SPREADSHEETS SERIES No. 0031SD

Wall Thickness Calculation of Torispherical Head Under Internal Pressure

ASME Section VIII Div 1 - Appendix 1-4 - Formulas for the Design of Heads Formed Under Internal Pressure

Appendix 1-4(d) Torispherical Heads with ts /L ≥ 0,002

(Enter values in yellow cells for calculations and in blue cells as information)

DATA INPUT

Design Conditions

Material

Design Pressure, Pd =

psig

Head Material

Head Material Type

Design Temperature, Td =

°F

Allowable Stress Head ⁽¹⁾, S =

psi

Joint efficiency, E =

Dimensions

Inner Diameter, Di =

in.

Corrosion Allowance, CA =

in.

Nominal wall thickness before forming ⁽²⁾, tn =

in.

Thickness after forming ⁽³⁾, tf =

in.

Inside knuckle radius ⁽⁴⁾, r =

in.

Inside knuckle radius (r = 0.06Do) =

Inside knuckle radius (r = 3tf) =

The inside knuckle radius shall be not less than 0.06Do but in no case less than 3tf =

Outside Diameter, Do =

in.

Inside spherical or crown radius^(4), L =

in.

Straight skirt length ⁽⁵⁾⁽⁶⁾, SK =

in.

Check If tr ≤ tf

Notes:

(1)

As per UG-32(d) Torispherical heads made of materials having a specified minimum tensile strength exceeding 70,000 psi (485 MPa) shall be designed using a value of S equal to 20,000 psi (138 MPa) at room temperature and reduced in proportion to the reduction in maximum allowable stress values at tempera ture for the material as shown in the appropriate table (see UG-23).

(2)

It is recommended a nominal thickness before forming 15% higher than the minimum specified thickness to ensure after forming thickness is above it.

(3)

As per UG-79 (d)(3) The reduction in weld thickness after forming shall not exceed 1/32 in. (1 mm) or 10% of the nominal thickness of the adjoining surface, whichever is less.

(4)

As per UG-32 (i) The inside crown radius to which an unstayed head is dished shall be not greater than the outside diameter of the skirt of the head. The inside knuckle radius of a torispherical head shall be not less than 6% of the outside diameter of the skirt of the head but in no case less than 3 times the head thickness.

(5)

As per UG-32(k) All formed heads, thicker than the shell and concave to pressure, intended for butt welded attachment, shall have a skirt length sufficient to meet the requirements of Figure UW-13.1, when a tapered transition is required. All formed heads concave to pressure and intended for butt welded attachment need not have an integral skirt when the thickness of the head is equal to or less than the thickness of the shell. When a skirt is provided, its thickness shall be at least that required for a seamless shell of the same inside diameter.

(6)

As per UG-32(l) Heads concave to pressure,intended for attachment by brazing, shall have a skirt length sufficient to meet the requirements for circumferential joints in Part UB.

CALCULATIONS

Torispherical Head

with tf/L ≥ 0.002

Thickness after forming adjusted for corrosion, nt =

in.

nt = tf - CA

Inner diameter of the skirt adjusted for corrosion, Lc =

in.

Lc = L + CA

Inside knuckle radius adjusted for corrosion, rc =

in.

rc = r + CA

Ratio of the inside crown radius to the inside knuckle radius, Lc/rc ⁽⁷⁾ =

Factor M =

M =

1/4 (3 +

(

)

0,5

)

Wall Thickness [APPENDIX 1-4(d)]

Minimum required thickness, tr =

in.

t =

P Lc M

2 S E - 0.2 P

Check If tr ≤ tf

t_r =

P Lc M

+ CA

2 S E - 0.2 P

Maximum working pressure [APPENDIX 1-4(d)]

Maximum working pressure for Torispherical Head, Pmax =

psig

Check If Pmax ≥ P

P =

2 S E nt

Lc M + 0.2 nt

Check

Limitations: tf/L ≥ 0.002

tf/L ≥ 0.002

Volume & Weight Calculation

Inside radius of the head skirt, Ri =

in.

R = Di/2

Inside spherical or crown radius, Li =

in.

Inside knuckle radius, ri =

in.

Li/Ri =

2ri/Ri =

Coefficient Ki =

K i =

- [(

)(

2ri

)]

0,5

Outside radius of the head skirt, Ro =

in.

R = Do/2

Outside spherical or crown radius, Lo =

in.

Outside knuckle radius, ro =

in.

Lo/Ro =

2ro/Ro =

Coefficient Ko =

Ko =

- [(

)(

2ro

)]

0,5

Inside Volume, Vi =

ft³

Vi =

(

π Di³ Ki

π Di² SK

)

/ 1728

Outside Volume, Vo =

ft³

Vo =

(

π Do³ Ko

π Do² SK

)

/ 1728

Weight =

lbs

W =

(Vo - Vi) ρm

Note:

(7)

As per note 1 in Table 1-4.2, L/r = 16,66 is the maximum ratio allowed by UG-32(i) when L equals the outside diameter of the skirt of the head.

RESULT

Design Conditions

Design Pressure, Pd =

psig

Design Temperature, Td =

°F

Material

Head Material

Dimensions

Outside Diameter, Do =

in.

Nominal wall thickness before forming, tn =

in.

Thickness after forming, tf =

in.

Inside spherical or crown radius, L =

in.

Inside knuckle radius, r =

in.

Maximum working pressure =

psig

Inside Volume =

ft³

Outside Volume =

ft³

Weight =

lbs

Discussion and References

Information about Wall Thickness Calculation of Torispherical Head Under Internal Pressure

ASME Section VIII Div 1 Appendix 1-4(d)

Standards, Paragraph & Appendix

ASME BPVC.VIII.1 Rules for Construction of Pressure Vessels

ASME BPVC SEC II-D Material Properties

ASME Section VIII Div 1 Appendix 1-4 Formulas for the Design of Formed Heads Under Internal Pressure

Torispherical Head with ts/L ≥ 0.002

Minimum required thickness [ASME VIII APP 1-4]

t =

P L M

2 S E - 0.2 P

Internal design pressure [APP 1-4]

P =

S E t

L M + 0.2 t

Where:

P: Design Pressure, in barg (psig)

S: Allowable Stress, in MPa (psi)

E: Welding Efficiency

L: Inside crown radius not greater than the outside diameter of the skirt, in mm (inches)

M: a factor in the equations for torispherical heads depending on the head

proportion L/r

M =

1/4 (3 +

(

)

0,5

)

t: Minimum required thickness of head after forming, in mm (inches) (*)

ts: Minimum specified thickness of head after forming, en mm (in.) ts shall be ≥ t

(*) The required thickness of a torispherical head for the case in which the inside crown radius to which an unstayed head is dished shall be not greater than the outside diameter of the skirt of the head. The inside knuckle radius of a torispherical head shall be not less than 6% of the outside diameter of the skirt of the head.

r = inside knuckle radius, in mm (inches)

Feactures

- High Availability
- Limitations: ts/ L ≥ 0.002, L ≤ D+2t, r ≥ 0.06*(D+2t)
- For t calculation will be considered L = D
- For heads with ts/L < 0.002, see Appendix. 1-4 (f)

Torispherical heads made of materials having a specified minimum tensile strength exceeding 70,000 psi (485 MPa) shall be designed using a value of S equal to 20,000 psi (138 MPa) at room temperature and reduced in proportion to the reduction in maximum allowable stress values at temperature for the material (see UG-23).