Eqn Reference Asme Bpvc R1s
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ASME BPVC Eqn Reference Reference: ASME BPVC Sec VIII Div 1 2007
UG-16 General Guidelines 1. The absolute minimum thickness of any vessel: t min = 116 in 2. Minimum thickness for water service fabricated from materials listed in table 3 and 1A in Section II Part D: t min = 3 32 in ; If temperatures below -20°F use allowables for 100°F (per UCS-23)
UG-27 Thickness of shells under internal pressure Definitions: t: minimum required thickness of shell, in. P: internal design pressure, psi. R: inside radius of the shell under consideration in the corroded condition, in. S: maximum allowable stress, psi. E: joint efficiency (see UW-12 for welded vessels; UG-53 for ligaments between openings)
Equations 1. Circumferential Stress (Longitudinal Joints): thickness not greater than half inside radius and P does not exceed 0.385SE PR PR0 a. Min Thickness: t = or t = based on O.D. SE − 0.6 P SE + 0.4 P SEt SEt b. Max Pressure: P = or P = based on O.D. R0 − 0.4t R + 0.6t 2. Longitudinal Stress (Circumferential Joint): thickness not greater than half inside radius and P does not exceed 1.25SE PR a. Min Thickness: t = 2 SE + 0.4 P 2SEt b. Max Pressure: P = R − 0.4t c. To be used only when Ecirc for the circumferential joint is less half of Elong. 3. Spherical Shells: Thickness does not exceed 0.356R and P does not exceed 0.665SE PR PR0 a. Min Thickness: t = or t = based on O.D. 2 SE − 0.2 P 2 SE + 0.8 P 2 SEt 2 SEt b. Max Pressure: P = or P = based on O.D. R0 − 0.8t R + 0.2t
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UG-32 Thickness of Formed Heads and Sections with Pressure on Concave Side Definitions: t: minimum required thickness of shell, in. P: internal design pressure, psi. D: Inside diameter of the head skirt; inside length of major axis for ellipsoidal head; Inside diameter of a conical head at the point under consideration perpendicular to longitudinal axis in the corroded condition, in. Di: Inside Diameter of conical portion of toriconical head at tangent to knuckle; Di = D − 2r (1 − cos α ) r: inside knuckle radius, in S: maximum allowable stress, psi. E: joint efficiency (see UW-12 for welded vessels) L: inside spherical or crown radius, in. α: half of the included (apex) angle of the cone at center line of the head
Equations: 1. Ellipsoidal Heads: ½ of minor axis equals ¼ of the inside diameter; 2:1 Ellipsoidal Head 2 1 D K = 2 + a. Shape Factor: 6 2h PDo K PDK b. Min Thickness: t = or t = based on O.D. 2 SE − 2 P( K − 0.1) 2 SE − 0.2 P 2 SEt 2 SEt c. Max Pressure: P = or P = using O.D. KD0 + 2t ( K − 0.1) KD + 0.2t d. An acceptable approximation of a 2:1 ellipsoidal head is one with a knuckle radius of 0.17D and spherical radius of .90D. 2. Torispherical Heads: .885 PL SEt a. t = or P = when the knuckle radius (r/L) > 6% of crown SE − 0.1P .885L + 0.1t radius, L/D < 1; t/L>0.002 b. For general torospherical heads where L
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3. Hemispherical Heads: Thickness is not to exceed 0.356L or P does not exceed 0.665SE PL 2SEt a. t = or P = 2 SE − 0.2 P L + 0.2t 4. Conical Heads and Sections (w/o transition knuckle) PD 2 SEt 2 cos α a. t = or P = 2 cos α (2 SE − 0.6 P ) D + 1.2t cos α 5. Toriconical Heads and Sections: knuckle radius neither less than 6% of O.D. nor less than 3x knuckle a. t for the cone is determined by equation 4 above using Di in place of D. Di b. t for the knuckle is determined by equation 3 with the substitution L = 2 cos α
UG-34 Unstayed Flat Heads and Covers Definitions C: a factor depending on attachment method (see UG-34 (d)). This factor includes a 0.667 factor increasing allowable stress by 1.5S. d: diameter as indicated in fig UG-34 (pg39 BPVC) adjusted for corrosion allowance. Note that ‘d’ does does not correspond to the cover diameter, rather it corresponds to the diameter subject to pressure, in. E: joint efficiency, equals 1.0 unless the head is multi-piece. hG: gasket moment arm, in. m: ratio of tr/ts, dimensionless. P: internal design pressure, psi. S: maximum allowable stress in tension, psi. t: minimum required thickness of flat head or cover, in. tr: required thickness of seamless shell, for pressure, in. ts: nominal thickness of shell, in. W: total bolt load, lbf.
Equations 1. Flat unstayed circular heads, covers and blind flanges CP SEt 2 a. t = d or P = SE Cd 2 b. Not for use where attachment is by bolt such that edge moments are present. c. For a seal plate C = 0.33 per fig UG-34(h). See UG34 (d) for less conservative factors. d. tr= required seamless shell thickness; ts = required shell thickness 2. Flat unstayed circular flanges attached by bolt causing edge moments CP 1.9WhG a. t = d ; W being calculated in accordance with formulas 3 & 4 of + SE SEd 3 Appendix 2 of the Code
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UG-37 Reinforcement Required for Openings in Shells and Heads Reinforcement is not required if: A ≥ A1 + A2 + A3 + A41 + A42 + A43 + A5 where A42 and A5 are 0 because no reinforcement is added where each of the areas must fall within the limits of reinforcement as described in UG-40. A: Total cross sectional area of opening in vessel. Includes nozzle area if Sn/Sv < 1.0 A1: Area in excess thickness of vessel within the limits of reinforcement A2: Area in excess thickness of nozzle outward of vessel within the limits of reinforcement. A3: Area in excess thickness of vessel penetrating vessel within the limits of reinforcement. A41: Outward nozzle weld area. A42: Outward reinforcement weld area. A43: Inward nozzle weld area A5: Reinforcement thickness within the limits of reinforcement NOTE: All excess areas A1-A4x do not include corrosion allowance. A5 is NOT affected by corrosion allowance. NOTE: UG-36 allows exemptions for certain openings. Usually openings of Ø2⅜” are exempt for shells of t>⅜” and in some cases openings to Ø3½” are exempt.
UG-40 Limits of Reinforcement 1. Parallel to the vessel wall (i.e. body pipe) the reinforcement limit as measured from the centerline of the opening is the greater of: a. The finished diameter d of the opening (i.e. non penetrating nozzle) b. The sum of the finished radius r, vessel thickness t, and nozzle thickness tn. 2. Perpendicular to the vessel wall (i.e. along the nozzle wall) the reinforcement limit as measured from the vessel surface the lesser of: a. Two and a half times the vessel wall thickness, 2.5 t b. Two and a half times the vessel wall thickness, 2.5 t + te.
UG-98 & UG-99 MAWP, Test Requirements, Design Pressure 1. UG-98: Maximum Allowable Working Pressure (MAWP) is the maximum pressure allowable at the top of the vessel considered in concert with the specified temperature at that pressure. 2. UG-99 Test Requirements: Normal test requirements include a test at 1.3 of the design pressure (was 1.5 until 1999) [times the lowest ratio of allowable stress at test temp to allowable at design temp]: S Pt = 1.3 × all / test S all / design NOTE: The test pressure for ASME BPVC is different from API 610, thus the pressure to be used 1.5 for an ASME BPVC design will be figured from Pdesign = MAWP * . 1.3
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UCS-66 Minimum Design Metal Temperature (MDMT) 1. Minimum Design Metal Temperature is the minimum temperature for which the material is certified for the designed service without requiring impact testing.
UW-3 Joint Categories Joint Categories are used to specify allowed joint types and degree of inspection. They are listed from relatively high stress joints to relatively lower stress joints.
Category A Joints Longitudinal & spiral welded joints within a main shell, joints connecting shells and communicating chambers, transitions in diameter, any welded joint in formed heads, or flat walls, and circumferential welds between hemispherical heads and connecting shells.
Category B Joints Circumferential joints within any walls, nozzles, within transitions of diameter, or between communicating chambers, and circumferential welds connecting formed heads to a main shell except for hemispherical heads.
Category C Joints Joints at flat heads & flanges
Category D Joints Joints connecting nozzles to main shells, heads, spheres, and transitions of diameter.
UW-11 Radiography Pay special attention to UW11 (a) (7)
UW-12 Joint Efficiency Add UW 16 stuff ... Radiography
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UG-16 General Guidelines 1. The absolute minimum thickness of any vessel: t min = 116 in 2. Minimum thickness for water service fabricated from materials listed in table 3 and 1A in Section II Part D: t min = 3 32 in ; If temperatures below -20°F use allowables for 100°F (per UCS-23)
UG-27 Thickness of shells under internal pressure Definitions: t: minimum required thickness of shell, in. P: internal design pressure, psi. R: inside radius of the shell under consideration in the corroded condition, in. S: maximum allowable stress, psi. E: joint efficiency (see UW-12 for welded vessels; UG-53 for ligaments between openings)
Equations 1. Circumferential Stress (Longitudinal Joints): thickness not greater than half inside radius and P does not exceed 0.385SE PR PR0 a. Min Thickness: t = or t = based on O.D. SE − 0.6 P SE + 0.4 P SEt SEt b. Max Pressure: P = or P = based on O.D. R0 − 0.4t R + 0.6t 2. Longitudinal Stress (Circumferential Joint): thickness not greater than half inside radius and P does not exceed 1.25SE PR a. Min Thickness: t = 2 SE + 0.4 P 2SEt b. Max Pressure: P = R − 0.4t c. To be used only when Ecirc for the circumferential joint is less half of Elong. 3. Spherical Shells: Thickness does not exceed 0.356R and P does not exceed 0.665SE PR PR0 a. Min Thickness: t = or t = based on O.D. 2 SE − 0.2 P 2 SE + 0.8 P 2 SEt 2 SEt b. Max Pressure: P = or P = based on O.D. R0 − 0.8t R + 0.2t
Page 1 of 5
UG-32 Thickness of Formed Heads and Sections with Pressure on Concave Side Definitions: t: minimum required thickness of shell, in. P: internal design pressure, psi. D: Inside diameter of the head skirt; inside length of major axis for ellipsoidal head; Inside diameter of a conical head at the point under consideration perpendicular to longitudinal axis in the corroded condition, in. Di: Inside Diameter of conical portion of toriconical head at tangent to knuckle; Di = D − 2r (1 − cos α ) r: inside knuckle radius, in S: maximum allowable stress, psi. E: joint efficiency (see UW-12 for welded vessels) L: inside spherical or crown radius, in. α: half of the included (apex) angle of the cone at center line of the head
Equations: 1. Ellipsoidal Heads: ½ of minor axis equals ¼ of the inside diameter; 2:1 Ellipsoidal Head 2 1 D K = 2 + a. Shape Factor: 6 2h PDo K PDK b. Min Thickness: t = or t = based on O.D. 2 SE − 2 P( K − 0.1) 2 SE − 0.2 P 2 SEt 2 SEt c. Max Pressure: P = or P = using O.D. KD0 + 2t ( K − 0.1) KD + 0.2t d. An acceptable approximation of a 2:1 ellipsoidal head is one with a knuckle radius of 0.17D and spherical radius of .90D. 2. Torispherical Heads: .885 PL SEt a. t = or P = when the knuckle radius (r/L) > 6% of crown SE − 0.1P .885L + 0.1t radius, L/D < 1; t/L>0.002 b. For general torospherical heads where L
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3. Hemispherical Heads: Thickness is not to exceed 0.356L or P does not exceed 0.665SE PL 2SEt a. t = or P = 2 SE − 0.2 P L + 0.2t 4. Conical Heads and Sections (w/o transition knuckle) PD 2 SEt 2 cos α a. t = or P = 2 cos α (2 SE − 0.6 P ) D + 1.2t cos α 5. Toriconical Heads and Sections: knuckle radius neither less than 6% of O.D. nor less than 3x knuckle a. t for the cone is determined by equation 4 above using Di in place of D. Di b. t for the knuckle is determined by equation 3 with the substitution L = 2 cos α
UG-34 Unstayed Flat Heads and Covers Definitions C: a factor depending on attachment method (see UG-34 (d)). This factor includes a 0.667 factor increasing allowable stress by 1.5S. d: diameter as indicated in fig UG-34 (pg39 BPVC) adjusted for corrosion allowance. Note that ‘d’ does does not correspond to the cover diameter, rather it corresponds to the diameter subject to pressure, in. E: joint efficiency, equals 1.0 unless the head is multi-piece. hG: gasket moment arm, in. m: ratio of tr/ts, dimensionless. P: internal design pressure, psi. S: maximum allowable stress in tension, psi. t: minimum required thickness of flat head or cover, in. tr: required thickness of seamless shell, for pressure, in. ts: nominal thickness of shell, in. W: total bolt load, lbf.
Equations 1. Flat unstayed circular heads, covers and blind flanges CP SEt 2 a. t = d or P = SE Cd 2 b. Not for use where attachment is by bolt such that edge moments are present. c. For a seal plate C = 0.33 per fig UG-34(h). See UG34 (d) for less conservative factors. d. tr= required seamless shell thickness; ts = required shell thickness 2. Flat unstayed circular flanges attached by bolt causing edge moments CP 1.9WhG a. t = d ; W being calculated in accordance with formulas 3 & 4 of + SE SEd 3 Appendix 2 of the Code
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UG-37 Reinforcement Required for Openings in Shells and Heads Reinforcement is not required if: A ≥ A1 + A2 + A3 + A41 + A42 + A43 + A5 where A42 and A5 are 0 because no reinforcement is added where each of the areas must fall within the limits of reinforcement as described in UG-40. A: Total cross sectional area of opening in vessel. Includes nozzle area if Sn/Sv < 1.0 A1: Area in excess thickness of vessel within the limits of reinforcement A2: Area in excess thickness of nozzle outward of vessel within the limits of reinforcement. A3: Area in excess thickness of vessel penetrating vessel within the limits of reinforcement. A41: Outward nozzle weld area. A42: Outward reinforcement weld area. A43: Inward nozzle weld area A5: Reinforcement thickness within the limits of reinforcement NOTE: All excess areas A1-A4x do not include corrosion allowance. A5 is NOT affected by corrosion allowance. NOTE: UG-36 allows exemptions for certain openings. Usually openings of Ø2⅜” are exempt for shells of t>⅜” and in some cases openings to Ø3½” are exempt.
UG-40 Limits of Reinforcement 1. Parallel to the vessel wall (i.e. body pipe) the reinforcement limit as measured from the centerline of the opening is the greater of: a. The finished diameter d of the opening (i.e. non penetrating nozzle) b. The sum of the finished radius r, vessel thickness t, and nozzle thickness tn. 2. Perpendicular to the vessel wall (i.e. along the nozzle wall) the reinforcement limit as measured from the vessel surface the lesser of: a. Two and a half times the vessel wall thickness, 2.5 t b. Two and a half times the vessel wall thickness, 2.5 t + te.
UG-98 & UG-99 MAWP, Test Requirements, Design Pressure 1. UG-98: Maximum Allowable Working Pressure (MAWP) is the maximum pressure allowable at the top of the vessel considered in concert with the specified temperature at that pressure. 2. UG-99 Test Requirements: Normal test requirements include a test at 1.3 of the design pressure (was 1.5 until 1999) [times the lowest ratio of allowable stress at test temp to allowable at design temp]: S Pt = 1.3 × all / test S all / design NOTE: The test pressure for ASME BPVC is different from API 610, thus the pressure to be used 1.5 for an ASME BPVC design will be figured from Pdesign = MAWP * . 1.3
Page 4 of 5
UCS-66 Minimum Design Metal Temperature (MDMT) 1. Minimum Design Metal Temperature is the minimum temperature for which the material is certified for the designed service without requiring impact testing.
UW-3 Joint Categories Joint Categories are used to specify allowed joint types and degree of inspection. They are listed from relatively high stress joints to relatively lower stress joints.
Category A Joints Longitudinal & spiral welded joints within a main shell, joints connecting shells and communicating chambers, transitions in diameter, any welded joint in formed heads, or flat walls, and circumferential welds between hemispherical heads and connecting shells.
Category B Joints Circumferential joints within any walls, nozzles, within transitions of diameter, or between communicating chambers, and circumferential welds connecting formed heads to a main shell except for hemispherical heads.
Category C Joints Joints at flat heads & flanges
Category D Joints Joints connecting nozzles to main shells, heads, spheres, and transitions of diameter.
UW-11 Radiography Pay special attention to UW11 (a) (7)
UW-12 Joint Efficiency
Page 5 of 5
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