Pressure Vessel Design Manual - PVManage

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246Pressure Vessel Design ManualLongitudinal Stressescompression will occur when the vessel is not pressurizedand the term PeD/4t will drop out.Pi D 48Mx Whsxt ¼ tension side ¼ þ4tpD2 t pDtIn the following equations, D is in inches. The term"48MX" is used for ft-lb or ft-kips. If in.-lb or in.-kips areused, then the term "4MX" should be substituted where"48MX" is used. The allowable stresses S1E1 or B may besubstituted in the equations for t to determine or verifythickness at any elevation. Compare the stresses orthicknesses required at each elevation against the thickness required for circumferential stress due to internalpressure to determine which one will govern. If there is noexternal pressure condition, assume the maximumElevationMxWnDsxc ¼ compression side ¼ ð ÞPe D 48Mx Wh 4tpD2 t pDt Allowable longitudinal stresses.tension : S1 E1 ¼tTensionS1E1CompressionσxtBσxc

Design of Vessel Supports247Table 4-20Coefficients for determining period of vibration of free-standing cylindrical shells having varying cross sections and 100.804590.0.0.0.Reprinted by permission of the Chevron Corp., San Francisco.Notescompression:0:125tA ¼RoB ¼ from applicable material chart of ASME Code,Section II, Part D, Subpart 3.Note: Joint efficiency for longitudinal seams incompression is 1.0.1. This procedure is for use in determining forces andmoments at various planes of uniform and nonuniform vertical pressure vessels.2. To determine the plate thickness required at anygiven elevation compare the moments from bothwind and seismic at that elevation. The larger ofthe two should be used. Wind-induced momentsmay govern the longitudinal loading at oneelevation, and seismic-induced moments maygovern another.

248Pressure Vessel Design ManualProcedure 4-9: Seismic Design – Vessel on Conical SkirtwT, wC ¼ Uniform load in shell, tension orcompression, Lbs/inDT ¼ Temperature differential in skirt; DT –70o Fl ¼ Damping FactorsLT ¼ Longitudinal tension stress, skirt, PSIsLC ¼ Longitudinal compressive stress, skirt,PSIsDT ¼ Stress in skirt due to DT loading, PSIsX ¼ Longitudinal bending stress in shell, PSIsr ¼ Allowable shear stress in shear band, PSIsw ¼ Allowable shear stress in weld, �¼¼¼¼¼¼¼F1 or F2 ¼MAA orBB¼Mb ¼MX or My ¼NNbPpT, pC¼¼¼¼QRmSSbttrV¼¼¼¼¼¼¼Vmax ¼W ¼W1 ¼W2 ¼ASME Code strain factor, dimensionlessArea of base plate supported on steel, in2Area required for one anchor bolt, in2Area of shear band, LS X tS, in2Allowable bearing pressure, PSIOD of vessel shell, inOD of skirt at base plate, inModulus of elasticity, PSIAllowable compressive stress, PSILoad at support points, LbsBearing pressure, PSIAllowable stress, tension, PSIMinimum specified yield strength of skirtat design temperature, PSISeismic load for upper or lower portion ofvesselOverturning moment due to earthquake,In-Lbs, at elevation A-A or B-BBending moment, In-LbsInternal bending moment in base plate, inlbsNumber of support pointsNumber of anchor boltsDesign pressure, PSIGLoad at top of skirt, tension or compression, Lbs/inLoad at support points, LbsMean radius of shell, inShell allowable stress, tension, PSIAllowable stress, anchor bolts, PSIThickness of shell, inThickness required, skirt, inBase shear, LbsGreater of V1 or V2, LbsWeight, operating, LbsWeight of vessel, insulation, piping, etcabove LOS. Include weight of contents ifcontents are supported above the LOS. Donot include weight of skirt, LbsWeight of vessel, insulation, piping, etc.,below LOS. Include weight of contents ifsupported below the LOS. Do not includeweight of skirt or base.FC.G.L2ALWwTSHEARBANDWCAL.O.S.pCpTBBf or Qf or QDC.L. of BOLTSIMPLE VESSEL DIAGRAMSEE NOTE 1V

Design of Vessel Supportsθ 30 MAX15 PREFERREDC.G. OF UPPERPORTIONF1VESSEL OD,DoHsL3W1L1AL.O.SθtSKAL4HSBBL2f or QtbecVmaxdDC.L. of BOLTF2SKIRT DIMENSIONSf or QW2C.G. OF LOWERPORTIONtSW1WTpTtWcLSpcSHELLθDETAIL OF FORCESHSW2DIMENSIONS OF SHEAR BAND249

250Pressure Vessel Design Manual(2) TYPE “A”INSUL. RINGSbbSEE DETAILBELOWLoad areaAbyAIR SPACEW.P.xxaHOT BOX SEGMENTAL RINGFOR TEMP 500 ºFINSULATIONTYPE “A” INSUL.RINGTYPE “B”INSUL. RINGINSULATE SHELLUNDER SKIRTBEFORE PLACINGON SUPPORTSKIRT VENTybLoad areaFIREPROOFINGPROVIDE 1/2” SQ.NUTS ON CENTERSFOR SUPPORTaxxBTM. BASE PLATESKIRT BASEDETAIL TYPESupportsteelyyBASE PLATE LOADINGSKIRT O.D., DSKREF. TAN. LINE(1) TYPE “B”INSULATION RING.SKIRT & BASE DETAILStsTable 4-21Maximum bending moment in a bearing plate with gussets45ºSKIRT BANDRa/b0.333.5.6661.01.52.03.0 NcL (4) 6 DIA. VENTSEQUALY SPACED15ºW.P.BLENDRDETAIL OF SHEAR BANDMxx [ :5by[‘0.0078 Bp.0293 Bp.0558 Bp.0972 Bp.1230 Bp.1310 Bp.1330 Bp2bb2b2b2b2b2b2Myx [ :5by[0( ).500 Bp( ).428 Bp( ).319 Bp( ).227 Bp( ).119 Bp( ).124 Bp( ).125 Bp( ).125 BpReprinted by permission of John Wiley & Sons, Inc.From Process Equipment Design, Table 10.3 (See Note 2.)l2l2l2l2l2l2l2l2

Design of Vessel SupportsCalculationCase 1: Simplified Approach (Note 1)GIVEN: Uniform load in skirt at ELEV A-ApT ¼ wT Cos qpC ¼ wC Cos q Allowable stress, skirt;D ¼L ¼F ¼W ¼L2 ¼Calculate moments;MAA ¼ F L21. Compression, FCAssume a thickness of skirt and calculate;A ¼ ð:125 tSK Þ ð:5 DSK Þ FC ¼ A E 2 :5 Fy2. Tension, FT S ¼ from ASME II D :66 FyMBB ¼ F LFT ¼ 1:2 SCase 2: Rigorous Approach (Note 2)GIVEN:HS ¼L3 ¼L4 ¼W2 ¼F2 ¼W1 ¼F1 ¼Vmax ¼ Greater of F1 or F2Mmax ¼ Greater of following;MAA ¼ F1 L3 Thickness required, skirt, trTension; tr ¼ pT FTComp; tr ¼ pC FCUse tSK ¼ Stress due to DT sDT ¼ 48 DT HS tb ½DO tSK Longitudinal stress in skirt due to loadings;Tension; sLT ¼ ðpT tSK Þ þ sDTComp; sLC ¼ ðpC tSK Þ þ sDTOr ¼ F2 L4MBB ¼ ðVmax HS Þ þ MmaxW ¼ W1 þ W2Shear RingDesign of Skirt Uniform loads in vessel at ELEV A-A; wT ¼ W p DO þ 4 MAA p DO 2 wC ¼ W p DO 4 MAA p DO 2 Find angle, q, by layout or calculation;X ¼ :5 ½ðD 2 eÞ ðDO þ 2 tS ÞTan q ¼ X ðHS tb Þq ¼1 2 Allowable shear stresses;Ring; sr ¼ :7 SWeld; sw ¼ :4 S Minimum length of shear band, LminLmin ¼ wC sr Size fillet welds, w1 and w2w ¼ w1 þ w2w ¼ wC ð:707 sw ÞUse w1 ¼ w2 ¼ Thickness required for shear band, tStS ¼ 2 w1Use tS ¼251

252Pressure Vessel Design ManualBase PlateThe base plate thickness depends on how the vessel issupported. The vessel can either have continuous supportor partial support. Partial support describes a vessel supported on 4 or 8 points on steel in a structure. Continuoussupport describes a concrete table top where there is fullwidth, 360o contact between the base plate and thesupport.Use Nb ¼db ¼Longitudinal Stress in Shell due to Shear Band Cross sectional area of shear band, ASAS ¼ LS tS Damping Factor, ll ¼ 1:285 ðRm tÞ1 2Case A: Full Support Maximum load, fNote: The maximum loading is assumed to occur atthe bolt circle.f ¼ W p D 4 MBB p D2 Longitudinal bending stress in shell, sXsX ¼ 6 M t2 Bearing pressure, fPf P ¼ f d BP Base plate thickness, tb :6 Fytb ¼ C 3 f P Bending moment in shell, M M ¼ P 2 l2 AS AS þ t LS þ 2 t l1 2Case B: Partial Support Load QQ ¼ W N MBB D Bearing pressure, fPf P ¼ Q Ab Maximum bending moment, Mb, from Table 4-21a b ¼Mb ¼ greater of MX or My Thickness of base plate, tb 1 2 tb ¼ 6 Mb :6 FyAnchor Bolts Determine if anchor bolts are required due to upliftNb At ¼ ½ð48 MBB DÞ W ½1 SbIf N b A t is negative, then anchor bolts are notrequired. Use minimum size and maximum spacingfor this case.If Nb At is positive then anchor bolts are required. Area required, AtAt ¼ ½ð48 MBB DÞ W ½1 Nb SbNotes1. The “Simplified Approach” is valid for average sizevessels where L/D 5 and the support point is nearthe C.G. of the vessel. The simplified approachapplies the full seismic force at the C.G. of thevessel.2. The “Rigorous Approach” is for vessel whereL/D 5 or the vessel is supported near the top orbottom of the vessel. In such cases the simplifiedapproach may not be adequate. In this case thevessel is divided into two parts; the upper and lowerpart. The division between the upper and lower partis the line of support.3. A third approach, not shown here, would be todetermine the loadings by determining the shearand moments at each weld plane for each partof the vessel. This procedure is illustrated inProcedure 4-8.4. The upper weight, W1, will produce a compressiveforce in the shell equal to W1 / A, where A is thecross sectional area of the vessel.5. The lower weight, W2, will produce a tensile forcein the vessel shell equal to W2 / A. This would beadditive to effects due to internal pressure.6. The effects of the unbalanced inward (or outward)load on the shell to cone junction should beevaluated for circumferential membrane andbending stresses, as well as longitudinal bendingstresses.

Design of Vessel Supports253F1LOSL3F1L4L3LOSF2L4F2LOWER PORTIONGOVERNSUPPER PORTIONGOVERNSMmax GREATER OF .MAA F1 L3OrF2 L4MBB (Vmax Hs) MmaxVmax Greater of F1 or F2Figure 4-39. Vessel supported on conical skirt (Influence of support positioning).Procedure 4-10: Design of Horizontal Vessel on Saddles [1,3,14,15]NotationAr ¼ cross-sectional area of composite ringstiffener, in.2E ¼ joint efficiencyE1 ¼ modulus of elasticity, psiCh ¼ seismic factorI1 ¼ moment of inertia of ring stiffener, in.4tw ¼ thickness of wear plate, in.ts ¼ thickness of shell, in.th ¼ thickness of head, in.Q ¼ total load per saddle (including piping loads,wind or seismic reactions, platforms, operatingliquid, etc.) lbWo ¼ operating weight of vessel, lbM1 ¼ longitudinal bending moment at saddles,in.-lbM2 ¼ longitudinal bending moment at midspan,in.-lbS ¼ allowable stress, tension, psiSc ¼ allowable stress, compression, psiS1–14 ¼ shell, head, and ring stresses, psiK1–9 ¼ coefficientsFL ¼ longitudinal force due to wind, seismic,expansion, contraction, etc., lbFT ¼ transverse force, wind or seismic, lbsx ¼ longitudinal stress, internal pressure, psisf ¼ circumferential stress, internal pressure, psi

254Pressure Vessel Design Manualse ¼ longitudinal stress, external pressure, psiss ¼ circumferential stress in stiffening ring, psish ¼ latitudinal stress in head due to internal pressure, psiFy ¼ minimum yield stress, shell, psiPPeKsmy¼¼¼¼¼internal pressure, psiexternal pressure, psipier spring rate,friction coefficientpier deflection, in.Figure 4-40. Typical dimensions for a horizontal vessel supported on two saddles.Figure 4-41. Stress diagram.

Design of Vessel SupportsFigure 4-42. Moment diagram.255

256Pressure Vessel Design Manual

Design of Vessel Supports257Transverse Load: Basis for EquationsMethod 1w3 ¼3FB E6FB3FB¼ 2O ¼22E 22EETherefore the total load, QF, due to force F is3FB3FBQ F ¼ w3 E ¼ 2 E ¼EEMethod 2 Unit load at edge of base plate, wu.Wu ¼ W1 þ W2 Derivation of equation for w2.ME2M ¼ FBZ ¼6ZThereforeM6FB¼ 2ZE Equivalent total load Q2.Q2 ¼ wu Es ¼This assumes that the maximum load at the edge of thebaseplate is uniform across the entire baseplate. This isvery conservative, so the equation is modified as follows: Using a triangular loading and 2/3 rule to developa more realistic “uniform load”FB3FBF1 ¼¼ð2 3ÞE2EThis method is based on the rationale that the load is nolonger spread over the entire saddle but is shifted to oneside. Combined force, ��Q2 ¼ F2 þ Q2 Angle, qH. FqH ¼ arctanQ Modified saddle angle, q1.q qHq1 ¼ 22

258Pressure Vessel Design ManualSaddle Reactions and Moments for Exchangers or Vessels with Offset SaddlesDue to.Load per SaddleDiagramFxFxQ1 ¼Ws L2 Fx BþL12AQ2 ¼Ws L3 Fx BþL12ABAFyC.G.FyðWs þ Fy ÞL2Q1 ¼L1ðWs þ Fy ÞL3Q2 ¼L1FyL3L2Q1Q2FzFzQ1 ¼WS L2 Fz BþL1L1WS L3 Fz BQ2 ¼þL1L1Q1L1Q2

Design of Vessel SupportsL1L2X1X259L3–X2W–Q1Q2WM2M1Note: W weight of vessel plus any impact factorsOAL ¼ L1 þ L2 þ L3 w ¼Q1 ¼ihw ðL1 þ L2 Þ2 L232L1wL222 M2 ¼ Q1Q1 L22wM3 ¼wL232Mx ¼wðL2 XÞ22Mx1 ¼wðL3 X2 Þ22Types of Stresses and AllowablesQ 2 ¼ W Q1M1 ¼WOALMx2 ¼M3 wðL2 þ X1 Þ2 Q 1 X12 S1 to S4: longitudinal bending.Tension : S1 ; S3 ; or S4 þ sx SECompression : S2 ; S3 ; or S4 se Scwhere Sc ¼ factor “B” or S or tsE1/16rwhichever is less.1. Compressive stress is not significant where Rm/t 200 and the vessel is designed for internal pressureonly.2. When longitudinal bending at midspan is excessive,move saddles away from heads; however, do notexceed A 0.2 L.3. When longitudinal bending at saddles is excessive,move saddles toward heads.

260Pressure Vessel Design Manual4. If longitudinal bending is excessive at both saddlesand midspan, add stiffening rings. If stresses are stillexcessive, increase shell thickness. S5 to S8 0.8S: tangential shear.1. Tangential shear is not combined with otherstresses.2. If a wear plate is used, ts may be taken as ts þ tw,providing the wear plate extends R/10 above thehorn of the saddle.3. If the shell is unstiffened, the maximum tangentialshear stress occurs at the horn of the saddle.4. If the shell is stiffened, the maximum tangentialshear occurs at the equator.5. When tangential shear stress is excessive, movesaddles toward heads, A 0.5 R, add rings, orincrease shell thickness.6. When stiffening rings are used, the shell-to-ringweld must be designed to be adequate to resist thetangential shear as follows:St ¼Qlballowable shear: pr in: circumferencein: of weld S11 þ sh 1.25 SE: additional stress in head.1. S11 is a shear stress that is additive to the hoopstress in the head and occurs whenever the saddlesare located close to the heads, A 0.5 R. Due totheir close proximity the shear of the saddleextends into the head.2. If stress in the head is excessive, move saddlesaway from heads, increase head thickness, or addstiffening rings. S9 and S10 1.5 S and 0.9Fy: circumferentialbending at horn of saddle.1. If a wear plate is used, ts may be taken as ts þ twproviding the wear plate extends R/10 above thehorn of the saddle. Stresses must also be checkedat the top of the wear plate.2. If stresses at the horn of the saddle are excessive:a. Add a wear plate.b. Increase contact angle q.c. Move saddles toward heads, A R.d. Add stiffening rings. S12 0.5Fy or 1.5 S: circumferential compressivestress.1. If a wear plate is used, ts may be taken as ts þ tw,providing the width of the wear plate is at leastpffiffiffiffiffib þ 1:56 rts :2. If the shell is unstiffened the maximum stressoccurs at the horn of the saddle.3. If the shell is stiffened the maximum hoopcompression occurs at the bottom of the shell.4. If stresses are excessive add stiffening rings. (þ)S13 þ sf 1.5 S: circumferential tensionstressdshell stiffened. ( )S13 ss 0.5Fy: circumferential compressionstressdshell stiffened. ( )S14 ss 0.9Fy: circumferential compressionstress in stiffening ring.Procedure for Locating SaddlesTrial 1: Set A ¼ 0.2 L and q ¼ 120 and check stress at thehorn of the saddle, S9 or S10. This stress will govern formost vessels except for those with large L/R ratios.Trial 2: Increase saddle angle q to 150 and recheckstresses at horn or saddle, S9 or S10.Trial 3: Move saddles near heads (A ¼ R/2) and return q to120 . This will take advantage of stiffness provided bythe heads and will also induce additional stresses in theheads. Compute stresses S4, S8, and S9 or S10. A wearplate may be used to reduce the stresses at the horn orsaddle when the saddles are near the heads (A R/2) andthe wear plate extends R/10 above the horn of the saddle.Trial 4: Increase the saddle angle to 150 and recheckstresses S4, S8, and S9 or S10. Increase the saddle angleprogressively to a maximum of 168 to reduce stresses.Trial 5: Move saddles to A ¼ 0.2L and q ¼ 120 anddesign ring stiffeners in the plane of the saddles usingthe equations for S13 and S14 (see Note 7).Total Saddle Reaction Forces, Q.Q ¼ greater of Q1 or Q2Longitudinal, Q1Wo FL BQ1 ¼þ2LsTransverse, Q2Wo 3Ft BQ2 ¼þ2EShell StressesThere are 14 main stresses to be considered in thedesign of a horizontal vessel on saddle supports:

Design of Vessel Supports261Figure 4-43. Chart for selection of saddles for horizontal vessels. Reprinted by permission of the American WeldingSociety.S1 ¼ longitudinal bending at saddles without stiffeners, tensionS2 ¼ longitudinal bending at saddles without stiffeners, compressionS3 ¼ longitudinal bending at saddles with stiffenersS4 ¼ longitudinal bending at midspan, tension atbottom, compression at topS5 ¼ tangential sheardshell stiffened in plane ofsaddleS6 ¼ tangential sheardshell not stiffened, A R/2S7 ¼ tangential sheardshell not stiffened except byheads, A R/2S8 ¼ tangential shear in headdshell not stiffened,A R/2S9 ¼ circumferential bending at horn of saddledshellnot stiffened, L 8RS10 ¼ circumferential bending at horn of saddledshellnot stiffened, L 8RS11 ¼ additional tension stress in head, shell not stiffened, A R/2S12 ¼ circumferential compressive stressdstiffened ornot stiffened, saddles attached or notS13 ¼ circumferential stress in shell with stiffener inplane of saddleS14 ¼ circumferential stress in ring stiffenerLongitudinal Bending S1, longitudinal bending at saddlesdwithout stiffeners, tension.8AH þ 6A2 3R2 þ 3H23L þ 4HM1S1 ¼ ð þ ÞK1 r 2 t s S2, longitudinal bending at saddlesdwithout stiffeners, compression.M1 ¼ 6Q

262Pressure Vessel Design ManualS9 ¼ ð ÞFigure 4-44. Saddle reaction forces.M1K7 r2 ts S3, longitudinal bending at saddlesdwith stiffeners.M1S3 ¼ ð Þ 2pr ts S4, longitudinal bending at midspan.S2 ¼ ð Þ3L2 þ 6R2 6H2 12AL 16AH3L þ 4HM2S4 ¼ ð Þ 2pr tsM2 ¼ 3QTangential Shear S5, tangential sheardshell stiffened in the plane ofthe saddle.32Q 6 L 2A 744 5prtsLþ H3 S6, tangential sheardshell not stiffened, A 0.5R.32S5 ¼K2 Q 6 L

Procedure 4-9: Seismic Design – Vessel on Conical Skirt Nomenclature A ¼ ASME Code strain factor, dimensionless Ab ¼ Area of base plate supported on steel, in 2 At ¼ Area required for one anchor bolt, in 2 AS ¼ Area of shear band, LS XtS,in 2 BP ¼ Allowable bearing pressure, PSI DO ¼ OD of vessel shell, in DSK ¼ OD of skirt at base plate, in E ¼ Modulus of elasticity, PSI

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