1、STP-PT-029-1EXTERNAL PRESSUREDESIGN INCREEP RANGESTP-PT-029-1 External Pressure Design in Creep Range Prepared by: Maan Jawad, Ph.D., P.E. and Donald Griffin, Ph.D. Global Engineering & Technology, LLC Date of Issuance: July 29, 2011 This report was prepared as an account of work sponsored by ASME P
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9、k, NY 10016-5990 ISBN No. 978-0-7918-3398-8 Copyright 2011 by ASME Standards Technology, LLC All Rights Reserved External Pressure Design in Creep Range STP-PT-029-1 iii Summary of Changes July 29, 2011 STP-PT-029-1 External Pressure Design in Creep Range The following changes have been made to the
10、first revision of STP-PT-029. Rev. 1 Page Location Change vi-vii Table of Contents Updated to reflect changes 3 table 2, row 8 Corrected from “9Cr-1M0-V” to “9Cr-1Mo-V” 5 last paragraph, line 3 Replaced “k ” with “kT” 5 equation (10) Removed “T” 6 paragraph 1 Inserted “K = kT” 6 equation (11) Replac
11、ed “1464” with “39,300” 6 equation (10) Removed “T” 6 equation (11) Replaced “1464” with “39,300” 7 bullet 2 Replaced “48” with “120” 7 bullet 3 Replaced “10,000” with “100,000” 7 section 3.3.1.1, line 3 Replaced “10,000” with “100,000” 7 section 3.3.1.1, line 3 Replaced “860” with “8,600” 7 equatio
12、n Removed “100”7 equation Replaced “48” with “120” 7 equation Replaced “5,880” with “94,100” 7 equation Replaced “” 7 paragraph 8 Replaced “5,880” with “14,200” 7 paragraph 8 Replaced “860” with “8,600” STP-PT-029-1 External Pressure Design in Creep Range iv Rev. 1 Page Location Change 7 section 3.3
13、.1.2, line 3 Replaced “10,000” with “100,000” 7 section 3.3.1.2, line 3 Replaced “380” with “3,800” 8 first equation Removed “10,000”8 first equation Replaced “48” with “120” 8 first equation Replaced “515” with “5,570” 8 paragraph 3 Replaced “515” with “5,570” 8 paragraph 3 Replaced “380” with “3,8
14、00” 8 section 3.3.1.3, line 1 Replaced “40” with “20” 8 section 3.3.1.3, line 2 Replaced “300” with “3,800” 8 second equation Removed “100,000”8 second equation Replaced “48” with “120” 8 second equation Replaced “2.94” with “2.96” 8 second equation Replaced “300” with “4,740” 8 paragraph 9 Replaced
15、 “300” with “4,740” 8 paragraph 9 Replaced “equal to” with “greater than” 8 paragraph 9 Replaced “300” with “3,800” 8 paragraph 9 Replaced “40” with “20” 11 equation (19) Replaced “K ” with “k ” 11 paragraph 5 Replaced “K ” with “k ” 11 paragraph 5 Replaced “(2) ” with “(1)” 12 equation (20) Removed
16、 “T” 12 paragraph 1 Inserted “K = kT” 13 bullet 4 Replaced “24.7” with “24,700” 13 paragraph 5 Removed “8” 14 paragraph 4 Removed “8” 15 bullet 3 Inserted “S = 20,700 psi at 1000F for short time” 15 bullet 4 Inserted “S = 6,300 psi at 1000F for 100,000 hours” 15 bullet 6 Replaced “1.0” with “1.5” 15
17、 paragraph 4 Inserted “This stress is 6,300 psi. Use B = 6,300 psi ” 15 paragraph 8 Removed “not” 16 paragraph 3 Replaced “low” with “high” External Pressure Design in Creep Range STP-PT-029-1 v Rev. 1 Page Location Change 16 bullet 1 Inserted “The ratio e/t of the cylinder is highly arbitrary and d
18、oes not have an influence on the results.” 16 bullet 1 Removed “assumed to have a very large Ro/t ratio. However, the ratio in this case is only 45.” 16 bullet 2 Replaced “get to be too conservative” with “become approximate” 16 paragraph 4 Removed “the conservative” 18 equation (29) Replaced “K ” w
19、ith “k ” 18 paragraph 5 Replaced “K ” with “k ” 18 paragraph 5 Replaced “(2) ” with “(1)” 19 equation (30) Removed “T” 19 paragraph 1 Inserted “K = kT” 20 paragraph 4 Replaced “1.0” with “1.5” 21 first equation Replaced “1.0” with “1.5” 21 first equation Removed “100,000”21 first equation Replaced “
20、0.55” with “16.9” 21 paragraph 2 Replaced “0.55 psi ” 21 paragraph 3 Replaced “inadequate” with “adequate” 21 bullet 1 Inserted “The ratio e/t of the cylinder is highly arbitrary and does not have an influence on the results.” 21 bullet 1 Removed “assumed to have a very large Do/t ratio. However, th
21、e ratio in this case is only 144.” 21 bullet 2 Replaced “get to be too conservative” with “become approximate” 23 equation (40) Replaced “Pa” with “1c” 23 equation (40) Removed “T” 23 equation (40) Replaced “0.588” with “0.353” STP-PT-029-1 External Pressure Design in Creep Range vi TABLE OF CONTENT
22、S Foreword . viii Abstract ix 1 INTRODUCTION 1 2 STRESS-STRAIN RELATIONSHIPS IN THE CREEP RANGE 2 3 AXIAL COMPRESSION OF TUBES AND COLUMNS . 4 3.1 Theoretical Derivations 4 3.2 Design Equations . 6 3.3 Applications . 7 3.3.1 Example 1 . 7 4 AXIAL COMPRESSION OF CYLINDRICAL SHELLS . 9 4.1 Theoretical
23、 Equations Below the Creep Range . 9 4.1.1 Elastic Buckling 9 4.1.2 Inelastic Buckling . 10 4.2 Theoretical Equations in the Creep Range . 11 4.3 Approximate Method Using Isochronous Stress-Strain Curves in the Creep Range . 12 4.4 Design Equations . 14 4.5 Applications . 14 4.5.1 Example 2 . 14 5 E
24、XTERNAL PRESSURE ON CYLINDRICAL SHELLS 17 5.1 Theoretical Equations Below the Creep Range . 17 5.2 Theoretical Equations in the Creep Range . 18 5.3 Approximate Method Using Isochronous Stress-Strain Curves 19 5.4 Design Equations . 19 5.5 Applications . 20 5.5.1 Example 3 . 20 6 EXTERNAL PRESSURE O
25、N SPHERICAL SHELLS . 22 6.1 Theoretical Equations Below the Creep Range . 22 6.2 Theoretical Equations in the Creep Range . 22 6.3 Approximate Method Using Isochronous Stress-Strain Curves 23 6.4 Design Equations . 23 6.5 Applications . 24 6.5.1 Example 4 . 24 7 EXTERNAL PRESSURE ON CONICAL SHELLS .
26、 26 References . 33 Acknowledgments . 35 Abbreviations and Acronyms . 36 External Pressure Design in Creep Range STP-PT-029-1 vii LIST OF TABLES Table 1 - Approximate Temperatures at Which Creep Becomes a Design Consideration for Various Materials (these temperatures may vary significantly for speci
27、fic product chemistry and failure mode under consideration). . 1 Table 2 - Temperature Range of Available Isochronous Stress-Strain Curves. . 3 LIST OF FIGURES Figure 1 - Creep Curves Conventionally Plotted as Strain vs Time at Constant Stress. 27 Figure 2 - Resultant Stress-Strain Curves Plotted as
28、 Stress vs Strain at Constant Time. . 27 Figure 3 - Isochronous Stress-Strain Curves for 2.25Cr-1Mo Steel at 1000F (ASME). 28 Figure 4 - Deflection in the Creep Range. 29 Figure 5 - External Pressure Chart for Carbon and Low-Alloy Steels with Yield Stresses of 30 ksi and Higher (ASME). 29 Figure 6 -
29、 External Pressure Chart for 2.25Cr-1Mo Steel at 1000F. 30 Figure 7 - Collapse Coefficients of Cylindrical Shells with Pressure on Sides and Ends, Edges Simply Supported, and P = 0.3 3. 31 Figure 8 - Geometric Chart for Cylindrical Shells Under External or Compressive Loadings (ASME). . 32 STP-PT-02
30、9-1 External Pressure Design in Creep Range viii FOREWORD This document was developed under a research and development project that resulted from ASME Pressure Technology Codes & Standards (PTCS) committee requests to identify, prioritize and address technology gaps in current or new PTCS Codes, Sta
31、ndards and Guidelines. This project is one of several included for ASME fiscal year 2009 sponsorship which are intended to establish and maintain the technical relevance of ASME codes & standards products. The specific project related to this document is project 09-03 (BPVC #2) titled “External Pres
32、sure Design in Creep Range”. Established in 1880, the American Society of Mechanical Engineers (ASME) is a professional not-for-profit organization with more than 127,000 members promoting the art, science and practice of mechanical and multidisciplinary engineering and allied sciences. ASME develop
33、s codes and standards that enhance public safety, and provides lifelong learning and technical exchange opportunities benefiting the engineering and technology community. Visit www.asme.org for more information. The ASME Standards Technology, LLC (ASME ST-LLC) is a not-for-profit Limited Liability C
34、ompany, with ASME as the sole member, formed in 2004 to carry out work related to newly commercialized technology. The ASME ST-LLC mission includes meeting the needs of industry and government by providing new standards-related products and services, which advance the application of emerging and new
35、ly commercialized science and technology and providing the research and technology development needed to establish and maintain the technical relevance of codes and standards. Visit www.stllc.asme.org for more information. External Pressure Design in Creep Range STP-PT-029-1 ix ABSTRACT At the prese
36、nt time the ASME Boiler and Pressure vessel code does not include rules for the design of components under external pressure and axial compressive loads in the time-dependent creep regime. A method is suggested in this report for designing components in the time-dependent creep regime. The design me
37、thodology is developed for columns and cylindrical shells under axial compression as well as cylindrical, spherical and conical shells under external pressure. An external pressure chart for 2.25Cr-1Mo steel was developed at 1000F to demonstrate the applicability of the methods developed in this rep
38、ort. In addition, variable factors of safety are imbedded in the design equations in order to transition from the design factors used in the time-independent External Pressure Charts of Section II to the lower design factors specified in Section III for time-dependent, creep buckling. STP-PT-029-1 E
39、xternal Pressure Design in Creep Range x INTENTIONALLY LEFT BLANKExternal Pressure Design in Creep Range STP-PT-029-1 1 1 INTRODUCTION The 2007 edition of the ASME Boiler and Pressure Vessel Code, Sections I and VIII, includes rules for the design of cylindrical, conical, spherical, ellipsoidal and
40、torispherical shells subjected to external pressure. Rules are also given for the design of cylindrical and conical shells under axial compressive loads. In addition, Section VIII gives rules for the design of structural members subjected to axial compressive loads such as heat exchanger tubes. All
41、of these rules are applicable at temperatures below the creep range of the material. The ASME code gives approximate temperatures above which creep becomes prominent as shown in Table 1. These temperature limits are approximate and serve as guidelines for design purposes and should not be thought of
42、 as absolute values for a given specified material. Table 1 - Approximate Temperatures at Which Creep Becomes a Design Consideration for Various Materials (these temperatures may vary significantly for specific product chemistry and failure mode under consideration). Material Temperature (F) Tempera
43、ture (C) Carbon and Low Alloy Steel 700-900 370-480 Stainless Steels 800-1000 425-535 Aluminum Alloys 300 150 Copper Alloys 300 150 Nickel Alloys 900-1100 480-595 Titanium and Zirconium Alloys 600-650 315-345 There are situations where it is beneficial for newly constructed boiler and pressure vesse
44、l components to operate at temperatures beyond the creep cut-off limits of the material. Thus, new design criteria are needed for establishing allowable compressive stress for various components. In this report, suggested procedures are presented to address the design of ASME components under compre
45、ssive and external pressure loads operating at elevated temperatures in the creep range. STP-PT-029-1 External Pressure Design in Creep Range 2 2 STRESS-STRAIN RELATIONSHIPS IN THE CREEP RANGE Theoretically 1 the relationship between stress and strain in the creep range can be expressed by Nortons e
46、quation: ndkdTHVc (1)Where: kc= constant n = creep exponent which is a function of material property and temperature ddTH = strain rate V stress This non-linear equation is difficult to use since it must be integrated to get the strain in a given component. However, when the stress field in the comp
47、onent stabilizes to a constant value after redistribution and when the strain value is relatively large, then Equation (1) may be replaced by the much simpler viscoelastic equation: nKHVc (2)Where: Kc= constant H = total strain Equation (2) is more practical to use for solving indeterminate structur
48、es than Equation (1) and it assumes the component represented by the viscoelastic Equation (2) is loaded in the same manner and has the same boundary conditions as when represented by the creep strain rate Equation (1). It also assumes that only secondary creep strain is considered and that the tota
49、l strain given by Equation (2) is approximately equal in magnitude to the creep strain rate given by Equation (1). Equation (2) and the stated assumptions mentioned above are collectively referred to as the Stationary Stress Method or the Elastic Analog Method 2, 3. It is applicable mainly in the secondary creep range which occurs after about 100 hours of service at elevated temperatures for materials used in ASME pressure vessels. The value of n in Equation (2) varies between 2 and 8 for most materials and corresponding te
