Fourier Series Analysis of Cylindrical Pressure Vessel Subjected to External Pressure

2009 ◽  
Author(s):  
Gurinder Singh Brar ◽  
Yogeshwar Hari ◽  
Dennis K. Williams
Keyword(s):  
Fourier Series ◽  
Pressure Vessel ◽  
Large Diameter ◽  
External Pressure ◽  
Pressure Vessels ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Cylindrical Pressure Vessel ◽  
Section Viii ◽  
Division 2

This paper presents the comparison of a reliability technique that employs a Fourier series representation of random asymmetric imperfections in a cylindrical pressure vessel subjected to external pressure. Comparison with evaluations prescribed by the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2 Rules for the same shell geometries are also conducted. The ultimate goal of the reliability type technique is to predict the critical buckling load associated with the chosen cylindrical pressure vessel. Initial geometric imperfections are shown to have a significant effect on the load carrying capacity of the example cylindrical pressure vessel. Fourier decomposition is employed to interpret imperfections as structural features that can be easily related to various other types of defined imperfections. The initial functional description of the imperfections consists of an axisymmetric portion and a deviant portion, which are availed in the form of a double Fourier series. Fifty simulated shells generated by the Monte Carlo technique are employed in the final prediction of the critical buckling load. The representation of initial geometrical imperfections in the cylindrical pressure vessel requires the determination of appropriate Fourier coefficients. Multi-mode analyses are expanded to evaluate a large number of potential buckling modes for both predefined geometries and associated asymmetric imperfections as a function of position within a given cylindrical shell. The probability of the ultimate buckling stress that may exceed a predefined threshold stress is also calculated. The method and results described herein are in stark contrast to the “knockdown factor” approach as applied to compressive stress evaluations currently utilized in industry. Recommendations for further study of imperfect cylindrical pressure vessels are also outlined in an effort to improve on the current design rules regarding column buckling of large diameter pressure vessels designed in accordance with ASME Boiler and Pressure Vessel Code, Section VIII, Division 2 and ASME STS-1.

Buckling of Axisymmetric, Homogeneous Cylindrical Shells With Random Imperfections: Monte Carlo Method

2005 ◽  
Author(s):  
Dennis Williams
Keyword(s):  
Monte Carlo ◽  
Cylindrical Shell ◽  
Pressure Vessel ◽  
Cylindrical Shells ◽  
Large Diameter ◽  
Buckling Load ◽  
Problem Solution ◽  
Critical Buckling Load ◽  
Asme Code ◽  
Section Viii

This paper presents the second of a series of solutions to the buckling of imperfect cylindrical shells subjected to an axial compressive load. In particular, the current problem reviewed is the case of a homogeneous cylindrical shell with random axisymmetric imperfections. The problem solution for the determination of the critical buckling load utilizes a statistical approach to define the random imperfections as opposed to the deterministic methods most often employed in the pressure vessel industry. The imperfections are treated as a random function of the axial (i.e., longitudinal) position on the shell. The Monte Carlo technique is utilized to create a large sample of random shell geometries from which to eventually calculate a critical buckling load for each randomly generated shell geometry. Having matched or predefined the statistical parameters (including the co-variance) of interest as determined from actual manufacturing statistics to the Monte Carlo simulation of shell geometries, the reliability of the critical buckling load is then calculated for the set of cylindrical shells with the random axisymmetric imperfections. The ASME Boiler and Pressure Vessel Code Section VIII fabrication tolerances as supplemented by ASME Code Case 2286-1 are reviewed and addressed in light of the findings of the current study and resulting solutions with respect to the critical buckling loads. The method and results described herein are in stark contrast to the “knockdown factor” approach currently utilized in ASME Code Case 2286-1. Recommendations for further study of the imperfect cylindrical shell are also outlined in an effort to improve on the current design rules regarding column buckling of large diameter shells designed in accordance with ASME Section VIII, Divisions 1 and 2 and ASME STS-1 in combination with the suggestions contained within Code Case 2286-1.

A Study of the Conservatism in ASME BPVC Section VIII Division 2 Opening Design for External Pressure

2019 ◽  
Author(s):  
Barry Millet ◽  
Kaveh Ebrahimi ◽  
James Lu ◽  
Kenneth Kirkpatrick ◽  
Bryan Mosher
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Pressure Vessel ◽  
External Pressure ◽  
The Other ◽  
Finite Element Analyses ◽  
Division 1 ◽  
Section Viii ◽  
Allowable Compressive Stress ◽  
Division 2

Abstract In the ASME Boiler and Pressure Vessel Code, nozzle reinforcement rules for nozzles attached to shells under external pressure differ from the rules for internal pressure. ASME BPVC Section I, Section VIII Division 1 and Section VIII Division 2 (Pre-2007 Edition) reinforcement rules for external pressure are less stringent than those for internal pressure. The reinforcement rules for external pressure published since the 2007 Edition of ASME BPVC Section VIII Division 2 are more stringent than those for internal pressure. The previous rule only required reinforcement for external pressure to be one-half of the reinforcement required for internal pressure. In the current BPVC Code the required reinforcement is inversely proportional to the allowable compressive stress for the shell under external pressure. Therefore as the allowable drops, the required reinforcement increases. Understandably, the rules for external pressure differ in these two Divisions, but the amount of required reinforcement can be significantly larger. This paper will examine the possible conservatism in the current Division 2 rules as compared to the other Divisions of the BPVC Code and the EN 13445-3. The paper will review the background of each method and provide finite element analyses of several selected nozzles and geometries.

scholarly journals An Ability to Adapt and Change

2014 ◽  
Vol 136 (11) ◽  
pp. 36-37
Author(s):  
Madiha El Mehelmy Kotb
Keyword(s):  
Life Cycle ◽  
Pressure Vessel ◽  
Pressure Vessels ◽  
Electronic Format ◽  
The World ◽  
Regulatory Approach ◽  
Section Viii ◽  
Division 2 ◽  
Service Inspection ◽  
Technical Services

This article reviews about the views of Madiha El Mehelmy Hotb, the Head of the Pressure Vessels Technical Services Division for Regie Du Batiment Du Quedec, on how ASME Boiler and Pressure Vessel Code has evolved over the years. Hotb reveals that during the 1980s, ASME’s regulatory approach covered all aspects of the life cycle of a boiler or a pressure vessel from design to being taken out of service. It also confirmed every step in between – fabrication, installation, repair and modification, and in-service inspection. During later years, the institution moved toward accreditation of authorized inspection agencies, changed the publication cycle from three years to two, eliminated addenda, and restructured the Code committees. New Section VIII and division 2 were written, and the Codes were published in digital electronic format. Hotb believes that the Code will continue to be widely used and adopted in future. It will have a bigger and larger input from all over the world and will have further outreach and adoption by far more countries.

Calculation of Working Pressure for Cylindrical Vessel Under External Pressure

2010 ◽  
Author(s):  
Gurinder Singh Brar ◽  
Yogeshwar Hari ◽  
Dennis K. Williams
Keyword(s):  
Monte Carlo ◽  
Cylindrical Shell ◽  
Pressure Vessel ◽  
External Pressure ◽  
Working Pressure ◽  
Geometric Imperfections ◽  
The Monte Carlo Method ◽  
Cylindrical Pressure Vessel ◽  
Section Viii ◽  
Initial Geometric Imperfections

Initial geometric imperfections have a significant effect on the load carrying capacity of asymmetrical cylindrical pressure vessels. This research paper presents a comparison of a reliability technique that employs a Fourier series representation of random asymmetric imperfections in a defined cylindrical pressure vessel subjected to external pressure. Evaluations as prescribed by the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2 rules are also presented and discussed in light of the proposed reliability technique presented herein. The ultimate goal of the reliability type technique is to statistically predict the buckling load associated with the cylindrical pressure vessel within a defined confidence interval. The example cylindrical shell considered in this study is a fractionating tower for which calculations have been performed in accordance with the ASME B&PV Code. The maximum allowable external working pressure of this tower for the shell thickness of 0.3125 in. is calculated to be 15.1 psi when utilizing the prescribed ASME B&PV Code, Section VIII, Division 1 methods contained within example L-3.1. The Monte Carlo method as developed by the current authors and published in the literature is then used to calculate the maximum allowable external working pressure. Fifty simulated shells of geometry similar to the example tower are generated by the Monte Carlo method to calculate the nondeterministic buckling load. The representation of initial geometric imperfections in the cylindrical pressure vessel requires the determination of appropriate Fourier coefficients. The initial functional description of the imperfections consists of an axisymmetric portion and a deviant portion that appears in the form of a double Fourier series. Multi-mode analyses are expanded to evaluate a large number of potential buckling modes for both predefined geometries and the associated asymmetric imperfections as a function of position within a given cylindrical shell. The method and results described herein are in stark contrast to the dated “knockdown factor” approach currently utilized in ASME B&PV Code.

Review of Section VIII, Division 1 and 2 Changes, 2008–2010

2010 ◽  
Author(s):  
Thomas P. Pastor
Keyword(s):  
Pressure Vessel ◽  
Pressure Vessels ◽  
Major Event ◽  
The Past ◽  
Division 1 ◽  
Section Viii ◽  
Division 2

Three years ago the major event within Section VIII was the publication of the new Section VIII, Division 2. The development of the new VIII-2 standard dominated Section VIII activity for many years, and a new standard has been well received within the industry. As expected with any new standard, some of the material that was intended to be published in the standard was not ready at the time of publication so numerous revisions have taken place in the last two addenda. This paper will attempt to summarize the major revisions that have taken place in VIII-2 and VIII-1, including a detailed overview of the new Part UIG “Requirements for Pressure Vessels Constructed of Impregnated Graphite”. I have stated in the past that the ASME Boiler and Pressure Vessel Code is a “living and breathing document”, and considering that over 320 revisions were made to VIII-1 and VIII-2 in the past three years, I think I can safely say that the standard is alive and well.

A Strength Calculation of a Nozzle Using Comparative Methods

2014 ◽  
Vol 601 ◽  
pp. 84-87 ◽  
Author(s):  
Serban Vasilescu ◽  
Costin Ilinca
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Pressure Vessels ◽  
Comparative Methods ◽  
The Finite Element Method ◽  
Finite Element Program ◽  
Element Program ◽  
Section Viii ◽  
Torsional Loads ◽  
Division 2

The stresses and deflections developed due to all piping loads produce some significant deformation in the nozzles of the pressure vessels. In this paper a spherical pressure vessel with two cylindrical nozzles are analyzed. The stresses in the nozzles are evaluated using two comparative methods: one of them represents the classical way of using the superposition of the axial, bending and torsional loads; the other one is based on the requirements of the ASME Boiler and Pressure Vessel Cod, Section VIII, Division 2 and is developed by a FE analysis. In order to obtain the loads (forces and moments) at the end of the nozzle a specialized finite element program has been used. This program (Coade Caesar 5.30) allows studying the strength and flexibility behavior of the pipes that connect the analyzed nozzle with the rest of the plant. The results obtained are compared in order to find when the using of the classical methods of strength of materials can be used as conservative approaches. The finite element method is applied in order to check the most important load cases that appear during the interaction between pipes and shell. In this respect the sustained (proper gravity loads), expansion (thermal loads) and occasional (wind and seismic loads) are combined in order to check all the requirements of ASME. This study contains also the effect of the pressure trust and the influence of the real geometry of the junction (nozzle-shell) in the peaks of the stresses.

Modernization of Pressure Vessel Design Codes ASME Section VIII, Division 2, 2007 Edition

2007 ◽  
Vol 129 (4) ◽  
pp. 754-758
Author(s):  
T. P. Pastor ◽  
D. A. Osage
Keyword(s):  
Pressure Vessel ◽  
Computer Aided Design ◽  
Pressure Vessels ◽  
Ease Of Use ◽  
Design Codes ◽  
Section Viii ◽  
Special Rules ◽  
The 1960S ◽  
Aided Design ◽  
Division 2

The technology for pressure equipment design continues to advance each and every day. The ASME Boiler and Pressure Vessel Code has been keeping pace with these advances over the last 92 years. As far back as the 1960s, it was recognized that the special requirements for design of pressure vessels operating at pressures over 2000 psi (13.7 MPa) called for special rules, and ASME issued Sec. VIII, Division 2 of Alternative Rules for Pressure Vessels. Since that time, the understanding of failure mechanisms and advances in material science, nondestructive testing, and computer-aided design has progressed to the stage where a new approach was needed not only in the content of design codes but in the way they are presented and organized. This paper introduces the newly issued ASME Sec. VIII, Division 2 of 2007 edition and explores the technical concepts included and the new format designed for ease of use. Included are results of test exercises sponsored by ASME giving actual applications of the new Code for design of vessels. This paper demonstrates ASME’s commitment to provide manufacturers and users of pressure equipment with the most up-to-date technology in easy to use standards that service the international market.

Proposed External Pressure Design Rules for Pressure Vessels for Human Occupancy

1980 ◽  
Vol 102 (4) ◽  
pp. 223-229
Author(s):  
J. R. Maison ◽  
E. M. Briggs
Keyword(s):  
Pressure Vessel ◽  
External Pressure ◽  
Pressure Vessels ◽  
Design Rules ◽  
Mathematical Development ◽  
Work Systems ◽  
Safety Code ◽  
Section Viii

The safety of externally pressurized manned diving bells, submersibles and underwater work systems resides in the ability of the system to rise to the surface in case of an emergency. Use of the ASME Boiler and Pressure Vessel Code Section VIII design rules, lead to unacceptably heavy structures, and thus substantially compromise the sought-for safety in underwater manned systems. A recognition on the part of the diving industry of the inherent limitations in using the ASME Boiler and Pressure Vessel Code for design of underwater pressure vessels, motivated the formation of the ASME Safety Code Committee on Pressure Vessels for Human Occupancy (PVHO) in 1974. A subcommittee of the PVHO Safety Code Committee was formed to address the specific problems of external pressure vessel design. The mathematical development which provided the basis for the proposed rules are presented. The restrictions imposed by the External Pressure Subcommittee are also presented.

Code Case 2286 Applied to the Design of Pressure Vessels

2003 ◽  
Author(s):  
Kanhaiya L. Bardia ◽  
Kim Nguyen ◽  
Manfred Lengsfeld ◽  
Donald G. LaBounty ◽  
Bernie Au
Keyword(s):  
Pressure Vessel ◽  
Petrochemical Industry ◽  
External Pressure ◽  
Pressure Vessels ◽  
Compressive Stresses ◽  
Division 1 ◽  
Shell Design ◽  
Asme Code ◽  
Section Viii ◽  
Sample Vessel

Code Case 2286-1 [1] of the ASME Boiler and Pressure Vessel Code [2][3] provides alternate rules for determining the allowable external pressure and compressive stresses for cylinders, cones, spheres, and formed heads in lieu of the rules of Section VIII, Divisions 1 and 2. The authors in this paper present a comparison of the longitudinal and circumferential compressive stresses in pressure vessels based on the methods outlined in Paragraph UG-28 of Division 1, Section VIII of the ASME Code and Code Case 2286-1. The Do/t ratio in this paper is limited to 600 which covers the majority of pressure vessel designs found in the petrochemical industry. A sample vessel shell design is presented applying both the ASME Code, Section VIII, Div. 1 method and that of Code Case 2286-1.

scholarly journals Finite Element Analysis of Gasket in Pressure Vessel

2021 ◽  
Vol 9 (11) ◽  
pp. 1390-1393
Author(s):  
Sanjana Jaishankara
Keyword(s):  
Pressure Vessel ◽  
Design Procedure ◽  
Pressure Vessels ◽  
Project Work ◽  
Element Analysis ◽  
Applied Loading ◽  
Sealing Performance ◽  
Riveted Joints ◽  
Section Viii ◽  
Division 2

Abstract: Pressure vessel is a closed container designed to hold liquids or gases at a pressure which are higher than the surrounding atmospheric pressure. These pressure vessels are not made as a single component but manufacture with an assembly of many other components and connected through bolted joints or riveted joints or welded joints. These joints are susceptible to failure and cause leakage of the liquid or gas which are very dangerous and sometimes causes heavy loss of life, health and property. Hence proper care has to be taken during the design analysis processes by following ASME section VIII division 1 which specifies the design-by-formula approach while division 2 contains a set of alternative rules based on design by Analysis (FEA) to determine the expected deformation and stresses that may develop during operation. The ASME section-VIII division-2 standards are used for the design of pressure vessel. Leakage in gasketed flanged joints have always been a great problem for the process industry. The sealing performance of a gasketed flanged joints depends on its installation and applied loading conditions. The present project work involves the design procedure and stress analysis (Structural Analysis) for the leak proof pressure vessel at the gasket under three different gasket conditions. Keywords: 1. FEM, 2. ASME, 3. ANSYS, 4. Gasket,5. Displacement,6. Stress

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