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Wall
Thickness Calculation of Ellipsoidal Head 2:1 Under Internal Pressure
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ASME
Section VIII Div 1 - Appendix 1-4 - Formulas for the Design of Heads Formed
Under Internal Pressure
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(Enter values in yellow cells for calculations and
in blue cells as information)
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DATA INPUT
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Design Conditions
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Material
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Design Pressure, Pd =
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psig
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Head
Material Specification
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Head
Material Type
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Design Temperature, Td =
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°F
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Allowable
Stress Head, S =
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psi
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Joint efficiency, E =
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Dimensions
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Inner
Diameter, Di =
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in.
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Corrosion Allowance, CA =
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in.
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Nominal wall
thickness before forming, tn =
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in.
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Thickness
after forming (1),
tf =
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in.
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Outside
Diameter, Do =
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in.
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Straight skirt length (2)(3), SK =
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in.
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Check If tr
≤ tf
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Notes:
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(1) 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.
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(2) 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.
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(3) 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.
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CALCULATIONS
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Ellipsoidal Head 2:1
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with tf/L ≥ 0.002
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Thickness after forming adjusted for corrosion, nt =
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in.
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nt = tf-CA
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Inner diameter with corrosion removed, D =
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in.
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D = Di + 2CA
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Inside depth of the
ellipsoidal head with corrosion removed, h
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in.
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For Ellipsoidal head 2:1 h = D/4
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Head Proportion = D/2h
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Factor K
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(The value is obtained from Table 1-4.1)
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Factor K1
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(The value is obtained from Table UG-37)
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Inside spherical or crown radius, L = k1D
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in.
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Inside knuckle radius (4), r =
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in.
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Wall Thickness
[APPENDIX 1-4(c)]
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Minimum required thickness, tr =
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in.
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tr =
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P D K
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+ CA
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2 S E - 0.2 P
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Check If tr ≤ tf
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Maximum working pressure
[APPENDIX 1-4(c)]
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Maximum working pressure for Ellipsoidal Head, Pmax =
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psig
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P =
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2 S E nt
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K D + 0.2 nt
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Check If Pmax ≥ P
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Check
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Limitations: tf/L ≥ 0.002
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tf/L ≥ 0.002
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Volume =
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ft³
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V =
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(
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π Di³
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+
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π Di² SK
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/ 1728
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24
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4
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Weight =
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lbs
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W =
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((
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π (Do³-Di³)
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+
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π (Do²-Di²) SK
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/
1728) ρm
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24
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4
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Note:
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(4) 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.
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RESULT
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Design Conditions
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Design Pressure, Pd =
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Design Temperature, Td =
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°F
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Material
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Head Material
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Dimensions
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Outside Diameter, Do =
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in.
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Nominal wall thickness before forming, tn =
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in.
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Thickness after forming, tf =
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in.
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Inner Diameter, Di =
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in.
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Inside spherical or crown radius, L =
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in.
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Inside knuckle radius, r =
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in.
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For Ellipsoidal head 2:1 h =
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in.
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Maximum working pressure =
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psig
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Volume =
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ft³
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Weight =
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lbs
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