Baixe Guia para aplicação ASME - VAsos de pressão e outras Notas de estudo em PDF para Engenharia Elétrica, somente na Docsity! aa a id o im o dm E res e O LEE To our children, Katherine, David, Susan, Nancy, and Thomas Jennifer and Mark Cover Phoro Courtesy of Nooter Corp. PREFACE TO SECOND EDITION The ASME Boiler and Pressure Vessel Code, Section VI, às a live and progressive document. Jt strives to contain the latest, safe and economical rules for the desiga. and construction of pressure vesseis, pressure vessel components, and hear exchangers. A majar improvement was made within the last year by changing the design margin on fensile strength front 4,0 to 3.5, This reduction. in the margin permits an increase in the allowable stress for many materizis with a resulting decrease in minimum required thickness. This was the first reduction in this design margin in 50 years and was based upon the many improvements in material properties, design methods, and inspection procedures during that time. Chapters and parts of chapters have been updated to incorporate the new allowable stresses and improve- ments which have been made in design methods since tais hook was originally issued. Some of thess changes are extensive and some are minor, Some of the examples in this book have changed completely and some remain unchanged. This book continues to be an easy reference for the latest methods of problem solving in Section VIT. James R. Farr Wadsworth, Qhio Masn E, Jawad 8t. Louis. Missouri July 2001 CONTENTS Preface Ackniowledgments List ví Pigures List of Tables Chapter 1 Background Information 11 introduction .. 1,2 Allowable Sresse: 13 Join Fiticiency Factors 14 Britto Fracture Considerations ... 1.5 Fatigue Requirements Lá Pressure Testing oí Vessels and Components ASME Code Requirements What Does à Hydrostatic or Pueumatic Pressme Test Do? .. 1.6.3 Pressure Test Requiverments for VIH-A 164 Pressure Test Requirements for VÍl-: Chapter 2 Cylindrical Shells 21 Introdection .. s, VID-E nt 2 Tensile For 2.2.4 Thin CyEndrical Shells . 222 Thick Cylindrical Sbelis Axiaf Compression 4 Extemal Pressure 241 External Pressure for Cylinders with Do! External Pressare for Cylinders vita Dois < 10 Empisical Equations Suffening Rings .. 24.5 Attachment of Stiftening Rings . 25 Cylindrical Shel! Eguations, VUL2 . 26 Miscellaneous Shells 26.1 Mitered Cylinders 262 Eltipúcal Shells pm Chapter 3 Spherical Shelis, Heads, and Transition Sections . 33 Introduckion .. erenentaraneo 32 Sphezical Shelis and Memispherical Heads, VII. 321 Internal Pressure in Spherical Shells and Pressure on Concave Hemispherical Heads 22 Extemal Pressure in Spheric Hemispherical Heads ........ 3,3 Spherical Shells and Hemispherical Hea Shells ané Pressure on Convex Si ix vii xiii xvii s7 7 57 s7 61 [e x Coments 34 -Ellipscidal Heads, VILA .... . 65 34,1 Pressure on the Concave Side es 34.2 Pressure on the Convex Side . & 35 Torispherical Heads, VIE .. 68 35.1 Pressore on the Concave Side 6% 3.8.2 Presnre on the Convex Si uq 36 llipsoida! and Torisplerical Heads, VIE “ 37 Coxical Sections, VI. 4 27.1 Infernal Pressure. ”a 372 Extemal Pressure 85 38 — Conival Sections, VS... 9s Capes é Flat Plates, Covers, and Flanges 4d Iriroducrioa . 42 Integral Flat Plates and Covers 42.1 Circular Mat Plates and Cov 42.2 Noncircuiar Flat Plutes and Covers . 43 Bolted Flat Plates, Covers, and Flanges 431 Gasket Requirements, Bolt Sizing, and Bolt Loudings 145 44 Fiat Plates and Covers With Bolting 106 44,1 Blind Flanges & Circular Flat Plates and Cove: 106 442 Noncircular Flar Plates and Covers 7 485 Openings in Flat Plates and Covers 107 451 Opening Diameter Does Not Exceed Half the Plate Diameter 107 45.2 Opening Diameter Exceeds Half the Plate Diameter .... 108 46 Bolted Flange Connections Wirh Ring Type Gaskeis 108 4.6.1 Standard Fanges 109 46.2 Special Flanges 118 47 Spherically Dished Cover 124 471 Definitions and Terminology . 12 &72 Types of Dished Covers . 125 Chapter 5 Openings st Inguduction . s2 Code Bases for Acceptability of Gpenine 53 Terms and Definitions 54 Reinforced Openings—General Requirements 544 Replacement Area 542 Reinforcement Limits 55 Reinforced Opening Rules, VI-i 5.51 Openings Wilh Inberent Compensation . Shupe and Size of Openings ......... 5. Area of Reinforcement Required . 5.54 Limits of Reintorcement 5.5 Area of Reinforcement Available... Openings Exceeding Size Limits of S só Reinforced Opening Rules, VII-Z 5.61 Definitions . 862 Openings Not Reguíring Reinforcement Catouletá 5.6.3 Shape and Size of Openings . 5.64 Area of Reinforcement Required. Limits of Reinforcement Available Reinforceme: “a “o us 5 po qo Daur E E312 Lisr or FiGURES Welded Joint Categories (ASME VHL-i) Category C Weld ..... e Impact. Vest Exemprion Curves (ASME VII-D . Charpy Impact-Test Requirements for Full Size Specimens for Carbon and Low Alloy Steels With Tenaile Strength of Less Than 95 ksi (ASME VII-J) Reduction of MDMT Without Impact Testing (ASME VIE-I) Fatigue Curves for Carbon, Low Alloy, Series 4XX, High Alloy Stccls, aid High Tensile Steels for Temperatures Not Excecding 700'F (ASME VII-2) . Comparison of Equations tor EHoop Siress in Chart for Carbon and Low Alloy 410 Stainless Steels . € Factor as 4 Function of R/T Qawad, 1994) . regis With Yield Stress of 30 Esi and Over, and Types 405 & Geometric Chart for Cylindrical Vessels Under External Pressure (Jawad and Tarr, 1989) . Some Lines ví Support of Cylindricai Shsils Under Extemal Pressure (ASME VIN-E) Some Details for A! Milered Bend Elliptical Cylinder . ing Suúllener Inherent Reinforcement for Large End of Conc-to-Cylinder Janstion (ASME VI valuos of Q for Large End vf Cone-to-Cylinder Junction (ASME VEN-Z) ... Inherent Reinforcement for Small End of Cone-to-Cylinder Junctior (ASME VII-2) Values of (Q for Small End of Cone-o-Cylinder Junciion Cosme q VEL) Some Acceptable Types oí Unsiayed Flat Heads and Covers Multiple Openings in the Rim of a Flat Head or Cover With a Large Central Opening xiii xiv List of Figures E45 Ring Flanges Sample Calceladon Sheet . 110 Ea6 — Welding Neck Flange Sample Calculation Sheet us Es7 Reverse Welting Neck Flange Sample Calculation She: Ho 43 Sphericalty Dished Covers With Bolling Flanges (ASME VEI-t) . 125 F48 Example Problem of Sphericalhy Dished Cover, Div. 1 128 51 Reinforcement Limits Parallel to Shell Surface . 135 52 Chart for Determining Valve of F for Angle & 138 53 Determination of Special Limits for Setting 4, for Use in Reinforcement Caleulations 139 Example Problem of Nozzle Reinforcement in Ellipsoida! Head, Div. 1... 141 Example Problem of Nozzle Reinforcemeut of 12 in, X 161, Manway Opening, Div. 1. 143 Example Problem of Nozzle Reinforcement of Riliside Nozzie, Div. 146 Example Problem of Nozzle Reintorcement of Hillside Nozzte, Div. 1 147 Example Problem of Nozile Rôirorenent Wath Conusiói Allowuie 182 o 152 . terms . 152 z:le Nomenciature and Dimensions (Depicts Gencral Configu 154 Limits of Reinforcing Zone for Alternative Nozrle Design ... 158 5 Example Problem of Nozsle Reinforcement in Elipsoida) Head, Div. 2 .. 159 E5.6 Example Problem of Nozele Reinforcement of 12in, X I6in. Manway O 162 E57 Example Problem of Nozae Reinfurcement of Series of Openings, Div. 1 165 64 Typical Forms of Welded Staybolts 1 62 Typical Weldod Stay for Jacketed Vessel 1 63 Some Accepiabie Types of Jackeled Vessels ra 64 Some Aceeprable Types of Closure Details .... 1%6 65 Some Acceptable Types of Penetration Details 180 : 66 Spiral Jackets, Hulf-Pipe and Oder Shapes 182 67 Factor K for NPS 2 Pipe Jacket .. 183 : As Factor K for NPS 3 Pipe lacker 184 E) Factor K for NPS 4 Pipe Jacke 185 610 Vessels of Rectangular Cross Section . 188 ; am Vessels of Rectangular Cross Section With Stay Plates ...... 190 : 612 Vessels of Obround Cross Section With end Without Stay Plawos and V. Section With a Stay Plate .. ' 194 6a Plate With Constant-Diameter Openings of Same or Different Diameters 192 614 Plate With Multidiametor Openings 193 : E68 — Example Problem of Noncircular Vessel, Div. 1 198 31 Various Heat-Exchanger Configurations (TEMA, 1999) . me : 72 Some “Pypical Tuhesheet Details for U-Iuhes (ASME, ZKH) 203 72 Tubesheet Geomeiry 205 IA Effective Poisson's Ratio and Moduius cf Elasticity (ASME, 2001) . x 75 Chart for Determining À (ASME, 2001) 208 26 Kixity Bactor, E (ASME, 2001) .. 209 ; 71 Some Typical Details for Fixed Tubeste: 214 Í z Zu E and Zw versus X, (ASME, 2001) 2 8 79 Valnes of O. Netween 0.0 and 0.8 . 1 t 1 740 Values of O: Between —ELK and 0.0. 223 : Tl Bellows-Type Expansion Joints 28 i 712 Flanged and Flued Expansion Joints 231 i Es.t eme 238 81 Linearizing Stress Distribution 240 E84 Modal of a Finiic Element Layout in a Fiat Head-to-Sheil Junction ... 243 a 82 Fatigde Curves for Carbon, Low Alloy, 4XX High Alloy, and High Suength Steeis for : Temperamres Not Exceeding 700º (ASME VHI-2) 246 Ba Cyclic Curves 247 AM 252 List of Figures xe 255 236 257 258 259 260 261 262 263 264 265 26 D.l-—Riug Flange With Ring-Type Gaskee Fig. D.2---Skp-On or Lap-loint Mange With Ring-Lype Gasket . Fig. D.3-—Weiding Neck Fiange With Ring-Type Gasket . Fig. D.4-—Reverse Welding Neck Flange With Ring-Typ Fig. D.5—Slip-On Flange With Full-Face Gasket . Fig, D.6-—Weiding Neck Flange Wiih Full-Face G: CHAPTER 1 BACKGROUND INFORMATION 1.1 INTRODUCTION In this chapter some general concepts and criteria pertuning to Section VIE are discussed, These include allowabie stress, factors of safety nt efficiency factors. brimle fracture, fatigue, and pressure testing. Detailed design and analysis reles for individual components are discussed in subsequent clapters. Sinee frequent reference wili be made to ASME Section VII Divisions 1 and 2, ihe following designation vil] be used from here on to facilitate such references. ASME Section VII, Division 1 Code will be designated by VIE, Similady, VIE-2 will designate the ASME Section VHI, Division 2 Code, Other ASME code sections such as Section H Part D will be referred to as ID. Equatons and paragraphs referenced in each of these divísions will be calicd out as they appear in their respective Code Divisions. Many design rules in VI and VIT-2 ave identical, These include flange design and external pressure requirements. In such cases, lhe rules of VH-) wili be discussed with a statement indicating that the rules of VITI-2 ate the same. Appendix A at the end of this book lists lhe paragraph numbers in VHE-1 that pertain to various components of pressure vessels. Section VHI requires the fabricator of the equipmem to be responsible for its design. Paragraphs UG- 22 in VIE and AD-ILO in VI-Z are given to assist the designer in considering he most commoniy encountered loads. They include pressure, wind forces, equipinent loads, and thermal considerations. When the designer takes exceptions fo these loasts githor because they are not applicable or they are unknown, then such exceptions must bc stated in the calcuiations. Similarly, any additional loading conditions considered by the designer that are not mentioned in fhe Code must be documented in the design calculations. Paragraphs U-2(a) and U-2(b) of VIII give guidance for some design requirements. VILI-2, paragraph AD-: HO and tho User's Design Specifications mentioned in AG-301 provide the loading conditions to be used by the manufacturer. Many design rules in VIE] and VIU-2 are included in lhe Appendiçes of these codes. These rules are for specific products or configurations. Rules that have been substantiated by experience and used by industry over a long period of time are in the Mandatory Appendices. New rules or rules that have limited applications are placed in the Non-Mundatory Appendives. Non-Mandatory rules may eventually be transferred to fhe Mandatory section of the Code after à period of use and verificanon of their safety and practicality. However, guidance-type appendices will remain in the Non-Mandartory se “ion of the Code. The rules in VII do not cover all applications and configurations. When rules are not available, Paragraphs U-2(d), U-2Mg), and UG-101 must be used. Paragraph U-2g) permits the engineer to design. components in lhe absence of rules in VILI-1. Paragraph UG-104 is for allowing proof testing to establish maximum allowable working pressure for components. In VHI-Z there are no rules similar to those in UG-I0I, since VINT-2 permits design by analysis as part of its requirements. This is detailed in Paragraphs AD-100(b), AD-140, AD-150, and AD-160 of VIT-2, 1 2 Chapter | 1.2 ALLOWABLE STRESSES The criteria for establishing allowable stress in VIH-1 are detailed in Appendix P of VEI-Í and Appendix | of TI-D and are sumimarized in Table 1.º. The allowable stress at design temperature for most maierials is or of 173.5 the minimum effective tensile strength or 2/3 the minimum yield stress of the material for temperatures below the creep and rupture values. The controlling allowable stress for most bolts is 3/5 the tensile strength. The minimum effective tensite stress at elevaled temperatures is obtained from: the actual tensile stress curve with some adjustments. The tensile stress valve obtained from the actual curve ata given temperature is multiplied by the lessor of 1.0 or the ratio of the minimum tensile stress at room temperature obtamed from ASTM Specificalion for the given material to the actual tensile stress at room temperature ohtaineil from the tensile strength curve. This quansity is then multiplied by the factor 1.1. The effective -tensile stress is then-equal to the-lessor of this quantity or the minimum tensile stress-at-room temperature given in ASTM. This procedure às illusirated in example 4.[ of Jawad and Farr (reference 14, Tound at hack of book). The 1.1 factor discussed above is a constant established by the ASME Code Committee. It is bascd em engineering judement thut takes into consideration many factors. Some of these include increase in tensile strength for most carbon and low alloy steels between room and elevated temperature; he desire to maintain a constant allowabie stress level between room temperature and 500ºF or higher for carbon steels; and the adjustment of minimum suwength data 10 average data. Above approximately 500ºF or higher the allowable stress for carbon steels is controlled by creep-ruptuze rather than tensile-yield criteria. Some materials may not exhibit such an increase in tensile stress, but the critecion for 1.1 is still applicable to practicaliy all materials in VHL. Table EI also gives additional criteria for creep and rupture at elevated temperatures. The criteria are based or creep at a specified strain and rupture at 100,000 hours. The 100,000 hours criterion for rupiure corresponds to about eleven years of continual use. However, VIT-Í does not limit the operating life of the equipraent to any specific number of hours, “The allowable stress criteria iu VEE-2 are given in TI-D of lhe ASME Code. The allowahle stress at ihe design temperature for most rnaterials is the smaller of 1/3 the tensile strength or 2/3 the yield stress. The design temperature for all materials in VIH-2 is kept below the creep and rupture values, Table 1.2 sumimarizes the aliowable stress criteria in VII-2, A sample of the allowable stress Tables listed in Section IIH-D of the ASME Code is shown in Table 1,3. X lists the chemicai composition of the material, its product form, specification number, grade. Unified Numbering System (UNS), size, and temper. This information, with very few oxceptions, is identical to that given ia ASTM for lhe materia! The Table also lists the ? and Group numbers of the material. The P numbers are used TO cross reference the material to corresponding welding processes and procedures listed in Section TX, “Welding and Brazing Qualifications,” of the ASME Code. The Table also lists the micimum yicld and tensike strengins of the material at room temperature, maximum applicable temperature tmit, Externai Pressure Chart reference, any applicable notes, and the suess values ai various Lemperalures. The designer may interpoiate between listed stress values, but is not permitted to extrapolate beyond the published values. Stress values for components in shear and bearing are given in various parts of VIII, VER-2. as well as TED. Paragraph UW-1S of VIT-L and AD-132 of VHI-2 lists the majority of these values. A summary of the altowable stress values for connections is shown in Table 1.4, Some material designations in ASTM as well as the ASME Code have been changed in the last 20 years. The change is necessitated by the introduction of subclasses of the same material or improved properties. Appendix B shows a cross reference between older and newer designations of some common materiais. The maximum design remperafares allowed in VIE cannot excesd those published in Secúon FD. VIH-! defines design temperature as the inean temperature through the cross section of a component. VII-2 defines design temperature as the mean temperature in the cross section of a component, bat the surface temperature cannot exceed the highest temperature listed in H-D for lhe material. This difference in the definition of temperature in VIH-1 and VIH-2 can be substantial in thick cross sections subjected to elevated temperatures. Background Informar TABLE 1.4 ALLOWABLE STRESS VALUES FOR WELDED CONNECTIONS . o MS Component Type of Stress Stress Value Reference Fillet weldl tension 0555 Um-Bia) Fillet weld shear 0498 UM-15Ãc) Groove weld tension 0748 UM-15(6) Groove weld shear 0.608 UW-35(0) Nozle neck shear 2705 uG-25(0) Dovei boits shear G.80s 1D Any location bearing 1.605 ID "E allgwabie stress tor VII constructiár: e o vHI-Z nn e Component Type of Stress Stress Value Reference Filiat weld tansion 0557 AD-920 Filiet weld shear 05Sy AD-920 Groove weld tension 0.755. AD-920 Groove weld shear 0758, AD-920 Nozele neck shear 068. AD-132% Any location bearing Ss, AD-132.1 “8, = stress intensity values for Vili-2 construction A E D) +B FIG. 1.1 WELDED JOINT CATEGORIES (ASME Viti-1) The pe o” construction and joint efficiency associated with each of joints A, B, €, and D is given in Table 1.5. “The categories refer to a location within a vessel rather than detail of construction. Thus, a Category C weld, which identifies the attachment of à fiange 19 a shell, can be either fillet, comer, or butt welded, as illusttated in Fig. 1.2. The Joint Efficiency Factors appiy only to lhe butt-welded joint in sketch tc). The factors do not apply to sketches (a) and (h) sinve they are not butt welded. The Joint Bfficiency Factors used to design a given component are dependent on the type of examination performed at the welds of the component. As an example, the Joint Efficiency Factor in a fully radiographed longitudinal seam of a shell course is & = 1.0. However, this number may have to be reduced, depending on the degree of examination ul the circumferential welds at either end of the longitudinal seam. Appendix B shows some typical components and their corresponding Joint Efficiency Factors. 6 Chapter 1 e TABLE 1.5 MAXIMUM ALLOWABLE JOINT EFFICIENCIES!* FOR ARC- AND GAS-WELDED JOINTS Dagree of Radiographic Examination Type Joint sont dl -b c No. Description Limitations Category Full? Spot? None 8 Butt joints es altalned by None AB,C&D 19 085 070 double-welting or ay other means which will obtain the same quailty cf deposited weld metal on the inside and outside vit suriates to agree iwith the requiraments af UW-S5, Welds using metal vacking sirips which remain in place are exclused. e Single-welded butl joint with (a) None except às shown in ABC&D GS 080 065 backing etrip cther than b) below those included under (1) (2) Circumierentiai butt jointe AB&C 090 080 ves wit- one plate ofíset, see UCA 3(6) and Fig. UW- 43.400. (3) Single-welded butt joint witnout — Circumfgrential but joimts onfy, AB&C NA NA 0.eo usa of backing strip not over 548 in. fhick and not over 24 in. outside diameter (9 Double full filict lap joimr tongitudinal joints not aver A NA NA 0.55 2/8 in. thiok Circumforentia! joints not over pac NA NA 2.85 5/8 in. thick (8 Single duilfibet [sp joimts with (2) Ciroumferentia! ioimts* for B NA NA 0.50 pluc welds corforming to attachment of heads no: over UmsIT 24 in. outside diameter io sheils not over 1/2 im. Ihick (b) Circumforantial joints for the attachment to sneils of c NA NA 0.50 jeckels not over 5/8 in. in nominal thickness were the distarce lrom the center of the plug weld to the adge of the plete is not jess than 1-122 times the diameier of the hole tor the plug. te) Single ful filot lap joints (8) For tne attachment of A&B NA NA 0.45 without plug weids heads convex to pressure to shels not over 5/8 in. required thickness. Only with use of filet weid on inside of sheils, or (b) Por atiachmont of heads A&B NA NA 0.45 having pressure on eithar side. To shells not over 24 in, inside diameter and not over 44 in. required thickness it fillet weld on outside cf head flange enty. Notas: (4) The singis factor showin for eacii combination of joint category and degree of radiagrapaio axemination raplaces Dota the stress reduction faclor and ne joint efficienoy factor considerations previsusiy used in this Division. (2) See UW-+2(a) and UW-5$. (3) Seo UW-:2(p) and UMy-52. (4) Joints asaching hemispher.cal heatis to shalis are excluded. (5) E = 1.0 for butt jointe in comprassion. (6) For Tyas No. 4 Catagory C joint, :imitation rot applicabie for bokted flenge connections. Background Information 7 (a) (o) FIG. 1.2 CATEGORY C WELD 10 Chapter t TABLE 1.6 ASSIGNMENT OF MATERIALS TO CURVES (ASME VIIL-1) GENERAL NOTES ON ASSIGNMENT UE MATERIALS TO CYRVES: ta) Curve 4 applios d (as all carbon aná Bt les dlloy steel plates, structoral shages, and bars Hut fisted In Curves 8, C, and U below; (2) SA-255 Graves WEB and WCC | cormatized and tempered or water-quenched and tempared; S4-217 Grade WD6 normalized and tempared or witer-quenched and tempered, É tb) Curve E applies to: (Ni SA-216 Braús WYCA ff normalized and tempered or water-quencned and temperos Sf-220 Grades WCB and INCG for Ahicknesses uol exceectiny 2 iny É produced 30 fire qrein practice ané snter-quenches and tempeced SA-2X? Grade WS It norrafized and tempere Sh-zgs Grades A anó E SAIA Grade A Sh-535 Grade 60 SA-S16 licacês 65 ang 70 if noz normalized 54612 Hi.not narmaiizes SA-66Z Grade 8 if not normalized; (2) excont for cast steeis, alt matérials of Curve A If produced to fine grain preetice ang normadsed wileh are not listed io Curves i Game D telow; 435 all pipe, ittings, (orcinas and subina not listed for Curves O and D selos; 44) parts permitiro under UG-4] shall be include in Curve B even when fabricuted From plate that otheruise omuld de assigned lo a cifferent corvo, , te) Curve € (a) SA-z02 Grades 21 and 22 if rormatized and tempered SA-302 Grades C anã D S4-336 F21 and F22 6 nosmaiized and tempsrec Sa-ag7 Grades 23 and 22 4 noematized and tempered SA-S16 Grades 55 and 60 M not normatized 54533 Grades E and St-bbz Grade 47 <as all materias of Gurec E If produced tu fine graia practice ani nosmalized ane not listed for Curve Di beiow. 40) Curse O sa-zo3 SA-5O8 Grade 2 SA-S36 il nortualized Sa-524 Classes 1 and 2 SA-537 Classes 4, 2, and 3 Sáb? é mormealiced Sanbbz UE nopmalized SA-P38 Grade A S4c738 Grade A with Ob and Y deliberatety asdeu in accordance walh the provisicns of the materia! snecifzation, no: colder tan =20ºF (-e9"c) 54738 Grade 6 not colder thau =20%F t-29º5) te) For bolting ar nuts, the Sollowlhg Impact eest exemption temperature sinal apply: Bolting Impact Test a Spre. Me. Exemption Temperature, “E sáiy3 es 20 saias B7 (24% it. dia, ano under) 55 4Over 23% in. to 7 ie, dacho) ao saios am 55 saias Bi6 -20 sa-so7 8 =20 Sasen t7, LIA, LIM, L43 hrapact tested Sagas 12 =20 sa35A He 5 Shase Bo +to saquo Na -26 sas Bas24 "o Bots Impact Tost , grade Exemption Temperature, saga 2, 2H, 2HM, 3,4, 1, 74, 8 and 16 sA-s40 sasmas -55 417 Nyiien no class or grade is shçun, all classes e grades nte included. tg) The foftowing shail apply 10 aii material assigrment noves. (E) Cooling rates faster than those obtained by cooling ir air, followed by termaering, as permilted by the material specification, are consigerod fo he equivalent fo normalizing or normalizing ans temperira heat trontmemis. (27 Fine grain practice Is defined as the procedure necessary to oltain a fine auslenitiz grain size as described in 5A-20. NOTES: (3) Tabuiar vaiues for this Flgure are provicad in Tabte ULS-66. 42) Castings net listed ia Genera! Notes (aj ang (b) above shais be impact sestee. Background informatico 11 steel or those with carbon steel operating beyond the scope of Paragraph UG-20(f) require an evaluation for brittle fractore in accordance with the rules of UCS-66. The procedure consists of E. Determining the goveming thickness in accordance with Fig. 1.3. 2. Using Fig. 14 to obtain the temperature that exempts the material from impact testing. If the specified Minimum Design Metal Temperamre, MDMT, is colder thas that obtained from the figure, then impact testing in accordance with Fig. 1.5 is required, The specified MDMT is usually given by the user, while the calculated MDMT is obtained from VHL. The celculated MDMT is kept equal to or colder ihan the specified MDMT. E Lp x Section K-x iga-ta (ga = ta (seamloss) or tg (welded) - - - E— ta Butt Visidod Components | t f (4 te to ut patente Ho Ho o t € E g ig a! te “+ 4 À femme) me PA e [1 OO) ta O to CONNOR tg = the thinner tag = the thinner tga = the thinner ofigorte ottgorte oftaorta NOTE: Using tg1, fg2, and ta. determine the warmest MDMT and use that as the permissible MDMT for the welded assembly. tb) Woided Connection with Reinforcomsnt Plato Added FG. 1.3 SOME GOVERNING THICKNESS DETAILS USED FOR TOUGHNESS (ASME VHL1) 12 Chaprr 1 tar =SAtror (A) moided ot nonweidady ; or namwelded) mto =" , farto “The governing thickness Cc or (A) isthe greater £ ofigr Or tça fc) Boltad Flat Hesd or Tubashoot and Flungo td) Integral let Hoad or Tubeshost Mori 4 tm a (For (A) welded or nonwelded) t8 / tg2 = thinnes ot ta 0º ig The governing thickness ot &) is the greater ef tai ot tga (gi Fist Hand or Tubeshast With a Corner Joint FIG. 1.3 (CONT'D) Background Information 15 140 120 À 109 so so N | | “0 Minimum Design Metal Tempereture, OF -20 NA. DN N NEN N À À -40 / e -F-t-d>--E-— E=Ttoo ça cc e a | memo | tro eme I impact testing required «so nd 0.394 1 2 3 4 5 Nominal Thickness, in. tLiraited to & in. tor Weided Construction) Fig. 1.4 HUPACT-TEST EXEMPTION CURVES (ASME VII-1) Stiffener For a 0.75-im. stiifener, Curve E of Table 1.6 is to be used. Using Fig. 1.4 and a goveming thickness of 0.75 in. we obtain a minimum temperature of 15ºF. Since siresses cannot be established from VII-1 rules, the MDMT = 1SSF. Pad The material will be normalized since it is 2.00 in. thick. Curve D of Fable 1.6 is used. From Fig. 1.4 and a governing thickness of 2.0 in., we obrain a minimum lemperature of — SF. Since stresses cannot de establisbed from VTE-1 íules, the MDMT = —SºR, 16. Chair 1 E 0.394 i: i l [o | I | ] | Minimum specified a t viela strength º ! 65 bsi E L Ê t é Í MM É do al 56 ksi >! : 5 MM 50 ksi E a ci =] — AI SR E Ja PA A] pr > «38 kal 8 Das Li 15 ma aee í I 19 + I ! t l Í o 10 29 »30 º Maximum Nomital Thicknass of Material or Well, in GENESAL NOTES. tal Interpaiatior. between yield strengths shown is pesmitted, 4) The minimure impact energy os one specimaa shali not be tess (han 2/3 of the average energy required for three specimens, tc) Matesiols produced and Impact tested in secaniance with SA-320, SA-333, SA-334, SA-350, SA-352, SA-420 and SA-?85 do net have ta satisfy Inese energy valvos. Thay are aceoptebe iemperatyre nox coider than the test temparatkrs when the energy values required by the appilcable ion ere : aterials tavinç à spesiffed minimum (onsilo strength of 85 ksi or more, see US-BstcHei(bl : tor use at minimum desiga metal FIG. 1.5 CHARPY IMPACT-TEST REQUIREMENTS FOR FULL SIZE SPECIMENS FOR CARBON AND LOW ALLOY STEELS WITH TENSILE STRENGTH OF LESS THAN 95 ksi (ASME VIH-1) Background Information 17 T 1.00 : ; 2 : | 3 Í É Ê | | E 0.80 + - z a Ê 7 ' — £ ; : É | E 060 4 “q t ! E : | Ê £ Í 5 £ ; a : i õ [a ; E 040 + = 03, 7 E . E F ; LPP IT, VA 7 du See UCS-G8(bN3) when ratios sre 0.35 and smaller Y o and smaiter 8 020 Ss & 7 DV 0.00 0 20 co Bo 100 420 140 “F [Sea UCS-Go(bii Nomenclatura (Note references to General Notes of Fig. UCS-66.2)) tr = required thickness of the component under consideration in the corroded condition for all applicable loadings [General Note [2], based on the applicable joint efficiency E [General Note (3), in. ta = nominal thickness of the component under consideration before coresion ailowance is deducted, in. corrosion alowanca, in. as defined in General Note (3). S* E* divided by the product of the maximum allowable stress value from Table UCS-23 times E, where S is the applied general primary membrane tensile stress end E and E* are as defined in General Note (3). c E Alternative Ratio vas FIG. 1.6 REDUCTION OF MDMT WITHOUT IMPACT TESTING (ASME VIH-1) Noxze Neck From Table 1.6, Curve B is to be used for a nozzle neck of 0.258-in, thickness. Frons Pig. 2.4, minimum temperature is -- 20ºF. The ratio of required thickness to actual thickness is 0.08/0,258 x 0.875 = 0.36 Using Fig. 1.6 and this ratio, we get 130ºF, Hence, MDMT = —-20 — —130 = LSF. 20 Chapér 1 a. The number of full range pressure cycles, including startup and shutdown. is less than the number of cycles determined from the appropriate fatigue chart, Fig. 1.7, with am 5, valve equal to 3 times the allowable design stress value, Sw. b. The range of pressure fluctuation cycles during operation does not excced P(L/3XS,! Sa), where P is the design pressure, S, is the siress obtained from the fatigue curve for the number of significant pressure cyeles, and $, is the allowabie str Significant pressure cyeles are defined as those that execed the quantity P(1/3)(5/8,). S is defined as 5 = 5, taken at 1US cycles when the pressure cycles are = MY. £ = So taken at actual number of cycles when the pressure cycles are >10*. c. The temperature difference between adjacent points during startup and shutdown does not exceed S,/(2Ew), where 5, is the valuc obtained from the applicable design fatigue curve for.the total specified number of startup and shutdown cycles. d. The temperature difference between adjacent points during operation does not exceed S,/(2Eo;). where 5, is the valne obtained from the applicable design fatigue curve Tor the total number of significant finctuations. Significant Auciuations is defined as those exceeding the quantity S/(2Ew), where S is as defined in (b) above. Adjacent points are defined in AD- 160.2, Condition A, Paragraph (c) of VHI-2. e. Range of significant temperature flucruation in cormponents that have materiais with different coefficient of expansion or modules of elasticity and thal do not exceed the quantity Sat l2idiy 04 — Es 49)], where a is the coefficient of therma! expansion und E is the modulus of elasticity. Significant temperature fluctuation is that which exceeds the value S/[HE, q — E; oo), where $ is as defined in (b) above. £ Range of mechanical loads does not result in stress intensíties whose range exceeds the 5, value obtained from the fatigue chari. notes: T Em 99 x 10 o [al Intarpotao for UTS 80-11 ha TE Tatão EO. comia tda vas al a fm f a somirtoinstrpoatic ot these cones Fortes so ks values ol 8a pa Fars visaagus Jd Ei! Tete, 1 Lin LAI tl i j “a o? Ed a 108 ns souber at rear FIG. 1.7 FATIGUE CURVES FOR CARBON, LOW ALLOY, SERIES 4XX, HIGH ALLOY STEELS, AND HIGH TENSILE STEELS FOR TEMPERATURES NOT EXCEEDING 700ºF (ASME VIII-2) Background Information 24 The third criterion for nozzles with nonintegral reinforcement is given in Paragraph AD-160.3 of VII-2 aná is very similar to Conditions A and B detailed above. Example 1.3 Problem A pressure vessel consisting of a shell and two hemispherical heads is constructed from SA 516-70 carbon stee] material. The self-reintorced nozzles in the vessel are made irom type SA 240-304 stainless steel material. The vessel is shut down six times a year for mainteriance, At startup, the full pressure of 300 psi and full temperature of 400ºF arc reached in two hours. The maximum AT between any nwo points during-stari-up-is-250ºF.-At normal operation, the AT.is negligíble. .At shutdown, the, maximum AT is 100“. Derermine the maximum number of years that this vesscl can be operated if a fatiguc evaluation is not performed. Let the cosfficient of expansion for carbon steel he 6,5 x 10 *in/in./ºF and that for stainless steel be 9.5 x 10Sin./in./ºF. Solution From Condition A, determine the number of eycles in one yeer. a. Number of full pressure cycles for one yoar is 6. b. This condition does not apply for this case. c. From the chart, the 250ºP difference ia temperature during start-up corresponds to 4 cyoles. The 100ºF difference in temperature during shutdown corresponds to | cycle. Thus total equivalent eycles due to temperature in one year is (4 + 1) 6 = 30 cycles. d. At nozale attachments, the quantity (9.5 X 107 — 6.5 x 1079) 400 is equal to 0.0012. Since this value is greater than 0.00034, the equivalent eycles per year = 6. Total cy per year due to (a), (c). and (d) = 6 + 306 = 42 Number of years to operate vessel if fatigue anatysis is not performed = 1000/42 = 23.8 ycars. Example 1.4 Problem A pressure vessel has an inside diameter of 60 in., intemal pressure oF 300 psi, and design temperature of 500ºF. The shell thiciness is 1/2 in. at an allowable stress level of 18,000 psi (maicrial tensile stress = 70 ksi). The ihickness of lhe hemispherical heads is 1/4 in. at an allowable stress fevel of 18,000 psi. Integrally reintorced nozzles are weldsu to the shell and are also comstrucied of carbon steel with an aliowahie stress of 18,000 psi At start-vp, the full pressure of 300 psi and full temperature of SO0SF are reached ín eight hours. The maximum AT between any tivo points during startup is 60ºF. At normal operation, the AY is negligible. AL shutdown, the maximum AT is 5QºE. Determine if the shell and heads are adequate for 100,00) cycles without the need [or fatigue analysis. From IF-D, the cocfficient of expansion for carbon steel is 725 X 10 * in./in./“E and the modulus of elasticity is 27.3 X 10º psi. Use Fig. 1.7 for a fatigue chart. Solurion Condition B is to be used. a. Three times allowable stress af the nozele location is = 3(18,000) = 54,800 psi. Using Fig. 1.7 for lhis value gives a fatigue life of 4200 cycles. b. This condition does not apply. 22 Chapter i e. Jrom Fig. 1.7, with 100,000 cycles, the value of S, = 20,000 pst. The value of Si/ QE) = 20,0002 X 37.3 X 10º X 7,25 X 1079 = 5!ºF. Since this value is less than 60ºE, the specified cycles are inadequate. The designer has two options in this situation. The first às to perform fatigue analysis, which is costly. The second option, if it is feasible, is to reduce the AT at startup to 51ºF. «. This condition does not apply. . This condition does not apply. This condition does not apply. mp Example 1.5 Problem in lixample 1.4, determine the required thickness of the shell and heads for 1,000,000 cycles without the need to perform fatigue analysis. Solution From Fig. 1.7, with a cycle life of 1,U(W,000, the value of 8, = [2,000 pst. From Condition B, subparagraph (a), the maximum stress valve for the shell is (12,000/3) = 4,000 psi. The needed shell thickness = 0,5 x 18,000/4000 = 2.25 in. The required head thickness = 0,25 X 18,000/4000 = 4.13 in. The maximum AY aí start-up or shuidown cannot excced 8,/(2Ee) = 1200002 X 27.3 x 10º x 7.25 x 107%) = 31ºF, otherwise a fatigue analysis is necessary. 16 PRESSURE TESTING OF VESSELS AND COMPONENTS 1.6.1 ASME Code Requirements Pressure vessels that are designed and constructed io VTN- rules, except those tested in accordance with the requirements of UG-10I, are required to pass either a hydrostatic test (TG-99) or a pnemnatic test (UG- 100) of the completed vessel before the vessel is U-stamped. Pressure vessels that are designed and constructed to VIN-2 rules also are required to pass either a hydrostatic test (Article T-3) or à pncumatic test (Article 1-4) before the U2-stamp is applied. Each component section of the ASME Boiler and Pressure Vessel Code has a pressure test reguirement that calls for a pressure test at or above the maximum allowable working pressure indicated on the nameplate or stamping and in the Manufacturer's Data Report before the appropriate Code stamp mark may be applied. Under certain conditions, à pneumatic test may be combined with or substituted for a hydrostatic test. When testing conditions require a combination cf a preumatie test with a hydrostatic test, the requirements for the pneumatic test shall be followed. In all cases, the term Aydrostatic refers not only to water being an acceptahie test medium, but also to oil and other fluids that are not dangerous or fiammable; likewise, pneinatic refers not onty to air, hut also Lo other nondangerous gases that may be desirable for “snif- fer” detection. 1.6.2 What Does a Hydrostatie or Preumatic Pressure Test Do? There is always a difference of opinion as to what is desired and what is accomplisted with a pressure test. Some persons believe that the pressure test is meant to devect major leaks, while others fecl Lat there should be no leaks. large or small. Some fecl that the test is necessary to invoke loadings and stresses that are equivalent to or exceed those loadings and stresses at operating conditions. Others feel that a pressure test is needed to indicate whether a gross error has been made in caleniations or fabrication. In some cases, if appears that the pressure testing may help round out comers or other undesirable wrinkles or may offer some sor of a stress rolicf to some components. db. A calculated primary membrane plus primary bending stress intensity Pp 4 Pi noLto exceed lhe limits given below: [Pa + PÃs 1355, when = 0675, as wi PS2355,- 15 P, when 0,675, <P, = 0905, a. - 1.642 Preumatic Test Requirements. A pneumatic test is permitted only when one of the follow- ing prevails: à Vessels cannot be safely filled with water duc Lo their design and support system: bi vesselk in which tades of testing liquid camnot be tolerated: When a pneumatic test is permitied in Hieu of a hydrostatic test, except for glass-lincd and enameled vessels, [he pneumatic test pressure at every point in the vesse! shall be 1.15 times the design pressure (or MANWP) to bs marked on the vessel multiplied by the ratio of the design stress intensity value at test temperature divided by the design stress intensity value at design temperature. For glass-lined or enameled vossels, the pneumatic test pressure shall be at least squal to, but need not exceed, the design pressure (or MAWP). The pneumatic test pressure shall not exceed a value that results in the following: a. A calculated primary membrane stress intensity P, Of 80% of the tabulated yield st ength 5, ar fest temperature; b. A caleulated primary membrane plus primary bending stress intensity Po + Ps not tu exceed the following limits: Em dh Pr = 1,205, when P, < 0.675, (4.3) E + B)<2205,- 15 P, when 0.678, < Py = 0805, (4 CHAPTER 2 CyLINDRICAL SHELLS 21 INTRODUCTION The rules for cylindrical shells in VIE and VITE-2 take into consideration internal pressure, external pressure, and axial Joads. The rules assumé a circular cross section wilh uniform thickness in the circumferential and longitudinal directions. Design requirements are not available far elliptic cylinders or cylinders with variable thicknesses and materiaf properties. However, sach construction is not prohibited in VII in accordance «with Peragraphs U-2(g) of VIH-1 and, AG-100(b) and (d) of VII-2. The design and loading conditions given in VIIL-I are discussed first in this chapter, followed by the rules in VEL. 22 TENSILE FORCES, VIHE-I The goveming equations and criteria for the design of cylindrical shelis under tensile forces are piven in several paragraphs of VI-4. The tensile forces arise from various loads such as those fisted in Paragraph UG-22 and include internal pressure, wind loads, and earthquake forces, 2.21 Thin Cylindrical Shells The required tbickness of a eylindrical shell due to internal pressure is determined from one of two equations listed in Paragraph UG-27. The equation for the required thickness in the circumferentiai tRrection, Fig. 2.14), due to internal pressure is given as to PRHSE — 16), when 0.5R or P< 03RSE (2.1) where E = Joint Efficiency Factor P = internal pressure R = internal radius S = allowable stress .in the material é == thickness of the cylinder This equation can be rewrirten to caleutate the maximum pressure when the thickness'is knowa. K takes the form P = SERIR + 065 23 2 3 Chapter 2 terms of the outside radius Ro. This equation, which is obtained from Eq. (2.1) by substituting (Ro — À) for R. is given in VIH-!, Appendia 1, Article 1-1, as 1= PRoi(SE + 04P) will E<05 or P< 038588 (0 P = Ser(Ro o 0.4) (2.8) VIU- does not given an equation for the thickuess in the iongitudinal direction in terms of outside radius Ro. Such an expression. can be obtained from Fg. (2.4) as 1 = PRoi(2SE + L4P) (2 erinterms of P; Eri (Ro LA) (2.10) Equations (2.1) through (2.10) are applicable to solid wall as well as layered wall construction. Layered vessels consist of thin: cylinders wrapped around cach other to form a thick cylinder, Fig. 2.3. At any given cross section, a-a, the total thickness consists of individual plate material as well] as weld seams. The Joint Etfciency Factor for the overall thickness of a lavered vessel is calculated frem the ratio E = (Ent 1 FIG. 2.3 Cylindrical Shelis 31 where E = overall Joint Efficiency Factor for the layered cylinder ; = Joint Efficiency Factor in a given layer += overall thickness of a layered cylinder 4 = thickness ol one layer The rules in VIII assume that the longitudinal welds in various layers are staggered in such a way lat in Eg. (2.11) is essentially equal to 1.0. Example 2.1 Problem A pressure vessel is constructed of SA 516-70 material and has an inside diumeter of 8. The internal design pressure is LOO psi at 450ºF. The corrosion allowance is 0.125 in., and the joint efficiency is 0,85. What is the required sheli thickness if the aliowable stress is 20,000 psi? Solution Refer to Paragraph UG-27 of VI-1. The quantity 0.385SE = 6545 psi is greater than the design pressure of 100 psi. Thus, Eq. (2.1) appics. The inside radius in the corroded conttion is equal to R= 48 + 6.125 = 48125 in. t = [PRI(SE — 0.6P)] + comasion = [100 X (48.125)/(20,000 x 0,85 — 0.6 x 100)] + 0.125 = pátin, The calculated thickness is less than 0.5R. Thus, Hg. (2.1) is applicable. A check of Eg. (2.4) for the required thickness in the longitudinal direcron will result in a t = Uzin, including corrosion allowance. This is about 60% af the lhickness obtained in the circumferential direction, Example 2.2 Problem A pressure vessel with am internal diameter of 120 in. has a shell thickness of 2.0 in. Determine the maximum pressure if the allowable stress is 20 Ksi. Assume E = 0,85, Solution For the circumferential direction, the maximum pressure is obtained from Eg. (2.2) as p 4 20,000 x 0.85 x 20/(60 + 0.6 x 20) 556 psi 32 Chapter 2 For the longitudinal direction, the maximum pressure is obtained from Eq. (2.5) as P=2x 20,000 x085xã260/(6)-— 4x 20 = 1349 psi Thus, tac maximum pressure permíssible in the vessel is 556 pst. Example 2.3 Problem. A vertical boiler is consuucted of SA. 516-70 material and built in accordance with the requirements of VERA. Té has an oulside diameter of 8 ft and an internal design pressure of 450 psi at 709ºK. The corrosion allowance is 0.128 in., und the joint efficiency is 1.0. Cafculate the required lhickness of the shell if the allowable stress is 17,500 psi. Also, calculate the maximum allowable additional tensile force in the axial dircetion lhai Me shel! can withstand at the design pressure. Solwtion Yrom Eg. (2.7) the required thickness is ' 450 X 48/(17,500 x LO + 04 x 450) + 0,125 H 1.222 + 0.125 = Las in. From Eg. (2.10), the maximum allowable axial pressure is p=2% 17,500X 10x LIA LZZ 924.0 psi Subtracting from this valve the internal pressure of 450 psi results in lhe additional equivalent pressure P'. that can be applied to the cylinder during operation. P' e U240 — 650 = 4740 psi Totai corroded metal area of cylinder = 7(Rj — R) = q(d8 — 46.718 = 3639 in? Hence, total allowable force in cylinder during operation is 363.9 Coylindrica! Shels 35 where Z=(PISE)+I or in Lerms of pressure, P. P=SsZ-n (2.20) where Z = (RotR$ = [RollRo — DF AM of the equations given so far are in terms of internal pressure only. VIil-i does not give uny equations for caloulating stresses in cvlinders resulting from wind and carthquake loads. One method of calculating these stresses is given in Section 2.3, Example 2.5 Problem Calculate the reguired shell thickness of an accumelator with P = 10,000 psi, KR = i8in, $ = 20,000 psi and E = 1.0. Assume à corrosion allowance of 0.25 in. Solution The quantity 0.3858E = 7700 psi is less than ths design pressure of 10,000 psi. Thus, Eq. (2.13) is applicable. (SE + PHSE - P) (20,000 x 1.0 -— 10,000)/(20.,000 x 1.0 -- 10,000) 30 1= Rg 1) u U825K3.00 — 1.0) 1336 im. Totalt = 13,36 + 0.25 = 13.61 in. Example 2.6 Problem What is the required thickness in Example 2.5 if the desiga pressure is 7650 psi and the corrosion allowance is zero? 36 Chapter 2 Solution The quantity 0.3855E = 7700 psi is greater than the design pressure 0f 7650 psi. Thes, Eq. (2.1) is applicable. ' PRIÇSE — 0.67) H 7650 X 18/(20,000 x 1,0 — 0,6 x 7650) = 894 im. Tlis of interest to determine lhe accuracy of Eg. (2.1) by comparing it with the theoretical Eg. (2,13), which gives Z=(SE+ PSE-P) = (20,000 x LO + 7650)/(20,000 x 10 — 7650) = 2239 re RE 1) K 18(2.23988 — 1.0) = 893. This comparison demonstrates the accuracy of the “simple-to-use” Eg. (2.1) over a wide range of R/t ratios. Example 2.7 Problem What is the maximum stress in a layered vessel subjected to an internal pressure of 15.(N0D psi? The putside diameter is 24 in., and the inside diameter is 1H in. Solution “Fhe thickness of 6.50 in. is greater than 0.5R. Thus, either Eq. (2.17) or Eq. (2.13) may he used, since both the outside and inside diameters are given. Both of these equations are in terms of the quantity Z, which is a function of stress $, Solving for $ in these equations is not easy. However, since both of these equations were derived from Fg. (2.12), we can use it directly to solve for S. Thus, SE = 15,000 12 + 5.5/UM — 5,5) 22,980 psi 23 AXIAL COMPRESSION Vessel components are frequendy subjected to, axial compressive stresses caused by such iteros as wind, dead loads, earthquake, and nozzle loads. The maximum compressive siress is limited by either the allowable tensile stress, using a Joint Efficiency Factor of 1.0, or the allowable compressive stress, whichever is less. The allowable tensile siress controls thick eylinders, while the alowable compressive stress controls thin Cylinárical Shelis 37 cylinders. The procedure for calculating the allowable axizl compressive stress im a cylinder is given in Peragraph UG-23 of VIH-2 and is based on a theoreticat equation with a large L/D ratio (lawad, 1994). Jr consists of caleulating the quentity A = QI25/(R/A (22) trair Ro = outside radius of the cylinder 1 = thickness anidthem using a stress-strainrdiagram furnished'by (ho ASME to determine the permissible axial compressive. stress, B. The ASME plois stress-sirain diagrams, called External Pressure Charts, for various materials at various lemperatures on a log-log scale. Ope such chart for carbon steel is shown in Fig. 2.4. The strain, A, is plorted along the horizontal axis, and a stress, B, along the vertical axis. The majority of the materials listed in the stress tahtes of EI-D or VII construction have a corresponding External Pressure Cnart (BPC), Tabular values of the curves in fhese charts are also given in TI-D, for example those showa in Table 2.1 for Fig. 2.4. TF the caieulated value of A falls to the left of the stress-suais line in a given External Pressuse Chart, then B must be calcuiated from the equation B = AE/3 (2.22) TABLE 2.1 TABULAR VALUES FOR FIG. 2.4 “F A B, psi ºF A B, psi 300 0.100 —04 0.145 +08 700 0.100 —c4 0.124 —08 0.765 —03 0411 +05 2.559 —05 0.685 04 0.500 014 0.100 02 9.808 0.800 o.119 0.300 0.101 +05 0.100 02 o. 128 0.500 04 o.i22 0.200 0.150 0,250 o.:39 0.390 0.163 0.100 +00 0.139 0.400 o.s70 0.590 o.172 Bos 0100 —04 o.tia +08 025 01 0.175 0.499 —08 0.569 +04 6.100 +00 c178 0.400 —02 ORA 0.150 0.805 500 0.100 —04 0.135 +03 0.200 0.849 0.663 —08 0.895 +04 0.300 cas 0.800 0.965 0.300 -01 0.124 +05 0.100 —02 0.101 +05 0.100 --00 0.124 0.250 0.121 0.390 0.124 seo 0.100 04 0.104 +03 0.800 n.149 0.247 -08 0.444 4.04 0.100 04 0.147 0.100 —02 0.605 0.150 0.155 0.450 0.689 0.200 ojos 0.200 o742 0.272 0.170 . 0.800 0.795 0.106 +00 0170 0,800 0.900 —0t 0,100 +00 0.112 40 Chapter 2 a 32 ps fo | i E : 8 z 24 pa” io i a oo! I t » 20 os I- Nr, boa » 1 t a 1 Solution Assume + = 3/8 in. Axial force = 60 » 25! = 31 ips Asial compressive stress = Jurce/area of material in skirt 311,000/m x 96 x 0,375 = 2750 psi The wind moment at thz bottom of skirt using à vessel projected area of 8 ft is M=ILXEXI XII MAH xXEXIA XI 26) + 20x 8x 26x (2612) Cylindrical Shelis 41 = 718,848 + 280,704 + 54,080 = 11152,632 feto Notice that in many applications, the projected area must be increased beyond 8 ft to Lake into consideration such items as insulation, laddets, and platforms. Also, lhe moment may have to be modified for shape and drag factors. The bending stress is obtained from the classical equation for the bending of beams: Stress = Me/I where e = maximum depth of the cross section from the neutral axis 4 = moment of ineriia M = applied moment and for thin circular cross sections, this equation reduces to Siress = M/tm) k 1,0153,632 X 12/67 x 48º x 0.375) = 4660 psi Total compressive stress = 2750 + 4660 = 410 psi The ailowable compressive stress is caleulated from Eq. (2.21). A = QI2SMAS/OITS) = (L00098 From Fig. 2.4 with A = 0.00098 and temperature of 200ºF, we get B = 12,000 psi, which is tho allowablc compressive stress. Thus, the selected thickness is adeguate at the bottom of the skirt. Note that the thickness would have been inadequate if the temperature at the bottom was 800ºF. Now let us check the thtickness at the iop of the skir. The axial stress due to dead load s: The bending moment becomes the same, M=Mx8XIXI6+IMA+I—1LG+MXEXI x (3/2 + 26-16) +20 x 8x 40x (10/20) 571,392 + 176,256 + 8000 755,648 filb 42 Chapter 2 Bending stress = 755,648 X IZMm x 48º x 0,375) = 3340 psi Total compressive stress = 2750 + 3340 = 6090 psi From Fig. 2.4 wilh À = 0.00098 and temperature of 800ºF, we get B = 7.000 psi. Thus, the selected thickness is adequate at the top of the skirt. H 3 8 3 a x $ Maximum tensile stress at bottom of skirt A 1910 psi Maximum tensile stress a top of skit = 3340 — 2750 590 psi Both of these values are less than 16,000 psi, which is the allowahle tensile stress for the skirt. These caleuiations show that é = 3/8 in. for the skirt is satisfactory. This lhickness may need to be increased in actual construction to take into account such items as opening reinforcementis, corrosion, out- of-roundness considerations, aad handling factors. Example 2.9 Problem What is the allowable compressive stress in an internal cylinder with D, — 24 ft. r = 3/lóin, and design temperature = 900ºF7 Use Fig. 2.4 for the External Pressure Chart. Solution From Eq. (2.21), A = 0,125/(120/0.1875) = 0.0002 From Fig. 2.4, this 4 value falis to the left of the curve for 900ºF, Therefore, Eg. (2.22) must be used. The value of E is obtained from Fig. 2.4 as 20.8 X 10º psi for 900ºF. Hence, allowanle compressive stress B is B = 00002 x 20,800,000/2 2080 psi 24 EXTERNAL PRESSURE External pressure on eylindrical shells causes compressive forces Lhat could lead to buckting. The equations for the buckling of cylindrical shells under external pressure are extremciy cumbersome to use direcily in Cylindriçal Shelis 45 His t t 1 ! nia nt 1 i NE + No ta) ta-2 ti ENotes (7! and (23] ANote (3!) ç sd ot nt3 q L t L t 1 i 1 | | | Fen a FA — fo-th te-2 to) tel te Notes (f) ang 21] TNote (3) ENore 43)] NOTES: (4) When tho cune-to eylinder or the knuokla-to-aylinder junotion is not a fine of support, tho nominal thickness of the cono, knuckto. or torinanical section ehait nox ba loss than the rminimum required thickness of the adjacent oyiindrical shell. (2) Calculations sheil be made using the diameter and carresponding thickness of onats section with dimonsion é as shown, (33 Wenien the cons-to-sylinder ar the knuokle-to-oylinder junotion ia a fine of support, the imament of inertia shall be provided in accordanca with 1-8. FIG. 2.7 SOME LINES OF SUPPORT OF CYLINDRICAL SHELLS UNDER EXTERNAL PRESSURE (ASME VINI) 46 Chapter 2 The allowable compressive hoop stress is then S= PR = 19.1 x 30/0575 K 1530 ps 242 External Pressure for Cylinders with Do/t < 10 When Dot is less than 10, the allowable extérial pressure is taken as the smaller of thé values deteimincd from the following two equations: Pa = (I6THDo!) — OBA B (2.28) Ro LD!) (2.29 where B is obtained as discussed above. For values of (Dy/f) of less than vr equal to 4, the A value is calcutated from A = LIADoy (2.30) For values of A greater than 0.10, use a value of 0,10. The value of Sis taken as the smaller of Two times the allowable tensile stress, or 0.9 times the yield stress of the materia! aí the design temperature. The yield stress is obtained ftom the lxternal Pressure Chart of lhe material by esing twice the valuc obtained from the extreme rigbt-hand side of the termination point of the appropriate temperature curve. The factor of safety in Egs. (2.28) and (2.29) varies from 3.0 for Dotr = t0 to about 1.67 for Do/t = 2. This gradual reduction in the factor of safety as the cylinder gets thicker is justified since buckling ceases to be a consideration and the factor of safety for externa! pressure is kept the same as that for internal pressure, which is 2/3 8, Example 2.11 Problem The inside cylinder of a jacketed vessel has an outside diameter of 20 in., a length of 72in.. and a thickness of 5 in. What is [he maximum allowable jacket pressure? Use Fig, 2.4 for an External Pressure Chart. Let the design temperature he 300ºF. The allowable stress from tension is 17,500 psi. Solution Caleulations give L/Do = 3.60 and D5/t = 4.0. And since Dot = 4.0, Eq. (2.30) must be used. Hence, As LISA “= 0,0688 From Fig. 2.4, B = 17,800 psi. Cylindrica! Shells 47 From Eq, (2.28). Pu = 2167/40) — 0.0823] 17,800 = 8160 psi The yield stress of the maicrial is (0.0)(28) or 32,040 psi. Twice tie altowable stress is 35,000 psi. Hence S = 32,040 psi is to be used. From Eq. (2.29), Po =x 32,040/40 — 1/40) = 12,020 psi Therefore, the alowable jacket pressure in accordance with VIN-1 is 8160 psi. Notice, however, that this pressure is greater than 0.385S, an indication that thick-shell equations may have to be used, Such eguations for external pressure are notin VIN-i yet. 24.3 Empirical Equations It is of interest to note that Fig. 2.6 can only be used for (Do/t) of up to 1080. Larger values are not permittcd presently by the ASML. One approximate equation (Tawad, 1994) that is frequently used by designers for large (Do/1) ratios was developed by the U.S. Navy and is given by P = O866E/(L/DoXDo! 1º (231) where E = modulus of elasticity, psi P = allowable external pressure, psi “This equation incorporates a factor of safety of 3 and a Poisson's ratio of 0,30. Many pressure vessels are subjected routinely to vacuum as well as axial loads from wind and dead load. Section VIH does not give any method for calculating the allowable compressive stress due to combined effect of vacuum and axial loads. One such method is given bv Bergman (Bergman, 1955). Tt uses an equivalent external pressure to account for the axial compression cffect on external pressure. Another method that is used to combine axial and extemal pressure is that of Gilbert (Gilbert and Polani, 1979). This method uses an interactive equation similar to the one used for calculating the buckling of heam columns. Example 2.12 Problem Solve Example 2.10 using Eq. (2.31). Solution From Example 2.10, + = 0,375in., L/Do = 4.0, Do/t = 160.00, and E = 27,000 ksi. Then from Eq. (2.31), P = 0866 x 27,000,000/64.0) 1607: = 181 ps This approximate value differs from the answer in Example 2.10 by about 6%. 50 Chapier 2 From Eq. (2.34), B = Q7S[IZ x 600/0025 + 0,25 X 3.07 140.0] = 200 psi Since this valve falls below the left end of the material line ip Fig. 2.4, we vse Eq. (2.35). 4 — 2 x 2110/29,0004100 = 0,000146 From Eg. (2.33), É = [600 x 140,000.25 — 0.25 x 3.0/140.0) 000N46]/14 = 13d in? Since this number is larger than the actual moment of inertia of the ring (0.56 in.9), the assumed ring is inadoquate and a larger ring is required. However, before such a new ring is chosen, let us use the effective moment Of inertia of the existing ring and shell and compare that to Eg. (2.33). From Eg. (2.33), = [6002 x 140,0(0.25 4 0,25 x 3.0/140.0) 0.000146]/10.9 1D2in* The effective centroid of the shell-ring section, Fig. E2.13(b), is h = [426 x 025 X (125 + 025 X 30(1.5 — 0,25)]/(4.26 x 0.25 + 0.25 x 30) = (0.796 in. The actual moment of inertia is “ 4 4.25 X 025/12 + 426 X 025 X 0677 — 0.25 X 3/12 + 0,25 X 30 x 0.954 0006 — 0.480 + 0.563 + 0,683 173 in 4 Thus, using the composite section results in a 1/4 in. X 3 in. stiffensr that is adequate. 24.5 Attachment of Stiffening Rings Details of lhe attachment of súffening rings to the shell are given in Fig. UG-20 of VELA, which is reproduced in Pig. 2.8. The welds must be able to support a radial pressure load from the shell of PL,. This is based on the code assumption that the suffening rings nrust support the total lateral load if the shell segments between the rings collapse, Also, the code requires that the welds support a shear load of 0.01 PLDo. This shear loud is arbitrary and is based on the assumption that if the rings buckle, bending moments | | — Aylindgica] Shels 51 Zinmio, CÊ Zin min. 24t max, s — dl. Ala kem ImLino Strggorvd Continuous Fiflet Wald intermittent Intormittant One Sisto, intermittant Vista Wata Other Sida S< 8t external stiffenare 5< 12r interna! stiffeners Stiffener M Y ê S Sheli / t w O) tl te) É s Continuous fui! penetration weid e) tel FIG. 2.8 SOME DETAILS FOR ATTACHING STIFFENER RINGS (ASME VIII-t) 52 Chapter 2 occur and generate shear forces, VIIL-1 also has other reguirements pertaining to sitch welding and gaps berween the rings and the shell. These requirements are given in Paragraphs UG-29 and UG-30 of VELI. Example 2.14 Problem Calculate the required size of the double fillet welds attaching the stiffening Ting shown in Fig. B2.13%b) àf Example 2.13 to the shell. Let the allowable tensile stress of SA 285-C at 100ºF he 15,700 psi. Salution “The radisi load, Fr onthe-rings is equal io PF. PL, = 120 x 140 = 1680 Ib/in, of circumference Allowable tensile stress in the filet weld from Table £.4 is 0.558 = 8635 psi. The Lotal load carried by weld is Total load = number of welds artaching ring X size 01 weld x allowable stress 2x wx 8635 Hence, the required weld size, W. is W = 1680/42 x 8635) 0.10in. Use 2 1/4in. continuous fillet welds, in accordance «ith the minimum requirements of UG-30€). Shearing force, V, on the weld is V = 001 FLDo 001 x 12 x 140 x 60 g 1008 o 4“ Allowabie shearing síress in fillet weld from Table 1.4 is 0.558 = 8635 psi. From strength of materials, the equation for shear stress is given by = Vo kh whsre Q is at the location of the weld, as shown im Fig. E2.13(b), and is given by O: 426 X 0,25(0,796 — 0.125) = Q7l in” | : é / Cyiindrical Shells 55 FIG. 2.9 MITERED BEND This is inadeguate, Try ( = 18125 in. (15.000 x 0.85 X 1.8125/24)(14 + O.64224/1,8125)º tan 20)) = 520 psi > 500 psi User = Main. 2.6.2 Eiliptical Shells Elliptical shells, Fig. 2.10, are encountered occasionally by the pressure vessel designer. The stressos, away from discontinuities. in the shell due to internal pressure can be approximated by using the membrane theory of ciliplical cylinders (Flugge, 1967). The basic equation for hoop stress is expressed as 1= PebisElo sin? db + bicos q? (24) where a = major radius of the ellipse, in b = minor radius of the ellipse, in, E = Joint Eifficiency Factor P = design pressure, psi S = allowable stress, psi t = thickness, in. & = angle as defined in fig. 2.10 S6 Chapter 2 | | Loo FIG. 2.10 ELLIPTICAL CYLINDER Example 2.17 Problem Solve Example 2.1 if the cylinder is the minor diameter equal to 92 in. cthiptical in cross section with the major diameter equal to 100 in. and Solution a = 50. 125in, b = 46125in., P = 100 psi, S = 20,000 psi, and E = 0.85 For b = 0º, Eg. (2.41) gives HO x 50.125? x 46. 0,000 x 0.85(50.125º sin? O + 46.125º cos? OP” + 0.125 1 0.320 + 0,125 = 045 in. For p = 90º, Eq. (241) gives E = 100 X SO 128º X 46,125%/20,000 x 0.85€50.125º sinê 90 + 46,125º cos! 90)? + 0.125 = 0,250 + 0.125 = 0375in. Lise f = 0.45 in. This thickness is about 10% higher than that for a cylinder with a circular cross section having an average diameter of 96 in. CHAPTER 3 SPHERICAL SHELLS, HEADS, AND TRANSITION SECTIONS 3.1 INTRODUCTION Sections VIII end VHI-2 contain rules for the design of spherical shells, heads and transition sections. Head configurations include spherical, hemispherical, torispherical, and elipawidal shapes. Transition sec- tions include conicai and toriconical shapes. The design rules for most of these shapes differ significantly in VIN-I and VÍI-2. This difference is due to the design approach used in developing the egrarions for V4-1 and VEN? En this chapter a brief description of the various kinds of heads is given. 3.2 SPHERICAL SHELLS AND BEMISPHERICAL HEADS, VIHI-1 3.2.1 Internal Pressure im Sphericai Sbelis and Pressure on Concave Side of Hemispherica! Heads The required thickness of a thin sphcrical shell due to internai pressure is listed in Paragraph UG-27 and is given by t— PRIGSE — 1,2P)3, when t< 0,356 or P< 0665SE (3.1) where E = Joint Efficiency Pactor P = imlemal pressure R = internal radius S = stress in the material 1 = thickness of the head This eguation can be rewritten to calculate the maximum pressure when the thickness is known. Tt then takes the form — 2SES(R + 0.20) (32) 57 Chanter 3 48 + 0.125 x ' 48.125 im, n The totai head thickness is t = PRI(QSE — 0.2P) — corrosion 100 X (48.125)/(2 x 20,000 x 0.85 — 0.2 x 100) + 0,125 = QI42 + 0.125 = 827 in. “Yhe calculated ibickness is less than 0.356R. Thos, Eg. (3.1) is applicable. Example 3.2 Problem A pressure vessel with an internal diameter of 120 in. has a head thickness of 1.6 in. Determine the maximum pressure if the allowable stress is 20 ksi. Assume £ = 0.85. Solution The maximum pressure is obtained from Eg. (3.2) as P=2x 26000 x 0685 10/60 + Mx 10) « 565 psi Example 3.3 Problem A vertical unfired boiler is constructed of SA 516-70 material and built in accordance with the requirements of VIILI. Tt has an outside dismeter of & ft and an infernal design pressure of 450 psi at 550 ºF. The corrosion allowance is 0.125 in. and the joint efficiency is 1.0. Caleulate the required thickness of the hemispherical head if he allowable stress is 19,700 psi. Solution From Eq. (3.4), the required head thickness is t= 450 X 48/2 X 19,700 X LO — 0.8 x 450) + 0.125 0,543 — 0.125 " 0.67 in. | ! Í 1 Spherical Shells, Heads, and Transition Sections 61 Example 3.4 Problem Calculate the required hemispherical head thickmess of an accumulator with O = 10,000 psi, R = 18 in, $ = 15,000 psi, and £ = 1.0, Assume a corrosion allowance of 0.25 in. Solution The quantity 0.665SE = 9975 psi is Jess than the design pressure of 10,000 psi. Thus. Fg. (3.6) applies. »é 4 USE + PJÇSE — 1) UVSENOO O LO “H10,000)/ (x LS 000 x LO - 10,0007 25 4 = PO 1) " (825%2.5'% — 10) = 652in. Total head thickness = 6.52 + 0.25 = 677 in The required thíckness of the shell for this vessei is calcntated in Example 2.5. Attaching the head to the sheil requires a transition with a 3:1 taper, as shown in Fig. UW-13.3 of VH-1. This taper, however, is impractical to make in this case since the thickness of the head is about two-thirds the radivs, One method of attaching the head to the shell is shown in Fig. E3.4, 3.22 External Pressure in Spherical Sbells and Pressure on Convex Side of Hemispherical Heads The procedure for calculating the external pressure on spherical sbells is given in Paragraph UG-28(d) of VIN-1 and consists of calculating the quamtity A = QIZS/(Rot) (330) eai utside radius of the spherica! sheil and then using a stress-strain diagram similar to Fig. 2.4 to determine a 8 valuo. The allowable externai pressure is calculated from Po = BiRolO ga 62 Chapter 3 = =13.61" FIG. E3.4 H ihe caiculated value of À falls o the left of the stress-strain line in a given lixternal Pressure Chart, then P, must be calculated from the equation Po = 00625E/ Ro! if (3.12) where E = modulus of clasticity of lhe material at design temperature The modulus cf elasticity, E, in Eg. (3.12) is obtained from the actual stress-strain diagrams fumished by the ASME, such as those shown in Fig. 24, Equations (3.10) and (3.11) are also applicable to hemispherical heads with pressure en the convex side, as mentioncd in Paragraph UG-33(c) of VII-?. This is illestrated in Fig. 3.1. For an applied internal pressure in compariment B. the hemispherical head def is subjected to convex pressure and Egs. (2.10) and (3.11) may be used. Sphezica! Shelis, Heads, and Trunsítion Sections 65 Example 3,7 Problem Determine the required thickness for a hemispherical head subjected to an internal pressure of 15,000 psi. LerS = 20ks,R = 20in. Solution P/S = 0.5. Since this ratio is larger than 0.4, Eg. (3.15) must be used. r= 20 (etsr) = 568 im. 34 ELLIPSOIDAL HEADS, VE-i 34.1 Pressure on the Concave Side A commonly esed ellipsoidal head has a ratio of base radius to depth of 2:1 (Fig. 3.29). The shape can be spproximated by a spherical radius of 0,9D and a knucide racius of 0.17D, as showa in Vig. 3.24b), The required thickness of 2:1 heads due to pressure on the concave side is given im Paragraph UG-32(d) of VI-1. The thickness is obtained from the following equation: 1 = PDI(SE — 028) (317) or in terms of required pressure, P- 28) + 020 (3.18) where D = inside base diameter E = Joint Efficiency [actor P = pressure on the concave side of the head S = allowable siress for the material é = thickness of the head Ellipsoidal hezds with a radius-to-depth ratio other than 2:1 may also be designed to the requirements of VHI-t. The governing equations are given im Appendix 1-4 of VIE-l as t= PDKIQSE — 02P) (3.19) where K = (UP + (DI end D/2h varies between 1.0 and 3.0. The £.0 factor corresponds to a homispherical head. The X equation is given in Article 1-4(6) of Appendix 1 of VIII. Equation (2.19) can bz expressed in terms of the teguired pressure as P = 2SEHED + 0.2) (3.20) 66 Chaprera tb) FIG. 3.2 These equations can also be writien in terms of the outside diameter, Do. Thus, t= PDKIDSE + 2RK — GM (321) or in terms of reguired pressure P = 2SEHEKDo — 24K — 0.0] (322 X is of interest to note that VIM-t does not give any P/S limitations for the above equations. Nor does it have any rules for ellipsoidal heads when the ratio of P/S is large, Spherical Shells. Neads, and Transition Sections 67 34.2 Pressure on the Convex Side The thickness needed to resist pressure on the convox side of an ellipsoidal head is given in Paragraph UG-33 of VIIL-1, The required thickness is the greater of the rwo thicknesses determined from the steps below. 1. Multiply the design pressure em the convex side by the factor 1.67, Then use this new pressure end a joint efficiency of E = 1.0 in the appropriate equations listed in Egs. (3.17) through (3.22) to determine the required thickness. 2. Determine first the crown radius of the ellipsoidal head. Then use this value as an equivalent spherical radius to calculate a permissíble external pressure in a manner similar to the procedure giver for spherical shells in Section 3.2.2. The procedure consists of calculating the quantity A = DI25HBDoli) (3.23) where A = strair E = function of the ratio Do/24, and is obtained from Teble 3.1 Do = outside base diameter of the ellipsoida! head += thickneas t Then, using a stress-strain diagram similar to Fig. 2.4, determine the B value. The allowable pressure is calculated from = BI(KoDo!t) (3.26) Jf the calculated value of A falls to the left of the stress-strain line in a given External Pressure Chart, then 4, must be calculated from the equation Po = 0.06255HKaDoi tb? 13.25) wliere E = modutus o elasticity of material ar design temperatore The modulus of elasticity, E. in q. (3.25) is obtained from the actual stress-suaiu diagrams, such as those shown in Fig. 2.4, furnished by the ASME, Example 3.8 Problem Caleulate the reguired thickness of a 2.2:1 head with an inside base diameter of 18 fL, design temperature of 100º, concave pressure of 200 psi, convex pressure of 15 psi, alowable stress is 17,500 psi, and joint efficiency of 0.85. The head is made of low-carhon steel. TABLE 3,1 FACTOR Ko, FOR AN ELLIPSOIDAL HEAD WiTHi PRESSURE ON THE CONVEX SIDE. Do!2ho 30 28 26 24 22 20 Ko 1.36 +27 118 1.08 0.99 0.90 Dof2ha 18 16 14 12 10 Ke 081 ora 0.65 0.57 0.50 70 Chapter 3 where M = (VAOB + Lit and £/r varies herween E. and 16,67. The [0 ratio corresponds to a hemispherical shell The M equation is given in Article 1-4td) of Appendix 1 of VHL. Equation (3.28) can be expressed in terms of the required pressure as P = 2SEH(IM — 0.28 (3.29) These equations can aiso be written in torms of the outside ratius, Lo, us i= PLoMI[DSE + PM — 02) (3.30) or in terms of required pressure, P = EMI, — UM — 0)! (3.31) The theoretical membrane suess diswibution in the circumferential, N,, and meridional, Ng, directions in, shallow heads due to internal pressure are shown in Fig. 3,4. Both the circumferential and meridional stresses at the crown of the head are tensile with a magnitude of $ = Pa?!2hr, However, at the base of the head, the meridional stress is tensile with magnitude S = Pa/2, while the circumferential stress is compressive with a value of S = (Pa/2)[2 — (a/b)]. This compressive stress, which is not considered by Eg. (3.28), could cause buckling o? the shallow head as ihe ratio of D/t increases. Onc way to avoid such failure is to calculate the thickness based on an equaúon (Shield and Dmeker, 1961) that takes buckling into consideration and is expressed as nP/S, = (033 + 5.5r/D)(s/E) + 28(1 = 2.2/Dt/LY — 00006 Sphexical Shelis, Heads, and Transition Sections 71 where D = base diameter of head. in. spherical cap radius, in. factor of safety P = design pressure, psi r = knuckle radius, in. 5, = yield stress of the material, psi é = thickness, in. This equation normally results in a thickness that is greater than thai calculated from Egs. (3.26), (3.28), ox (3.30) for shallow heads with large D/t ratios. Paragraph UG-32(e) ot VIII states that the maximum aliowable stress Used tó calculate the rêquiréa thickness of torispherical heads cannot exceed 20 ksi, regardless of the strength of the material. This requirement was added in the code ty prevent the possibility of buckling of the heads as the thickness is reduced due to the use of materials with higher strength. 35.2 Pressure on the Convex Side For pressure on the convex design, the buckling rules for calculating F&D head thicknesses are the same as those for elipsaidal heads, with the exception that the ontside crowm radius of the F&D head is used in lieu of the quantity KDo. Example 3.9 Problem Calculate the required thickness of an F&D head with an inside base diameter of 18 ft. design temperature of 100ºF, internal (concave) pressure of 200 psi, external (convex) pressure of 15 psi, allowable stress is H7,500 psi, and joint efficiency of 0.85, The head is made of low-carbon steel. Solution For Concave Pressure Using L = 2160 im, r = 0.06 x 216 = 130 in, and M = (1/43 + (216/1338) = 1.77, we get from Eg. (3.28) 1 (200 x 216.0 X LINA X 17,500 x 0,85 — 0.2 x 200) = 258 in. For Convex Pressure ! Find the pressure and the thickmess, P= 67X 5=25ips io (231 x 260 X TDI X 17,500 X 10 — 0.2 X 25,15 72 Chapter 3 2, Leti = 2.58 in. Then Quiside radius = 216 + (2 X 2.58) = 22L.16 in. From Eig. (3.23), A = 0,125/(221.16/2,58) = 0.0015 Prom-Fig:2:4; 8-=-14;000 psi: P, = 14,000/(221.16/2.58) = 163 psi > 15 psi Thus, / = 2,58 in. 36 ELLIPSOIDAL AND TORISPHERICAL HEADS, VIF-2 The required thickness for ellipsoidal as well as torispherical heads is obtained from Paragraph AD-204 and Article 4-4 of VIE-2. The procedure utilizes a chart, Fig. 3.5, which takes into consideration the possibility of buckling of thin shallow heads, as discussed in the previous section. The design consists ví caleuaúng the quantities P/S and 7/D fist and then using Fig. 3.5 to obtain lhe quantity 1/L, and thus +. The thiciness for 2:1 ellipsoida! heads is obiained by using the 7/D = 0.17 curve, while the thickness for a standard F&D head is obtained by using the 7/D — 0.06 curve. Figure 3.5 is plotted from the following equation: tos Let (3.32) + A + A — 126176643 — 4,5524592 (1/D) + 28.933179 (r/DY 0.66298796 — 2.2470836 (1/D) + 15.682985 (r/D)In(P/8)] 878909 x 107! — 0.42262179 (r/D) + 1,8878333 (/DYWIn(P 75)? D = base diameter, in. L = crowu radius, in. P = design pressure, psi + = erown radius, it S = allowable stress, psi r= thickness Example 3.10 Problem An F&D head wilh a 6% Enuckle is subjected to 4U psi of pressure. What is the required tickness if D = 168 in. Use VIIE-2 and then VIL-I rules. S = 20,000 psi for VITE-2, and 15,000 psi for VH-1. Spherical Shells, Heads, and Transition Sections 2 Br I Portion of a cont Í , tar tby tel tar ter FIG. 3.6 P- 28E: cos ailDo - H2 — Lê cos o) (3.36) Hquations (3.33) to (2.36), which are applicable at any angle «, are limited by VEFi to a = 30º. When the angle « exceeds 30º, then VEN-I reguires a knuckle at the large end. as shown in Pig. 3.6(c) and (e). This type of construction will be discussed later in this section. After determining the thickness of the cone for internal pressure, the designer must evaluate the cone- to-shell junction. The cone-to-shelf juncion at the large end of the cone is in compression due to interual pressure, in most cases. The designer must check the junction for required reintorcement needed to contain the unhalanced forces in accordance with Paragraph 1-5 of Appendix £ of VIH-I. The required area is obtained from Ar = EQ RAS EN — Atajtana (3.37) where, Ay = Tequired area at the large end of the cone, in 4º, = Joint Efficieney Factor of the longitudinal joint in the cylinder 76 Chapher3 ae E. = modulus of elasticity of the cone, psi E, = modulus of elasticity of the reinforcing ring, psi E, = modulus qf clasticity of the cylinder, psi k when additional area of reinforcement is not required 3/S,E, but not less than 1.0 when a stiffening ring is required xial Toad at the large end, Fb/in., including pressure end-load R, = large radius of the cons, in. allowable stress in the cone, psi = allowable stress in the reinforcing Ling. psi Ilowable stress in the cylinder, psi E, for the reinforcing ring on the sheil So for ihe, reirforcing ring on the, cone 2 A = angle obtained from Tahte 3.º The area calculated from Eq. (3.37) mast be fumished at the junction. Part of this area may be available at the juncuon as excess area. This excess area can be calculated from the equation Aa E o RUIDO + (ho — &XRibiicos a” (3.38) where Aa, = available area at the junction, in? += minimum requixed thickness of the shell, im. * = nominal cone thickness, in. minimum required thickness of the cone, im. nominal shell tuickness, in. 1 this excess area is less than that calculaied trom Eq. (3.37), then additional area in the form of stiffening rings must be added. The cone-to-shell junction at the small end of the cone is ir tension due to intemal pressure, in most The designer must check the junction for required reinforcement in accordance with Paragraph 1-5 of Appendiz | of VITI-I. The required area at the small end of the cone is obtained from em Ag e ORAS EXT Ato) tm a (3.39) where A, = required area at the small end of the cone, in? Q, = axial load (including pressure end load) at small end, Fo/in. R, = small radivs of the cons, in. À = angle obtained trom Table 3.3 TABLE 3.2 VALUES OF 4 FOR JUNCTIONS AT THE LARGE CYLINDER DUE TO INTERNAL PRESSURE PISES 0.001 0.002 0.903 0.004 0.005 A, deg 1 15 18 2 23 PISE, 0.006 0.007 0.008 9.009 à, deg. 35, 27 285 30 NOTE: (IPA = 30º for greater values ot P/S,E.. : à | i : | | | Spherical Sheils. Heads, and Transiliun, Sections 77 The area calculated from Eq. (3.39) must be fumished at the junctiun. Part of this area may be available at the junetion as excess area. This excess arca can be calculated from the equation As OTBARANE — O + (1 — cos a) (3.40) Hf this excess area is less taan that calcudated from Eq. (3.39), then additional arca in the form of stiffening rings must bo added. When the angle a exceeds 30º, VINI requires a knuckle at the large end, as shown io Fig. 3,6tc) and (e). The required thickness for the kmnckic (called a flauge) at the large end of the cone is obtained from the equation += PLHIÇSE — 0.20) 4 where M= (UA + Un] L=D/2cosa D. = inside diameter at the knuckle-to-cone junction D-W4 - cosa) = insíde knuckle radius, in. Equation (3.41) can be expressed in terms of the required pressure P = 28EHEM + 020) [624] Equations (3.41) and (3.42) cam also be written in terms of the outside diameter, Ds, as t= PLMITSE + PM — 02] (3.43) or in terms of required pressure, P — 28EM [MI — HM — 0,2) (3.44) When a kmnckie is uxcd at the cone-to-sheil junction, the diameter at the large end of the cone is stighuly less than the diameter of the cone without a knuckle, as shown in Fig. 3.6. Thus. the design of the cone as given by Eg. 3.33 is based on diameter D, rather than om the shelf diameter. ASME VII-I does not give rules for the design of knucktes (fues) at the small end of cones. One desiga method uses the pressure-area procedure (Zick and Germain, 1963) to obtain the requirod thickness. Referring TABLE 3.3 VALUES OF 4 FOR JUNCTIONS AT THE SMALL CYLINDER DUE TO INTERNAL PRESSURE PISE, 0.002 0.005 ooo 002 0.04 A, deg 4 5 9 12.5 175 PISEs 008 0.10 oest 4, dep. 24 27 30 NOTE: (1) 4 = 80º for greater values of P/S,E,