Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME ASME PTB-7-2014 Criteria for Shell-and-Tube Heat Exchangers According to Part UHX of ASME Section VIII-Division Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME PTB-7-2014 CRITERIA FOR SHELL-AND-TUBE HEAT EXCHANGERS ACCORDING TO PART UHX OF ASME SECTION VIII DIVISION Prepared by: Francis Osweiller OSWECONSULT Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME Date of Issuance: June 16, 2014 This document was prepared as an account of work sponsored by ASME Pressure Technology Codes and Standards (PTCS) through the ASME Standards Technology, LLC (ASME ST-LLC) Neither ASME, the author, nor others involved in the preparation or review of this document, nor any of their respective employees, members or persons acting on their behalf, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe upon privately owned rights Reference herein to any specific commercial product, process or service by trade name, trademark, manufacturer or otherwise does not necessarily constitute or imply its endorsement, recommendation or favoring by ASME or others involved in the preparation or review of this document, or any agency thereof The views and opinions of the authors, contributors and reviewers of the document expressed herein not necessarily reflect those of ASME or others involved in the preparation or review of this document, or any agency thereof ASME does not “approve,” “rate”, or “endorse” any item, construction, proprietary device or activity ASME does not take any position with respect to the validity of any patent rights asserted in connection with any items mentioned in this document, and does not undertake to insure anyone utilizing a standard against liability for infringement of any applicable letters patent, nor assume any such liability Users of a code or standard are expressly advised that determination of the validity of any such patent rights, and the risk of infringement of such rights, is entirely their own responsibility Participation by federal agency representative(s) or person(s) affiliated with industry is not to be interpreted as government or industry endorsement of this code or standard ASME is the registered trademark of The American Society of Mechanical Engineers No part of this document may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher The American Society of Mechanical Engineers Two Park Avenue, New York, NY 10016-5990 ISBN No 978-0-7918-6945-1 Copyright © 2014 by THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS All Rights Reserved Printed in the U.S.A Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME PTB-7-2014: Criteria for Shell-and-Tube Heat Exchangers According to Part UHX of ASME Section VIII Division TABLE OF CONTENTS Foreword x Abbreviations and Acronyms xi PART INTRODUCTION 1 SCOPE 2 HISTORICAL BACKGROUND 3 TYPES OF HEAT EXCHANGERS COVERED TYPES OF TS CONFIGURATIONS LOADING CASES STRUCTURE OF PART UHX 10 STRUCTURE OF THE DOCUMENT 11 NOTATIONS 12 References—Part 13 PART TUBESHEET CHARACTERISTICS 14 SCOPE (UHX-11.1) 15 NOTATIONS 16 DESIGN ASSUMPTIONS (UHX-11.2) 17 LIGAMENT EFFICIENCIES (UHX-11.5.1) 18 4.1 Introduction 18 4.2 Historical Background 19 4.3 LE in Part UHX (UHX-11.5.1) 20 EFFECTIVE ELASTIC CONSTANTS (UHX-11.5.2) 25 5.1 Introduction 25 5.2 Historical Background 25 5.3 The Square Pattern Problem 26 5.4 Synthesis of Results 27 5.5 Determination of EEC for the Full Range of μ* (0.1≤μ*≤1.0) 27 5.6 Determination of EECs for UHX Rules (UHX-11.5.2) 28 5.7 Conclusion 28 References—Part 32 PART ANALYICAL TREATMENT OF FIXED TUBESHEET HEAT EXCHANGERS 33 SCOPE (UHX-13.1) 34 HISTORICAL BACKGROUND 35 GENERAL 36 3.1 TS Configurations (UHX-13.1) 36 3.2 Notations (UHX-13.3) 37 3.3 Loading Cases (UHX-13.4) 40 3.4 Design Assumptions (UHX-13.2) 41 3.5 Basis of Analytical Treatment 42 3.5.1 General 42 3.5.2 Free Body Diagram 43 AXIAL DISPLACEMENTS AND FORCES ACTING ON THE TUBES AND ON THE SHELL 45 4.1 Axial Displacement and Force Acting on the Tubes (Figure 18) 45 4.2 Axial Displacement and Force Acting on the Shell 46 DEFLECTION AND LOADS ACTING ON THE TUBESHEET 48 iii Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME PTB-7-2014: Criteria for Shell-and-Tube Heat Exchangers According to Part UHX of ASME Section VIII Division 5.1 5.2 5.3 5.4 5.5 Equivalent Plate Resting on an Elastic Foundation 48 Determination of Integration Constants A and B 51 Deflection 53 Net Effective Pressure 53 Rotation 53 5.6 Shear Force 54 5.7 Bending Moment 55 5.8 Conclusion 55 TREATMENT OF THE UNPERFORATED RIM 56 6.1 Edge Loads Applied on Shell and Channel at their Connection to the TS 56 6.2 Equilibrium of the Unperforated Rim 58 6.3 Edge Loads Va and Ma Applied to the Tubesheet 61 EQUIVALENT PRESSURE ACTING ON TUBESHEET 64 7.1 Definition 64 7.2 Determination of Pe 65 STRESSES IN THE HEAT-EXCHANGER COMPONENTS 68 8.1 TS Net Effective Pressure 68 8.2 TS Axial Displacement 68 8.3 TS Rotation 69 8.4 Stresses in the Tubesheet 69 8.5 Axial Membrane Stress in Tubes 72 8.6 Stresses in the Shell 74 8.7 Stresses in the Channel 76 DETERMINATION OF THE ALLOWABLE STRESS LIMITS 78 9.1 General Considerations 78 9.2 Allowable Stress Limit in the Tubesheet 79 9.3 Allowable Stress Limit in the Tubes 79 9.4 Allowable Membrane Stress Limit in the Shell 79 9.5 Allowable Membrane + Bending Stress Limit in the Shell 79 9.6 Allowable Membrane + Bending Stress Limit in the Channel 79 9.7 Conclusions 80 10 ADDITIONAL RULES 81 10.1 Effect of Different Shell Thickness and Material Adjacent to the TS (UHX-13.6) 81 10.2 Effect of Plasticity at Tubesheet-Shell-Channel Joint (UHX-13.7) 82 10.3 Effect of Radial Thermal Expansion Adjacent to the Tubesheet (UHX-13.8) 84 10.4 Calculation Procedure for Simply Supported Tubesheets (UHX-13.9) 87 10.5 Tubesheet Effective Bolt Load (UHX-8) 87 10.6 Tubesheet Flange Extension (UHX-9) 88 10.7 HE Set-up with a Thin-Walled Expansion Joint (UHX-13.16) 90 10.8 HE Set-up with a Thick-Walled Expansion Joint (UHX-13.17) 90 11 HOW TO USE THE RULES 92 iv Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME PTB-7-2014: Criteria for Shell-and-Tube Heat Exchangers According to Part UHX of ASME Section VIII Division 12 CHECKING OF THE RESULTS 93 12.1 Comparison with FEA 93 12.2 Comparison with CODAP French Rules 95 12.3 Comparison with TEMA Rules 99 12.4 Comparison with Circular Plates Subject to Pressure 105 12.5 Conclusions 108 References—Part 109 PART FLOATING TUBESHEETS 110 SCOPE 111 HISTORICAL BACKGROUND 112 GENERAL 113 3.1 TS Configurations (UHX-14.1) 113 3.2 Notations 114 3.3 Loading Cases (UHX-14.4) 117 3.4 Design Assumptions (UHX-14.2) 118 3.5 Basis of Analytical Treatment 119 3.5.1 General 119 3.5.2 Free Body Diagram for ST TS 120 3.5.3 Free Body Diagram for FL TS 121 AXIAL DISPLACEMENTS AND FORCES ACTING ON THE TUBES AND ON THE SHELL 123 4.1 Axial Displacement and Force Acting on the Tubes (Figure 42) 123 4.2 Axial Displacement and Force Acting on the Shell (Figure 43) 124 DEFLECTION AND LOADS ACTING ON THE TUBESHEET 125 5.1 Equivalent Plate Resting on an Elastic Foundation (Figure 44) 125 5.2 Determination of Integration Constants A and B 126 TREATMENT OF THE UNPERFORATED RIM 127 6.1 Edge Loads Applied on Shell and Channel at their Connection to the TS 127 6.2 Equilibrium of the Unperforated Rim 127 6.2.1 Due to Axial Loads 127 6.2.2 Due to Applied Moments 133 6.2.3 Edge Loads Va and Ma Applied to the Tubesheet 133 EQUIVALENT PRESSURE ACTING ON THE TUBESHEET 134 STRESSES IN THE HEAT-EXCHANGER COMPONENTS 135 DETERMINATION OF ALLOWABLE STRESS LIMITS 136 10 ADDITIONAL RULES 137 11 HOW TO USE THE RULES 138 11.1 Stationary TS 138 11.2 Floating TS 138 11.3 Calculation Procedure 138 11.4 Calculation Using a Fixed TS HE Software 139 References—Part 140 PART ANALYTICAL TREATMENT OF U-TUBE TUBESHEET HEAT EXCHANGERS 141 SCOPE 142 HISTORICAL BACKGROUND 143 v Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME PTB-7-2014: Criteria for Shell-and-Tube Heat Exchangers According to Part UHX of ASME Section VIII Division GENERAL 144 3.1 TS Configurations (UHX-12.1) 144 3.2 Notations 144 3.3 Loading Cases (UHX-12.4) 146 3.4 Design Assumptions (UHX-12.2) 147 3.5 Basis of Analytical Treatment 147 3.5.1 General 147 3.5.2 Free Body Diagram 148 TREATMENT OF THE PERFORATED TUBESHEET 150 TREATMENT OF THE UNPERFORATED RIM 151 5.1 Edge Loads Applied on Shell and Channel at their Connection to the TS 151 5.2 Equilibrium of the Unperforated Solid Rim 151 STRESSES IN THE HEAT-EXCHANGER COMPONENTS 156 6.1 Stresses in the Tubesheet 156 6.2 Stresses in the Shell and Channel 156 6.3 Determination of Stresses using the Fixed TS Rules 157 DETERMINATION OF THE ALLOWABLE STRESS LIMITS 158 ADDITIONAL RULES 159 8.1 Effect of Plasticity at the Tubesheet-Shell-Channel Joint (UHX-12.5) 159 HOW TO USE THE RULES 160 10 COMPARISON WITH TEMA RULES 161 10.1 TEMA Formula 161 10.2 Numerical Comparisons 161 References—Part 163 PART SUMMARY AND CONCLUSIONS 164 SUMMARY AND CONCLUSIONS 165 Annex A — Values of Effective Elastic Constants from Various Authors 168 Annex B — Values of Effective Elastic Constants for the Full Range of μ (0.1≤μ*≤1.0) 170 Introduction 170 Curves (From [13] ) 170 Numerical Values (From [13] ) 171 Polynomials 176 Annex C — Poisson’s Ratio in Tubes and Shell 177 Annex D — Shell Pressure Acting on the Expansion Joint Sidewalls 179 Annex E — Differential Pressure Acting on the Equivalent Solid Plate 180 Annex F — Solution of Differential Equation w(x) 182 Annex G — Coefficients Zd, Zv, Zw, Zm; Qm, Qv; Qα, Qβ; Fm, Ft 184 Annex H — Radial Displacement and Rotation of the Shell at its Connection with the Ring 189 Radial Displacement Due to Internal Pressure Ps 189 Radial Displacement and Rotation Due to Edge Loads Qs and Ms 190 Radial Displacement Due to Internal Pressure and Edge Loads 190 Channel 190 Annex I — Shell-to-Ring Connection in Radial Direction 191 vi Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME PTB-7-2014: Criteria for Shell-and-Tube Heat Exchangers According to Part UHX of ASME Section VIII Division Annex J — Minimum Length of Shell and Channel when Integral with the TS 193 Annex K — Formulas for a Hemispherical Channel when Integral with the TS 195 Radial Displacement Due to Internal Pressure Pc 195 Radial Displacement and Rotation Due to Edge Loads Qs and Ms 195 Radial Displacement Due to Internal Pressure and Edge Loads 196 Annex L — Equilibrium of Ring Subjected to Edge Moments 197 Annex M — Direct Determination of the Equivalent Pressure 204 Annex N — Formulas To Be Used When Pe=0 208 Net Effective Pressure: q(x) 208 Axial Displacement: w(x) 208 Rotation: θ(x) 208 Bending Stress: σ(x) 208 Shear Stress:(x) 209 Axial Stress in Tubes: σt(x) 209 Annex O — Tabular and Graphical Representation of Coefficient Ft(x) 210 Annex P — Tabular and Graphical Representation of Coefficient Fm(x) 227 Annex Q —Tabular and Graphical Representation of Coefficient FQ(x) 238 Annex R — Determination of the Allowable Buckling Stress Limits 250 Annex S — Common Intersection of Curves σt(x) 254 General 254 Determination of Common Intersection xo for σt(x) 254 Generalization to Other Stresses 255 Annex T — Determination of Stresses in U-Tube TS HEs Using the Fixed TS Rules 256 Annex U — Calculation of a U-Tube TS Using Floating or Fixed TS HE Software 259 MATHCAD EXAMPLES Annex V — UHX-13 – Example E4.18.7 (PTB-4 2013 Edition) with General Equations 260 Annex W — UHX-14 – Example E4.18.8 (PTB-4 2013 Edition) Stationary 306 Annex X — UHX-14 – Example E4.18.8 (PTB-4 2013 Edition) Floating 335 Annex Y — UHX-12 – Example E4.18.4 (PTB-4 2013 Edition) 364 LIST OF TABLES Table — Values for E*/E and for Triangular Pattern from Meijers [12] 26 Table — Values of E*/E and for Square Pattern in Pitch and Diagonal Directions from Slot and O’Donnell [7] 27 Table — Comparison of TEMA and ASME TS Thicknesses for U-tube HEs 162 Table — Comparison of Effective Elastic Constants E* and Values by Various Theoretical Methods for Plane Stress Problem 168 Table — Values of Curves * as a Function of μ* for Ratios h/p=0.1, 0.15, 0.25, 0.5, 1.0 and 2.0 for Triangular Pattern 172 Table — Values of Curves * as a Function of μ* for Ratios h/p=0.1, 0.15, 0.25, 0.5, 1.0 and 2.0 for Square Pattern 173 LIST OF FIGURES Figure — Three Types of Tubesheet Heat Exchangers Figure — Tubesheet Configurations vii Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME PTB-7-2014: Criteria for Shell-and-Tube Heat Exchangers According to Part UHX of ASME Section VIII Division Figure — Ligament Area in the Actual Tubesheet 18 Figure — Ligament Orientation in the Actual Tubesheet 19 Figure — Ligament Efficiency Used in TEMA 20 Figure — TS Equivalent Diameter Do 20 Figure — TS with Unperforated Lanes 22 Figure — Tube Expansion Depth Ratio ρ=lt,x/h 22 Figure — Pass Partition Groove on Tubeside of the TS 24 Figure 10 — Pitch and Diagonal Directions for Square Pattern 26 Figure 11 — Curves and Tables for the Determination of E*/E and (Triangular Pattern) 29 Figure 12 — Curves and Tables for the Determination of E*/E and (Square Pattern) 30 Figure 13 — Curves E*/E for Square Pattern Obtained from Polynomial Approximation Given in Figure 12 31 Figure 14 — Fixed Tubesheet Heat Exchanger 34 Figure 15 — Tubesheet Configurations 36 Figure 16 — Analytical Model Used in Design Method 43 Figure 17 — Free Body Diagram of the Analytical Model 44 Figure 18 — Axial Displacement of Tubes 45 Figure 19 — Axial Displacement of the Shell 46 Figure 20 — Loads Acting on the TS 48 Figure 21 —TS Displacement 49 Figure 22 —TS Displacement of the Unperforated Ring and Connection to Shell 52 Figure 23 — Ring Equilibrium of the TS 58 Figure 24 — Equivalent Pressure and Axial Force Acting on Plate 64 Figure 25 — Bending Stress Distribution Throughout the TS for Q3=0.0 and Xa=1, 3, 5, 7, 10 and 15 71 Figure 26 — Shell with Increased Thickness Adjacent to TSs 81 Figure 27 — Temperature Gradient at TS-Shell-Channel Joint 85 Figure 28 — Tubesheet Flanged Extension 89 Figure 29 — Minimum Required Thickness of the Tubesheet Flanged Extension 90 Figure 30 — Comparison of Tube Stresses Calculated Per UHX and FEA (Example E4.18.7) 94 Figure 31 — Tube Stress Distribution Obtained by UHX, CODAP and FEA throughout the TS from r = to r = ao 99 Figure 32 — TEMA and ASME-CODAP Coefficient F for X Varying from X=0 to X=20 101 Figure 33 — TEMA Coefficient F 101 Figure 34 — TEMA Design Range 101 Figure 35 — Coefficient Fq as a Function of X for SS and CL TS 104 Figure 36 — Floating Tubesheet Heat Exchangers 111 Figure 37 — Stationary Tubesheet Configurations 113 Figure 38 — Floating Tubesheet Configurations 114 Figure 39 — Analytical Model Used in Design Method 120 Figure 40 — Free Body Diagram of the Analytical Model for the ST TS 121 Figure 41 — Free Body Diagram of the Analytical Model for the FL TS 122 Figure 42 — Axial Displacement of Tubes 123 Figure 43 — Axial displacement of the Shell 124 Figure 44 — Loads Acting on TS 125 Figure 45 — TS Displacement 126 Figure 46 — Ring Equilibrium of the ST TS 127 Figure 47 — Ring Equilibrium of the FL TS 128 Figure 48 — Immersed Floating TS HE 130 Figure 49 — Externally Sealed Floating TS HE 131 Figure 50 — Internally Sealed Floating TS HE 132 Figure 51 — U-tube Tubesheet Heat Exchangers 142 viii Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME PTB-7-2014: Criteria for Shell-and-Tube Heat Exchangers According to Part UHX of ASME Section VIII Division Figure 52 — TS Configurations 144 Figure 53 — Free Body Diagram of the Analytical Model for the TS 149 Figure 54 — Ring Equilibrium of the TS 152 Figure 55 — Synthesis of E*/E and Values from [1], Provided by Various Authors for Triangular and Square Pattern 169 Figure 56 — Curves of Effective Elastic Constants for the Full Range of μ* (0.1≤μ*≤1.0) 170 Figure 57 — Radial Displacement due to Internal Pressure 189 Figure 58 — Radial Force at Tubesheet Periphery 191 Figure 59 — Ring Radial Displacement 191 Figure 60 — Hemispherical Head 195 Figure 61 — Configuration a 197 Figure 62 — Configuration b 199 Figure 63 — Configuration c 201 Figure 64 — Configuration d 201 Figure 65 — Pressures Ps and Pt Acting on TS 204 Figure 66 — Pressure Ps Acting on Bellows Joint… 205 Figure 67 — Effect of t Due to Pressures Ps and Pt 205 Figure 68 — Pressure Pt Acting on the Channel Head … 206 Figure 69 — Tube Buckling 251 Figure 70 — Determination of Buckling Safety Factor, FS 253 Figure 71 — Graphs Giving σt(x) and Ft(x) for the Loading Cases (ASME 2013) 254 ix Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 3/16 degF := R set Farenheit temp - TEMPERATURE Data Ta := 70⋅ degF Tubesheet T := 400.0⋅ degF Shell Ts := 400.0⋅ degF Shell Design Temp Ambiant temperature Tubesheet Design Temp Channel Tc := 400.0⋅ degF Channel Design Temp - MATERIAL Data TUBESHEET Material is SA-516/gr70 lb S := 20000.0⋅ E := 27.7⋅ 10 ⋅ TS allowable stress @ T in TS elastic modulus @ T in lb Sa := 22000.0⋅ lb TS allowable stress @ T a in TUBE Material is SA-179 lb StT := 13400⋅ lb EtT := 27.7⋅ 10 ⋅ Tube allowable stress @ T Tube elastic modulus @ T in in SHELL Material is SA-516/gr70 lb Ss := 20000.0⋅ lb lb Sys := 32500.0⋅ Shell elast mod @ Ts in ν s := 0.3 Shell allowable P+S stress @ Ts in in Es := 27.7⋅ 10 ⋅ lb SPSs := 65000.0⋅ Shell allow stress @ T s Shell yield stress @ Ts in Shell Poisson' ratio CHANNEL Material is SA-516/grade70 Sc := 20000.0⋅ lb Channel allow stress @ Tc in Ec := 27.7⋅ 10 ⋅ lb 2 Channel allowable P+S stress @Tc in Channel elast modulus @ Tc Syc := 32500.0⋅ in ν c := 0.3 lb SPSc := 65000.0⋅ lb in Channel Poisson's ratio ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 367 Channel yield stress @ Tc Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 4/16 - Flange BOLT LOADS data (from Table UHX-8.1) Maximum and Minimum Flange DESIGN BOLT LOADS Flange BOLT LOADS for GASKET SEATING Condition Wm1s := 656000.0⋅ lb Shell flange Design bolt load Ws := 656000⋅ lb Shell flange bolt load for Gasket Seating Wm1c := 0.0⋅ lb Wc := 0.0⋅ lb Channel flange Design bolt load ( Wm1max := max Wm1s , Wm1c ) Channel flange bolt load for Gasket Seating ( Wm1max = 656000.0 lb Wmax := max Ws , Wc ) Wmax = 656000.0 lb Determination of EFFECTIVE BOLT LOAD W* for each Configuration a , b , c , d Configuration a Configuration b and c Configuration d ⎛Wm1c ⎞ ⎜ 0.0⋅ lb ⎟ W*b := ⎜ ⎜Wm1c ⎟ ⎜ ⎝0.0⋅ lb ⎠ ⎛⎜ Wm1c ⎞ ⎜ Wm1s ⎟ W*d := ⎜ ⎟ ⎜Wm1max ⎟ ⎜ 0.0⋅ lb ⎝ ⎠ ⎛0.0⋅ lb ⎞ ⎜ 0.0⋅ lb ⎟ W*a := ⎜ ⎜0.0⋅ lb ⎟ ⎜ ⎝0.0⋅ lb ⎠ W*c := W*b W* := Configuration e and f ⎛0.0⋅ lb ⎞ ⎜W m1s ⎟ W*e := ⎜ ⎜Wm1s ⎟ ⎜ ⎝0.0⋅ lb ⎠ W*f := W*e W*a if Config = "a" W*b if Config = "b" ∨ Config = "c" W*d if Config = "d" W*e if Config = "e" ∨ Config = "f" ⎛ 0.000 ⎞ ⎜ 656000.000 ⎟ W* = ⎜ lb ⎜656000.000 ⎟ ⎜ ⎝ 0.000 ⎠ Minimum required thickness h r of the TS flanged extension (from UHX-9) Gasket moment arm h G := For flanged Configurations b , d (extended as a flange) , e 1.9Wm1s S⋅ Gs ⋅ hG , h G = 17.500 in See UHX-9.5b 1.9Wm1c h rG := For unflanged Config.c , f from UHX-9.5a ⎛⎜ h rD := max ⎜ ⎝ C − Gc S⋅ Gc ⋅ hG 1.9Wc Sa ⋅ Gc ( ⎞ ⎠ h rD = 5.804 in ⋅ h G h rG = 0.000 in ) h r := max hrD , hrG h r = 5.804 in ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 368 For unflanged Config.d , C See UHX-9.5c Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 5/16 Start of Calculations UHX-12.5.1 Step Determine D , µ, µ* and h' g from UHX-11.5.1 : D o := ⋅ ro + d t D o = 26.250 in ⎡ ⎛ EtT ⎞ ⎛ StT ⎞ ⎤ ⋅⎜ ⋅ ρ , ( dt − 2tt)⎥ ⎝ E ⎠⎝ S ⎠ ⎦ d* := max ⎢d t − 2⋅ tt⋅ ⎜ ⎣ p p* := 1− ( ⋅ AL , 4D o ⋅ p π ⋅ Do µ := p − dt p d* = 0.636 in µ = 0.250 µ* := ) p* = 1.035 in p* − d* p* µ* = 0.385 UHX-12.5.2 Step Calculate coefficients ρs and ρc and moment MTS ρ s := Ds if ( Config = "a" ) ∨ ( Config = "b" ) ∨ ( Config = "c" ) Do ρ s = 1.233 Gs if ( Config = "d" ) ∨ ( Config = "e" ) ∨ ( Config = "f" ) Do ρ c := Dc if ( Config = "a" ) ∨ ( Config = "e" ) ∨ ( Config = "f" ) Do ρ c = 1.181 Gc if ( Config = "b" ) ∨ ( Config = "c" ) ∨ ( Config = "d" ) Do MTS := Do 16 ⋅ ⎡⎣ ρ s − ⋅ ⎛⎝ρ s + 1⎞⎠ ⋅ Ps − ρ c − ⋅ ⎛⎝ρ c + 1⎞⎠ ⋅ Pt ⎤⎦ ( ) ( ) ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 369 ⎛− 12129.924 ⎞ ⎜ 16467.238 ⎟ MTS = ⎜ lb ⎜ 4337.314 ⎟ ⎜ ⎝ 0.000 ⎠ Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 6/16 UHX-12.5.3 Step Determine E*/E and ν* relative to h/p from UHX-11.5.2 h p = 3.500 UHX-12.5.4 β s := β c := ⎡⎣( Dc + tc) ⋅ tc⎤⎦ Es⋅ ts h δ s := ⎛⎜ −1 ) CHAN = "CYL" νs ⎞ ⎠ ( Ec⋅ tc in 2⎞ lb λ s = × 10 ⎠ λ c := 6⋅ Dc in h 6⋅ ⎛⎝1 − ν c ⎞⎠ h'c := h⋅ β c h's 3 kc = 5.064 × 10 lb h'c = 1.431 ⎛⎜ h'c ⎝ ⋅ kc⋅ ⎜1 + h'c + if SS = "NO" ∧ ( Config = "a" ∨ Config = "b" ∨ Config = "c" ) 2⎞ λ c = 7.591 × 10 ⎠ lb in −1 δ s = × 10 in lb νc ⎞ ⎠ if SS = "NO" ∧ CHAN = "CYL" ∧ ( Config = "a" ∨ Config = "e" ∨ Config = "f" ) −5 β c = 0.409 otherwise ⎛ − νc ⎞ ⎜ 4Ec⋅ tc ⎝ ⎠ Dc in SS = "NO" ⎛ ⎜1 − 4Ec⋅ tc ⎝ Dc kc := β c⋅ ⎠ ⋅ ks⋅ ⎜1 + h's + ⎛ ⎜1 − 4Es⋅ ts ⎝ ( if SS = "NO" ∧ ( Config = "a" ∨ Config = "e" ∨ Config = "f" ) 0.5 ⎝ β s = 0.000 0.25 h's = 0.000 0⋅ in lb δ c := if SS = "NO" ∧ ( Config = "a" ∨ Config = "b" ∨ Config = "c" ) ks = × 10 lb 2⎞ Ds in 6⋅ ⎛⎝1 − ν s 6⋅ Ds ( From right pages above ) otherwise in h's := h⋅ β s λ s := ν* = 0.318 otherwise in ⎡12⋅ ⎛1 − ν c2⎞⎤ ⎣ ⎝ ⎠⎦ ks := β s⋅ lb 0.25 0.5 ⎡⎣( Ds + ts) ⋅ ts⎤⎦ 0⋅ E* = 1.222 × 10 Use SS=YES for Simply Supported calculation in a nd step (see UHX-13.9) ⎡12⋅ ⎛1 − ν s2⎞⎤ ⎣ ⎝ ⎠⎦ 0⋅ E = 0.441 Calculate coefficients shell and channel parameters:β, k, λ, δ and ω : Step SS = "NO" E* µ* = 0.385 −1 0⋅ in lb ) if SS = "NO" ∧ CHAN = "HEMI" ∧ ( Config = "a" ∨ Config = "e" ∨ Config = "f" ) otherwise ( ω s := ρ s⋅ ks⋅ β s⋅ δ s⋅ + h's ) ω s = 0.000 in ( ω c := ρ c⋅ kc⋅ β c⋅ δ c⋅ + h'c ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 370 ) ω c = 7.013 in δ c = 1.18 × 10 −1 in lb Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 UHX-12.5.5 F := 7/16 K := Step Calculate diameter ratio K and coefficient F : ⎡ − ν* ⋅ λ + λ + E⋅ ln( K) ⎤ if ( Config = "a" ) ( s c )⎥ ⎢ ⎣ E* ⎦ ⎡ − ν* ⋅ λ + E⋅ ln( K) ⎤ if ( Config = "b" ) ∨ ( Config = "c" ) ( s )⎥ ⎢ ⎣ E* ⎦ − ν* ⎡ ⎤ ⋅ ( E⋅ ln( K) )⎥ if ( Config = "d" ) ⎢ E* ⎣ ⎦ − ν* ⎡ ⎤ ⋅ ( λ c + E⋅ ln( K) )⎥ if ( Config = "e" ) ∨ ( Config = "f" ) ⎢ ⎣ E* ⎦ A Do K = 1.419 F = 0.964 otherwise UHX-12.5.6 Step Calculate moment M* acting on the unperforated TS rim : ( MTS + ω c⋅ Pt − ω s⋅ Ps) M* := if ( Config = "a" ) C − Gc ⎛ ⎞ ⋅ W* if ( Config = "b" ) ⎜MTS − ω s⋅ Ps − 2⋅ π⋅ Do ⎝ ⎠ G1 − Gc ⎛ ⎞ ⋅ W* if ( Config = "c" ) ⎜MTS − ω s⋅ Ps − 2⋅ π⋅ Do ⎝ ⎠ Gc − Gs ⎛ ⎞ ⋅ W* if ( Config = "d" ) ⎜MTS + 2⋅ π⋅ Do ⎝ ⎠ C − Gs ⎛ ⎞ ⋅ W* if ( Config = "e" ) ⎜MTS + ω c⋅ Pt + 2⋅ π⋅ Do ⎝ ⎠ G1 − Gs ⎛ ⎞ ⋅ W* if ( Config = "f" ) ⎜MTS + ω c⋅ Pt − 2⋅ π⋅ Do ⎝ ⎠ ⎛− 7571.674 ⎞ ⎜ 26907.802 ⎟ M* = ⎜ lb ⎜19336.128 ⎟ ⎜ ⎝ 0.000 ⎠ 0lb otherwise UHX-12.5.7 Step Calculate the max bending moments M p ( at the periphery) , Mo ( at the center) : M* − Mp := Do 32 ( ⋅ F⋅ Ps − Pt 1+F M := ) ⎛3017.568 ⎞ ⎜ 6825.214 ⎟ Mp = ⎜ lb ⎜9842.782 ⎟ ⎜ ⎝ 0.000 ⎠ ⎛max⎛ ⎝ ⎜ ⎜max⎛ ⎝ ⎜ Mmax := ⎜max⎛ ⎝ ⎜ ⎜max⎛ ⎝ ⎝ Mo := Mp + Mo Mo Mo Mo , Mp , Mp 2 , Mp , Mp ⎞⎞ ⎠ ⎞⎟ ⎠⎟ ⎞⎟ ⎠⎟ ⎞ ⎠⎠ Do 64 ⋅ ( + ν* ) ⋅ Pe ⎛20202.132 ⎞ ⎜ 30044.913 ⎟ Mmax = ⎜ lb ⎜ 9842.782 ⎟ ⎜ ⎝ 0.000 ⎠ Mo if SS = "OUI" ∧ ( Config = "a" ∨ Config = "b" ∨ Config = "c" ) Mo if SS = "OUI" ∧ ( Config = "a" ∨ Config = "e" ∨ Config = "f" ) Mmax otherwise ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 371 ⎛−20202.132 ⎞ ⎜ 30044.913 ⎟ Mo = ⎜ lb ⎜ 9842.782 ⎟ ⎜ ⎝ 0.000 ⎠ ⎛20202.132 ⎞ ⎜ 30044.913 ⎟ M=⎜ lb ⎜ 9842.782 ⎟ ⎜ ⎝ 0.000 ⎠ Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 Summary : 8/16 ⎛ 0.000 ⎞ ⎜ 656000.000 ⎟ W* = ⎜ lb ⎜656000.000 ⎟ ⎜ ⎝ 0.000 ⎠ ⎛− 12129.924 ⎞ ⎜ 16467.238 ⎟ MTS = ⎜ lb ⎜ 4337.314 ⎟ ⎜ ⎝ 0.000 ⎠ ⎛− 7571.674 ⎞ ⎜ 26907.802 ⎟ M* = ⎜ lb ⎜19336.128 ⎟ ⎜ ⎝ 0.000 ⎠ ⎛3017.568 ⎞ ⎜ 6825.214 ⎟ Mp = ⎜ lb ⎜9842.782 ⎟ ⎜ ⎝ 0.000 ⎠ ⎛−20202.132 ⎞ ⎜ 30044.913 ⎟ Mo = ⎜ lb ⎜ 9842.782 ⎟ ⎜ ⎝ 0.000 ⎠ ⎛20202.132 ⎞ ⎜ 30044.913 ⎟ M=⎜ lb ⎜ 9842.782 ⎟ ⎜ ⎝ 0.000 ⎠ UHX-12.5.8 Step Calculate the tubesheet bending stress σ : ⎛h − h'g ⎞ ⎜ ⎜h − h'g ⎟ h := ⎜ ⎟ ⎜h − h'g ⎟ ⎜h − h' g⎠ ⎝ Effective Groove depth h'g := max( hg − ct , 0) h'g = 0.000 in ⎛3.5000 ⎞ ⎜ 3.5000 ⎟ h = ⎜ in ⎜3.5000 ⎟ ⎜ ⎝3.5000 ⎠ a) Maximum tubesheet stress for loading cases 1,2,3,4 σ := ⎛25669.233 ⎞ ⎜ 38175.669 ⎟ =⎜ ⎜12506.435 ⎟ ⎜ ⎝ 0.000 ⎠ 6⋅ M ( µ* ⋅ h − h'g ) σ ( σ max := max σ , σ , σ , σ ) lb in lb σ max = 38175.7 in σ allow := ⋅ S σ allow = 40000.0 lb in ( Tubesheet_bending_Design := if σ max > σ allow , "NOT OKAY" , "OKAY" ) h r := b) Minimum required thickness of the TS flanged extension for configurations b and e: Tubesheet_bending_Design = "OKAY" 1.9Wc C − Gc ⋅ if Config = "b" S⋅ Gc 1.9Ws C − Gs ⋅ if Config = "e" S⋅ Gs 0⋅ in otherwise ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 372 h r = 1.589 in Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 9/16 UHX-12.5.9 Step Calculate the maximum tubesheet shear stress ⎛ ⎜ ⎜ Note : If |Pe| τ allow , "NOT OKAY" , "OKAY" ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 9/16 373 ) Tubesheet_bending_Design = "OKAY" Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 UHX 12.5.10 Step 10 10/16 Determine the shell stresses a) shell membrane stress ⎛0⋅ lb ⎞ ⎜ ⎜ in ⎟ ⎜ lb ⎟ ⎜0⋅ ⎟ ⎜ in2 ⎟ σ zero := ⎜ ⎟ ⎜0⋅ lb ⎟ ⎜ in2 ⎟ ⎜ ⎟ ⎜0⋅ lb ⎟ ⎜ ⎝ in ⎠ ⎡ ⎤ Ds ⎢ ⎥ ⋅ Ps ⎢ 4⋅ ts⋅ ( Ds + ts) ⎥ ⎣ ⎦ σ sm := ⎛0.000 ⎞ ⎜ 0.000 ⎟ σ sm = ⎜ ⎜0.000 ⎟ ⎜ ⎝0.000 ⎠ if ( Config = "a" ) ∨ ( Config = "b" ) ∨ ( Config = "c" ) σ zero otherwise b) shell bending stress: σ sbb := ⎡ − ν* D o ⎛ ⎢ ⋅ ks⋅ β s⋅ δ s⋅ Ps + ⋅ ⋅ ⋅ ⎜1 + ⎢ ⎝ E* h ts ⎣ σ sb := σ sbb if ( Config = "a" ) ∨ ( Config = "b" ) ∨ ( Config = "c" ) ⎛⎜ ⋅ ⎜ Mp + ⎠⎝ h's ⎞ Do ⎞⎤ ⎥ ⎠ ⎥⎦ ⋅ Pe 32 σ zero otherwise c) total shell stress: σ s := ⎯⎯⎯⎯⎯⎯⎯ → σ sm + σ sb ( ) ⎛0.000 ⎞ ⎜ 0.000 ⎟ σs = ⎜ ⎜0.000 ⎟ ⎜ ⎝0.000 ⎠ ( ) lb σ smax := max σ s ⎛0.000 ⎞ ⎜ 0.000 ⎟ σ sb = ⎜ ⎜0.000 ⎟ ⎜ ⎝0.000 ⎠ σ smax = 0.0 lb in lb in in σ sallow := 1.5⋅ Ss σ sallow = 30000.0 lb in ( Shell_design := if σ smax > σ sallow , "NOT OKAY" , "OKAY" ) Shell_design = "OKAY" Note :If the shell stress is greater than σallows, but is less than S PSs, then Elastic/Plastic procedure "EP" can be used SPSs = 65000 lb in ( EP_shell := if σ sallow ≤ σ smax ≤ SPSs , "EP may be applied" , "EP procedure is not applicable" EP_shell = "EP procedure is not applicable" ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 374 ) lb in Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 UHX 12.5.10 11/16 Step 10 Determine the channel stresses a) channel membrane stress: σ cm := ⎡ ⎤ Dc ⎢ ⎥ ⋅ Pt ⎢ 4⋅ tc⋅ ( Dc + tc) ⎥ ⎣ ⎦ ⎛7900.711 ⎞ ⎜ 0.000 ⎟ σ cm = ⎜ ⎜7900.711 ⎟ ⎜ ⎝ 0.000 ⎠ if ( Config = "a" ) ∨ ( Config = "e" ) ∨ ( Config = "f" ) σ zero otherwise lb in b) channel bending stress: σ cbb := ⎡ − ν* D o ⎛ ⎢ ⋅ kc⋅ ( β c⋅ δ c⋅ Pt) − ⋅ ⋅ ⋅ ⎜1 + ⎢ E* h ⎝ tc ⎣ σ cb := ⎛⎜ ⋅ ⎜ Mp + ⎠⎝ h'c ⎞ Do ⎞⎤ ⎥ ⎠ ⎥⎦ 32 ⋅ Pe σ cbb if ( Config = "a" ) ∨ ( Config = "e" ) ∨ ( Config = "f" ) σ zero otherwise ⎛ 54418.403 ⎞ ⎜ − 56955.170 ⎟ σ cb = ⎜ ⎜ −2536.767 ⎟ ⎜ ⎝ 0.000 ⎠ lb in c) total channel stress: ⎯⎯⎯⎯⎯⎯⎯ → σ c := σ cm + σ cb ( ) ⎛62319.114 ⎞ ⎜ 56955.170 ⎟ σc = ⎜ ⎜10437.478 ⎟ ⎜ ⎝ 0.000 ⎠ lb ( ) σ cmax := max σ c lb σ cmax = 62319.1 in in σ callow := 1.5⋅ Sc σ callow = 30000.0 lb in ( Channel_design := if σ cmax > σ callow , "NOT OKAY" , "OKAY" ) Channel_design = "NOT OKAY" Note : If the channel stress is greater than σallowc, but is less than S PSc, then Elastic/Plastic procedure "EP" can be used SPSc = 65000 lb in ( EPchannel := si σ callow < σ cmax ≤ SPSc , "EP May Be Applied" , "EP is not Applicable" EPchannel = "EP May Be Applied" ⎛0⋅ lb ⎞ ⎜ ⎜ in ⎟ ⎜ lb ⎟ ⎜0⋅ ⎟ ⎜ in2 ⎟ σ zero := ⎜ ⎟ ⎜0⋅ lb ⎟ ⎜ in2 ⎟ ⎜ ⎟ ⎜0⋅ lb ⎟ ⎜ ⎝ in ⎠ ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 375 ⎛1⋅ lb ⎞ ⎜ ⎜ in ⎟ ⎜ lb ⎟ ⎜1 ⋅ ⎟ ⎜ in2 ⎟ σ zero1 := ⎜ ⎟ ⎜1⋅ lb ⎟ ⎜ in2 ⎟ ⎜ ⎟ ⎜1⋅ lb ⎟ ⎜ ⎝ in ⎠ ) Copyright c 2014 by the American Society of Mechanical Engineers No reproduction may be made of this material without written consent of ASME ExampleE4.18.4-U TUBE TS(AnnexY) from PTB4 12/16 UHX13.7 Simplified Elastic Plastic Procedure Calculation procedure for the effect of plasticity at the tubesheet, channel or shell joint This procedure applies only to Configurations a,b,c and Design Loading Cases 1, , , in the following conditions: -for integral shell (config a,b,c) when 1.5S s