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BS EN 13480‑3:2017
BSI Standards Publication
Metallic industrial piping Part 3: Design and calculation
BS EN 13480‑3:2017
BRITISH STANDARD
National foreword This British Standard is the UK implementation of EN 13480‑3:2017. It supersedes BS EN 13480‑3:2012 which is withdrawn. The UK participation in its preparation was entrusted to Technical Committee PVE/10, Piping systems. A list of organizations represented on this committee can be obtained on request to its secretary. This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. © The British Standards Institution 2017 Published by BSI Standards Limited 2017 ISBN 978 0 580 98618 5 ICS 23.040.01 Compliance with a British Standard cannot confer immunity from legal obligations.
This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 September 2017. Amendments/corrigenda issued since publication
Date
Text affected
BS EN 13480‑3:2017
EN 13480-3
EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM
June 2017
ICS 23.040.01
Supersedes EN 13480-3:2012
English Version
Metallic industrial piping - Part 3: Design and calculation Tuyauteries industrielles métalliques - Partie 3 : Conception et calcul
Industrielle metallische Rohrleitungen - Teil 3: Konstruktion und Berechnung
This European Standard was approved by CEN on 21 June 2017. CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member. This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION C O M I TÉ E URO P É E N D E N O RM ALI S ATI O N E U RO P ÄI S C H E S KO M I T E E F Ü R N O RM U N G
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels © 2017 CEN
All rights of exploitation in any form and by any means reserved worldwide for CEN national Members.
Ref. No. EN 13480-3:2017 E
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
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Contents
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European foreword .................................................................................................................................................... 10
1 2
Normative references ................................................................................................................................. 12
Terms, definitions, symbols and units ................................................................................................. 13 Terms and definitions ................................................................................................................................ 13 Symbols and units ........................................................................................................................................ 13
Design of piping components under internal pressure ................................................................. 30 Straight pipes ................................................................................................................................................. 30 Pipe bends and elbows ............................................................................................................................... 30 General ............................................................................................................................................................. 30 Symbols ............................................................................................................................................................ 31 Required wall thicknesses ........................................................................................................................ 31 Mitre bends..................................................................................................................................................... 32 General ............................................................................................................................................................. 32 Symbols ............................................................................................................................................................ 32 Effective radius of mitre bend ................................................................................................................. 33 Multiple mitre bends .................................................................................................................................. 33 Single mitre bends ....................................................................................................................................... 34
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Design stresses .............................................................................................................................................. 26 General ............................................................................................................................................................. 26 Time independent nominal design stress .......................................................................................... 27 Steels other than austenitic steels ......................................................................................................... 27 Austenitic steels ............................................................................................................................................ 27 Nickel and / or chromium alloy steels .................................................................................................. 28 Steels castings ................................................................................................................................................ 28 Additional requirements for steels with no specific control ........................................................ 28 Time dependent nominal design stress .............................................................................................. 29 General ............................................................................................................................................................. 29 Steels ................................................................................................................................................................. 29 Nickel and/or chromium alloy steels.................................................................................................... 30 ‐
5 5.1 5.2 5.2.1 5.2.2 5.2.3 5.2.4 5.2.5 5.3 5.3.1 5.3.2 5.3.3
Basic design criteria .................................................................................................................................... 15 General ............................................................................................................................................................. 15 Loadings .......................................................................................................................................................... 15 General ............................................................................................................................................................. 15 Combination of loads .................................................................................................................................. 16 Loads for dimensioning ............................................................................................................................. 16 Other loads to be taken into account .................................................................................................... 18 Design conditions ......................................................................................................................................... 19 Thickness ........................................................................................................................................................ 22 Tolerances ...................................................................................................................................................... 25 Joint coefficient ............................................................................................................................................. 25 Dimensioning of piping components subject to pressure ............................................................. 26
6 6.1 6.2 6.2.1 6.2.2 6.2.3 6.3 6.3.1 6.3.2 6.3.3 6.3.4 6.3.5
4 4.1 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.3 4.4 4.5 4.6
Scope ................................................................................................................................................................. 12
3 3.1 3.2
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6.3.6 6.4 6.4.1 6.4.2 6.4.3 6.4.4 6.4.5 6.4.6 6.4.7 6.4.8 6.4.9 6.4.10 6.5 6.5.1 6.5.2 6.5.3 6.6 6.6.1 6.6.2 6.6.3 6.6.4
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Adjacent straight pipe sections of mitre bends ................................................................................. 34 Reducers .......................................................................................................................................................... 34 Conditions of applicability ........................................................................................................................ 34 Specific definitions ....................................................................................................................................... 35 Specific symbols and abbreviations ....................................................................................................... 35 Conical shells .................................................................................................................................................. 36 Junctions general ........................................................................................................................................ 37 Junction between the large end of a cone and a cylinder without a knuckle .......................... 37 Junction between the large end of a cone and a cylinder with a knuckle ................................ 40 Junction between the small end of a cone and a cylinder .............................................................. 41 Offset reducers .............................................................................................................................................. 43 Special forged reducers .............................................................................................................................. 43 Flexible piping components ...................................................................................................................... 44 General ............................................................................................................................................................. 44 Expansion joints ............................................................................................................................................ 44 Corrugated metal hose assemblies ........................................................................................................ 46 Bolted flange connections ......................................................................................................................... 47 General ............................................................................................................................................................. 47 Symbols ............................................................................................................................................................ 47 Standard flange ............................................................................................................................................. 47 Non standard flange .................................................................................................................................... 48
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7 7.1 7.1.1 7.1.2 7.1.3 7.1.4 7.1.5 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5
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Design of ends under internal pressure ............................................................................................... 48 Dished ends ..................................................................................................................................................... 48 Symbols ............................................................................................................................................................ 48 Hemispherical ends ..................................................................................................................................... 49 Torispherical ends ....................................................................................................................................... 50 Ellipsoidal ends ............................................................................................................................................. 51 Calculation of .............................................................................................................................................. 52 Circular flat ends ........................................................................................................................................... 56 General ............................................................................................................................................................. 56 Symbols ............................................................................................................................................................ 56 Unstayed flat circular ends welded to cylindrical shells/pipes ................................................... 58 Unstayed flat circular bolted ends.......................................................................................................... 65 Reinforcements of openings in unstayed flat ends .......................................................................... 71
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Openings and branch connections ......................................................................................................... 74 General ............................................................................................................................................................. 74 Symbols ............................................................................................................................................................ 74 Limitations ...................................................................................................................................................... 75 Thickness ratio .............................................................................................................................................. 75 Openings in the vicinity of discontinuities .......................................................................................... 77 Types of reinforcement .............................................................................................................................. 79 Calculation method ...................................................................................................................................... 80 Elliptical openings and oblique branch connections ....................................................................... 80 Reinforcing pads ........................................................................................................................................... 82 Dissimilar material of shell and reinforcements .............................................................................. 82 Extruded outlets ............................................................................................................................................ 82 Forged tee ........................................................................................................................................................ 82 Branches in bends or elbows .................................................................................................................... 83 Screwed in branches ................................................................................................................................... 83 Isolated openings .......................................................................................................................................... 84 General ............................................................................................................................................................. 84 Unreinforced openings ............................................................................................................................... 87
8 8.1 8.2 8.3 8.3.1 8.3.2 8.3.3 8.3.4 8.3.5 8.3.6 8.3.7 8.3.8 8.3.9 8.3.10 8.3.11 8.4 8.4.1 8.4.2
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8.4.3 8.4.4 8.5 8.5.1 8.5.2 8.6 8.6.1 8.6.2 8.6.3
Design of piping components under external pressure ................................................................. 97 General ............................................................................................................................................................. 97 Symbols and elastic stress limits ............................................................................................................ 99 Symbols ............................................................................................................................................................ 99 Elastic stress limits .................................................................................................................................... 101 Cylindrical pipes, elbows and mitre bends ....................................................................................... 101 Determination of lengths ........................................................................................................................ 101 Interstiffener collapse .............................................................................................................................. 103 Overall collapse of stiffened pipes ....................................................................................................... 105 Stiffener stability ........................................................................................................................................ 106 Heating/cooling channels ....................................................................................................................... 109 Reducers (conical shells) ........................................................................................................................ 110 Dished ends .................................................................................................................................................. 112 Hemispherical ends ................................................................................................................................... 112 Torispherical ends ..................................................................................................................................... 113 Ellipsoidal ends ........................................................................................................................................... 113
10 10.1 10.2 10.3 10.3.1 10.3.2 10.4 10.4.1 10.4.2 10.5
Integral attachments ................................................................................................................................. 130 General ........................................................................................................................................................... 130 Allowable stresses ..................................................................................................................................... 130 Symbols .......................................................................................................................................................... 131 Hollow circular attachments .................................................................................................................. 133 Limitations .................................................................................................................................................... 133 Preliminary calculations ......................................................................................................................... 133 Analysis of attachments welded to pipe with a full penetration weld .................................... 135 Analysis of attachments welded to pipe with fillet or partial penetration weld ................ 136 Rectangular attachments ........................................................................................................................ 136 Limitations .................................................................................................................................................... 136 Preliminary calculations ......................................................................................................................... 136 Analysis of attachments welded to pipe with a full penetration weld .................................... 138 Analysis of attachments welded to pipe with fillet or partial penetration weld ................ 139 Stress analysis of the run pipe ............................................................................................................... 139 Shear stress analysis in attachment .................................................................................................... 141
Design for cyclic loading .......................................................................................................................... 113 General ........................................................................................................................................................... 113 Exemption from detailed fatigue analysis ........................................................................................ 113 Fatigue design for cyclic pressure ........................................................................................................ 114 Equivalent full load cycles ....................................................................................................................... 114 Simplified fatigue analysis ...................................................................................................................... 114 Fatigue design for thermal gradients ................................................................................................. 129 General ........................................................................................................................................................... 129 Design guidance .......................................................................................................................................... 129 Fatigue design for combined loads ...................................................................................................... 130
11 11.1 11.2 11.3 11.4 11.4.1 11.4.2 11.4.3 11.4.4 11.5 11.5.1 11.5.2 11.5.3 11.5.4 11.6 11.7
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Reinforced openings with di / Di < 0,8 .................................................................................................. 87 Reinforced single openings with 0,8 < d/D 1,0 .............................................................................. 93 Adjacent openings ........................................................................................................................................ 93 Unreinforced openings............................................................................................................................... 93 Reinforced openings with d/D 0,8 ...................................................................................................... 93 Design of special piping components .................................................................................................... 94 Cylindrical Y pieces ..................................................................................................................................... 94 Spherical Y pieces ........................................................................................................................................ 95 Triform reinforced branches ................................................................................................................... 96
9 9.1 9.2 9.2.1 9.2.2 9.3 9.3.1 9.3.2 9.3.3 9.3.4 9.3.5 9.4 9.5 9.5.1 9.5.2 9.5.3
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11.7.1 Hollow circular attachments ................................................................................................................. 141 11.7.2 Rectangular attachments ........................................................................................................................ 141 11.8 Alternative calculation methods .......................................................................................................... 141
12 Flexibility analysis and acceptance criteria ..................................................................................... 141 12.1 Basic conditions ......................................................................................................................................... 141 12.1.1 General .......................................................................................................................................................... 141 12.1.2 Loading conditions .................................................................................................................................... 142 12.1.3 Allowable stresses ..................................................................................................................................... 142 12.2 Piping flexibility ......................................................................................................................................... 144 12.2.1 General .......................................................................................................................................................... 144 12.2.2 Basic conditions ......................................................................................................................................... 144 12.2.3 Displacement strains ................................................................................................................................ 144 12.2.4 Displacement stresses ............................................................................................................................. 145 12.2.5 Stress range ................................................................................................................................................. 146 12.2.6 Cold pull ........................................................................................................................................................ 146 12.2.7 Properties for flexibility analysis ........................................................................................................ 147 12.2.8 Supporting conditions ............................................................................................................................. 147 12.2.9 Expansion joints ......................................................................................................................................... 149 12.2.10Flexibility analysis .................................................................................................................................... 149 12.3 Flexibility analysis .................................................................................................................................... 151 12.3.1 General .......................................................................................................................................................... 151 12.3.2 Stress due to sustained loads ................................................................................................................ 152 12.3.3 Stress due to sustained and occasional or exceptional loads .................................................... 152 12.3.4 Stress range due to thermal expansion and alternating loads ................................................. 153 12.3.5 Additional conditions for the creep range ........................................................................................ 154 12.3.6 Stresses due to a single non repeated support movement ........................................................ 154 12.3.7 Determination of resultant moments ................................................................................................ 155 12.3.8 Alternative method for stress calculation ........................................................................................ 157 12.3.9 Reactions ...................................................................................................................................................... 157 12.4 Fatigue analysis .......................................................................................................................................... 157 12.5 Vibration ....................................................................................................................................................... 157
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13 13.1 13.1.1 13.1.2 13.1.3 13.1.4 13.1.5 13.2 13.2.1 13.2.2 13.2.3 13.3 13.3.1 13.3.2 13.3.3 13.3.4 13.3.5 13.3.6 13.4
Pipe Supports .............................................................................................................................................. 158 General requirements .............................................................................................................................. 158 General .......................................................................................................................................................... 158 Classification of supports ........................................................................................................................ 158 Additional definitions .............................................................................................................................. 159 Boundaries ................................................................................................................................................... 161 Pipe supports welded to the pipe ........................................................................................................ 163 Selection of pipe supports ...................................................................................................................... 164 General .......................................................................................................................................................... 164 Detail design of pipe supports .............................................................................................................. 165 Support location ......................................................................................................................................... 166 Constant hangers/base mounted (pedestal) constant supports .............................................. 166 General .......................................................................................................................................................... 166 Load deviation from calibrated load .................................................................................................. 166 Site adjustment of the calibrated load ............................................................................................... 166 Travel reserve (Overtravel) ................................................................................................................... 166 Blocking......................................................................................................................................................... 167 Identification Marking/Name plate .................................................................................................... 167 Variable load spring hangers and base mounted (pedestal) variable load spring supports ........................................................................................................................................................ 167 13.4.1 General .......................................................................................................................................................... 167
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13.4.2 Tolerance on spring rate ......................................................................................................................... 168 13.4.3 Travel reserve (Overtravel) ................................................................................................................... 168 13.4.4 Blocking ......................................................................................................................................................... 168 13.4.5 Name plate .................................................................................................................................................... 168 13.5 Rigid struts ................................................................................................................................................... 169 13.6 Shock arrestors (shock absorber, snubber) ..................................................................................... 169 13.7 Sliding supports .......................................................................................................................................... 170 13.8 Anchors .......................................................................................................................................................... 170 13.9 Documentation of supports .................................................................................................................... 170 13.10 Marking of supports .................................................................................................................................. 170 13.11 Manufacturing of pipe supports ........................................................................................................... 170 13.11.1Material requirements ............................................................................................................................ 170 13.11.2Design temperatures for support components .............................................................................. 171 13.11.3Design details .............................................................................................................................................. 172 13.11.4Determination of component sizes ..................................................................................................... 173 13.11.5Welded connections ................................................................................................................................. 174 13.11.6Threaded connections ............................................................................................................................. 176 13.11.7Additional requirements on springs .................................................................................................. 177 13.11.8Design details for rigid struts ............................................................................................................... 177 13.11.9Design details for shock arrestors (shock absorbers, snubbers) ............................................ 178 13.11.10Design details for shock arrestors (shock absorbers, snubbers) .......................................... 179
Annex A Dynamic analysis ......................................................................................................... 180 A.1 General ........................................................................................................................................................... 180 A.2 Analysis by calculation ............................................................................................................................. 180 A.2.1 Seismic events ............................................................................................................................................. 180 A.2.2 Rapid valve closure ................................................................................................................................... 184 A.2.3 Flow induced vibration ............................................................................................................................ 187 A.2.4 Safety valve discharge .............................................................................................................................. 189 A.2.5 Allowable stresses ..................................................................................................................................... 192 A.3 Alternative means of design verification........................................................................................... 192 A.3.1 Comparative studies ................................................................................................................................. 192 A.3.2 Full scale testing ......................................................................................................................................... 192 A.3.3 Reduced scale testing ............................................................................................................................... 192
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Annex C Expansion joints ........................................................................................................... 201 C.1 Incorporation of expansion joints into piping systems ................................................................ 201 C.1.1 General ........................................................................................................................................................... 201 C.1.2 Types of expansion joints ........................................................................................................................ 202 C.1.3 Design of expansion joints ...................................................................................................................... 202 C.1.4 Designing with expansion joints ........................................................................................................... 203 C.1.5 Analyses and calculation ......................................................................................................................... 205 C.1.6 Cold pull ......................................................................................................................................................... 206 C.2 Maximum spacing for unrestrained axially compensated straight runs ............................... 206 C.2.1 General ........................................................................................................................................................... 206 C.2.2 Calculation rules ......................................................................................................................................... 206
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Annex B More accurate calculation of bends and elbows ................................................. 193 B.1 General ........................................................................................................................................................... 193 B.2 Symbols and units ...................................................................................................................................... 193 B.3 Required wall thickness .......................................................................................................................... 194 B.4 Calculation .................................................................................................................................................... 195 B.4.1 Calculation of wall thickness .................................................................................................................. 195 B.4.2 Stress calculation ....................................................................................................................................... 197
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C.2.3 C.3 C.3.1 C.3.2
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Maximum spacing for defined conditions ........................................................................................ 207 Indication for the design of expansion joints .................................................................................. 209 General .......................................................................................................................................................... 209 Information for the system analyst ..................................................................................................... 209
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Annex D Flanges ............................................................................................................................... 210 D.1 Purpose ......................................................................................................................................................... 210 D.2 Specific terms and definitions ............................................................................................................... 210 D.3 Specific symbols and abbreviations .................................................................................................... 211 D.4 General .......................................................................................................................................................... 212 D.4.1 Introduction ................................................................................................................................................ 212 D.4.2 Use of standard flanges without calculation .................................................................................... 212 D.4.3 Bolting............................................................................................................................................................ 213 D.4.4 Flange construction .................................................................................................................................. 215 D.4.5 Machining ..................................................................................................................................................... 215 D.4.6 Gaskets .......................................................................................................................................................... 215 D.5 Narrow face gasketed flanges ............................................................................................................... 216 D.5.1 General .......................................................................................................................................................... 216 D.5.2 Bolt loads and areas .................................................................................................................................. 219 D.5.3 Flange moments ......................................................................................................................................... 220 D.5.4 Flange stresses and stress limits .......................................................................................................... 220 D.5.5 Narrow face flanges subject to external pressure ......................................................................... 226 D.5.6 Lap joints ...................................................................................................................................................... 226 D.5.7 Split ring flanges ........................................................................................................................................ 229 D.6 Full face flanges with soft ring type gaskets .................................................................................... 230 D.6.1 Specific symbols and abbreviations .................................................................................................... 231 D.6.2 Bolt loads and areas .................................................................................................................................. 231 D.6.3 Flange design ............................................................................................................................................... 232 D.6.4 Full face flanges subject to external pressure ................................................................................. 233 D.7 Seal welded flanges ................................................................................................................................... 233 D.8 Reverse narrow face flanges .................................................................................................................. 234 D.8.1 Internal pressure ....................................................................................................................................... 234 D.8.2 External pressure ...................................................................................................................................... 236 D.9 Reverse full face flanges .......................................................................................................................... 236 D.9.1 General .......................................................................................................................................................... 236 D.9.2 Design following method of D.5 ............................................................................................................ 236 D.9.3 Design following method of D.6 ............................................................................................................ 238 D.10 Full face flanges with metal to metal contact .................................................................................. 240 D.10.1 General .......................................................................................................................................................... 240 D.10.2 Specific symbols and abbreviations .................................................................................................... 240 D.10.3 Design ............................................................................................................................................................ 241
Annex E Design of branch connections in piping accessories ......................................... 243 E.1 Scope .............................................................................................................................................................. 243 E.1.1 General .......................................................................................................................................................... 243 E.2 Reinforcement ............................................................................................................................................ 245 E.2.1 Angles and areas ........................................................................................................................................ 245 E.2.2 The following condition shall be satisfied: ....................................................................................... 245 E.3 Flexibility analysis .................................................................................................................................... 246
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Annex F Testing during operation in the case of cyclic loading ................................... 248 F.1 Testing during operation ........................................................................................................................ 248 F.2 Measures to be taken when the calculated fatigue life has been reached ............................ 248
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Physical properties of steels ................................................................................... 250
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G.1 G.2 G.2.1 G.2.2 G.2.3 G.2.4 G.2.5 G.3
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General ........................................................................................................................................................... 250 Physical properties .................................................................................................................................... 250 Density ........................................................................................................................................................... 250 Differential coefficient of linear expansion ...................................................................................... 251 Specific thermal capacity......................................................................................................................... 251 Thermal diffusivity .................................................................................................................................... 251 Poisson's ratio ............................................................................................................................................. 251 Physical properties of steels .................................................................................................................. 251
Annex H Flexibility characteristics, flexibility and stress intensification factors and section moduli of piping components and geometrical discontinuities ........................ 257
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Annex I Production testing of spring supports and shock arrestors (shock absorbers) .................................................................................................................................................... 267 I.1 Constant load supports ............................................................................................................................ 267 I.2 Variable spring supports ......................................................................................................................... 267 I.3 Shock arrestors ........................................................................................................................................... 267
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Type testing of support components ........................................................................ 272
Annex K Attachment of supports to structures .................................................................. 274 K.1 Attachment of supports to concrete structures .............................................................................. 274 K.2 Attachment to metallic structures ....................................................................................................... 275 K.2.1 Standard bolts ............................................................................................................................................. 275 K.2.2 Friction grip bolts ...................................................................................................................................... 275 K.2.3 Welding .......................................................................................................................................................... 275
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Annex M Design guidance for structural components ..................................................... 280 M.1 Linear type components subjected to bending ............................................................................... 280 M.1.1 General ........................................................................................................................................................... 280 M.1.2 Supplementary verifications for linear type supports ................................................................. 280 M.2 Stability of plate type supports ............................................................................................................. 282 M.3 Anchorage plates or equivalent anchorage components ............................................................ 282 M.3.1 General ........................................................................................................................................................... 282 M.3.2 Design of simple anchorage plates ...................................................................................................... 282 M.3.3 Fixing plates with stiffening gussets ................................................................................................... 283 M.3.4 Load calculations for anchorages fixed in concrete ...................................................................... 283
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Recommended gaskets for industrial piping ..................................................... 340
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Documentation of supports ........................................................................................ 284
Annex O Alternative method for checking branch connections ..................................... 286 O.1 Scope ............................................................................................................................................................... 286 O.2 Symbols .......................................................................................................................................................... 286 O.3 Design and checking of the branch connection ............................................................................... 288 O.3.1 Limit value for the load due to pressure only for straight pipes without opening ............ 288 O.3.2 Determination of the minimum thicknesses under loading due to pressure only ............ 289 O.3.3 Checking of the thicknesses selected for the combination of pressure loading and loadings due to external loads .............................................................................................................. 289
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Annex L Buckling of linear type supports ............................................................................ 276 L.1 General ........................................................................................................................................................... 276 L.2 Symbols .......................................................................................................................................................... 276 L.3 Basic formulae ........................................................................................................................................... 277 L.4 Allowable compressive stress ............................................................................................................... 277 L.5 Buckling length ........................................................................................................................................... 278
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Annex Q Simplified pipe stress analysis ............................................................................... 342 Q.1 General .......................................................................................................................................................... 342 Q.2 Simplified procedure ................................................................................................................................ 342 Q.2.1 General .......................................................................................................................................................... 342 Q.2.2 Specification of allowable spacing of supports ............................................................................... 342 Q.2.3 Check of elasticity ...................................................................................................................................... 342 Q.3 Explanatory notes for Table Q.1 ........................................................................................................... 344 Q.4 Symbols ......................................................................................................................................................... 346 Q.5 Indices fL ........................................................................................................................................................ 346 Q.6 Explanatory notes to Q.2.2 ..................................................................................................................... 347 Q.6.1 Specification of allowable spacing of supports ............................................................................... 347 Q.7 Conversion of the allowable lengths ................................................................................................... 348 Q.7.1 Other support conditions ....................................................................................................................... 348 Q.7.2 Other parameters ...................................................................................................................................... 348 Q.8 Additional single loads ............................................................................................................................ 349 Q.8.1 General .......................................................................................................................................................... 349 Q.9 Explanatory note on Figure Q.2 ............................................................................................................ 352 Q.9.1 General .......................................................................................................................................................... 352 Q.9.2 Required pipe leg length L1 , for f1 from the nomogram ............................................................... 354 Q.9.3 Required pipe leg length L2 , for f2 from the nomogram .............................................................. 354
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Annex Y History of EN 13480 3 ................................................................................................ 359 Y.1 Differences between EN 13480 3:2012 and EN 13480 3:2017................................................. 359
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Annex ZA Relationship between this European Standard and the Essential Requirements of EU Directive 2014/68/EU aimed to be covered ........................................... 361
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Bibliography .............................................................................................................................................................. 362
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5
,
Flanges and their joints — Bolting — Part 4: Selection of bolting for equipment subject to the Pressure Equipment Directive 97/23/EC
E
N
1
5
1
5
‐
4
:
2
0
1
0
,
Flanges and their joints — Design rules for gasketed circular flange connections — Part 1: Calculation method
E
N
1
5
9
1
‐
1
:
2
0
1
3
,
Flanges and their joints — Design rules for gasketed circular flange connections — Part 2: Gasket parameters
E
N
1
5
9
E
E
N
N
1
‐
2
:
2
0
1
1
9
0
0
8
,
9
2
3
0
(
4
a
:
l
l
2
p
0
a
0
r
4
,
t s
)
,
Eurocode 3: Design of steel structures
Metallic products — Types of inspection documents
Seamless steel tubes for pressure purposes — Technical delivery conditions — Part 2: Non alloy and alloy steel tubes with specified elevated temperature properties
E
N
1
0
2
1
6
‐
E
N
1
E
N
1
3
4
8
N
1
3
4
8
E
E
E
N
N
1
1
‐
2
:
2
3
3
3
4
4
4
4
8
8
0
1
3
,
5
‐
0
‐
1
:
2
‐
2
:
2
0
0
0
‐
‐
3
4
5
:
:
:
2
2
2
0
1
0
1
1
0
0
0
1
1
4
,
7
,
7
,
7
,
7
,
Unfired pressure vessels — Part 3: Design
Metallic industrial piping — Part 1: General
Metallic industrial piping — Part 2: Materials
Metallic industrial piping — Part 4: Fabrication and installation
Metallic industrial piping — Part 5: Inspection and testing
Welding — Fusion welded joints in steel, nickel, titanium and their alloys (beam welding excluded) — Quality levels for imperfections
E
N
I
S
O
5
8
1
7
:
2
0
0
7
T
e
c
12
h
n
i
c
,
a
l
C
o
r
r
i
g
e
n
d
u
‐
m
1
:
2
0
0
6
)
(
I
S
O
5
8
1
7
:
2
0
0
3
,
c
o
r
r
e
c
t e
d
v
e
r
s
i
o
n
:
2
0
0
5
,
i
n
c
l
u
d
i
n
g
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
3 Terms, definitions, symbols and units
3.1 Terms and definitions
F
a
o
p
r
t h
p
l
y
.
e
p
u
r
p
o
s
e
s
o
f
t h
i
s
P
a
o
T
S
a
p
r
t h
b
e
l
e
c
i
t
o
f
‐
t h
i
s
E
u
r
o
p
e
a
n
S
t
a
n
d
a
r
d
,
t h
e
t e
r
m
s
a
n
d
d
e
f i
n
i
t i
o
n
s
g
i
v
e
n
i
n
E
N
1
3
4
8
0
‐
1
3.2 Symbols and units F
r
e
3
f i
p
.
c
2
u
‐
s
r
1
y
p
o
a
m
s
p
b
e
p
o
s
l
l
o
y .
s
f
t h
i
s
P
a
r
t
o
f
t h
i
s
E
u
r
o
p
e
a
n
S
t a
n
d
a
r
d
,
t h
e
s
y m
b
o
l
s
a
n
d
u
n
i
t s
g i
v e
n
i
n
E
N
1
3
4
8
0
‐
1
a
n
d
i
n
a
r
e
d
e
f i
n
e
d
i
n
t h
e
r
e
l
e
v
a
n
t
s
u
b
‐
c
l
a
u
s
e
s
.
13
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
‐
Table 3.2 1 — General symbols and units
Symbol
P
m
a
R
Description m
a
x
i
m
u
m
p
r
e
s
s
u
r
e
o
b
t a
i
n
e
d
f r
o
m
t h
e
d
e
s
i
g
n
b
y
Unit
f o
r
m
u
l
a
e
o
r
r
e
l
e
v
a
n
t
p
r
o
c
e
d
u
r
e
s
f o
r
M
P
a
(
N
/
m
m
²
)
x
g
m
R, r b
a
PSa
‐
r
i
a
a
v
x
d
i
e
i
i
n
m
c
u
o
m
m
a
p
l
l
o
o
n
e
n
w a
t
b
l
e
p
r
e
s
s
u
r
e
b
a
m
r
m
t
e
H
m
i
t h
S
n
i
s
i
m
t e
u
m
m
p
m
e
a
n
v a
m
e
a
n
v a
l
s
e
u
p
r
e
a
e
c
t u
o
f
i
f i
r
e
t h
e
i
e
d
s
v a
g
s
r
t r
l
e
e
u
a
s
e
t e
s
o
r
w
f
u
t h
h
i
c
p
a
p
n
h
e
r
t h
y
e
l
e
a
d
l
e
a
d
r
s
i
e
o
l
o
d
s
m
t r
t e
t o
a
1
t o
a
1
e
n
m
%
%
g
p
c
t h
e
r
r
a
a
e
e
e
e
t
t u
p
c
r
e
e
l
o
l
o
a
l
c
u
l
a
t i
o
n
t e
m
p
e
r
a
t u
r
e
w h
e
n
M
P
a
(
N
/
m
m
²
)
n
g
a
t i
o
n
i
n
1
0
0
0
0
0
2
0
0
0
0
0
h
M
M
P
a
(
N
/
m
m
(
N
/
m
m
²
)
1
S
l
u
e
o
f
t h
e
s
t r
e
s
s
w
h
i
c
h
s
c
r
p
e
n
g
a
t i
o
n
i
n
h
P
a
²
)
2
S
t
R
T
m
i
TS
n
e
h
o
2
0
m
a
q
u
n
u
r
x
i
v a
s
%
a
e
s
)
l
t i
u
o
w
f r
m
o
u
e
n
h
m
m
o
e
f
a
r
t
a
e
h
l
l
c
t
b
e
o
r
e
t h
e
e
y
p
c
t h
m
e
w a
a
b
e
n
l
r
o
e
u
n
d
v
p
s
i
s
a
t e
i
l
t
u
d
p
u
m
r
e
e
e
p
e
r
r
.
s
e
s
d
i
t r
e
t e
o
n
n
g
m
b
t h
p
a
e
n
a
r
d
a
s
t
o
i
u
f
n
r
d
e
t h
,
i
c
t
a
,
e
r
t e
a
e
d
n
s
b
d
u
l
y
f o
t s
t h
r
d
e
t h
o
e
s
e
s
t a
c
n
n
o
o
d
n
t
a
s
d
i
r
d
d
e
s
e
v i
,
r
a
f o
e
d
t e
r
l
t h
i
b
f e
y
e
t i
m
m
m
o
a
e
r
t e
r
T
e
i
(
t h
a
i
a
l
n
M
n
P
a
(
N
/
m
m
²
)
e
r
a
t u
r
e
°
C
Z
3
s
c
c
e
c
o
t i
r
r
o
o
n
s
i
m
o
o
n
d
o
u
r
l
e
u
r
s
o
f o
s
i
r
o
a
n
p
a
l
i
l
p
o
e
m
w a
n
c
e
(
s
e
e
F
i
g
u
r
e
4
.
3
‐
1
)
m
m
m
0
c
a
1
b
s
o
l
u
t e
v a
l
u
e
o
f
t h
e
n
e
g
a
t i
v
e
t o
l
e
r
a
n
c
e
t a
k e
n
f r
o
m
t
h
e
m
a
t e
r
i
a
l
s
t a
n
d
a
r
d
(
s
e
e
m
m
F
c
i
g
t h
i
u
n
r
n
e
i
4
n
.
g
3
‐
a
1
l
l
)
o
w
a
n
c
e
f o
r
p
o
s
s
i
b
l
e
t h
i
n
n
i
n
g
d
u
r
i
n
g
m
a
n
u
f a
c
t u
r
i
n
g
p
r
o
c
e
s
s
(
s
e
e
F
i
g
u
r
e
m
m
2
4
e
a
.
3
n
‐
a
1
l
)
y
s
i
s
t h
i
c
k n
e
s
s
o
f
a
c
o
m
p
o
n
e
n
t
u
s
e
d
f o
r
t h
e
c
h
e
c
k
o
f
t h
e
s
t
r
e
n
g
t h
(
s
e
e
F
i
g
u
r
e
4
.
3
‐
m
m
a
1
e
)
n
o
m
i
n
a
l
t h
i
c
k n
e
s
s
o
n
d
r
a
w i
n
g
s
(
s
e
e
F
i
g
u
r
e
4
.
3
‐
1
)
m
m
n
e
o
e
r
o
r
d
e
r
e
d
t h
i
c
k n
e
s
s
(
s
e
e
F
i
g
u
r
e
4
.
3
‐
1
)
m
m
d
m
i
n
i
m
u
m
r
e
q
u
i
r
e
d
t h
i
c
k n
e
s
s
w
i
t h
a
l
l
o
w a
n
c
e
s
a
n
d
t o
l
e
r
a
n
c
e
s
(
s
e
e
m
m
r
F
f
d
fcr
i
g
e
D
u
s
e
i
s
r
g
i
e
4
n
g
s
n
.
3
t r
s
‐
1
e
t r
s
e
)
s
s
(
s
i
s
e
n
e
c
t h
l
e
a
c
u
r
s
e
e
e
5
p
)
r
M
a
n
g
e
M
P
P
a
a
(
(
N
N
/
/
m
m
m
m
²
²
)
)
ff
p p t
D
e
s
i
g
n
s
t r
e
s
s
f o
r
f l
e
x
i
b
i
l
i
t y
a
n
a
l
y
s
i
s
M
P
a
c
a
l
c
u
l
a
t
i
o
n
p
r
e
s
s
u
r
e
(
s
e
e
4
.
2
.
3
.
4
)
M
P
a
o
p
e
r
a
t i
n
g
p
r
e
s
s
u
r
e
(
s
e
e
4
.
2
.
3
.
1
)
M
P
a
o
c
a
l
c
u
l
a
t i
o
n
t e
m
p
e
r
a
t
u
r
e
(
s
e
e
4
.
2
.
3
.
5
)
°
C
o
p
e
r
a
t i
n
g
t e
m
p
e
r
a
t u
r
e
(
s
e
e
4
.
2
.
3
.
2
)
°
C
o
z
(
N
/
m
m
²
)
(
N
/
m
m
²
)
c
c
t
j
o
a
i
d
n
d
t
i
c
t i
o
o
e
n
f f i
a
l
c
i
t
e
h
F
14
i
g
u
r
e
4
.
3
‐
1
)
n
i
t
c
(
s
k n
e
e
e
s
s
4
.
5
r
)
e
s
‐
u
l
t i
n
g
f r
o
m
t h
e
s
e
l
e
c
t i
o
n
o
f
t h
e
o
r
d
e
r
e
d
t h
i
c
k n
e
s
s
(
s
e
e
m
m
(
N
/
m
m
²
)
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
PS
a
A
l
l
p
r
e
s
s
u
r
e
s
f o
r
c
a
l
c
u
l
a
t i
o
n
p
u
r
p
o
s
e
s
a
r
e
i
n
M
P
a
(
N
/
m
m
²
)
a
n
d
i
s
i
n
b
a
r
.
‐
b
i
T
h
e
i
m
o
f o
n
m
o
s
i
e
u
l
l
o
d
a
e
n
t s
w
i
i
n
g
s
u
b
s
c
r
i
p
t s
a
p
p
l
y
:
d
e
4 Basic design criteria
4.1 General T
p
h
u
T
c
m
N
u
s
b
I
l
l
v
o
t h
P
i
t r
c
e
s
c
i
i
s
i
p
r
t i
e
i
t i
o
o
n
o
s
p
t i
r
o
o
i
s
,
a
u
n
.
s
g
i
a
l
g
e
e
p
g
c
r
F
b
m
e
y
n
s
r
,
e
s
p
r
r
k n
e
.
n
c
y
o
p
i
t e
w
l
d
p
b
n
c
c
.
h
h
i
i
i
n
n
h
t
g
o
c
a
f
h
i
n
s
h
a
P
d
t h
s
l
e
l
c
a
l
e
c
b
r
a
a
e
t
l
s
n
c
h
i
n
u
t a
a
l
l
g
a
l
a
c
t i
k e
o
o
n
p
n
n
i
p
l
d
i
r
n
y
t i
u
t o
f o
o
l
n
e
a
r
s
c
o
s
.
e
r
a
t i
n
g
a
n
d
t e
s
t i
n
g
c
o
n
d
i
t i
o
n
s
a
s
w
e
l
l
a
s
p
r
e
s
e
t ,
c
o
l
d
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c
p
s
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l
u
n
i
m
t
i
t e
f o
r
d
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e
a
c
n
h
a
c
c
o
a
m
s
p
e
o
b
n
e
y
n
c
t ,
a
l
s
o
e
a
b
d
i
n
a
g
s
,
i
s
b
f a
i
l
y
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g
r
e
e
o
m
m
o
e
d
t r
e
i
c
a
a
n
l
d
t h
i
s
e
E
d
g
u
e
r
d
o
p
c
e
a
l
a
c
n
u
l
S
a
t a
t i
n
o
d
n
a
r
r
u
d
l
d
e
s
o
,
e
o
s
r
n
e
o
x
t
i
p
n
e
r
d
i
i
c
m
a
e
t e
n
a
t a
l
c
a
m
l
c
e
u
t h
l
a
o
t i
d
o
s
n
r
t o
u
j
l
u
e
s
,
i
t i
t
i
f y
s
t
t h
h
e
e
d
d
i
e
s
m
i
e
g
n
n
s
e
i
r
o
'
s
n
s
r
e
a
s
n
p
d
o
n
t h
s
i
i
b
c
i
l
k n
i
t
e
y
s
t o
s
e
s
r
o
r
n
u
r
h
o
l
a
t i
o
n
m
e
t h
o
d
s
s
h
a
l
l
b
e
u
s
e
d
i
n
t h
i
s
P
a
r
t ,
a
l
t h
o
u
g
h
s
o
m
e
c
o
m
p
o
n
e
n
t s
m
i
g
h
t
e
x
h
i
b
i
t
p
l
a
s
t i
c
v
a
c
e
a
s
t h
a
r
d
l
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19
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
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BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
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21
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
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BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
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Figure 4.3 1 — Thickness (applicable to straight pipes as well as bends) when ordered with mean wall thickness
‐
23
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
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Figure 8.6.1 1 — Forged Y piece
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BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
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r
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e
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e
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
‐
Figure 9.1 1 — Internal stiffening rings with a reinforced cut out
‐
9.2 Symbols and elastic stress limits
9.2.1 Symbols F
o
T
a
r
b
t h
l
e
e
3
p
.
2
u
‐
r
1
p
.
o
s
e
‐
s
o
f
c
l
a
u
s
e
9
,
t h
e
s
y
m
b
o
l
s
g
i
v e
n
i
n
T
a
b
l
e
9
.
2
.
1
‐
1
s
h
a
l
l
a
p
p
l
y
i
n
a
d
d
i
t i
o
n
t o
t h
o
s
e
g
i
v
e
n
i
n
99
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
‐
Table 9.2.1 1 — Additional symbols for the purposes of clause 9
Symbol A A A A
Description
c
r
o
s
s
‐
s
e
c
t i
o
n
a
l
a
r
e
a
o
f
s
t i
f f e
n
e
r
p
l
u
s
e
f f e
c
t i
v e
l
e
n
Unit
g
t h
o
f
s
h
e
l
l
m
m
²
a
r
e
a
o
f
f l
a
n
g
e
m
m
²
f
c
r
o
s
s
‐
s
e
c
t i
o
n
a
l
a
r
e
a
o
f
s
t i
f f e
n
e
r
m
m
²
s
a
r
e
a
o
f
w
e
b
m
m
²
w
m
L
e
Et L
‐
u
s
o
n
e
d
s
e
u
t i
l
u
f f e
F
i
g
s
o
n
u
e
r
f
d
e
e
l
s
l
a
e
9
s
n
.
t i
g
3
.
c
i
t h
1
‐
t y
o
1
o
f
f
t h
m
e
a
s
t e
h
e
r
l
l
i
a
l
o
f
p
a
r
t
u
n
d
e
r
c
o
n
s
i
d
e
r
a
t i
o
n
a
t
d
e
s
i
g
n
t e
m
p
e
r
a
t u
r
e
,
t
M
P
a
(
N
/
m
m
m
m
m
m
²
)
c
R R R
r
a
d
i
u
s
t o
p
a
r
t
o
f
t
h
e
s
t
i
f f e
n
e
r
f u
r
t h
e
s
t
f r
o
m
t h
e
s
h
e
l
l
(
s
e
e
F
i
g
u
r
e
9
.
3
.
4
‐
1
)
m
m
f
m
e
a
n
r
a
d
i
u
s
o
f
t h
e
c
y
l
i
n
d
r
i
c
a
l
,
s
h
e
l
l
s
o
r
s
e
c
t i
o
n
s
m
m
m
r
a
d
i
u
s
o
f
t h
e
c
e
n
t r
o
i
d
o
f
t h
e
s
t
i
f f e
n
e
r
c
r
o
s
s
s
e
c
t i
o
n
(
s
e
e
F
i
g
u
r
e
9
.
3
.
4
‐
1
)
m
m
s
R p0,2 t R
p0,2
S S ,
m
i
n
i
m
u
m
0
,
2
%
p
r
o
o
f
s
t r
e
n
g
t h
a
t
t e
m
p
e
r
a
t u
r
e
o
f
p
i
p
e
M
P
a
(
N
/
m
m
²
)
s
m
i
n
i
m
u
m
0
,
2
%
p
r
o
o
f
s
t r
e
n
g
t h
a
t
t e
m
p
e
r
a
t u
r
e
o
f
s
t i
f f e
n
e
r
M
P
a
(
N
/
m
m
²
)
t
e
l
a
s
t i
c
s
t r
e
s
s
l
i
m
i
t s
f o
r
s
h
e
l
l
a
n
d
s
t i
f f e
n
e
r
,
r
e
s
p
e
c
t
i
v e
l
y
M
P
a
(
N
/
m
m
²
)
s
e e e
A
n
a
l
y
s
i
s
w a
l
l
t h
i
c
k n
e
s
s
o
f
t h
e
s
h
e
l
l
m
m
a
t h
i
c
k n
e
s
s
o
f
f l
a
n
g
e
o
f
s
t i
f f e
n
e
r
s
e
c
t i
o
n
m
m
f
t h
i
c
k n
e
s
s
o
f
w e
b
o
f
s
t i
f f e
n
e
r
s
e
c
t i
o
n
m
m
w
h
h
e
r
x
a
t e
d
i
r
a
n
l
a
h
l
h
e
i
e
g
i
g
h
h
t
t
o
f
o
s
f
a
t i
d
f f e
i
s
n
h
e
e
r
d
b
e
e
n
d
t w
e
m
e
n
f l
a
n
g
e
s
m
m
m
s
I
4
s
e
c
o
n
d
m
o
m
e
n
t
o
f
a
r
e
a
o
f
t h
e
c
o
m
p
o
s
i
t e
c
r
o
s
s
s
e
c
t i
o
n
o
f
t h
e
s
t i
f f e
n
e
r
a
n
d
e
f f e
c
t
i
v e
m
m
c
l
e
n
t h
k
s
k
r
a
f a
g
o
f e
c
t h
u
o
g
t y
t o
r
h
f
f a
d
s
h
t h
c
e
e
t o
p
e
e
l
c
r
l
a
e
n
c
t i
t r
n
o
i
g
d
w i
o
f
t h
t h
i
e
t
a
c
o
b
o
m
u
b
i
t
n
a
e
n
d
a
s
x
e
i
c
s
p
t i
o
a
n
r
a
l
l
e
l
t o
t h
e
a
x
i
s
o
f
t h
e
c
y l
i
n
d
e
r
p
a
s
s
i
n
g
‐
n
d
i
n
g
o
n
t h
e
f a
b
r
i
c
a
t i
o
n
o
f
s
t i
f f e
n
e
r
‐
s
n
n p p p
n
c
y
n
u
u
m
m
b
b
e
e
r
r
o
o
f
c
f
c
i
i
r
r
c
c
u
u
m
m
f e
f e
r
r
e
e
n
n
t i
t i
a
a
l
l
w
w
a
a
v
v
e
e
s
s
f o
f o
r
r
a
a
s
t i
u
f f e
n
s
t i
n
e
d
f f e
n
c
e
y
d
l
i
n
p
d
a
r
e
t
r
‐
o
f
c
y
l
i
n
d
e
r
‐
l
s
p
t h
e
e
c
o
i
f i
r
e
e
d
t i
c
e
a
x
l
t
e
e
l
r
a
n
s
a
t i
l
d
c
i
e
n
s
s
i
g
t a
n
b
i
p
l
i
r
e
t y
s
s
p
u
r
r
e
e
s
s
M
u
r
e
o
f
a
s
t i
f f e
n
e
d
c
y l
i
n
d
e
r
M
P
P
a
a
(
(
N
N
/
/
m
m
m
m
²
²
)
)
n
t h
e
o
r
e
t i
c
a
l
e
l
a
s
t i
c
i
n
s
t a
b
i
l
i
t y
p
r
e
s
s
u
r
e
f o
r
c
o
l
l
a
p
s
e
o
f
p
e
r
f e
c
t
c
y l
i
n
d
r
i
c
a
l
s
h
e
l
l
M
P
a
(
N
/
m
m
²
)
m
To be continued
100
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
Table 9.2.1 1
Symbol p
(
c
o
c
a
l
c
u
l
a
t e
d
l
o
w e
r
b
o
u
n
d
c
o
l
l
a
p
s
e
p
r
e
t i
n
u
e
d
)
‐
‐
Description
n
s
s
u
r
e
Unit
M
P
a
(
N
/
m
m
²
)
r
p
p
r
e
s
s
u
r
e
a
t
w h
i
c
h
m
e
a
n
c
i
r
c
u
m
f e
r
e
n
t
i
a
l
s
t r
e
s
s
i
n
c
y l
i
n
d
r
i
c
a
l
s
h
e
l
l
m
i
d
w
a
y
b
e
t w
e
e
n
M
P
a
(
N
/
m
m
²
)
y
s
p
y
r
t i
p
r
f f e
e
s
n
s
e
u
r
r
s
e
r
c
e
a
a
u
c
s
h
i
e
n
s
g
y
c
i
i
e
r
c
l
d
u
p
m
o
i
f e
n
r
t
e
o
n
f
t i
m
a
l
a
y
t e
i
e
r
l
i
d
a
l
o
f
s
t i
f f e
n
e
r
M
P
a
(
N
/
m
m
²
)
s
r
a
d
i
u
s
o
f
t
h
e
p
o
i
n
t
o
n
t h
e
s
t i
f f e
n
e
r
w e
b
c
l
o
s
e
s
t
t o
t h
e
s
h
e
l
l
a
b
o
u
t
w
h
i
c
h
r
o
t a
t i
o
n
i
s
m
m
i
a
R b
s
s
R a
u
d
m
i
u
e
s
d
:
i
s
n
e
t h
e
F
e
i
s
g
t i
u
r
f f e
e
9
n
.
e
3
.
r
t r
4
‐
1
i
p
p
i
n
g
c
a
l
c
u
l
a
t i
o
n
(
s
e
e
F
i
g
u
r
e
9
.
3
.
4
‐
1
)
m
m
i
w i
w
p
r
d
o
t h
j
e
o
c
f
t i
t h
n
g
e
s
w
i
t i
d
f f e
t h
n
o
e
f
r
f l
i
a
n
n
c
g
o
e
n
o
t a
f
c
s
t
t i
w
f f e
i
t h
n
e
s
r
h
e
l
l
m
m
m
m
f
m
e
a
n
e
l
a
s
t
i
c
c
i
r
c
u
m
f e
r
e
n
t i
a
l
s
t r
a
i
n
a
t
c
o
l
l
a
p
s
e
‐
p
a
r
a
m
e
t e
r
f o
r
s
t i
f f e
n
e
r
s
‐
m
a
x
i
m
u
m
s
t r
e
s
s
i
n
h
e
a
v
y
s
t i
f f e
n
e
r
M
P
a
(
N
/
m
m
²
)
s
i
n
s
t a
b
i
l
i
t
y
s
t r
e
s
s
a
t
w
h
i
c
h
s
i
d
e
w
a
y
s
t
r
i
p
p
i
n
g
o
c
c
u
r
s
M
P
a
(
N
/
m
m
²
)
i
a
n
g
l
e
o
f
i
n
c
l
i
n
a
t i
o
9.2.2 Elastic stress limits
T
h
e
e
l
f o
S
a
r
s
f o
S
n
r
c
o
R
a
s
n
t r
a
e
u
p0,2 t
R
Ss
t i
u
s
s
s
t e
t e
n
i
n
m
i
t i
i
t s
c
s
s
h
t e
a
e
l
o
f
c
o
n
i
c
a
l
s
h
e
l
l
t o
a
x
i
s
°
i
l
l
s
:
b
e
:
(
R1,25 t
t i
c
(
s
t e
e
l
s
:
(
R 1,25s t
(
9.3.1 Determination of lengths
l
e
.
2
2
.
.
2
2
‐
‐
1
2
)
)
n
9
.
2
.
2
‐
3
)
p0,2
e
9
.
9.3 Cylindrical pipes, elbows and mitre bends
h
9
p0,2
Ss
T
p0,2 s t
s
l
n
g
t h
s
L
a
n
d
L
s
h
a
l
l
b
e
d
e
t e
9
.
2
.
2
‐
4
)
r
m
i
n
e
d
f r
o
m
F
i
g
u
r
e
9
.
3
.
1
‐
1
.
c
101
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
Key a
)
b
c
)
)
S
i
P
P
‐
n
i
i
g
p
p
l
e
e
e
p
w
s
i
i
p
t h
w
i
e
e
t h
n
f l
d
a
n
g
e
c
o
n
n
e
c
t i
o
n
Figure 9.3.1 1 — Determination of lengths in cylindrical pipes (continued)
102
‐
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
Key d
e
)
)
N
P
P
O
i
p
p
E
e
e
w
w
i
i
t h
t h
b
m
L
e
i
m
n
d
t r
e
e
a
o
r
b
s
u
e
r
e
l
n
e
b
d
d
o
w
o
n
e
x
t r
a
d
o
‐
s
9.3.2 Interstiffener collapse
h
f o
a
)
l
e
l
Figure 9.3.1 1 — Determination of lengths in cylindrical pipes
T
‐
i
T
t h
o
w
E
i
i
s
c
n
t i
py
k n
g
m
e
p
a
s
r
t
s
o
e
c
o
e
a
S ea Rm
f
d
v
t h
u
a
l
r
e
e
u
s
.
e
h
e
l
l
w
i
t h
i
n
t h
e
u
n
s
t i
f f e
n
e
d
l
e
n
g
t h
L
s
h
a
l
l
b
e
n
o
t
l
e
s
s
t
h
a
n
t h
a
t
d
e
t
e
r
m
i
n
e
d
b
y
t
h
e
f o
r
e
a
a
n
d
c
a
l
c
u
l
a
t e
p
a
s
f o
l
l
o
w
s
:
y
(
9
.
3
.
2
‐
1
)
103
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
b
)
C
a
l
c
‐
u
l
h
e
r
i
a
t e
p
u
s
i
n
g
t h
e
s
a
m
e
v
a
Rm
n
h
e
e
s
i
c
y
l
c
)
n
C
a
d
l
f o
r
e
c
h
o
s
e
c
a
l
c
L
c
f o
r
c
a
l
c
u
l
a
t i
o
n
o
p
f
:
y
(
a
u
l
u
l
a
t e
d
f r
o
m
:
n
i
n
t e
g
e
r
≥
2 ea 1 2 Rm2 1 2
2 2 2 n cyl 1 Z
(
2
t o
m
i
n
i
m
i
z
e
t h
e
v a
l
u
e
o
p
f
pr
i
s
a
d
t e
pm
pr
/
;
pm
/
pm
/
e
t
e
r
pm
m
/
i
n
py
e
a
d
n
i
n
d
a
d
c
e
c
t e
o
r
r
d
m
i
a
n
n
e
c
e
w
pr
/
i
t
h
py
9
.
f r
3
o
.
1
d
)
C
a
l
/
0
‐
0
0
c
u
l
2
)
9
.
3
.
2
‐
3
)
m
,
,
2
1
5
2
0
4
5
0
,
,
5
T
a
b
l
2
0
5
0
5
0
,
,
7
3
5
7
e
9
.
3
1
5
9
.
3
.
2
‐
4
)
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2
‐
1
.
0
,
,
0
4
1
9
9
5
0
,
,
2
6
5
0
4
1
5
0
,
,
5
6
1
7
9
5
0
,
,
7
7
5
2
,
0
2
,
2
5
2
,
5
2
,
7
5
3
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0
3
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2
5
3
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5
,
7
5
4
5
0
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7
8
0
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8
0
2
5
0
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8
2
2
0
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8
3
5
5
0
,
8
4
9
0
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8
6
1
3
,
7
5
4
,
0
4
,
2
5
4
,
5
4
,
7
5
5
,
0
5
,
2
5
0
,
8
7
0
,
8
7
9
0
,
8
8
6
5
0
,
8
9
5
5
0
,
9
0
4
5
0
,
9
1
3
5
0
,
9
1
6
5
5
,
5
5
,
7
5
6
,
0
6
,
2
5
6
,
5
6
,
7
5
7
,
n
0
d
a
b
o
v
e
a
0
t e
pr k p
104
2
0
py py
‐
a
pr
2
py py
/
.
(
0
py
py
/
pr
py py
/
3
m
/
.
Table 9.3.2 1 — Cylindrical straight pipes and reducers (hoop stress governing) pm
9
Rm L
n
a
e
s
e
Z
a
r
u
1 1 2 2 Z n2 2 n cyl 1 cyl 2 1 Z2
w
l
m
E t ea
pm
w
t h
e
,
9
p
2
r
2
e
s
5
s
u
0
r
e
pr
,
9
2
f r
8
o
5
m
0
pr
/
py
,
9
3
a
4
n
5
d
0
py
w
h
,
i
9
c
4
h
0
s
5
h
a
0
l
l
c
o
n
,
9
f o
4
r
6
5
m
t o
0
t h
e
,
9
f o
5
l
l
2
o
5
w
0
i
n
g
:
,
9
5
8
5
(
9
.
3
.
2
‐
5
)
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
w
h
e
r
e
=
x
c
e
pr
a
d
j
u
i
s
s
1
t
f o
f
p
i
I
l
t e
e
d
r
s
u
s
v
f o
5
o
s
l
s
p
v
t
e
t e
t h
n
e
i
l
c
d
e
a
i
l
n
t h
f i
;
c
a
c
a
s
t i
kp
e
p
p
l
i
c
a
t i
o
n
s
w h
e
r
a
)
e
f o
C
l
a
l
l
o
c
h
e
h
b
)
e
i
a
c
)
C
a
a
r
e
l
l
c
c
u
r
e
,
q
n
g
t h
u
c
p
a
l
u
e
o
p
s
u
f r
l
o
a
t i
m
:
Et Ic
3 m Lc
l
c
k
m
a
y
b
e
i
n
c
r
e
a
s
e
d
b
y
a
g
r
e
e
m
e
n
t
b
e
t w
e
e
n
t h
e
p
a
r
t i
e
s
i
s
e
r
w
a
e
d
h
s
s
v
e
r
u
a
e
m
l
u
k
e
e
d
i
=
s
v
1
a
o
,
l
b
5
u
o
n
s
s
h
a
l
l
b
e
p
e
r
f o
r
e
t a
m
i
1
o
n
,
e
f
e
2
d
5
.
s
a
.
h
a
l
l
b
e
i
n
c
r
e
a
s
e
d
o
r
t h
e
s
p
a
c
i
n
g
o
f
s
t i
f f e
n
e
r
s
s
h
a
l
l
b
e
e
d
.
n
3
pn
f
s
(
h
a
l
l
c
o
n
f o
r
m
t o
t h
e
f o
l
l
o
w
i
n
g
:
9
.
3
.
3
‐
1
)
(
9
.
3
.
3
‐
2
)
i
l
s
e
a
f o
f o
s
r
l
s
t e
f a
r
e
s
p
s
c
s
h
o
r
l
i
d
t h
a
y
b
l
l
f r
b
o
c
a
t e
f o
a
n
e
m
i
r
d
m
o
e
r
d
h
s
k ks p
n
:
c
r
e
a
s
o
t i
,
e
t
f o
f f e
e
d
.
i
r
n
t h
m
e
r
e
r
e
s
d
(
a
s
h
d
i
t i
g
d
i
f f e
h
t i
r
o
n
e
n
e
s
i
a
r
s
d
l
(
u
o
l
a
r
o
l
w
s
h
t r
e
r
e
e
a
s
s
s
v i
i
d
e
e
u
s
r
)
a
.
s
l
s
t r
e
s
s
e
s
)
;
t i
f f e
n
i
n
g
s
h
a
l
l
b
e
p
r
o
v
i
d
e
d
o
r
t h
e
p
i
p
e
s
S e R R 1 2 s a
f
(
9
.
3
.
3
‐
3
)
2 m
u
s
k n
p ys
c
v
pn
f
C
t e
ks
t h
a
g
1,2 1,33
ks
I
l
n
kk
pn w
u
R
pn
T
w i
e
h
r
n
,
9.3.3 Overall collapse of stiffened pipes T
‐
k e
l
a
t e
t h
e
k ks Ss p p ys
m
a
x
i
m
u
m
s
t r
e
s
s
i
n
t h
kk E R( n ( p 1 )0k,005 k p) 2
t
m
n
e
s
t
i
f f e
n
e
r
f r
o
m
:
sp
(
9
.
3
.
3
‐
4
)
s
105
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
w
h
‐
e
r
e
n2
max ( Rm R f ) Xc ea / 2; Xc e 2 a 2
Xc
=
=
T
h
1
‐
e
f o
s
f
p
i
e
p
q
e
(
r
f o
t r
i
r
e
n
s
e
s
u
a
t h
t i
i
o
c
9
.
3
.
3
‐
5
)
L A ea R R c s m s 2
t e
x
r
n
t e
0 s Ss I
Ae
1
r
s
a
n
h
l
s
a
a
l
l
t i
l
s
f f e
t i
c
o
n
f f e
n
e
n
f o
r
s
e
r
;
r
.
n
3
.
3
‐
6
)
t o
:
s
(
.
(
k n
9
s
m
(
e
9
s
.
s
3
.
s
3
h
‐
7
a
l
)
l
i
b
s
e
n
i
o
n
c
t
f u
r
e
a
l
f i
s
e
l
l
d
e
.
d
,
e
i
t h
e
r
a
d
d
i
t i
o
n
a
l
o
r
h
e
a
v
i
e
r
s
t i
f f e
n
i
n
g
s
h
a
l
l
b
e
p
r
o
v i
d
e
9
d
.
3
o
.
3
r
‐
7
t h
)
e
9.3.4 Stiffener stability
T
a
o
)
e
n
F
1
s
u
o
)
r
r
e
a
l
s
t h
a
t i
e
t e
r
f f e
s
a
n
t r
e
l
s
e
s
r
s
t a
o
e
r
e
f o
C
r
f o
r
C =
106
F
s
i
e
h
a
,
t h
t h
l
l
a
c
e
n
o
f o
f l
n
a
f o
l
l
t
r
o
w
b
m
a
i
r
n
g
c
a
l
c
u
l
a
F
i
a
g
o
n
s
s
h
a
l
l
b
e
p
e
r
f o
r
m
e
d
t o
t h
e
f o
l
l
o
w
Ss
i
n
g
:
l
u
l
r
b
e
e
s
:
(
u
2
r
e
s
9
.
3
.
4
‐
1
a
)
,
b
)
a
n
d
d
)
:
.
3
.
4
‐
1
)
3 8 e f wf3 hs e w
9
.
3
.
4
‐
1
c
)
ef wf3
:
(
9
.
3
.
4
‐
2
)
ri 6 hs ew 6 ef wf 2 hs ef 2
9
ri 6 h s e w 1 2 e f wf 2 h s e f
t i
i
p
g
t y
r
p ys
h
i
l
C =
s
i
t h
i Et C
w h
b
4 hs ew 3 e f w f hs ew 3 e f w f
(
9
.
3
.
4
‐
3
)
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
Key a
)
b
c
)
d
)
E
)
E
I
‐
x
E
t e
x
x
n
r
t e
t e
t
e
n
r
r
r
a
n
n
n
l
a
a
a
l
l
l
s
T
L
T
t i
s
s
s
f f e
t i
t i
t i
n
f f e
f f e
f f e
e
n
n
n
r
e
e
e
r
r
r
CGs
CGc
w
h
e
r
C
e
t h
lps
e
C
e
n
e
t r
n
e
o
t r
f f e
i
o
c
d
i
t
d
i
o
v
f
o
e
s
f
l
s
e
1 , 56 Ri e
t i
f f e
t i
n
n
f f e
g
e
n
t h
,
r
e
r
p
l ps
,
l
u
i
s
s
e
g
i
f f e
v e
c
n
t
i
v
b
e
y
:
l
e
n
g
t h
o
f
s
h
e
l
l
(
Figure 9.3.4 1 — Types of stiffeners other than flat bar
2
)
I
f
c
o
t h
n
hs ew
e
f o
r
s
t i
m
f f e
t o
n
e
t h
r
e
i
s
f o
l
f l
l
o
a
‐
n
w
i
g
e
n
d
g
:
a
t
t h
e
e
d
g
e
f a
r
t h
e
s
t
f r
o
m
t h
e
s
h
e
l
l
,
p
r
o
p
o
r
9
.
3
.
4
‐
4
)
t i
o
n
s
o
f
s
t i
f f e
n
e
r
s
s
h
a
l
l
Et p ys E max 1 ,1 t ; 0 , 67 Ss p Ss
(
9
.
3
.
4
‐
5
)
107
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
‐
o
r
Et p ys E max 0,5 1 t ; 0 ,32 Ss p ef Ss
wf
b
)
f o
r
a
f l
T
h
a
e
b
t
b
a
r
s
t i
f f e
n
e
r
,
t h
e
s
t r
e
s
s
s
h
a
l
l
(
c
o
n
f o
r
m
t o
t h
e
f o
l
l
o
w
i
n
g
:
p ys
r
l
e
e
9
hs / R m
3
.
s
(
.
4
h
a
l
l
b
e
c
a
l
c
u
l
a
t
e
d
f r
o
m
v
a
l
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e
s
o
b
t
a
i
n
e
d
f r
o
m
T
a
b
l
e
9
.
3
.
4
‐
1
f o
r
i
n
t e
r
n
a
l
s
t i
f f e
n
e
r
s
9
o
.
3
r
.
4
f r
i
3
.
4
‐
2
f o
r
e
x
t
e
r
n
a
l
s
t i
f f e
n
e
r
s
.
0
,
0
1
‐
0
,
0
2
0
,
0
4
0
,
0
6
0
,
0
8
0
,
1
0
0
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1
2
0
,
1
4
0
,
1
6
0
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1
8
0
,
2
0
0
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1
1
9
0
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2
3
9
0
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3
9
5
0
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7
7
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7
7
8
0
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8
1
0
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1
9
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1
3
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1
5
8
0
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1
7
6
0
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2
3
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4
6
6
1
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4
6
6
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8
6
5
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6
9
0
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1
2
3
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1
7
6
1
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1
4
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3
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8
7
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1
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1
5
7
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8
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3
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6
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9
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2
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1
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4
3
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1
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2
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2
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3
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5
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6
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9
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5
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4
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9
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6
8
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3
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9
0
3
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9
8
1
1
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0
6
8
1
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0
5
8
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,
8
9
4
0
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9
6
1
1
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0
3
4
1
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1
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0
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2
0
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7
0
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,
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1
4
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8
5
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4
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4
1
8
0
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5
9
9
0
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6
2
3
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6
5
2
0
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7
3
4
0
,
7
7
3
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8
1
6
0
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9
0
3
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9
6
1
1
,
0
1
9
0
,
4
2
7
N
N
n
108
O
O
o
T
T
t
E
E
b
‐
6
)
2
.
i
Table 9.3.4 1 — Values of i / Et hs / e w 2 for internal flat bar stiffeners
n cyl
9
4 p Ss
i
w
a
1
e
2
e
F
x
t
r
S
a
o
i
p
r
n
o
i
c
l
n
e
a
t
e
r
m
e
d
i
a
t e
v
a
l
u
e
s
i / Et h s / e w 2
t e
d
b
e
y
o
n
d
t h
a
t
v a
l
o
i
u
hs / R m
f
s
e
.
l
i
m
i
t e
d
u
s
t o
e
a
l
o
m
g
a
a
x
r
i
i
t h
m
u
m
m
i
c
v
i
a
n
l
t e
u
e
r
p
o
o
f
l
1
a
,
t i
1
o
4
,
n
.
v a
l
u
e
s
o
f
t h
e
e
x
p
r
e
s
s
i
o
n
s
h
o
u
l
d
‐
7
o
)
m
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
Table 9.3.4 2 — Values of i / Et hs / e w 2 for external flat bar stiffeners
hs / R m
n cyl 2
‐
0
,
0
1
0
,
0
1
1
0
‐
,
0
1
2
0
,
0
1
5
0
,
0
2
0
,
0
2
5
0
,
0
3
0
,
0
4
0
,
0
4
5
0
,
0
1
2
0
0
0 0
,
0
1
3
2
,
0
1
4
4
0
3
0
,
0
2
5
4
0
,
0
4
6
7
5
0
,
0
7
6
6
0
,
1
2
0
6
8
,
0
3
0
3
,
0
4
9
2
0
,
0
1
8
0
0
,
0
0
,
0
3
7
4
7
3
4
,
0
2
4
1
0
,
0
5
5
0
,
0
,
0
,
7
1
3
8
3
2
6
9
6
5
0
,
0
3
6
6
0
,
0
8
4
6
0
,
1
7
5
0
,
0
2
8
4
0
,
0
5
1
7
0
,
8
6
0
0
,
1
3
0
,
0
3
1
1
0
,
0
5
7
0
0
,
0
6
8
7
0
,
1
3
7
0
,
1
1
9
0
,
2
6
8
0
,
0
5
3
7
0
,
1
0
3
0
,
0
9
5
5
0
,
1
5
3
0
,
2
6
3
0
,
5
3
7
1
,
4
0
,
6
1
,
4
7
9
0
,
1
2
6
0
,
2
1
1
0
,
1
8
7
0
,
3
4
0
0
,
6
7
7
0
,
3
6
1
0
,
8
8
1
a
6
4
a
7
0
,
1
8
3
0
,
2
4
2
0
0
,
2
1
1
,
3
5
6
8
a
8
0
,
2
7
9
9
0
,
4
3
8
0
,
3
3
1
0
,
5
4
1
0
,
9
9
8
0
,
3
9
0
0
,
6
7
6
1
,
4
2
0
1
0
,
1
,
6
4
8
,
9
2
a
4
9
a
1
0
0
,
7
3
6
a
1
,
4
9
0
1
1
hs / R m
n cyl 2
3
0
,
0
5
0
,
0
6
0
,
0
8
0
,
1
0
0
,
1
2
0
,
1
4
0
,
1
6
0
,
1
8
0
,
2
0
0
,
0
6
2
2
0
,
1
5
7
0
0
,
0
7
5
5
0
,
2
0
1
0
,
5
8
1
0
,
1
0
3
0
,
3
1
0
0
,
1
3
0
,
4
6
3
0
,
1
6
4
0
,
6
9
5
0
,
1
9
8
1
,
1
0
0
,
2
3
1
,
9
9
6
,
2
7
7
0
,
3
2
4
a
2
a
4
0
,
3
9
5
,
4
1
4
a
1
,
4
6
5
a
T
N
N
e
O
s
T
e
E
T
p
O
e
T
O
x
N
h
r
E
e
E
v
1
3
l
u
e
2
s
a
s
F
s
S
i
o
n
s
B
a
o
i
r
r
n
h
u
i
c
o
c
e
p
n
e
u
k l
i
r
o
t e
v i
r
d
m
e
e
d
d
t o
i
a
l
d
n
g
n
c
o
a
t
n
b
n
o
e
t
e
o
o
r
N
F
e
c
O
i
T
c
h
g
h
h
r
o
T
u
e
a
o
E
r
u
l
e
i
s
n
i
g
n
c
S
e
s
n
l
9
h
n
.
e
e
l
3
l
.
l
s
5
t h
h
u
‐
s
s
c
1
h
h
a
.
n
h
s
n
c
s
e
h
u
l
a
s
n
b
‐
a
n
c
r
e
l
e
l
s
a
u
a
a
s
e
t t a
r
e
n
a
b
v a
l
l
e
u
i
e
e
s
c
a
h
h
l
s
a
e
o
l
d
l
.
x
c
c
t r
u
r
a
p
f o
o
r
l
n
n
s
t e
o
r
m
e
d
i
a
t e
hs / R m
f
v a
u
l
s
u
e
e
l
s
o
t o
g
b
a
r
e
i
i
n
t h
t e
m
i
r
c
p
i
o
l
n
a
t e
t e
r
d
p
o
l
a
t i
o
n
.
2 i
a
s
t e
>
1
l
d
0
,
i
m
b
e
i
t e
y
o
d
n
t
d
hs / R m
o
a
t h
>
0
a
,
m
t
0
a
v a
1
u
x
l
n
i
u
d
m
e
e
r
.
u
m
v
a
l
u
e
o
f
1
,
1
4
,
v
a
l
u
e
s
o
f
t h
e
e
x
t e
r
n
a
l
p
r
e
s
s
u
r
e
.
a
p
p
l
y
f o
r
t h
e
t h
i
c
k n
e
s
s
o
f
a
c
y
l
i
n
d
e
r
t o
w
h
i
c
h
c
i
r
c
u
m
f e
r
e
n
t i
a
l
h
e
a
t i
n
g
k n
o
w n
a
s
h
e
m
i
c
o
i
l
s
o
r
l
i
m
p
e
t
c
o
i
l
s
.
T
y
p
i
c
a
l
f o
r
m
s
o
f
c
o
n
s
t r
u
c
t i
o
n
a
r
e
s
h
o
w
n
i
n
a
a
i
e
i / Et h s / e w
9.3.5 Heating/cooling channels T
t
l
l
l
l
b
b
e
e
i
d
g
e
n
s
o
i
g
r
e
n
d
e
d
a
,
n
u
d
s
i
n
t h
e
g
c
t h
h
a
e
n
r
n
u
e
l
l
e
s
s
o
m
f
a
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BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
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BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
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‐
111
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
‐
9.5 Dished ends
9.5.1 Hemispherical ends
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e
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
9.5.2 Torispherical ends
T
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s
t
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c
f
c
e
a
o
r
t h
u
n
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e
m
f
d
n
p
f a
p
a
o
r
v o
o
n
m
r
o
u
a
m
b
r
e
a
g
a
a
n
l
b
b
i
l
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l
t
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n
y
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i
.
g
r
e
t h
e
s
t y
T
s
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o
h
e
r
i
d
n
f
e
g
u
o
t r
a
l
t c
f a
s
a
i
l
e
r
s
h
u
n
d
‐
t o
t r
s
r
g
e
e
e
t h
s
n
i
t h
s
s
o
s
e
i
e
s
t i
g
f
a
a
v
r
t h
v o
n
e
e
e
d
t e
d
a
w
t h
a
i
a
r
w e
l
e
n
i
d
n
l
c
e
d
h
f
o
i
a
a
m
m
r
f
d
p
e
m
e
t a
l
h
e
r
a
i
r
o
n
s
g
f e
n
u
h
h
s
c
e
f a
o
u
t i
s
c
l
t r
.
e
o
n
s
s
W i
t u
d
s
r
b
i
e
;
g
e
e
a
k s
;
t h
n
p
t h
d
q
u
e
e
a
l
n
f e
o
c
t o
t c
t
h
i
o
r
s
‐
s
e
n
g
r
n
o
e
s
t
a
i
t i
n
t e
r
v
o
e
t i
t h
s
c
a
t e
e
n
d
e
l
o
t h
s
r
a
t
g
e
.
.
g
w
h
i
g
.
i
s
m
t h
h
e
o
e
r
o
q
t e
t h
u
a
m
l
s
p
s
e
u
r
t r
r
f a
e
a
s
t u
c
s
e
r
f i
a
e
n
m
s
i
p
r
e
s
l
i
d
h
;
t u
u
d
c
e
e
,
i
t h
n
e
c
r
c
e
y
a
c
l
s
i
i
c
n
g
s
w a
t r
e
n
l
l
g
t h
t h
i
c
o
k n
f
t h
e
e
s
s
r
m
a
e
d
t e
u
r
i
c
a
e
l
s
s
f a
a
t i
n
d
g
u
r
e
e
;
d
u
c
e
t h
e
c
o
m
p
o
n
e
n
t '
s
o
r
r
.
r
m
.
a
2
.
c
r
n
s
i
n
w i
e
e
e
3
i
e
n
p
i
r
b
t a
t o
3
n
h
v e
t h
s
h
g
d
t h
e
n
e
a
s
r
e
t
l
.
r
l
l
b
i
n
o
g
d
.
W h
t h
a
l
u
t o
e
o
e
c
p
o
O
e
o
w
r
v
a
e
e
e
b
r
p
p
r
l
e
e
a
i
e
f o
r
r
c
n
g
n
r
a
a
t i
t i
o
l
u
m
o
o
v
a
e
y
m
e
n
n
r
e
b
d
,
e
a
i
l
n
r
e
s
g
f r
r
f o
p
m
l
o
o
r
e
e
c
a
a
y
m
f
l
t h
i
s
a
u
e
l
r
t e
o
e
l
r
a
y
e
i
f o
a
r
d
v
s
a
i
r
i
n
n
m
n
c
r
n
a
g
y
o
s
c
o
d
,
o
l
u
p
e
s
c
h
s
t h
e
s
t c
t e
i
‐
t i
s
n
.
e
s
n
g
h
s
d
o
i
t i
u
u
l
r
v e
i
d
n
m
g
b
e
t
a
h
c
t e
e
o
r
o
n
s
i
a
p
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l
e
d
s
r
e
,
c
a
r
t i
e
a
n
d
n
g
r
p
w
h
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e
d
r
u
i
n
c
o
e
d
d
i
t h
(
s
m
e
e
e
e
n
n
s
1
i
u
0
o
m
.
3
n
i
b
.
e
2
n
.
g
r
7
o
.
a
3
n
f
)
d
f o
o
s
n
r
m
t h
p
o
e
n
w
e
n
h
o
t s
l
e
o
f
p
i
p
t h
i
e
n
g
p
i
s
p
y s
i
n
t e
g
.
m
T
,
h
t h
e
e
s
c
m
a
a
l
l
l
c
u
e
s
l
a
t
t i
o
v a
l
n
u
s
e
o
,
r
r
o
;
.
n
a
10.3.2.2 Symbols F
a
n
e
.
t e
t
o
.
u
f t e
o
t a
t i
g
g
o
d
e
s
s
h
t e
1
d
.
n
s
e
m
r
s
f i
‐
r
i
e
n
d
e
n
m
r
.
,
.
e
o
n
t u
o
e
g
c
k n
o
e
c
r
e
o
o
b
g
i
a
.
e
w h
t o
u
,
c
a
g
d
c
C
l
.
t u
a
i
e
l
n
e
e
c
l
b
t h
u
e
a
t i
c
p
u
n
d
g
e
b
r
e
,
f a
o
f a
l
t i
d
r
l
r
n
u
t e
e
6
n
r
n
y c
f
g
o
a
c
o
o
h
E
g
t h
a
t e
O
o
i
s
f a
l
a
p
o
N
a
t
o
s
s
e
s
o
f
1
0
.
3
.
2
,
t h
e
s
y
m
b
o
l
s
g
i
v
e
n
i
n
T
a
b
l
e
1
0
.
3
.
2
‐
1
s
h
a
l
l
a
p
p
l
y
i
n
a
d
d
i
t i
o
n
t o
t h
o
s
e
g
i
v
e
n
i
n
117
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
‐
Table 10.3.2 1 — Additional symbols for the purposes of 10.3.2
Symbol
Ft
‐
Description
Unit
t
e
m
p
e
r
a
t u
r
e
i
n
f l
u
e
n
c
e
f a
c
t o
r
‐
*
k
n
u
m
b
e
r
o
f
i
n
t e
r
v
a
l
s
o
f
d
i
f f e
r
i
n
g
p
r
e
s
s
u
r
e
f l
u
c
t u
a
t i
o
n
s
w
h
i
c
h
t o
g
e
t h
e
r
f o
r
m
t h
e
l
o
a
d
‐
c
p p
F
o
l
l
e
c
t i
v
e
p
r
e
s
s
u
r
e
f l
u
c
t u
a
t i
o
n
r
a
n
g
e
(
d
o
u
b
l
e
a
m
p
l
i
t u
d
e
)
M
P
a
(
N
/
m
m
²
)
c
o
r
r
e
c
t i
o
n
f a
c
t o
r
t o
t a
k e
a
c
c
o
u
n
t
o
f
t h
e
i
n
f l
u
e
n
c
e
o
f
t h
e
w a
l
l
t h
i
c
k n
e
s
s
‐
d
N
o
N
a
*
2
2
d
w
t i
a
n
b
l
g
e
n
n
u
u
m
m
b
b
e
e
r
r
o
f
o
l
f
l
o
o
a
a
d
d
c
c
y c
y
c
l
l
e
e
s
s
‐
w i
t h
a
p
r
e
s
s
u
r
e
f l
u
c
t u
a
t i
o
n
r
a
n
g
e
p p
*
e
t e
r
m
i
n
i
n
g
c
a
l
c
u
l
a
t i
o
n
t e
m
p
e
r
a
t u
r
e
d
u
r
i
n
g
t h
e
l
o
a
d
c
y c
l
e
‐
°
C
n
o
t i
o
n
a
l
p
s
e
u
d
o
‐
e
l
a
s
t i
c
s
t r
e
s
s
a
m
p
l
i
t u
d
e
M
P
a
(
N
/
m
m
²
)
n
a
o
t i
o
n
a
l
e
n
d
u
r
a
n
c
e
v a
l
u
e
s
M
P
a
(
N
/
m
m
²
)
s
t r
e
s
s
f a
c
t o
r
‐
d
e
s
i
g
n
s
t r
e
s
s
f
0
u
p
e
r
s
c
r
i
p
t s
S
u
p
e
r
s
c
r
i
p
t
u
u
p
b
e
s
r
c
s
r
c
i
r
p
i
p
t
a
n
d
s
t
K
n
u
b
s
c
r
i
p
t s
:
a
c
c
o
r
d
i
n
g
t o
5
.
2
a
t
2
0
°
C
M
P
a
(
N
/
m
m
²
)
m
a
m
i
x
i
m
u
m
v
a
l
u
e
,
e
.
g
.
p
u
m
b
e
n
r
i
i
m
n
d
u
e
m
x
v
e
.
a
g
.
l
u
e
N
,
e
.
g
.
p
K
10.3.2.3 Determination of allowable number of load cycles
T
o
q
d
u
a
e
t e
t i
o
r
n
m
:
i
n
e
t h
e
a
l
l
o
w a
b
l
e
n
u
m
b
e
r
o
f
l
o
a
d
c
y c
l
e
s
,
2
*
s
h
a
l
l
b
e
c
a
l
c
u
l
a
t e
d
i
n
a
c
c
o
r
d
a
n
c
e
T
h
e
p
r
e
s
e
s
s
f p 2
t o
T
c
g
h
e
i
e
r
v
s
t a
118
e
t r
i
n
e
w
i
t h
t h
e
s
u
r
e
P
s
m
t r
a
s
D
S
e
2
S
o
a
a
f
S
l
r
l
l
l
e
a
t
p
f o
r
a
a
p
i
x
p
h
a
l
l
b
e
d
e
(
t e
r
m
i
n
e
d
a
s
a
l
l
o
w
a
b
l
e
p
r
e
s
s
u
r
e
w i
t h
f u
l
l
u
t i
l
i
s
a
t i
o
n
o
f
t h
e
n
o
m
i
1
n
0
a
l
.
3
d
.
2
e
s
‐
i
1
g
)
n
i
n
g
c
o
m
p
o
n
e
n
t
f r
o
m
t h
e
d
i
m
e
n
s
i
o
n
a
l
e
q
u
a
t i
o
n
s
i
n
c
l
a
u
s
e
s
6
t o
9
a
n
d
1
1
,
r
e
a
r
r
a
n
g
e
d
0
.
s
c
s
o
f a
m
c
p
t o
o
n
r
e
n
t
s
h
g
e
a
o
l
l
r
m
e
e
p
t r
r
y
e
s
a
e
r
i
n
s
t
i
t h
n
g
e
i
n
u
p
p
p
r
a
e
c
r
t i
l
c
i
m
a
l
i
t
s
i
o
f
t u
a
t h
t i
e
o
s
n
t r
s
e
o
s
r
s
s
f a
e
l
e
c
c
t o
t e
r
s
d
f o
f r
r
o
d
m
i
m
T
a
e
b
n
l
s
e
i
o
1
n
0
.
i
n
3
.
g
2
‐
c
4
o
.
n
d
i
t i
o
n
s
o
f
a
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
T
o
t a
k
e
a
c
c
o
u
n
t
o
f
t h
e
i
n
f l
u
e
n
c
e
o
f
t h
e
c
o
m
p
o
n
e
n
t
s
i
z
e
o
n
t h
e
c
y c
l
i
c
l
o
a
d
s
t r
e
n
g
t h
,
a
c
o
r
r
e
c
‐
t i
o
n
f a
c
t o
r
F
d
s
h
a
l
l
b
e
t a
k e
n
f o
o
r
f r
o
m
F
i
g
u
r
e
w
a
l
l
t h
i
c
k n
e
s
s
e
s
e
o
r
>
2
5
m
m
i
n
a
c
c
o
r
d
F
o
e
F
a
r
l
o
n
f o
e
r
v
a
t h
y
l
o
A
l
l
y
W i
t e
t e
c
l
e
t h
m
n
g
m
c
a
c
s
a
l
c
y
,
u
c
l
r
1
l
e
i
a
0
.
3
.
2
e
a
t i
u
w a
l
s
o
n
t a
n
d
,
e
‐
l
l
n
2
r
a
t u
.
T
t h
d
t h
r
e
h
e
f a
c
c
a
e
o
i
r
c
f o
n
k n
d
s
i
s
l
.
l
e
f o
o
r
a
a
r
d
c
t u
f e
t o
r
F
s
h
a
l
t
f o
r
a
l
d
o
e
t
F
o
T
r
h
f u
e
n
r
s
t*
r
e
r
r
y
e
c
i
l
e
n
e
t e
f l
a
c
l
t i
e
r
l
1
o
o
e
B
i
t i
s
t e
c
n
a
l
0
l
0
b
°
s
i
e
C
w a
n
o
t e
r
b
f
l
e
t h
u
l
a
t i
,
O
f r
o
T
E
m
l
b
e
l
i
m
i
t e
d
t o
F
e
s
s
s
h
a
l
=
0
,
6
4
.
1
0
.
3
.
2
‐
2
)
l
b
e
t a
k e
n
a
s
t h
e
d
e
t e
r
m
i
n
i
n
g
h
e
a
t
t r
e
a
t m
e
n
t
d
i
a
m
e
t e
r
f r
o
m
t h
e
w
r
a
i
n
t i
g
o
s
n
:
h
a
l
l
b
e
d
e
f i
n
e
d
a
s
t h
e
d
e
t
e
r
m
i
n
i
n
g
c
a
l
c
u
l
a
t i
o
n
t e
m
p
e
r
a
t u
r
e
d
u
r
i
n
g
(
d
f a
c
t o
r
s
s
h
a
l
l
b
e
r
e
l
a
t e
d
t o
t h
i
s
d
e
t e
r
m
i
n
i
n
g
t
e
m
p
e
r
a
t u
r
e
t*
o
f
t h
e
r
e
l
e
1
v
0
a
.
3
n
.
t
2
l
‐
o
3
a
)
d
n
p
c
e
e
r
a
f a
t u
c
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119
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
‐
Figure 10.3.2 2 — Correction factor Fd to take into account the wall thickness
‐
Key (
a
(
b
t*
)
a
)
:
:
u
s
f e
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t e
r
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t e
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t i
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a
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t i
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m
p
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a
t u
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e
Figure 10.3.2 3 — Correction factor Ft* to take into account temperature influence
120
‐
EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
‐
‐
BS EN 13480‑3:2017
Figure 10.3.2 4 — Allowable number of load cycles for design temperature < 100 °C and wall thickness < 25 mm
121
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
T
c
h
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c
m
p
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Table 10.3.2 2 — Calculation constants B
‐
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m
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1
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‐
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BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
a
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1
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6
Table 10.3.2 4 — Stress factors for structural forms 1
l
m
a
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p
D
c
s
10.3.2.4 Stress factors for structural forms E
e
‐
6
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W e
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K 1
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d
(continued)
123
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
‐
Table 10.3.2 4 (continued)
N
1
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8
D
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2
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e
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f r
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t r
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f r
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l
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n
1
3
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0
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d
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2
t
b
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t h
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s
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b
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t
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2
K
3
124
(continued)
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
Table 10.3.2 4 (continued)
N
o
2
.
D
5
i
a
g
r
a
m
D
S
e
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c
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p
n
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n
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o
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z
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l
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n
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f r
r
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n
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t h
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h
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w
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m
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m
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t e
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:
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t h
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3
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m
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n
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k ‐
w
s
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d
:
p
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F
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3
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K 2
3,0
(continued)
125
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
‐
Table 10.3.2 4 (continued)
N
3
o
.
D
4
i
a
g
r
a
m
D
S
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n
d
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p
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t
t i
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(
d
C
i
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d
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d
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r
n
a
;
)
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l
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3
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4
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l
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d
l
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k n
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.
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p
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d
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d
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t h
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5
.
1
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a
m
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p
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d
f o
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m
a
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d
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t h
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t ‐
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f ‐
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s
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f i
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a
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l
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1
0
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3
.
2
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5
1
.
1
t o
1
.
3
126
(continued)
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
Table 10.3.2 4 (continued)
N
o
D
i
a
g
r
a
m
D
e
s
c
r
i
p
t i
o
‐
.
2
S
e
a
m
l
e
s
s
n
o
C
r
w
e
l
d
e
d
b
e
n
d
o
n
W e
d
l
i
d
t i
o
f o
n
r
s
m
C
a
n
d
l
a
s
s
t h
o
u
t ‐
o
f ‐
r
o
u
n
d
n
e
s
s
c
l
a
s
s
i
f i
c
a
t i
o
n
a
s
e
e
w i
s
5
‐
n
o
.
1
.
1
T
a
b
l
e
1
0
.
3
.
2
‐
5
t o
1
.
3
h
a
F
o
r
m
a
x
i
m
u
m
a
l
l
o
w a
b
l
e
w e
l
d
o
f f s
e
t
0
,
5
e
w i
t h
m
a
x
i
m
u
m
o
f
3
m
m
a
c
c
o
r
d
i
n
g
t
o
E
N
I
S
O
5
8
1
7
,
r
a
t i
n
g
g
r
o
u
p
B
b
F
o
r
a
d
d
i
t i
o
n
a
l
l
i
m
i
t s
f o
r
w e
l
d
o
f f s
e
t
s
F
o
r
m
a
x
i
m
u
m
a
l
l
o
w a
b
l
e
w
e
l
d
o
f f s
e
s
h
c
t
e
e
E
0
,
N
1
1
e
3
a
4
c
8
c
o
0
r
‐
4
d
i
.
n
g
t o
E
N
I
S
O
5
8
1
7
,
r
a
t i
n
g
g
r
o
u
p
B
Table 10.3.2 5 — values for pipes and bends with out of roundness
‐
‐
e D
‐
‐
/
u
D
e
u
=
=
O
0
,
0
0
5
0
,
0
1
0
,
0
2
5
0
,
0
5
0
,
1
0
0
,
1
5
0
,
2
0
%
1
,
1
6
1
,
2
7
1
,
3
5
1
,
2
5
1
,
1
4
1
,
1
0
1
,
0
7
2
%
1
,
3
1
1
,
5
4
1
,
6
9
1
,
5
1
1
,
2
9
1
,
2
0
1
,
1
5
3
%
1
,
4
7
1
,
8
1
2
,
0
4
1
,
7
6
1
,
4
3
1
,
2
9
1
,
2
2
4
%
1
,
6
3
2
,
0
8
2
,
3
9
2
,
0
2
1
,
5
7
1
,
3
9
1
,
3
0
5
%
1
,
7
8
2
,
3
5
2
,
7
4
2
,
2
7
1
,
7
2
1
,
4
9
1
,
3
7
6
%
1
,
9
4
2
,
6
2
3
,
0
8
2
,
5
2
1
,
8
6
1
,
5
9
1
,
4
4
7
%
2
,
0
9
2
,
8
9
3
,
4
3
2
,
7
8
2
,
0
0
1
,
6
9
1
,
5
2
8
%
2
,
2
5
3
,
1
6
3
,
7
8
3
,
0
3
2
,
1
5
1
,
7
8
1
,
5
9
9
%
2
,
4
1
3
,
4
3
4
,
1
3
3
,
2
8
2
,
2
9
1
,
8
8
1
,
6
7
2
,
,
7
7
3
5
4
2
,
4
1
,
9
,
7
0
o
=
u
w
o
T
a
u
E
%
t s
(
m
=
N
%
1
1
D
m
D
l
t
l
i
d
e
d
m
a
t h
–
o
V
i
+
a
x
i
f
a
c
k n
r
l
o
u
e
u
e
m
D
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i
t r
e
n
s
c
e
s
l
s
e
u
s
s
d
e
s
a
i
n
a
t
g
r
t h
t h
e
e
e
1
1
.
4
o
a
e
i
.
d
o
.
s
.
n
s
.
t
1
a
c
1
n
1
n
t t a
1
e
b
r
d
i
a
n
n
g
n
d
t h
c
o
1
e
n
1
.
a
d
i
t i
5
b
o
f o
s
o
n
s
l
.
r
u
a
t
t e
t a
c
h
v a
l
m
u
e
e
n
s
t s
o
t h
f
a
t
m
s
a
h
x
i
a
l
m
l
a
u
l
m
s
o
l
b
o
e
a
c
d
s
h
e
o
c
c
k e
c
u
d
r
f o
r
i
n
r
g
a
l
n
n
a
l
s
c
u
t e
g
l
a
g
a
r
c
t e
a
r
l
o
d
a
s
i
n
a
t t a
s
c
t h
c
h
e
c
o
m
r
e
w
d
n
a
l
a
n
t s
l
c
s
e
h
t h
i
w
a
c
l
l
i
t h
b
k n
e
e
s
C
c
s
l
a
o
u
n
o
s
s
f
e
i
d
t h
5
e
e
.
r
e
d
p
i
a
p
s
e
l
o
s
c
h
a
a
l
l
l
.
B
b
e
e
n
d
c
l
i
n
a
g
s
s
s
i
t r
f i
e
e
d
s
s
e
a
s
s
c
s
a
e
u
c
l
l
t h
i
c
k n
e
s
s
o
f
t h
e
p
i
p
e
s
h
a
l
l
b
e
c
o
m
b
i
n
e
d
w
i
t h
s
t r
e
s
s
e
s
r
e
s
u
l
t i
n
g
f r
o
m
s
o
a
l
0, 5
t
u
t e
n
g
t h
m
t h
n
h
t r
e
m
s
r
w
w
r
,
i
a
c
g
a
m
.
m
d
e
h
a
r
t o
l
5
s
v
s
.
u
a
e
a
e
s
d
e
e
p
m
t t
i
h
e
d
c
o
n
s
e
l
t h
p
p
e
m
i
e D 2
i
c
e
e
1
u
e
i
r
t t a
g
t h
r
r
s
i
e
d
g
e
f i
i
r
a
o
s
e
p
1
t e
a
u
t
p
l
a
a
e
t i
c
t o
a
e
e
c
e
c
r
n
d
s
e
,
s
c
e
r
e
i
2,5
n
c
y s
e
e
h
a
u
n
d
p
t y
n
a
g
h
a
p
e
i
n
i
w
s
i
t h
i
t s
s
s
T
v e
T
q
e
o
u
t h
e
a
g
p
t
f
s
a
n
n
r
r
l
.
g
e
.
e
l
l
n
t h
t s
m
d
o
n
s
l
e
e
i
r
r
t h
o
n
a
t
s
i
d
l
n
.
o
f o
m
r
n
1
p
n
a
y
h
1
i
s
a
t e
s
f o
e
i
f o
t
t
f e
n
c
a
s
n
h
t e
a
e
c
e
o
f f i
g
t
d
r
n
c
m
a
m
p
s
t r
e
s
e
n
s
o
c
e
y
a
a
t h
i
t h
n
n
e
i
f
t t a
a
h
n
i
e
r
t i
e
h
o
t o
t r
b
p
a
d
c
t h
i
c
t s
h
r
d
o
I
a
t r
d
o
l
r
i
.
n
c
n
r
m
j
m
s
T
s
u
a
p
t t a
e
t
o
l
e
i
t t a
o
w
s
a
u
i
h
4
a
n
e
t .
t
o
p
a
.
h
a
s
i
t i
p
c
t h
n
h
a
t s
l
a
1
e
m
e
e
n
o
t r
m
m
m
n
u
l
n
n
m
h
l
d
i
h
11.2 Allowable stresses T
v
w
s
a
t t a
s
o
e
g
e
l
g
i
h
n
a
g
e
s
h
c
e
t h
p
t
t s
x
e
m
h
n
i
l
a
t o
e
g
a
n
s
e
p
n
e
c
a
p
b
h
n
c
t t a
b
d
l
n
c
e
m
i
i
t t a
i
l
r
m
r
c
e
a
d
t a
t t a
h
l
s
d
l
a
v
h
g
e
c
s
p
n
h
i
T
a
r
t t a
e
L
o
l
t
N
m
t e
h
g
c
a
h
o
u
o
r
g
E
l
r
o
e
T
r
c
o
g
i
T
e
h
c
a
t t a
t h
s
t e
t r
r
m
e
11 Integral attachments
I
r
r
:
e
n
d
d
b
a
r
y
y
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
a
n
e
d
s
x
t
h
P
e
a
+
l
c
a
o
l
l
+
+
+
y
n
g
w i
+
P
+
P
b
Qf
l
i
1
,
s
;
t h
5
1
,
8
2
,
7
t h
fh
e
f o
l
l
i
o
w
n
c
i
n
a
g
s
e
:
o
f
s
u
s
t a
i
n
e
d
l
o
a
d
s
;
i
n
c
a
s
e
o
f
s
u
s
t a
i
n
e
d
a
n
d
o
c
c
a
s
i
o
n
a
l
l
o
a
d
s
;
i
n
c
a
s
e
o
f
e
x
c
e
p
t i
o
n
a
l
l
o
a
d
s
;
i
fh
L
‐
fh
L
P
p
d
P
b
m
a
L
P
o
m
b
m
P
l
n
P
m
P
r
n
c
a
s
e
o
f
r
e
s
t r
a
i
n
e
d
t h
e
r
m
a
l
e
x
p
a
n
s
i
o
n
o
f
t h
e
p
i
p
i
n
g
s
y s
t
e
m
;
a
P
+
P
m
+
P
b
+
Q fh
L
+
f
i
n
p
w h
e
r
e
m
P
L
P
b
F
o
C
F
v
l
r
a
o
o
d
u
r
n
s
p
i
s
t h
a
i
s
n
e
g
o
s
f
y
s
s
u
t e
s
t a
m
.
i
n
e
d
l
o
a
e
p
r
i
m
a
r
y
m
e
m
b
r
a
n
e
s
t r
e
s
s
;
i
s
i
s
t h
e
p
r
o
n
r
3
e
u
i
t h
.
2
.
a
n
d
r
e
s
t r
a
i
n
e
d
t h
e
r
m
a
l
e
x
p
a
n
s
i
o
n
o
f
t h
e
p
r
i
m
a
r
y
l
o
c
a
l
m
e
m
b
r
a
n
e
s
t r
e
s
s
;
t h
e
i
m
a
r
y
b
e
n
d
i
n
g
s
t r
e
s
s
;
i
t e
5
r
s
.
r
e
e
m
n
t h
a
t i
e
o
s
n
e
c
o
o
n
d
a
r
y
fa , fh
f
b
s
e
e
n
e
d
e
i
n
q
g
u
a
s
t r
t i
o
e
n
s
s
s
.
(
1
2
.
1
.
3
.
1
e
p
)
t
o
(
1
2
.
1
.
3
.
4
)
,
t h
e
d
e
s
i
g
n
s
t r
e
s
s
f
i
s
d
e
f i
n
e
d
i
n
s
s
i
s
h
e
t h
a
e
r
o
s
r
11.3 Symbols F
s
t r
y ,
e
a
s
n
s
d
e
s
s
(
h
a
a
l
v e
l
b
r
e
a
l
g
i
e
m
v
i
a
t e
l
u
d
e
)
t o
,
t h
1
,
5
e
e
q
u
i
v
a
u
r
p
o
s
l
e
n
t
s
t r
e
s
s
e
s
h
a
l
l
‐
b
e
c
a
l
c
u
l
a
t e
d
a
c
c
o
r
d
i
n
g
t o
t h
e
q
f for time independent design
i
d
M
c
p
e
i
P
Q
a
.
e
s
o
f
1
1
.
4
t o
1
1
.
6
,
t h
e
s
y
m
b
o
l
s
g
i
v e
n
i
n
T
a
b
l
e
1
1
.
3
‐
1
s
h
a
l
l
a
p
p
l
y
i
n
a
d
d
i
t i
o
n
t o
t h
o
s
e
g
i
v
e
n
131
BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
‐
Table 11.3 1 — Additional symbols for the purposes of 11.4 to 11.6
Symbol A A A
‐
Description
h
a
l
f
c
r
o
s
s
s
e
c
t i
o
n
a
r
e
a
o
f
c
i
r
c
u
l
a
r
h
o
l
l
o
w
a
t
t a
c
h
Unit
m
e
n
t
m
m
²
m
c
r
o
s
s
s
e
c
t i
o
n
a
r
e
a
o
f
c
i
r
c
u
l
a
r
h
o
l
l
o
w
a
t t a
c
h
m
e
n
t /
r
e
c
t a
n
g
u
l
a
r
a
t
t a
c
h
m
e
n
t
m
m
²
t
t
o
t a
l
f i
l
l
e
t
w e
l
d
t h
r
o
a
t
a
r
e
a
m
m
²
w
d
a
t t a
c
h
m
e
n
t
i
n
s
i
d
e
d
i
a
m
e
t e
r
f o
r
c
i
r
c
u
l
a
r
h
o
l
l
o
w
a
t
t a
c
h
m
e
n
t
m
m
i
d
a
t t a
c
h
m
e
n
t
o
u
t s
i
d
e
d
i
a
m
e
t e
r
f o
r
c
i
r
c
u
l
a
r
h
o
l
l
o
w
a
t t a
c
h
m
e
n
t
m
m
o
D e e
o
u
t s
i
d
e
d
i
a
m
e
t e
r
o
f
r
u
n
p
i
p
e
m
m
o
n
o
m
i
n
a
l
r
u
n
p
i
p
e
w a
l
l
t h
i
c
k n
e
s
s
m
m
n
n
,
f
f
n
o
m
i
n
a
l
a
t t a
c
h
m
e
n
t
w
a
l
l
t h
i
c
k n
e
s
s
m
m
t
d
e
s
i
g
n
s
t r
e
s
s
(
s
e
e
5
.
2
)
M
P
a
(
N
/
m
m
²
)
a
l
l
o
w a
b
l
e
s
t r
e
s
s
r
a
n
g
e
(
s
e
e
1
2
.
1
.
3
)
M
P
a
(
N
/
m
m
²
)
a
fcr
f
d
e
s
i
g
n
s
t r
e
s
s
i
n
t h
e
c
r
e
e
p
r
a
n
g
e
(
s
e
e
5
.
3
)
M
P
a
(
N
/
m
m
²
)
a
l
l
o
w
a
b
l
e
s
t r
e
s
s
a
t
m
a
x
i
m
u
m
m
e
t a
l
t e
m
p
e
r
a
t u
r
e
(
s
e
e
1
2
.
1
.
3
)
M
P
a
(
N
/
m
m
²
)
h
L
h
a
l
f
l
e
n
g
t h
o
f
a
t t
a
c
h
m
e
n
t
i
n
c
i
r
c
u
m
f e
r
e
n
t i
a
l
d
i
r
e
c
t i
o
n
o
f
t h
e
r
u
n
p
i
p
e
f o
r
r
e
r
e
c
t a
n
g
u
l
a
r
M
m
M
m
1
a
L
t t a
h
a
l
c
f
h
l
m
e
n
e
g
n
t
t
h
o
f
a
t t a
c
h
m
e
n
t
i
n
l
o
n
g
i
t u
d
i
n
a
l
d
i
r
e
c
t i
o
n
o
f
t h
e
r
u
n
p
i
p
e
f o
r
c
t a
n
g
u
l
a
r
2
a
M
l
t t a
o
n
c
g
h
i
m
t u
e
d
i
n
n
t
a
l
b
e
n
d
i
n
g
m
o
m
e
n
t
a
p
p
l
i
e
d
t o
t h
e
a
t t a
c
h
m
e
n
t
(
v e
c
t o
r
n
o
r
m
a
l
t o
t h
e
N
m
m
L
a
M
c
t t a
i
r
c
c
h
u
m
m
e
f e
n
r
t
e
a
n
n
t i
d
a
l
r
u
b
n
e
n
p
d
i
i
p
n
e
g
c
e
m
n
o
t r
m
e
e
l
i
n
n
t
e
a
)
p
p
l
i
e
d
t o
t h
e
a
t t a
c
h
m
e
n
t
(
v
e
c
t o
r
p
a
r
a
l
l
e
l
t o
t h
e
N
m
m
N
r
M
u
t o
n
r
p
s
i
i
o
p
n
e
a
c
l
e
n
m
t r
o
e
m
l
e
i
n
n
e
t
)
a
p
p
l
i
e
d
t o
t h
e
a
t t a
c
h
m
e
n
t
(
v
e
c
t o
r
n
o
r
m
a
l
t o
t
h
e
r
u
n
p
i
p
e
c
e
n
t r
e
N
m
m
T
l
p
i
c
n
a
e
l
)
c
u
l
a
t i
o
n
p
r
e
s
s
u
r
e
M
P
a
(
N
/
m
m
²
)
c
Q Q R
c
l
i
r
c
u
m
f e
r
e
n
t i
a
l
s
h
e
a
r
l
o
a
d
a
p
p
l
i
e
d
t o
t h
e
a
t t a
c
h
m
e
n
t
N
1
o
n
g
i
t u
d
i
n
a
l
s
h
e
a
r
l
o
a
d
a
p
p
l
i
e
d
t o
t h
e
a
t t a
c
h
m
e
n
t
N
2
m
e
a
n
r
a
d
i
u
s
o
f
r
u
n
p
i
p
e
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BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
11.4 Hollow circular attachments
11.4.1 Limitations T
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BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
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BS EN 13480‑3:2017 EN 13480 3:2017 (E) Issue 1 (2017 06)
‐
Table 11.4.2 1 — Factors for hollow circular attachments
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