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-3 , April 2019, URL: https://www.ijtsrd.com/papers/ijtsrd23531.pdf
Paper URL: https://www.ijtsrd.com/engineering/mechanical-engineering/23531/design-and-analysis-of-crankshaft-for-internal-combustion-engine/md-hameed
Pins require very little service and total failure seldom occurs. Wear, pitting, and scoring are the usual troubles
encountered with pins. In this paper, going to apply induction hardening process on pins and its comparison will
be done with existing pins. Different hardening thickness or case depth will be applied and analysis will be done
to interpret the results. Case depth of 1mm, 2mm or 2.5mm will be taken in induction hardening process.
Caterpillar 320dl excavator model is taken for study. Material used for the pins is EN8 grade of steel. And
different material used for the pin for analysis purpose will be bronze alloy, Titanium. The main objective in this
project is to determine the appropriate induction hardening case depth to be used in manufacturing pins.ThreedHiympeenrsmioensh
m aondde Alsn osfy sp iwnisl lu bseed u sined e xtoc aavnaatloyrz ew tihlle bsetr ecsres astteadtu uss oinng t hCea ptiianVs.5 T shoef tmwaarxei,m mumes hdienfgo rwmiallt iboen ,d monaex iumsuinmg
stress point and dangerous areas are found by the stress analysis.
Finite Element Analysis of Connecting Rod for Two Wheeler and Optimization of...IRJET Journal
This document presents a finite element analysis of a connecting rod for a two-wheeler under static load conditions. A connecting rod from a Hero Splendor motorcycle was modeled in CREO and analyzed in ANSYS. Two materials, C70S6 steel and structural steel, were considered. For each material, the maximum and minimum von Mises stress, principal stress, elastic strain, shear stress, and total deformation under an applied load of 677N were determined. For C70S6 steel, the maximum total deformation was 0.01271 mm and minimum was 0.00164 mm. The maximum elastic strain was 1.960×10^-4 and minimum was 4.218×10^-6. For structural steel,
Here are the steps to model the structural steel support:
1. Add a structural steel material (e.g. A36)
2. Define steel sections (e.g. W8x10, W6x15)
3. Add steel elements between the pipe supports and ground
4. Specify the pipe support nodes as CNODEs for the steel elements
5. Run analysis
6. Check stresses in steel
7. Check effect on piping loads and stresses
This models the structural aspect of the supports and incorporates it into the full piping analysis. It allows evaluation of both the piping and support system.
behavior of reterofitted steel structures using cost effective retrofitting t...iit roorkee
This document summarizes research on retrofitting techniques for steel structures. It focuses on comparing the fatigue performance of a 120-year-old riveted steel bridge girder to a new equivalent welded girder. Finite element models are created to analyze stresses in the girders when uncracked, cracked, and retrofitted. Retrofitting involves adding plates with bolts to the bottom flange near the mid-span where cracking is most critical. Results show retrofitting normalizes the stress distribution and eliminates the effect of cracking, extending the design life of the old structure in a cost-effective way compared to replacement.
Given:
Stresses:
i) 350 N/mm2 for 85% of time
ii) 500 N/mm2 for 3% of time
iii) 400 N/mm2 for 12% of remaining time
Material: Plain carbon steel 50C
Using Miner's rule:
For stress i)
N1/Nf1 = 0.85
Where, N1 is no. of cycles component can withstand at stress 350 N/mm2
Nf1 is no. of cycles to failure at stress 350 N/mm2
Similarly, for other stresses:
N2/Nf2 = 0.03
N3/Nf3 = 0.12
Equ
The document discusses stress concentration and fatigue failure in machine elements. It defines stress concentration as the localization of high stresses due to irregularities or abrupt changes in cross-section. Stress concentration can be reduced by avoiding sharp changes in cross-section and providing fillets and chamfers. Fatigue failure occurs when fluctuating stresses cause cracks over numerous load cycles. The endurance limit is the maximum stress amplitude that causes failure after an infinite number of cycles. Factors like stress concentration, surface finish, size, and mean stress affect the endurance limit. Designs should minimize stress raisers and protect against corrosion to prevent fatigue failures.
The document discusses design considerations for machine elements subjected to fluctuating loads. It covers topics such as stress concentration, fatigue failure, endurance limit, factors affecting fatigue strength, and methods to reduce stress concentration and improve fatigue life. Stress concentration occurs due to discontinuities and can be reduced by avoiding abrupt changes in cross-section and providing fillets. Fatigue failure is caused by fluctuating stresses and depends on factors like the number of cycles and mean stress. The endurance limit is the maximum stress amplitude a material can withstand without failure under completely reversed loading. Surface finish, size, and mean stress affect the endurance limit.
FINITE ELEMENT ANALYSIS OF GAS FOIL BEARINGSIRJET Journal
The document discusses finite element analysis of gas foil bearings. Three different gas foil bearing models (GFB1, GFB2, GFB3) were created with varying parameters like journal diameter, foil thickness, number of bumps, etc. Finite element analysis was performed on the models in ANSYS to determine stiffness values. The bearing models were subjected to varying loads and temperatures. Deflection values increased linearly with increasing load. Stiffness decreased with increasing temperature difference between the bearing and ambient temperature. Plots of load-deflection and stiffness-temperature were obtained. The finite element analysis provided stiffness coefficients of the gas foil bearings at different operating conditions.
Design Optimization and Analysis of a Steam Turbine Rotor GroovesIOSR Journals
1. The document describes a finite element analysis performed to optimize the design of steam turbine rotor grooves.
2. The analysis evaluated different fillet radii ranging from 13 to 50 mm to determine the maximum principal stress and stress concentration factor.
3. The optimal design was found to have a fillet radius of 40 mm, which reduced the stress concentration factor to 1.152 and deformation to 0.066121 mm.
ESTIMATION OF CREEP PARAMETERS IN AN ISOTROPIC UNIFORM COMPOSITE CYLINDERijiert bestjournal
In applications such as pressure vessel for industr ial gases or a media transportation of high- pressurized fluids and piping of nuclear reactors,the cylinder has to operate under severe mechanical and thermal loads,causing significant c reep hence reduced service life (Gupta and Phatak,2001;Tachibana and Iyoku,2004;Hagihara a nd Miyazaki,2008). As an example,in the high temperature engineering test reactor,the temp erature reaches of the order of 900 oC (Tachibana and Iyoku,2004). The piping of reactor cooling system are subjected to high temperature and pressure and may be damaged due to high heat generated from the reactor core (Hagihara and Miyazaki,2008). A number of studies pertaining to creep behaviour of the cylinder assume the cylinder to be made of monolith ic material. However,under severe thermo mechanical loads cylinder made of monolithic materi als may not perform well. The weight reduction achieved in engineering components,resul ting from the use of aluminum/aluminum base alloys,is expected to save power and fuel due to a reduction in the payload of dynamic systems. However,the enhanced creep of aluminum an d its alloys may be a big hindrance in such applications. Aluminum matrix composites offer a unique combination of properties,unlike many monolithic materials like metals and alloys,w hich can be tailored by modifying the content of reinforcement.
Optimization in mechanical seal design for api 682 category i applications ij...Dr.Vikas Deulgaonkar
The paper covers development of mechanical seal design to optimize the adaptive part for API 682 category 1 applications. Under the guidelines of Forschungskuratorium Maschinenbau (FKM) the static strength is investigated using local stresses. Static structural load case is carried out on the adaptive parts with non-average element-nodal stresses. The new design performance is investigated using finite element analysis in terms of equivalent stress. Improved features in the design and their effects on manufacturing benefits, seal performance leading final product cost/weight optimization are discussed. Evaluation of centrifugally cast stainless steel raw material instead of forged wrought raw material is discussed.
IRJET- Minimisation of Maintenance Actions through Design Analysis of Hydraul...IRJET Journal
This document discusses the design analysis and optimization of a hydraulic cylinder for use in trailers. It aims to minimize maintenance needs through design improvements. The document presents a 3D model and finite element analysis of a two-stage hydraulic cylinder. The analysis examines stress distribution under working conditions. The design was optimized to improve reliability, functionality, safety, and reduce costs. Various failure modes of hydraulic cylinders are also briefly discussed, along with causes and troubleshooting methods. The goal is to design a hydraulic cylinder that requires fewer maintenance actions through an improved design informed by modeling and analysis.
IRJET- Minimisation of Maintenance Actions through Design Analysis of Hyd...IRJET Journal
This document discusses the design analysis and optimization of a hydraulic cylinder for use in trailers. It aims to minimize maintenance needs through design improvements. The document begins with an introduction on trailers and hydraulic cylinders. It then reviews previous literature on hydraulic cylinder design analysis using modeling software. This includes analyzing stresses on different materials, seal performance, and fatigue life. The document then discusses failures that can occur in hydraulic cylinders due to issues like seal leakage. It aims to optimize the design of a two-stage hydraulic cylinder through modeling and analysis to reduce failure risks and lower maintenance needs.
This document compares two finite element models of a heat exchanger tube-to-tubesheet joint subjected to transient thermal loading. Model I represents tubes as beam elements while Model II represents tubes as spring elements. Both models are analyzed at two time points on the thermal loading curve. Results show that maximum stresses and deformations calculated by the two models are similar, with Model II requiring 38% less computational time. Therefore, using spring elements to model tubes provides a feasible way to determine joint stresses within a reasonable solution time frame for transient thermal-structural analysis of heat exchanger tube-to-tubesheet joints.
EFFECT OF PARTICLE CONTENT IN ANALYSIS OF CREEP IN AN ISOTROPIC UNIFORM COMPO...ijiert bestjournal
The following paper discusses the effect of particl e content in analysis of creep in an isotropic uniform composite cylinder. The paper is a part of the series of papers published under the analysis of creep in an isotropic uniform composite cylinder.
EFFECT OF PARTICLE CONTENT IN ANALYSIS OF CREEP IN AN ISOTROPIC UNIFORM COMPO...ijiert bestjournal
The following paper discusses the effect of particl e content in analysis of creep in an isotropic uniform composite cylinder. The paper is a part of the series of papers published under the analysis of creep in an isotropic uniform composite cylinder.
This document discusses a finite element analysis of fatigue in a piston ring. It begins with an introduction to piston rings and their importance. It then describes conducting a finite element analysis to model the stresses on a piston ring under different loading conditions like gas pressure, thermal loading, and contact with the piston. The analysis identified fatigue-critical locations and calculated fatigue lives. Figures 1-8 show results of the modeling like stress distributions, deformed shapes, and comparisons of coating and uncoated rings. The conclusion is that fatigue remains an issue for piston rings and manufacturers are working to reduce weight while increasing power, further challenging fatigue life.
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Determinação dos momentos de reação de juntas de expansão carndânica e dobradiça
1. ______________________________
1
Ger. Desenvolvimento, Engenheira Química – TEADIT
2
Ger. Eng.,Engenheiro Mecânico – TEADIT
3
Diretor Técnico, Engenheiro Mecânico – TEADIT
4
Engenheira de Equipamentos, Engenheira Mecânica – PETROBRAS
5
Consultor Sênior, Engenheiro Mecânico – PETROBRAS
IBP3298_10
DETERMINATION OF GIMBAL AND HINGED EXPANSION
JOINTS REACTION MOMENTS
Ana M. F. Sousa1
, José C. Veiga2
, Nelson Kavanagh3
Jordana L. Veiga4
, Jorivaldo Medeiros5
Copyright 2010, Instituto Brasileiro de Petróleo, Gás e Biocombustíveis - IBP
Este Trabalho Técnico foi preparado para apresentação na Rio Oil & Gas Expo and Conference 2010, realizada no período de 13 a
16 de setembro de 2010, no Rio de Janeiro. Este Trabalho Técnico foi selecionado para apresentação pelo Comitê Técnico do evento,
seguindo as informações contidas na sinopse submetida pelo(s) autor(es). O conteúdo do Trabalho Técnico, como apresentado, não
foi revisado pelo IBP. Os organizadores não irão traduzir ou corrigir os textos recebidos. O material conforme, apresentado, não
necessariamente reflete as opiniões do Instituto Brasileiro de Petróleo, Gás e Biocombustíveis, seus Associados e Representantes. É
de conhecimento e aprovação do(s) autor(es) que este Trabalho Técnico seja publicado nos Anais da Rio Oil & Gas Expo and
Conference 2010.
Resumo
Este trabalho propõe um método para estimar, mais próximo da realidade, as forças de reação em juntas de expansão
metálicas do tipo cardânicas e dobradiças. Foram analisados os resultados de testes de movimento, sob pressão,
desenvolvidos para realizar os ensaios de juntas de expansão de grandes diâmetros, a serem instaladas em uma unidade
de craqueamento catalítico fluido (FCC), de uma refinaria. Foram analisados as várias componentes que influenciam nas
forças de reação de uma junta de expansão: efeito mola do fole, atrito dos pinos das articulações, componente lateral de
força de pressão, atrito de componentes estruturais diversos e propostos modelos teóricos, que pudessem melhor
representar estas influências. Comparados os resultados reais dos ensaios com o modelo teórico, foram analisados
estatisticamente e proposto uma equação final, para o cálculo de momentos de reação. Algumas componentes de forças
de pressão e de atrito, que não são consideradas nos cálculos feitos pela norma de projeto do EJMA (“Expansion Joints
Manufacturer Association”), são acrescentadas à constante de mola, para melhor estimar os momentos de reação devido
ao movimento angular da junta de expansão.
Abstract
This paper proposes a method to estimate, closer to actual situations, the reaction loads in gimbal and hinged metal
expansion joints. It was analyzed the movement test results, under pressure, developed to test large diameter expansion
joints, to be installed in a fluid catalytic cracking unit (FCC) from a refinery. It was analyzed the several components
from the expansion joint reaction loads: bellows spring effect, hinges pin friction, lateral pressure component force,
structural hardware friction and were proposed theoretical models, which could better represent those influences.
Comparing the actual test results with the theoretical models, they were statistically analyzed and it was proposed the
final equation for the reaction moment. Friction and some media pressure forces, which are not considered in the current
EJMA standard (“Expansion Joints Manufacturer Association”), were added to the bellows spring rate to better estimate
the expansion joint angular movement reaction moment.
1. Introduction
Expansion joints are used by the industry in process piping and ducts to compensate the thermal expansion and
provide the proper pipe flexibility. A pipe line is considered flexible if the pipe stresses and the equipment connection
loads are lower than an acceptable level.
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The ASME Process Piping code B31.3 [1] establishes the rules and values for the maximum allowable stresses
in a process piping system. In addition, rotating equipment like steam turbines , compressors, pumps and
turbo-expanders, have the maximum allowable nozzle loads specified by the manufacturer or by an industry specific
standard such as the NEMA SM23 [2] for steam turbines and turbo-expanders.
In a paper by the authors [3] metal bellows expansion joints actual reaction forces were compared with the
theoretical values as per standards of the Expansion Joint Manufactures Association (EJMA) [4] equations. Since
EJMA does not consider effects like friction and components interference there is a discrepancy in the calculations that
can show an increase in the actual pipe stresses and equipment nozzle loads.
This Paper presents a series of equations, based upon 13 large gimbal (Fig. 1) and hinged (Fig. 2) expansion joints
pressure and movements tests, that take into account the loads not considered by the EJMA calculations. These
equations can be used to estimate with higher precision the reaction forces in piping systems with metal bellows
expansion joints.
Figure 1. Gimbal expansion joint Figure 2. Hinged expansion joint
2. Expansion Joint Reaction Forces
The media pressure and the movement acting in a gimbal or hinged expansion joints causes reaction loads
calculated according to EJMA equations. The source of these reaction loads may be attributed to the following effects:
- Bellows spring effect: a metal bellows acts like a spring when it is flexed by the piping movement (Fig. 3).
- Pressure thrust: as a flexible element the media pressure creates a pressure thrust force (Fig. 4) that acts on
expansion joint hinges.
In addition to these loads, other loads may be attributed to reactions as defined bellow:
- Hinges pin friction: as the expansion joints move, there is friction force acting on the hinge pins (Fig. 5). This
force is due to the pressure thrust, joint weight and external forces.
- Lateral pressure force: in a rotated bellows the difference between expanded and contracted sides generates a
lateral force
- Hinges Arm friction: the rubbing effect of the arms (Fig. 5) creates a friction force that opposite to their
rotation.
- Sleeve Seal friction: expansion joints with inner sleeves may have a seal to hold inside bellows insulation.
The seal creates a force which opposes the angular movement as shown in Fig. 6.
The forces acting on the expansion joint create an angular moment which can be expressed as follows:
Mav = Mb + Mpf + Mlpf + Marm + Ms (1)
In the following paragraphs each reaction moment is analyzed.
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Figure 3. Spring effect Figure 4. Thrust pressure
Figure 5. Hinged pin / arms friction Figure 6. Inner sleeve seal friction
2.1. Moment Due to Bellows Spring Rate
The standard EJMA (Expansion Joint Manufacturers Association), state the spring rate calculation considering
only the bellows spring effect.
Mb = α * kα (2)
2.2. Moment Due to Pin Friction
The pressure thrust force acting on an expansion joint hinge can reach very high values. For examples, in one of
the joints tested, during the preparation of this paper, it reached 112 ton (248000 lbf) at its maximum test pressure.
Consequently, it is necessary to account accurately and reduce the hinge pin friction.
An expansion joint, installed in a process piping to compensate thermal growth, is under a low frequency
movement. A process which starts-up and stays for long periods at a steady-state, once the process temperature has been
reached and hinges will not move.
In Fig. 7, see the sketch of the angular movement and the pin friction moment, due to the pin load.
The hinges pin moment can be written as:
Mpf = Fp * µp * d/2 (3)
4. Rio Oil & Gas Expo and Conference 2010
4
Figure 7. Pin friction moment
The pin static friction coefficient value “µp” depends of several conditions, like materials, hardness, surface
finishing, presence of dirty and others. The most part of expansion joints applications use some steel pin straight in
contact with the arms steel or with a metal sleeve, not using any lubricant and usually, in this condition the “µp” value is
from 0.25 to 0.9 and this values can change due to environmental conditions. The choice of the proper pin and arm or
sleeve metal must be carefully studied during the expansion joint design.
It is not part of this paper to analyze pin and sleeve materials. Further studies are necessary to evaluate the best
choices. The focus of this paper is to show the importance of pin/sleeve friction loads.
If the hinges pin and sleeves are not properly hardened, the pressure thrust force may create a galling effect at
their contact surface, increasing the moment necessary to move the joint. To avoid galling the pins can be hardened or
adopt some other solution. In the expansion joints tested, for this paper, the pins were hardened using stellite, with
grinding surface finishing. In order to check the friction coefficient of stellite x stellite, it was developed a test using
different contact pressures, considering that the media pressure would cause a pin contact pressure from 47 MPa to 73
MPa (6.8 ksi to 10.5 ksi). The test results for stellite friction coefficient were from 0.13 to 0.14. For this study we
considered a friction coefficient of 0.14.
2.3. Moment Due to the Lateral Pressure Force
As shown in Fig. 8, as the expansion joint rotates, one side of the bellows expands and the opposite side
contracts. The difference between the expanded and contracted areas (Fig.9) will generate a force in the opposite
direction of the rotation. The moment due to the differential area can be written as follows:
Mlpf = Fb * H / 2 (4)
Where:
Fb = P * Ad (5)
H = L / 2 (6)
Figure 10 shows an angular sector equals to half of the total rotation angle α. A side view (X-X) of this sector is
shown in Fig. 11. The shaded portions are the differential areas between the expanded and contracted sides of the
rotated bellows.
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Figure 8. Lateral pressure force Figure 9. Bellows differencial areas
Figure 10. Bellows angular sector Figure 11. Bellows angular view X-X
As shown in Fig. 12, it was considered a partial area, from the total differential area, to calculate in an easiest
way. So the equation is:
Ad = 8* Ac (7)
Figure 12. Differential areas
Considering the radius R in the view XX divided in “n” equal parts, the partial differential area can be
calculated as follows:
6. Rio Oil & Gas Expo and Conference 2010
6
( ( ) )ii
n
i
i
AA
HH
Ac −∗
−
= +
−
=
∑ 1
1
0 2
(8)
Where:
∗=
−
4
tan
2
α
i
i
B
HH
(9)
( ) 5.022
ii ARB −= (10)
So the equation becomes:
( ( ) ( ) )ii
n
i
i AAARAd −∗
∗−∗= +
−
=
∑ 1
5.01
0
22
4
tan8
α
(11)
In this study, it was adopted a division in 10 equal parts, so the equation becomes:
( ( ) ( ) )ii
i
i AAARAd −∗
∗−∗= +
=
∑ 1
5.09
0
22
4
tan8
α
(12)
Table 2 shows values of the differential areas Ad for the diameters and movements of this paper.
Table 2. Bellows sides area differences
ID mm
(in)
1650
(65)
1900
(75)
1930
(76)
α (°) Ad (cm²)
1 196,3 262,4 268,5
1,5 294,4 393,7 402,8
2 392,5 524,9 537,1
2,5 490,7 656,1 671,4
3 588,8 787,4 805,6
3,5 687,0 918,6 939,9
4 785,2 1049,9 1074,2
4,5 883,3 1181,2 1208,6
5 981,5 1312,4 1342,9
2.4. Moment Due to Hinges Friction
The friction between hinges will increase the moment required to move the expansion joint. This friction can
not be accurately accounted for. Bending due to welding thermal stresses can reduce the gap between arms increasing
their rubbing.
2.5. Moment Due to Inner Sleeve Seal
The expansion joints, with internal refractory insulation, may be fitted with a metal seal between sleeves as
shown in Fig. 13. This seal usually is a steel wire braid with steel mesh filler.
If the seal is aligned with the hinge pin, it will slide between the internal sleeves when the expansion joint is
subjected to an angular movement as shown in Fig. 13. If the seal is not aligned, it will slide as well as compress with
7. Rio Oil & Gas Expo and Conference 2010
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the joint rotation as shown in Fig. 14. Both the sliding movement and the seal compression will generate a force, and
consequently, a moment that can not be accurately calculated.
Figure 13. Sleeve seal centered Figure 14. Sleeve seal not centered
3. Analysis of Large Expansion Joints Test Results
Pressure and movement tests were performed by the authors [3] with 13 large expansion joints. A summary of
the test results are shown in Fig. 17 to 22. The actual moment values (black lines) are larger than the values calculated
by the EJMA equations (green lines). Figure 15 shows a picture of a joint being tested and Fig. 16 shows a schematic
drawing of the test device.
The force on hinges is affected by the weight of the test device and its value was excluded from calculations.
The actual values can be as high as 3 times when compared with the EJMA equations results. Angles in the 1 to 2
degrees range increase the error. This difference can result large errors in the pipe flexibility analysis.
To minimize this error, at the piping design time, the actual values were compared with the theoretical values in
order to define a correction factor (CR) to account for the uncertainties.
We have seen that is possible to calculate moment due to bellows spring rate (Mb), media pressure (Mlpf) and
pin friction (Mpf), so the eq. (1) in theory can be calculated and becomes as eq. (13).
Mavt = Mb + Mlpf + Mpf (13)
The value of CR can be used as a correction factor to adjust the Eq. (13) in order to have values closer to the
actual expanded joint.
Figure 15. Movement test Figure 16. Movement test
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EJ ID1930mm P=3.6bar
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
0 1 2 3 4 5 6
Movement Angle (°)
Moment(N.m)
Present
Theory
Proposed
Theory
EJ ID1930mm P=2.3bar
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
0 1 2 3 4 5 6
Movement Angle (°)
Moment(N.m)
Present
Theory
Proposed
Theory
Figure 17. Test result 1 vs. theory Figure 18. Test result 2 vs. theory
EJ ID1908mm P=3.6bar
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
0 1 2 3 4 5 6
Movement Angle (°)
Moment(N.m)
Present
Theory
Proposed
Theory
EJ ID1908mm P=2.3bar
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
0 1 2 3 4 5 6
Movement Angle (°)
Moment(N.m)
Present
Theory
Proposed
Theory
Figure 19. Test result 3 vs. theory Figure 20. Test result 4 vs. theory
EJ ID1650mm P=3.5bar
0
10000
20000
30000
40000
50000
60000
70000
0 1 2 3 4 5 6
Movement Angle (°)
Moment(N.m)
Present
Theory
Proposed
Theory
EJ ID1650mm P=2.1bar
0
10000
20000
30000
40000
50000
60000
0 1 2 3 4 5 6
Movement Angle (°)
Moment(N.m)
Present
Theory
Proposed
Theory
Figure 21. Test result 5 vs. theory Figure 22. Test result 6 vs. theory
Thus, the ratio of actual value and Mavt is defined as moment Ratio (MR ) shown in Eq. (14).
MR = Ma / Mavt (14)
The moment ratios calculated using Eq.(14), for test pressures of 2.2 bar and 3.5 bar were feed into the
Statgraphics Centurion software [5] to determine the best probability distribution for the data.
According to box-and-whisker plot for each pressure test, the variability is similar within each sample. The
mean comparison shows the same behavior of variability. It means that pressure does not have influence on MR;
consequently all data can be used to determine the probability distribution.
9. Rio Oil & Gas Expo and Conference 2010
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A distribution fitting procedure was performed to find a probability that provides a suitable model for the
experimental data in order to determine MR tolerance limits. From this procedure, experimental data of MR can be
adequately modeled by Weibull, as shown in Fig. 23, which compare frequency histogram to the estimated probability
density according Weibull distribution.
Figure 23. MR histogram vs. Weibull distribution
Table 3 shows the calculated MR and its respective probability obtained from the fitted Weibull distribution.
Table 3. MR values probabilities
MR Probability, %
1.15 95.0
1.19 97.5
1.23 99.0
1.26 99,5
1.31 99.9
The values shown in Table 3 can be used as a correction factor (CR). The selection of the MR value, used as CR,
will depend upon how critical the application is. Thus the expansion joint estimated moment can be expressed as in Eq.
(15) below.
Mejt=Mavt* CR (15)
For example, the respective MR value of a probability of 99.5% is 1.26. Using this number as CR, the Mejt
calculated from Eq. (15) is plotted, in red lines, against the joint actual test results, as shown in Fig. 17 to 22.
4. Conclusion
Based upon test values it is possible to improve the EJMA reaction moment, represented by Eq. (2), which is
considering just the bellows spring effect, by adding the friction and pressure forces effects with a correction factor. So,
it is suggested to use Eq. (16), to calculate the angular moment for gimbal and hinged expansion joints, due to angular
rotation.
Mejt=(Mb + Mlpf + Mpf )* CR (15)
Using this equation at the design time will prevent an underestimation of the expansion joints reaction loads,
which are critical in rotating equipment like turbines and turbo-expanders.
Additional studies are necessary to evaluate the CR variation according to the pin/sleeve different materials and
environment exposure.
10. Rio Oil & Gas Expo and Conference 2010
10
5. Nomenclature
Ad = Differential area
Aeff = Effective bellows area
CR = Correction factor
D = Bellows inside diameter
Fb = Force due to the differential area
Fe = External forces (weight, etc)
Fp = Tf + Fe = Total transversal force in the pin
L = Bellows length
Ma = Actual moment calculated from expansion joint tests
Marm = Moment due to hinges friction
Mav = Total moment in a EJ with angular movement
Mb = Bellows angular moment due to bellows spring rate
Mejt = Theoretical moment in a expansion joint
Mlpf = Moment due to the lateral pressure force
Mpf = Moment due to pin friction
Ms = Moment due to inner sleeve seal friction
P = Pressure
R = D / 2
Tf = Aeff . P = pressure thrust force calculated per EJMA equations
d = Pin diameter
kα = Bellows angular spring rate
α = Movement angle
µp = Pin friction coefficient
6. References
(1) ASME B31.3 – 2006 Process Piping, chapter II and appendix A, ASME Code for Pressure Piping, B31,
New York, NY, USA.
(2) NEMA SM23 – 1991(R1997, R2002), Steam Turbines for Mechanical Drive Service, section 8.4, Steam
Piping Systems, NEMA Standards, Rosslyn, VA, USA .
(3) Veiga J.C., Medeiros J., Veiga J.L.B.C., PVP2009-77828, “Analysis of FCC Expansion Joints Movement
Test”, 2009 ASME Pressure Vessel and Piping Conference , Prague, Czech Republic.
(4) EJMA – 9th
edition, section 4, Standards of the Expansion Joint Manufacturers Association, Inc.,
Terrytown, NY, USA.
(5) Statgraphics Centurion XV version 15.2.00 – Edition Profissional, StatPoint Technologies, Inc., Warrenton,
VA, USA.