Design Calculations for High Pressure Vessel - Above 1000PSI

Dear cadtrans

The following equations with its related terms are derived from ASME BPVC, Section VIII, Div. 1, which you can proceed the required design:

♦ UG-27 Thickness of Shells Under Internal Pressure (In terms of inside diameter)

where, t = Min. required thickness of shell (in.)

R = Inside radius of shell (in.)

P = Internal design pressure, or max. allowable working pressure (taking into consideration the static head of fluid) (psi)

S = Max. allowable stress of shell material (psi)

E = Min. joint efficiency, percent

UG-27(c) Cylindrical Shells :

UG-27(C)(1) Circumferential (hoop) Stress (Longitudinal Joints) t < 0.5 R or P < 0.385 SE : t = PR/(SE-0.6P)

UG-27(C)(2) Longitudinal Stress (Circumferential Joints) t < 0.5 R or P < 1.25 SE : t = PR/(2SE+0.4P)

UG-27(d) Spherical Shells : t < 0.356 R or P < 0.665 SE : t = PR/(2SE-0.2P)

 UG-32 Formed Heads, and Sections, Pressure on Concave Side

where, t = Min. required thickness of head (in.)

D = Inside dia. of head skirt (in.)

P = Internal design pressure, or max. allowable working pressure (taking into consideration the static head of fluid) (psi)

S = Max. allowable stress of shell material ((psi)

L = Inside spherical or crown radius = K₁ D (in.) [APP. 1-4(b)]

K₁= Spherical radius factor, [see Table UG-37]

UG-32(d) Ellipsoidal Heads :

where, K = Factor depends on ratio of major to minor axis D/2h= 1/6 [2 + (D/2h)²] …. [see Table 1-4.1] & [APP. 1-4(c)] : t = PDK/(2SE-0.2P)

UG-32(e) Torispherical Heads : [For knuckle radius 6% L and L = OD of skirt]

Torispherical heads made of materials having a specified min. tensile strength > 80 000 psi, shall be designed using S = 20 000 psi at room temp. and reduced in proportion to the reduction in max. allowable stress values at temp. for the material. [see UG-23)]: t = 0.885PL/(SE-0.1P)

UG-32(f) Hemispherical Heads : t < 0.356 L or P < 0.665 SE : t = PR/(2SE-0.2P)

UG-32(g) Conical Heads and Sections : where a = 0.5 induced angle of cone at centerline of the head, and a < 30 deg : t = PD/2 cos a (SE-0.6P) ..... (4)

UG-32(h) Toriconical Heads and Sections :

● The required thickness of the conical portion (knuckle radius > 6% OD of head skirt & > 3 knuckle thk.) shall be determined by Formula (4) of UG-32 (g) above, using D_i in place of D : t = PD_i/2 cos a (SE-0.6P)

● The required thickness of the knuckle shall be determined by Formula (3) of Appendix 1-4(d), in which,

L = D_i /(2 cos a) (in.)

L_o = Outside spherical or crown radius (in.)

D_i = ID of conical portion = D -2 r (1- cos a) (in.)

r = Inside knuckle radius (in.)

M = 1/4 [ 3 +ÖL/r ] …….. [Table 1-4.2]

t = PLM/(2SE-0.2P) and t = PL_oM/[2SE+P(M-0.2)] .... [App. 1-4(d)]

 APPENDIX-1 Supplementary Design Formulas

1.1 Thickness of Cylindrical and Spherical Shells under Internal pressure, in terms of outside diameter.

where, t = Min. required thickness of shell (in.)

D = ID of head skirt, or inside length of the major axis of ellipsoidal head, or ID of cone head (in.)

D_o = OD of head skirt or outside length of the major axis of ellipsoidal head, or OD of a cone (in.)

R_o = Do / 2 (in.)

P = Internal design pressure, or max. allowable working pressure (taking into consideration the static head of fluid) (psi)

S = Max. allowable stress of shell material (psi)

(1) For Cylindrical Shells : t = PR_o/(SE+0.4P)

(2) For Spherical Shells : t = PR_o/(2SE+0.8P)

1.4 Formulas for the Design of Formed Heads under Internal Pressure, in terms of outside diameter.

1.4(c) Ellipsoidal Heads^*:

Where, K = 1/6[2+(D/2h)²] and h = 0.5 minor axis of ellipsoidal head (in.):

t = PDK/(2SE-0.2P) .... (1) and t = PD_oK/[2SE+2P(K-0.1)] ..... (2)

* Ellipsoidal heads designed under K > 1.0 and all torispherical heads made of materials having a specified min. tensile strength > 80 000 psi shall be designed using a value of S = 20 000 psi at room temp. and reduced in proportion to the reduction in max. allowable stress values at temp. for the material as shown in the appropriate table (see UG-23).

1.4(d) Torispherical Heads :

where, L_o = Outside spherical or crown radius (in.),

M = 1/4 [ 3 +√L/r ] [Table 1-4.2] and L/r = Ratio of inside crown radius to the inside knuckle radius, in.: t = PLM/(2SE-0.2P) ... (3) and t = PL_oM/[(2SE+P(M- 0.2)] .... (4)

(f) Conical Heads : t = PD/[2 cos a (SE-0.6P)] ... (5) and t = PD_o/[2 cos a (SE+0.4P)] ... (6)

 APPENDIX-1 Supplementary Design Formulas

1.2 Thick Cylindrical Shells under Internal Pressure, in terms of inside and outside diameters.

where, t = Min. required thickness of shell, in.

R = Inside radius of shell course under consideration, in.

R_o = Outside radius of shell course under consideration, in.

P = Internal design pressure, or max. allowable working pressure (taking into consideration the static head of fluid), psi

S = Max. allowable stress of shell material, psi

(a)(1) Circumferential Stress (longitudinal joints) : t > 0.5 R or P > 0.385 SE : t = R (Z^1/2 – 1) = R_o (Z^1/2 – 1)/ Z^1/2, where, Z = (SE+P)/(SE-P)

(a)(2) longitudinal Stress (circumferential joints) : t > 0.5 R or P > 1.25 SE : t = R (Z^1/2 – 1) = R_o (Z^1/2 – 1)/ Z^1/2, where, Z = (P/SE)+1

1.3 Thick Spherical Shells under Internal Pressure, in terms of inside and outside diameters.

For wholly spherical vessel and hemispherical head : t > 0.356 R or P >0.665 SE : t = R (Y^1/3 – 1) = R_o (Y^1/3 – 1)/ Y^1/3, where, Y = 2(SE+P)/(2SE–P)