SPREADSHEETS SERIES No. 0031SA

Wall Thickness Calculation of Torispherical Head Under Internal Pressure

ASME Section VIII Div 1 - UG-32 - Formed Heads, and Sections, Pressure on Concave Side

UG-32(d) Torispherical Heads with ts /L ≥ 0,002

(Enter values in yellow cells for calculations)

DATA INPUT

Design Conditions

Material

Design Pressure, Pd =

barg

Head Material Specification ⁽¹⁾⁽²⁾

Design Temperature, Td =

°C

Allowable Stress Head ⁽³⁾, S =

MPa

Welding Efficiency, E =

Dimensions

See Table UW-12

Inside diameter of the head skirt, Di =

Corrosion Allowance, CA =

Nominal wall thickness before forming ⁽⁴⁾, tn =

Minimum specified thickness after forming ⁽⁵⁾, tf =

Minimum required thickness after forming, tr =

Outside diameter of the head skirt, Do =

Inside knuckle radius is 6% of the inside crown radius ⁽⁶⁾, r =

Check inside knuckle radius is in no case less than 3 times the head thickness (t)

Straight skirt length ⁽⁷⁾⁽⁸⁾, SK =

Check If tr ≤ tn

Check If tr ≤ tf

Notes:

(1)

S ≤ 66.66% of σy @ temp.

(2)

S > 66.66% but < 90% of σy @ temp.

(3)

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).

(4)

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

(5)

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.

(6)

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.

(7)

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.

(8)

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 =

nt = tf-CA

Inside spherical or crown radius adjusted for corrosion, Lc ⁽⁹⁾ =

Lc = Do + CA

Inside knuckle radius, r =

Wall Thickness [UG-32(d)]

Minimum required thickness after forming, t =

t =

0.885 P Lc

S E - 0.1 P

Minimum required thickness after forming, tr =

t_r =

0.885 P Lc

+ CA

S E - 0.1 P

Check If tr ≤ tf

Maximum allowable working pressure [UG-32(d)]

Maximum allowable working pressure for Torispherical Head, MAWP =

barg

MAWP =

S E nt

0.885 Lc + 0.1 nt

Check If MAWP ≥ P

Check

Limitations: tf/L ≥ 0.002

Inside Volume =

m³

V =

(

0.0847 Di³

π Di² SK

)

/ 10⁹

Weight =

W =

((

0.0847 (Do³-Di³)

π (Do²-Di²) SK

)

/ 10⁹) ρm

Note:

(9)

As per UG-32(d) the inside crown radius shall be equals the outside diameter of the skirt [see UG-32(i)]

RESULT

Design Conditions

Design Pressure, Pd =

barg

Design Temperature, Td =

°C

Material

Head Material

Dimensions

Outside diameter of the head skirt, Do =

Nominal wall thickness before forming, tn =

Thickness after forming, tf =

Inside spherical or crown radius, L =

mm (L = Do)

Inside knuckle radius, r =

Maximum allowable working pressure, MAWP =

barg

Inside Volume =

m³

Weight =

Discussion and References

Information about Wall Thickness Calculation of Torispherical Head Under Internal Pressure

ASME Section VIII Div 1 UG-32(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 - UG-32 - Formed Heads, and Sections, Pressure on Concave Side

Torispherical Head with ts/L ≥ 0.002

Minimum required thickness [ASME VIII UG-32(d)]

t =

0.885 P L

S E - 0.1 P

Internal design pressure [UG-32(d)]

P =

S E t

0.885 L + 0.1 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)

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).