Design Of Vertical Pressure Vessel Using Pvelite Software

Design Of Vertical Pressure Vessel Using Pvelite Software

Binesh P Vyas Student, Mechanical Department, VJTI, Maharashtra, India,

R. M. Tayade Professor, Mechanical

Department, VJTI, Maharashtra, India,

Ankit D Kumbhani Student, Mechanical Department, VJTI, Maharashtra, India,

Abstract

Pressure vessels are widely used in various industries. A vertical pressure vessel has been designed using graphical based software named PVElite. For designing of vertical leg supported pressure vessel some input parameters like volume, inside diameter, design pressure (either inside pressure or external pressure), temperature, material, processing fluid. Etc. is required. PVElite gives thickness of shell, thickness of head, height of head, thickness of nozzle, manhole. The high stresses at intersections are caused by discontinuity shear stresses and moments which exist to maintain compatibility at the junctions. PVElite calculate this local stresses according to welding research council (WRC) 107.

Key words: Vertical Pressure Vessel, Design using PVElite, Local stress analysis using PVElite.

1. INTRODUCTION

   Pressure vessels are the container for fluid and gases under high pressure. Due to high pressure, stresses are induced in pressure vessel, if this stresses are more than the permissible stresses then the failure of pressure vessel occurs. So it is necessary to manufacture pressure vessels under standard codes. A code is a standard that has been adopted by one or more governmental bodies and has the force of law, or when it has been incorporated into a business contract. Codes specify requirements of design, fabrication, inspection and testing of pressure vessels. A detailed study of various parts of pressure vessels like shell, head support, flanges, nozzles etc. is carried out according to rules of ASME code section VIII, Division I. Due to mathematical calculation designing of pressure vessel becomes tedious but by using software like PVElite designing of pressure vessel can be done easily. In the case of shell, opening requiring reinforcement in vessel under internal pressure the metal removed must be replaced by the metal of reinforcement. In addition to providing the area of reinforcement, adequate welds must be provided to attach the metal of reinforcement and the induced stresses must be evaluated.

2. ANALYSIS OF PRESSURE VESSEL USING PVELITE AND DISCUSSION

   1. Design condition Design pressure: 0.245 MPa Design temperature: 150 Material: SA240 M 316L Corrosion allowance: Nil

      process fluid : D M Water ( Non Lethal ) Process fluid sp. Gravity: 1.00

      Wind load/ snow load: Not applicable Seismic load: AS per IS-1893, Zone III

   2. Result and Discussion

      In PVElite software we have to enter input data that is required for pressure vessel element and then we have to select its components like head, shell, pipe and legs etc. And its calculate its o/p value like thickness, shell/head height and all other result as show in bellow. Pressure vessel contains fluid so while designing we have to also consider static pressure due to fluid. Static pressure is equal * g *

      h. Where, = density of fluid, g= gravity and h= height up to which vessel contain fluid.

      PVElite also show analyzes result as follow: Inside Corroded Head Depth [h]:

      = L Sqrt ((L – Di / 2) * (L + Di / 2 – 2 * r ) )

      = 1000.00 Sqrt ((1000.00 -1000.00 /2)*(1000.00

      +1000.00 /2-2*100.00))

      = 193.774 mm.

      M factor for Torispherical Head:

      = (3+sqrt ((L+CA)/(r + CA))) /4 per Appendix 1-4 (b & d)

      = (3+sqrt ((1000.000 +0.0000)/ (100.000

      +0.0000)))/4

      = 1.540

      Fig. 1 torispherical head Thickness Due to Internal Pressure [Tr]:

      = (P*(L+CA)*M)/(2*S*E-0.2*P) per Appendix 1- 4 (d)

      = (259.397*(1000.0000+0.0000)*1.5406)/(2*87.43*0.8 5-0.2*259.397)

      = 2.6898 + 0.0000 = 2.6898 mm.

      Max. All. Working Pressure at Given Thickness [MAWP]:

      Less Operating Hydrostatic Head Pressure of 14.397 KPa.

      = (2*S*E*(T-CA))/(M*(L+CA)+0.2*(T-CA)) per

      Appendix 1-4 (d)

      = (2*87.43*0.85*(3.0000))/(1.5406*(1000.0000+0.000 0)+0.2*(3.0000))

      = 289.305 – 14.397 = 274.908 KPa.

      Actual stress at given pressure and thickness [Sact]:

      = (P*(M*(L+CA)+0.2*(T-CA)))/(2*E*(T-CA))

      = (259.397*(1.5406*(1000.0000+0.0000)+0.2*(3.0000

      )))/(2*0.85*(3.0000))

      = 78.392 N./mm²

      Required Thickness of Straight Flange = 1.749 mm. Percent Elongation per UHA-44 (75*tnom/Rf)*(1- Rf/Ro) 4.369 %

      Generally industry used mm unit system but we can change it into other system because soft ware provide this facility and also design code are given so can use any of it. For pressure vessel we used ASME SEC VIII division I and also material can change and according to material software used materials all data like max. Allowable stress etc.

      Fig. 2 cylindrical shell input parameter Thickness Due to Internal Pressure [Tr]:

      = (P*(D/2+Ca))/(S*E-0.6*P) per UG-27 (c)(1)

      = (257.253*(1000.0000/2+0.0000))/(87.43*0.85- 0.6*257.253)

      = 1.7345 + 0.0000 = 1.7345 mm.

      Max. All. Working Pressure at Given Thickness [MAWP]:

      Less Operating Hydrostatic Head Pressure of 12.253 KPa.

      = (S*E*(T-Ca))/((D/2+Ca)+0.6*(T-Ca)) per UG- 27 (c)(1)

      = (87.43*0.85*(2.0000))/((1000.0000/2+0.0000)+0.6*2

      .0000)

      = 296.534 – 12.253 = 284.282 KPa.

      Actual stress at given pressure and thickness [Sact]:

      = (P*((D/2+CA)+0.6*(T-CA)))/(E*(T-CA)) =

      (257.253*((1000.0000/2+0.0000)+0.6*(2.0000)))/(0. 85*(2.0000))

      = 75.849 N./mm²

      Percent Elongation per UHA-44 (50*tnom/Rf)*(1- Rf/Ro) 0.596 %

      In this pressure vessel there are four nozzles including manhole. Here I show only one manholes input parameter and its calculation given by PVElite. Here I selectee nozzle with RF pad and input all parameter including nozzle orientation.

      Fig. 3 manhole M input parameter

      Nozzle Sketch

      | |

      | |

      | |

      | |

      /| |

      /| \| |

      | \ | |

      | \ | |

      | \| |

      Fig. 4 Insert Nozzle with Pad, no inside projection

      NOZZLE CALCULATION, Description: man hole M

      ASME Code, Section VIII, Division 1, 2007, UG-37 to UG-45

      Actual Nozzle Inside Diameter Used in Calculation 428.650 mm.

      Actual Nozzle Thickness Used in Calculation

      14.275 mm.

      Nozzle input data check completed without errors.

      Reqd thickness per UG-37(a)of Torispherical Head, Tr [Int. Press]

      = (P*(L+CA)*M)/(2*S*E-0.2*P) App. 1-4 (d)

      = (245.00*(1000.0000+0.0000)*1.00)/( 2*87*1.00-0.2*245.00)

      = 1.4016 mm.

      Reqd thickness per UG-37(a)of Nozzle Wall, Trn [Int. Press]

      = (P*(D/2+CA))/(S*E-0.6*P) per UG-27 (c)(1)

      = (245.00*(428.6504/2+0.0000))/(87*1.00- 0.6*245.00)

      = 0.6016 mm.

      UG-40, Thickness and Diameter Limit Results : [Int. Press]

      Effective material diameter limit, Dl 857.3008 mm. Effective material thickness limit, no pad Tlnp 7.5000 mm.

      Effective material thickness limit, pad side Tlwp 7.5000 mm.

      Results of Nozzle Reinforcement Area Calculations:

      AREA AVAILABLE, A1 to A5

      Area Required , Ar 6.008 cm² Area in Shell, A1 6.852 cm²

      Area in Nozzle Wall, A2 = 2.051 cm² Area in Inward Nozzle, A3 = 0.000 cm² Area in Welds,A4 = 0.407 cm²

      Area in Pad , A5 = 8.568 cm²

      TOTAL AREA AVAILABLE, Atot = 17.878 cm²

      The Internal Pressure Case Governs the Analysis. Nozzle Angle Used in Area Calculations

      90.00 Degs.

      The area available without a pad is Sufficient.

      The area avalable with the given pad is Sufficient. Reinforcement Area Required for Nozzle [Ar]:

      = (Dlr*Tr+2*Thk*Tr*(1-fr1)) UG-37(c)

      = (428.6504*1.4016+2*(14.2748- 0.0000)*1.4016*(1-1.0000))

      = 6.008 cm²

      Areas per UG-37.1 but with DL = Diameter Limit, DLR = Corroded ID:

      Area Available in Shell [A1]:

      = (DL-Dlr)*(ES*(T-Cas)-Tr)-2*(Thk-

      Can)*(ES*(T-Cas)-Tr)*(1-fr1)

      = (857.301-428.650)*(1.00*(3.0000-0.000)- 1.402)-2*(14.275-0.000)

      *(1.00*(3.0000-0.0000)-1.4016)*(1-1.0000)

      = 6.852 cm²

      Area Available in Nozzle Wall, no Pad [A2np]:

      = ( 2 * min(Tlnp,ho) ) * ( Thk – Can – Trn ) * fr2

      = ( 2 * min(7.50 ,63.60 ) ) * ( 14.27 – 0.00 – 0.60 )

      * 1.0000 )

      = 2.051 cm²

      Area Available in Nozzle Wall, with Pad [A2wp]:

      = ( 2 * Tlwp)*( Thk – Can – Trn )* fr2

      = ( 2 * 7.5000 ) * ( 14.2748 – 0.0000 – 0.6016 ) *

      1.0000

      Area Available in Welds, no Pad [A4np]:

      = Wo² * fr2 + ( Wi-Can/0.707 )² * fr2

      = 6.0000² * 1.0000 + (0.0000)² * 1.0000

      = 0.360 cm²

      Area Available in Welds, with Pad [A4wp]:

      = (Wo² – Ar Lost)*Fr3+((Wi-Can/0.707)² – Ar Lost)*Fr2 + Wp²*Fr4

      = (0.1575) * 1.00 + (0.0000) * 1.00 + 25.0000² *

      1.00

      = 0.407 cm²

      Area Available in Pad [A5]:

      = (min (Dp, DL)-(Nozzle OD))*(min (Tp, Tlwp, Te))*fr4

      = (600.0000 – 457.2000) * 6.0000 * 1.00

      = 8.568 cm²

      UG-45 Minimum Nozzle Neck Thickness Requirement: [Int. Press.]

      Wall Thickness per UG45 (a), tra = 0.6016 mm. Wall Thickness per UG16 (b), tr16b = 1.5875 mm. Wall Thickness per UG45 (b) (1), trb1 = 2.1592 mm. Check UG16 (b) Min. Thickness, trb1 = Max (trb1, tr16b) = 2.1592 mm.

      Std. Wall Pipe per UG45 (b)(4), trb4 = 8.3344 mm. Wall Thickness per UG45 (b),

      trb = Min(trb1, trb4) = 2.1592 mm.

      Final Required Thickness, tr45 = Max (tra, trb) = 2.1592 mm.

      Available Nozzle Neck Thickness = .875 * 14.2748 = 12.4905 mm. --> OK

      M.A.W.P. Results for this Nozzle (Based on Areas) at this Location Approximate M.A.W.P. for given geometry 289.305 KPa.

      Weld Size Calculations, Description: man hole M

      Intermediate Calc. for nozzle/shell Welds Tmin 6.0000 mm. Intermediate Calc. for pad/shell Welds Tmin Pad 6.0000 mm.

      Results Per UW-16.1:

      Required Thickness Actual Thickness

      Nozzle Weld4.2000 = 0.7 *TMIN 4.2420 = 0.7 *

      WO mm.

      Pad Weld 3.0000 = 0.5*Tmin Pad 3.5350 = 0.7 * WP mm.

      The Drop for this Nozzle is: 26.3982 mm.

      The Cut Length for this Nozzle is, Drop + Ho + H + T: 93.0000 mm.

      Manhole or hand hole is required for inspection or cleaning and repair work and which one is selected is depend on pressure vessel diameter

      .As per UG-46 (f) (1) vessel less than 450 mm & over 300 mm I.D should have at least two hand hole and I.D more than it should have man hole. According to UG-46 (g) (1) a circular manhole shall not be less than 400 mm I.D. Below Figure show input parameter and analysis of leg support with base plate.

      Fig. 5 Pipe Leg support input parameter RESULTS FOR LEGS: Hydro Test Case Description: LEGS

      Legs attached to: bottom dishend

      Section Properties: Circular Steel Pipe: PIPE

      India ISI Structural Steel Data

      Leg Length from Attachment to Base Leglen 700.000 mm.

      Number of Legs Nleg 3

      Cross Sectional Area for PIPE Aleg 14.377 cm² Section Inertia (strong axis) 125.583 cm**4 Section Inertia (weak axis) 125.583 cm**4 Section Modulus (strong axis) 28252.760 mm.³ Section Modulus (weak axis) 28252.760 mm.³ Radius of Gyration ( strong axis ) 29.555 mm. Radius of Gyration (weak axis ) 29.555 mm.

      Leg Orientation – Strong Axis

      Overturning Moment at top of Legs 0.0 Kg-m. Total Weight Load at top of Legs, W 1574.2 Kgf Total Shear force at top of Legs 0.0 Kgf Additional force in Leg due to Bracing, Fadd 0 Kgf Occasional Load Factor , Occfac 1.000

      Effective Leg End Condition Factor, k 1.000 Pipe Leg inside Diameter 77.927 mm.

      Pipe Leg outside Diameter 88.900 mm Note: The Legs are Not Cross Braced

      The Leg Shear Force includes Wind and Seismic Effects

      Maximum Shear at top of one Leg [Vleg]:

      = (Max (Wind, Seismic) + Fadd ) * ( Imax / Itot )

      = (0.0 + 0.0) * (125.6 / 376.75)

      = 0.00 Kgf

      Axial Compression, Leg furthest from N.A. [Sma]

      = ((W/Nleg) + (Mleg/(Nlegm*Rn)))/Aleg)

      = ((1574 / 3) + (0 /( 1 * 547.45 )))/ 14.377 )

      = 3.58 N /mm² Axial Compression, Leg closest to N.A. [Sva]

      = ( W / Nleg ) / Aleg

      = (1574 / 3) / 14.377

      = 3.58 N./mm²

      Allowable Comp. for the Selected Leg (KL/r < Cc) [Sa]:

      = Occfac * ( 1-(kl/r)²/(2*Cc²))*Fy /

      ( 5/3+3*(Kl/r)/(8*Cc)-(Kl/r³)/(8*Cc³)

      = 1.00 * (1-(23.68)²/ (2 * 127.18²)) * 248 / (5/3+3*(23.68)/(8* 127.18 )-( 23.68³)/(8*

      127.18³)

      = 140.53 N./mm² Bending at the Bottom of the Leg closest to the N.A. [S]:

      = (Vleg * Leglen * 12 / Smdsa)

      = (0.00 * 700.00 * 12 / 28252.76)

      = 0.00 N./mm²

      Allowable Bending Stress [Sa]:

      = (0.6 * Fy * Occfac)

      = (0.6 * 248 * 1.00)

      = 148.93 N./mm²

      AISC Unity Check [Sc]( must be < or = to 1.00 ) :

      = (Sma/Sa)+(0.85*S)/((1-Sma/Spex)*Sb)

      = (3 /140 )+( 0.85 *0.000 )/(( 1 -3 /1867 ) *148 )

      = 0.0255

      LEG BASEPLATE Analysis, including Moments

      Pipe Leg

      Base Plate Available Area (AA):

      = B * D

      = 150.00 * 150.00

      = 225.00 cm² Clearance between the Bolt and the Leg Edge (BCL):

      = z – BOD / 2

      = 20.00 – 16.00 / 2

      = 12.00 mm.

      Moment at Base plate (MOMENT):

      = Vleg * Lleg

      = 0.00 * 700.00

      = 0.00 Kg-m.

      Bearing Pressure (FC):

      = P / AA

      = 524.72 / 225.00

      = 228.69 KPa. m = (MAX (B, D) – 0.707 * POD) / 2.0

      = (150.00 – 0.707 * 0.00) / 2.0

      = 43.57 mm.

      The Base plate Required Thickness (TREQ):

      = (3 * FC * m² / (1.5 * SBA)) ½

      = (3 * 228.69 * 43.57² / 206.85)½

      = 2.51 mm.

      Base plate Lifting Moment (MBB):

      = Rmleg + V * Length

      = 0.00 + 0.00 * 700.00

      = 0.00 Kg-m.

      Required Total Bolt Area per Leg (ABREQB): per H. Bednar

      = (1 / STBA) * ((4 * MBB / (Nlegm * OD)) – P)

      = (1 / 129.63) * ((4 * 0.00 / (1 * 1006.00)) –

      524.72)

      = -0.3970 cm² --> (No tension in bolts) Summary of Results:

      Actual Required Pass/Fail Base plate Thickness ( mm. ): 14.000 2.510

      Pass

      Bolt Root Area (D. Moss)( cm² ):1.44 0.00

      Pass

3. LOCAL STRESSES ANALYSIS USING PVELITE

   Fig. 6 hollow attachment at shell

   When pressure vessels have to be connected to a piping system, the attachment of nozzles to the crown becomes inevitable. There have been numerous detailed analyses of torispherical shells with radial nozzles, being subjected to various loadings. The nozzle has been singled out as a potential source of weakness in the sense that high stresses occur here. If stresses are within the limit than PVElite shown joint is safe. Here only radial load and shear force V2 is consider and shear force V1 is not consider because of unidirectional loading and moment doe to this force are not excepted in this example. Local stress analysis of manholes input parameter window is shown below.

   Fig.7 Local stress analysis of man hole Input Echo, WRC107 Item 1, Description: manhole M

   Diameter Basis for Vessel Vbasis ID Cylindrical or Spherical Vessel Cylsph Spherical Corrosion Allowance for Vessel Cas 0.0000 in. Vessel Diameter Dv 78.740 in.

   Vessel Thickness Tv 0.118 in. Design Temperature 301.98 F Vessel Material SA-240 316L Vessel Cold S.I. Allowable Smc 16700.00 psi Vessel Hot S.I. Allowable Smh 12680.24 psi Attachment Type Type Round WRC107 Attachment Classification, Holsol Hollow Diameter Basis for Nozzle Nbasis ID Corrosion Allowance for Nozzle Can 0.0000 in. Nozzle Diameter Dn 16.876 in.

   Nozzle Thickness Tn 0.562 in.

   Nozzle Material SA-312 TP316L

   Nozzle Cold S.I. Allowable SNmc 16700.00 psi Nozzle Hot S.I. Allowable SNmh 12680.24 pi Thickness of Reinforcing Pad Tpad 0.236 in. Diameter of Reinforcing Pad Dpad 23.622 in. Design Internal Pressure Dp 35.535 psig Include Pressure Thrust No External Forces and Moments in WRC 107 Convention:

   Radial Load (SUS) P 839.7 lb. Longitudinal Shear (SUS) (Vl) V1 0.0 lb. Circumferential Shear (SUS) (Vc) V2 301.9 lb. Circumferential Moment (SUS) (Mc) M1 0.0 ft.lb. Longitudinal Moment (SUS) (Ml) M2 0.0 ft.lb. Torsional Moment (SUS) Mt 0.0 ft.lb.

   Use Interactive Control No

   WRC107 Version Version March 1979 (B1 & B2)

   Include Pressure Stress Indices per Div. 2 No Compute Pressure Stress per WRC-368 No

   WRC 107 Stress Calculation for Sustained loads: Radial Load P 839.7 lb. Circumferential Shear (VC) V2 301.9 lb. Longitudinal Shear (VL) V1 0.0 lb. Circumferential Moment (MC) M1 0.0 ft.lb. Longitudinal Moment (ML) M2 0.0 ft.lb. Torsional Moment MT 0.0 ft.lb.

   Dimensionless Parameter: U = 2.40

   TAU = 15.51

   RHO = 4.00 (0.63)

   Below all value taken from respective figure than given in welding Research council bulletin 107. By using PVElite software its easy to get its value and reduce time otherwise we have to do little iteration and its tedious work.

   Dimensionless Loads for Spherical Shells at Attachment Junction:

   ————————————————————

   Curves read for 1979 B1/B2 Figure Value Location

   ———————————————————— N(x) * T / P SP 7 0.02237

   M(x) / P SP 7 0.00205 N(x)*T *SQRT(Rm * T) /MC SM 7 0.02019 M(x) *SQRT(Rm * T ) /MC SM 7 0.00160 N(x) * T *SQRT(Rm * T) /ML SM 7 0.02019 M(x) *SQRT(Rm * T ) /ML SM 7 0.00160 N(y) * T / P SP 7 0.02957

   M(y) / P SP 7 0.00406 N(y) * T * SQRT (Rm * T ) / MC SM 7 0.03386 M(y) * SQRT (Rm * T) / MC SM 7 0.00292

   N(y) * T * SQRT (Rm * T) / ML SM 7 0.03386 M(y) * SQRT (Rm * T) / ML SM 7 0.00292

   Stress Concentration Factors Kn = 1.00, Kb = 1.00

   Stresses in the Vessel at the Attachment Junction:

   ————————————————————————

   Stress Values at

   Type of (psi )

   ———————————————————————–

   Stress Load| Au Al Bu Bl Cu Cl Du Dl

   ———————————————————————–

   Rad. Memb. P -149 -149 -149 -149 -149 -149 -149 -149

   Rad. Memb. MC 0	0	0	0	0	0	0	0	Rad. Memb. MC |	0	0	0	0	0	0	0	0
   Rad. Bend. MC 0	0	0	0	0	0	0	0	Rad. Bend. MC |	0	0	0	0	0	0	0	0
   Rad. Memb. ML 0	0	0	0	0	0	0	0	Rad. Memb. ML |	0	0	0	0	0	0	0	0
   Rad. Bend. ML 0	0	0	0	0	0	0	0	Rad. Bend. ML |	0	0	0	0	0	0	0	0

   Rad. Memb. MC 0	0	0	0	0	0	0	0	Rad. Memb. MC |	0	0	0	0	0	0	0	0
   Rad. Bend. MC 0	0	0	0	0	0	0	0	Rad. Bend. MC |	0	0	0	0	0	0	0	0
   Rad. Memb. ML 0	0	0	0	0	0	0	0	Rad. Memb. ML |	0	0	0	0	0	0	0	0
   Rad. Bend. ML 0	0	0	0	0	0	0	0	Rad. Bend. ML |	0	0	0	0	0	0	0	0

   Rad. Bend. P -82 82 -82 82 -82 82 -82 82

   Stress Concentration Factors Kn = 1.00, Kb = 1.00

   Stresses in the Vessel at the Edge of Reinforcing Pad

   —————————————————————

   | Stress Values at

   Type of | (psi)

   —————|———————————————

   Stress Load| Au Al Bu Bl Cu Cl Du Dl

   —————|———————————————–

   Rad. Memb p -1309 -1309 -1309 -1309 -1309 -1309 -1309 –

   1309

   Rad. Bend. P | -3575 3575 -3575 3575 -3575 3575 -3575

   3575

   Tot. Rad. Str. -231 -67 -231 -67 -231 -67 -231 -67

   ———————————————————————— Tang. Memb. P -197 -197 -197 -197 -197 -197 -197 -197

   Tang. Bend. P -162 162 -162 162 -162 162 -162 162

   |

   Tot. Rad. Str.| -4884 2266 -4884 2266 -4884 2266 -4884

   2266

   —————————————————————

   Tang. Memb. MC 0	0	0	0	0	0	0 0 Tang. Bend -1083 1083 -1083 1083 -1083 1083 -1083 1083
   Tang. Bend. MC 0	0	0	0	0	0	0 0 Tang. Memb. MC | 0 0 0 0 0 0 0 0
   Tang. Memb. ML 0	0	0	0	0	0	0 0	Tang. Bend. MC |	0	0	0	0	0 0	0 0
   Tang. Bend. ML 0	0	0	0	0	0	0 0	Tang. Memb. ML |	0	0	0	0	0 0	0 0

   Tang. Memb. MC 0	0	0	0	0	0	0 0 Tang. Bend -1083 1083 -1083 1083 -1083 1083 -1083 1083
   Tang. Bend. MC 0	0	0	0	0	0	0 0 Tang. Memb. MC | 0 0 0 0 0 0 0 0
   Tang. Memb. ML 0	0	0	0	0	0	0 0	Tang. Bend. MC |	0	0	0	0	0 0	0 0
   Tang. Bend. ML 0	0	0	0	0	0	0 0	Tang. Memb. ML |	0	0	0	0	0 0	0 0

   Tang. Memb. P -391 -391 -391 -391 -391 -391 -391 -391

   Tot. Tang. Str. -360 -34 -360 -34 -360 -34 -360 -34

   ———————————————————————— Shear VC 30 30 -30 -30 0 0 0 0

   Shear VL	0	0 0 0	0 0	0	0
   Shear MT	0	0 0 0	0 0	0	0
   Tot. Shear	30	30 -30 -30	0 0	0	0

   ————————————————————————

   Str. Int. 367 85 367 85 360 67 360 67

   ————————————————————————

   Unit less Prm: U = 5.47

   TAU = 0.00 (20.52)

   RHO = 0.00 (0.21)

   Dimensionless Loads for Spherical Shells at Pad edge:

   ————————————————————

   Curves read for 1979 B1/B2 Figure Value

   ————————————————————

   SR 2	0.02175
   SR 2	0.00990
   SR 3	0.01691
   SR 3	0.01053
   SR 3	0.01691
   SR 3	0.01053
   SR 2	0.00650
   SR 2	0.00300
   SR 3	0.00507
   SR 3	0.00317
   SR 3	0.00507
   SR 3	0.00317

   SR 2	0.02175
   SR 2	0.00990
   SR 3	0.01691
   SR 3	0.01053
   SR 3	0.01691
   SR 3	0.01053
   SR 2	0.00650
   SR 2	0.00300
   SR 3	0.00507
   SR 3	0.00317
   SR 3	0.00507
   SR 3	0.00317

   N(x) * T / P M(x) / P

   N(x) * T * SQRT(Rm * T ) / MC M(x) * SQRT(Rm * T ) / MC N(x) * T * SQRT(Rm * T ) / ML M(x) * SQRT(Rm * T ) / ML

   N(y) * T / P M(y) / P

   N(y) * T * SQRT(Rm * T ) / MC M(y) * SQRT(Rm * T ) / MC N(y) * T * SQRT(Rm * T ) / ML M(y) * SQRT(Rm * T ) / ML

   Tang. Bend. ML | 0 0 0 0 0 0 0 0

   Tot. Tang. Str.|-1475 692 -1475 692 -1475 692 -1475 692

   —————————————————————-

   Shear VC | 68 68 -68 -68 0 0 0 0

   Shear VL | 0 0	0	0	0	0	0	0
   Shear MT | 0 0	0	0	0	0	0	0
   |
   Tot. Shear| 68 68	-68	-68	0	0	0	0

   Str. Int. | 4886 2269 4886 2269 4884 2266 4884 2266

   —————————————————————-

   WRC 107 Stress Summations:

   Vessel Stress Summation at Attachment Junction

   ————————————————————————

   Type of Stress Values at Stress Int.(SUS) (psi)

   —————|——————————————————–

   Location Au Al Bu Bl Cu Cl Du Dl

   —————|——————————————————– Rad. Pm 1974 1974 1974 1974 1974 1974 1974 1974

   Rad. Pl -149 -149 -149 -149 -149 -149 -149 -149

   Rad. Q -82 82 -82 82 -82 82 -82 82

   ———————————————————————— Long. Pm 1974 1974 1974 1974 1974 1974 1974 1974

   Long. Pl -197 -197 -197 -197 -197 -197 -197 -197

   Long. Q -162 162 -162 162 -162 162 -162 162

   ————————————————————————

   Shear Pm	0	0	0	0	0	0	0	0
   Shear Pl	30	30	-30	-30	0	0	0	0
   Shear Q	0	0	0	0	0	0	0	0

   ————————————————————————

   Pm 1974 1974 1974 1974 1974 1974 1974 1974

   ———————————————————————— Pm+Pl 1839 1839 1839 1839 1824 1824 1824 1824

   ———————————————————————— Pm+Pl+Q 1749 1957 1749 1957 1742 1939 1742 1939

   ————————————————————————

   Type of Max. S.I. S.I. Allowable Result Stress Int. psi

   ————————————————————————

   (2) F.A. Leckie and R.K. Penny, "Stress Concentration Factors for the Stresses at Nozzle Intersections in Pressure Vessels", Welding

   Pm (SUS)	1974	12680	Passed		Research Council, Bulletin 90, 1963.
   Pm+Pl (SUS)	1839	19020	Passed	(3)	R.K.Penny and F.A. Leckie, "Solution for the

   Pm (SUS)	1974	12680	Passed		Research Council, Bulletin 90, 1963.
   Pm+Pl (SUS)	1839	19020	Passed	(3)	R.K.Penny and F.A. Leckie, "Solution for the

   Pm+Pl+Q (TOTAL) 1957 44070 Passed

   ————————————————————————

   WRC 107 Stress Summations:

   Vessel Stress Summation at Reinforcing Pad Edge

   ————————————————————————

   Type of Stress Values at

   Stress Int. (psi )

   —————|——————————————————–

   Location | Au Al Bu Bl Cu Cl Du Dl

   —————|——————————————————–

   Rad. Pm 5922 5922 5922 5922 5922 5922 5922 5922

   Rad. Pl -1309 -1309 -1309 -1309 -1309 -1309 -1309 -1309

   Rad. Q -3575 3575 -3575 3575 -3575 3575 -3575 3575

   ———————————————————————— Long. Pm 5922 5922 5922 5922 5922 5922 5922 5922

   Long. Pl -391 -391 -391 -391 -391 -391 -391 -391

   Long. Q -1083 1083 -1083 1083 -1083 1083 -1083 1083

   ————————————————————————

   Shear Pm	0	0	0	0	0	0	0	0
   Shear Pl	68	68	-68	-68	0	0	0	0
   Shear Q |	0	0	0	0	0	0	0	0

   ————————————————————————

   Pm 5922 5922 5922 5922 5922 5922 5922 5922

   ————————————————————

   Pm+Pl 5536 5536 5536 5536 5531 5531 5531 5531

   ———————————————————————— Pm+Pl+Q 4448 8192 4448 8192 4447 8189 4447 8189

   ————————————————————————

   ———————————————————————–

   Type of Stress Int.	Max. S.I. psi	S.I. Allowable	Result
   —————|——————————————————–
   Pm (SUS)		5922	12680	Passed
   Pm+Pl (SUS)		5536	19020	Passed
   Pm+Pl+Q (TOTAL)		8192	44070	Passed
   ————————————————————————

4. Conclusion

   Design of pressure vessel by using PVElite gives accurate analysis result and also reduces time. Further research need to explore environmental parameter such as earthquake, thermal load, fluctuation load and so on. Moreover dynamic processes in design need to employ for optimization instead of fixing the input parameter. High stresses occurred at intersection of head and nozzle Welding Research council (WRC) bulletin gives formulation for calculating this stresses.

5. References

(1) Stress analysis of torispherical shell with radial nozzle by Amran Ayob Faculty of Mechanical engineering, University Teknologi Malaysia, 81310 Skudai, Johor.

Stresses at Nozzles in Pressure Vessels",

Welding Research Council, Bulletin 90, 1963.

1. ASME Boiler & Pressure Vessel Code: Rules for Construction of Pressure vessels, (ASME VIII),

   Division1, 2007

2. Moss, Dennis. Pressure Vessel Design Manual. Third Edition, Gulf Professional Publishing Inc, Burlington, 2004.

3. Megyesy, Eugene F., Pressure Vessel Handbook. Eleventh Edition, Pressure Vessel Publishing Inc. Tulsa., Oklahoma. 2001.

4. R. Farr, James. And H. Jawad, Maan, Guide Book for the Design of ASME Section VIII Pressure Vessel, ASME Press, New York, 2001.

5. Jimit Vyas and Mahavir Solanski, Design and Analysis of Pressure Vessel, Dissertation, U.V. Patel College of Engineering, Gujarat, 2008

6. PVElite and PV CodeCalc 2008.