SPREADSHEETS SERIES No. 0029SD

Wall Thickness Calculation of Ellipsoidal Head Under Internal Pressure

ASME Section VIII Div 1 - Appendix 1-4 - Formulas for the Design of Formed Heads Under Internal Pressure ⁽⁹⁾

Appendix 1-4(c) Ellipsoidal Heads

(Enter values in yellow cells for calculations)

DATA INPUT

Design Conditions

Material

Design Pressure, Pd =

psig

Head Material Specification ⁽¹⁾⁽²⁾

Design Temperature, Td =

°F

Allowable Stress Head, S =

psi

Welding Efficiency, E =

Dimensions

See Table UW-12

Inside Diameter of the head skirt, Di =

in.

Corrosion Allowance, CA =

in.

Nominal wall thickness before forming ⁽³⁾, tn =

in.

Minimum specified thickness after forming ⁽⁴⁾, tf =

in.

Minimum required thickness after forming, tr =

in.

Inside depth of the ellipsoidal head with corrosion removed, h ⁽⁵⁾ =

in.

Head Proportion = Di/2h ⁽⁶⁾ =

Outside Diameter of the head skirt, Do =

in.

Straight skirt length ⁽⁷⁾⁽⁸⁾, SK =

in.

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)

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

(4)

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.

(5)

For Ellipsoidal head 2:1 h = DI/4

(6)

Head Proportion = Di/2h (Ratio between 3 and 1)

(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.

(9)

The formula for the typical 2:1 elliptical head is listed in paragraph UG-32(c) of ASME Code Section VIII, Division 1. The general formula for all elliptical heads within the dimensional scope is addressed in Appendix 1-4. Factor K varies depending on the shape of the ellipse.

CALCULATIONS

Ellipsoidal Head

with tf/L ≥ 0.002

Thickness after forming adjusted for corrosion, nt =

in.

nt = tf-CA

Inner diameter with corrosion removed, D =

in.

D = Di + 2CA

Inside depth of the ellipsoidal head with corrosion removed, h

in.

(For Ellipsoidal head 2:1 h = D/4)

Head Proportion = D/2h

Factor K ⁽¹⁰⁾

(The value is obtained from Table 1-4.1)

Factor K1

(The value is obtained from Table UG-37)

Inside spherical or crown radius, L = k1D

in.

Inside knuckle radius ⁽¹¹⁾, r =

in.

Wall Thickness [APPENDIX 1-4(c)]

Minimum required thickness after forming, t =

in.

t =

P D K

2 S E - 0.2 P

Minimum required thickness after forming, tr =

in.

t_r =

P D K

+ CA

2 S E - 0.2 P

Check If tr ≤ tf

Maximum allowable working pressure [APPENDIX 1-4(c)]

Maximum allowable working pressure for Ellipsoidal Head, MAWP =

psig

MAWP =

2 S E nt

K D + 0.2 nt

Check If MAWP ≥ P

Check

Limitations: tf/L ≥ 0.002

tf/L ≥ 0.002

Volume =

ft³

V =

(

π Di³

π Di² SK

)

/ 1728

Weight =

lbs

W =

((

π (Do³-Di³)

π (Do²-Di²) SK

)

/ 1728) ρm

Note:

(10)

As per ASME VIII-1 EndNote 90. Ellipsoidal heads designed under K > 1.0 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 as shown in the appropriate table (see UG-23).

(11)

As per UG-32(c) An acceptable approximation of a 2:1 ellipsoidal head is one with a knuckle radius of 0.17D and a spherical radius of 0.90D.

RESULT

Design Conditions

Design Pressure, Pd =

Design Temperature, Td =

°F

Material

Head Material

Dimensions

Outside Diameter, Do =

in.

Nominal wall thickness before forming, tn =

in.

Thickness after forming, tf =

in.

Inner Diameter, Di =

in.

Inside spherical or crown radius, L =

in.

Inside knuckle radius, r =

in.

For Ellipsoidal head 2:1 h =

in.

Maximum allowable working pressure, MAWP =

psig

Volume =

ft³

Weight =

lbs

Discussion and References

Information about Wall Thickness Calculation of Ellipsoidal Head 2:1 Under Internal Pressure

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

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

ASME Section VIII Div 1 Table UG-37 Value of Spherical Radius Factor K1

ASME Section VIII Div 1 Table 1-4.1 Value of Factor K

Ellipsoidal Head with ts/L ≥ 0.002

Minimum required thickness [ASME VIII.1 App 1-4(c)]

t =

P D K

2 S E - 0.2 P

Internal design pressure [ASME VIII.1 App 1-4(c)]

P =

2 S E t

K D + 0.2 t

Where:

P: Design Pressure, in bar (psig)

D: Inside Diameter (in a corroded condition), in mm (inches)

L = K1D for ellipsoidal heads in which K1 is obtained from Table UG-37.

S: Allowable Stress, in Mpa (psi)

E: Welding Efficiency

K: a factor in the equations for ellipsoidal heads depending on the head

proportion D/2h. K is obtained from Table 1-4.1

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

r = inside knuckle radius, in mm (inches)

Feactures

- High Availability
- Supports higher pressures than the Torispherical
- Ellipsoidal head has one-half the minor axis, h, equal to one-fourth of the inside diameter of the head skirt, D
- An acceptable approximation of a 2:1 ellipsoidal head is one with a knuckle radius of 0.17D and a spherical radius of 0.90D
- For heads with ts/L < 0.002 see Appendix. 1-4 (f)