SPREADSHEETS SERIES No. 0028SB

Wall Thickness Calculation of Conical Section Under Internal Pressure

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

UG-32(f) Conical Heads and Sections (Without Transition Knuckle)

(Enter values in yellow cells for calculations)

DATA INPUT

Design Conditions

Material

Design Pressure, Pd =

psig

Conical Section Material Specification ^{(1 to 7)}

Design Temperature, Td =

°F

Allowable Stress Conical Section, S =

psi

Welding Efficiency, E =

Dimensions

See Table UW-12

Large End Inside Diameter, Di =

in.

Corrosion Allowance, CA =

in.

Small End Inside Diameter, di =

in.

Undertolerance Allowance ^(8)(9)(10), U1 =

default value = 0

Nominal wall thickness, tn =

in.

Minimum required thickness (Large End), tr =

in.

Length of Conical Section, Lc =

in.

(Large End) If tr ≤ tn acceptable

(Small End) If tr ≤ tn acceptable

Notes:

(1)

S ≤ 66.66% of σy @ temp.

(2)

S > 66.66% but < 90% of σy @ temp.

(3)

(t ≤ 2¹/₂)

(4)

(2¹/₂ < t ≤ 4)

(5)

(4 < t ≤ 6)

(6)

Tensile strength of the Section IX reduced section tension test is not less than 100 ksi.

(7)

Tensile strength of the Section IX reduced tension test less than 100 ksi but not less than 95 ksi.

(8)

As per UG-16(c) Mill Undertolerance. Plate material shall be ordered not thinner than the design thickness. Vessels made of plate furnished with an undertolerance of not more than the smaller value of 0.01 in. (0.25 mm) or 6% of the ordered thickness may be used at the full design pressure for the thickness ordered. If the specification to which the plate is ordered allows a greater undertolerance, the ordered thickness of the materials shall be sufficiently greater than the design thickness so that the thickness of the material furnished is not more than the smaller of 0.01 in. (0.25 mm) or 6% under the design thickness.

(9)

As per UG-16(d) Pipe Undertolerance. If pipe or tube is ordered by its nominal wall thickness, the manufacturing undertolerance on wall thickness shall be taken into account except for nozzle wall reinforcement are a requirements in accordance with UG-37 and UG-40. The manufacturing undertolerances are given in the several pipe and tube specifications listed in the applicable Tables in Subsection C. After the minimum wall thickness is determined, it shall be increased by an amount sufficient to provide the manufacturing undertolerance allowed in the pipe or tube specification

(10)

If you are ordering a head or other such fitting that is formed from plate, such as an elliptical, torispherical head, etc, you do not need to include the undertolerance. You do need to account for thinning during the forming of the head. Calculations should be done based on the minimum thickness after forming. The vendor of such heads should provide that information.

CALCULATIONS

Conical Sections

Wall Thickness [ASME UG-32(f)]

Undertolerance thickness, U2 =

in.

U2 = tn*U1

Nominal thickness adjusted for corrosion and undertolerance, nt =

in.

nt = tn-CA-U2

Large End Inside diameter with corrosion & undertolerance removed, D =

in.

D = Di+2CA+2U₂

Small End Inside diameter with corrosion & undertolerance removed, d =

in.

d = di+2CA+2U₂

One‐half of the included (apex) angle of the cone, α ≤ 30ᵒ =

deg.

α =

arctan

(

0.5 (D - d)

)

Minimum required thickness (Large End), t =

in.

t =

P D

2 cos α (S E - 0.6 P)

Minimum required thickness (Large End), tr =

in.

tr =

P D

+ CA

2 cos α (S E - 0.6 P)

Nominal wall thickness, tn =

in.

Check If tr ≤ tn (Large End)

Minimum required thickness (Small End), t =

in.

t =

P d

2 cos α (S E - 0.6 P)

Minimum required thickness (Small End), tr =

in.

tr =

P d

+ CA

2 cos α (S E - 0.6 P)

Nominal wall thickness, tn =

in.

Check If tr ≤ tn (Small End)

Maximum allowable working pressure [ASME UG-32(f)]

Maximum allowable working pressure for Conical Sections, MAWP =

psig

MAWP =

2 S E nt cos α

D + 1.2 nt cos α

Inside Volume =

ft³

V_i =

1/3*π*Lc(R_i² + r_i² + R_ir_i ) / 1728

Outside Volume =

ft³

V_o =

1/3*π* Lc(R_o² + r_o² + R_or_o ) / 1728

Weight =

lbs

W =

(Vo - Vi) ρm

RESULT

Design Conditions

Design Pressure, Pd =

psig

Design Temperature, Td =

°F

Material

Conical Section Material

Dimensions

Large End Inside Diameter, Di =

in.

Small End Inside Diameter, di =

in.

Nominal wall thickness, tn =

in.

Length of Conical Section, Lc =

in.

Maximum allowable working pressure, MAWP =

psig

Inside Volume =

ft³

Outside Volume =

ft³

Weight =

lbs

Discussion and References

Information about Wall Thickness Calculation of Conical Section Under Internal Pressure

ASME Section VIII Div 1 paragraph UG-32(f)

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 paragraph UG-32 Formed Heads, and Sections, Pressure On Concave Side

Conical Sections (Without Transition Knuckle)

Minimum required thickness [ASME UG-32(f)]

t =

P D

2 Cos α (S E - 0.6 P)

Internal design pressure [ASME UG-32(f)]

P =

2 S E t cos α

D + 1.2 t cos α

Where:

P: Design Pressure, in PSIG

S: Allowable Stress, in PSI

E: Welding Efficiency

D: Inside diameter of a conical section at the point under consideration, measured perpendicular to the longitudinal axis, in inches

t: Minimum required thickness, in inches

α = one‐half of the included (apex) angle of the cone at the centerline of the section

Feactures

- Used as transitions in diameter change of vessels.
- Limitations: α ≤ 30°
- A reinforcing ring shall be provided when required by the rule in 1-5(d) and 1-5(e).