SPREADSHEETS SERIES No. 0035SA

Wall Thickness Calculation of Toriconical Heads Under Internal Pressure

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

UG-32(g) Toriconical Heads and Sections (With Transition Knuckle)

(Enter values in yellow cells for calculations)

DATA INPUT

Design Conditions

Material

Design Pressure, Pd =

barg

Toriconical Section Material Specification ⁽¹⁾⁽²⁾

Design Temperature, Td =

°C

Allowable Stress Toriconical Section, S =

MPa

Welding Efficiency, E =

Dimensions

See Table UW-12

Large End Inside Diameter, D =

Small End Inside Diameter, d =

Corrosion Allowance, CA =

Nominal wall thickness before forming ⁽⁶⁾, tn =

Undertolerance Allowance ^(3)(4)(5), U1 =

default value = 0

Minimum specified thickness after forming ⁽⁷⁾, tf =

Minimum required thickness Cone Section (Large End), tr =

(Large End) Inside knuckle radius ⁽⁸⁾, R =

Check inside knuckle radius is neither less than 6% of the outside diameter of the head skirt

Check inside knuckle radius of a torispherical head shall be not less than 3 times the knuckle thickness (t_k)

(Small End) Inside knuckle radius ⁽⁸⁾, r =

Check inside knuckle radius is neither less than 6% of the outside diameter of the head skirt

Check inside knuckle radius of a torispherical head shall be not less than 3 times the knuckle thickness (t_k)

Outside diameter of the Large End, Do =

Outside diameter of the Small End, do =

Length of Conical Section, X =

( Large End) If t_r ≤ t_f acceptable

(Large End) If t_kr ≤ t_f acceptable

(Small End) If t_r ≤ t_f acceptable

(Small End) If t_kr ≤ t_f acceptable

Notes:

(1)

S ≤ 66.66% of σy @ temp.

(2)

S > 66.66% but < 90% of σy @ temp.

(3)

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.

(4)

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

(5)

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.

(6)

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

(7)

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.

(8)

As per UG-32(g) Toriconical Heads and Sections. The required thickness of the conical portion of a toriconical head or section, in which the knuckle radius is neither less than 6% of the outside diameter of the head skirt nor less than three times the knuckle thickness.

CALCULATIONS

Toriconical Heads

Wall Thickness [ASME UG-32(g)]

Undertolerance thickness, U2 =

U2 = tn*U1

Nominal thickness adjusted for corrosion and undertolerance, nt =

nt = tn-CA-U2

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

D_c = D+2CA+2U₂

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

d_c = d+2CA+2U₂

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

deg.

α =

arctan

(

0.5 (D_c - d_c)

)

(Large End) Inside knuckle radius with corrosion & undertolerance removed,R_c =

R_c = R+CA+U₂

(Small End) Inside knuckle radius with corrosion & undertolerance removed, r_c =

r_c = r+CA+U₂

(Large End) ID of the conical portion with corrosion & undertolerance removed, D_i =

Di = D_c−2R_c(1−cos α)

(Small End) ID of the conical portion with corrosion & undertolerance removed, d_i =

di = d_c−2r_c(1−cos α)

Minimum required thickness (Large End), t =

t =

P Di

2 cos α (S E − 0.6 P)

Minimum required thickness (Large End), tr =

t_r =

P Di

+ CA

2 cos α (S E − 0.6 P)

Minimum specified thickness after forming, tf =

Check If tr ≤ tf (Large End)

Minimum required thickness (Small End), t =

t =

P di

2 cos α (S E − 0.6 P)

Minimum required thickness (Small End), tr =

t_r =

P di

+ CA

2 cos α (S E − 0.6 P)

Minimum specified thickness after forming, tf =

Check If tr ≤ tf (Small End)

Knuckle Thickness [ASME UG-32(g) & App 1-4(d)]

Inside spherical or crown radius (Large End), L_L ⁽⁹⁾ =

L_L =

2 x cos α

Factor depending on the head proportion (Large End) L/r_c, M_L =

M_L =

(

3 + (L/R_c)^1/2

)

Minimum required knuckle thickness (Large End), t_k =

t_k =

P L_L M_L

2 S E − 0.2 P

Minimum required knuckle thickness (Large End), t_kr =

t_kr =

P L_L M_L

+ CA

2 S E − 0.2 P

Check If t_kr ≤ t_f (Large End)

Inside spherical or crown radius (Small End), L_s ⁽⁹⁾ =

L_s =

2 x cos α

Factor depending on the head proportion (Small End) L/r_c, M_s =

M_s =

(

3 + (L/r_c)^1/2

)

Minimum required knuckle thickness (Small End), t_k =

t_k =

P L_s M_s

2 S E − 0.2 P

Minimum required knuckle thickness (Small End), t_kr =

t_kr =

P L_s M_s

+ CA

2 S E − 0.2 P

Check If t_kr ≤ t_f (Small End)

Maximum allowable working pressure Cone Section [ASME UG-32(g)

Maximum allowable working pressure for Toriconical Head, MAWP_C =

barg

MAWP_C =

2 S E nt cos α

Di + 1.2 nt cos α

Maximum allowable working pressure Knuckle [ASME App 1-4(d)]

Maximum allowable working pressure for Knuckle, MAWP_K =

barg

MAWP_K =

2 S E nt

L_L M_L + 0.2 nt

Volume & Weight Calculation

Inside Volume

Large End Inside diameter, D =

Diagrama, Dibujo de ingeniería

Descripción generada automáticamente

Small End Inside diameter, d =

(Large End) Inside knuckle radius, R =

(Small End) Inside knuckle radius, r =

α =

deg.

X =

L₂ = R * sin(α) =

L₃ = r * Tan(α/2) =

L₁ = X - L₂ - L₃ =

ID of the conical portion, D₁ = D – 2R(1 – cos α) =

D₂ = D - 2R =

Outside Volume

Outside diameter of the Large End, D_o =

Outside diameter of the head Small End, d_o =

(Large End) Outside knuckle radius, R_o =

(Small End) Outside knuckle radius, r_o =

α =

deg.

X =

L₂ = R_o * sin(α) =

L₃ = r_o * Tan(α/2) =

L₁ = X - L₂ - L₃ =

OD of the conical portion, D₁ = D_o – 2R_o(1 – cos α) =

D₂ = D_o - 2Ro=

Inside Volume

V₁ =

m³

V₁ =

(

πL₁(D₁² + D₁d + d²)

)

/ 10⁹

V₂ =

m³

V₂ =

(

πL₂(D₁² + D₁D₂ + D₂²)

)

/ 10⁹

V₃ =

m³

V₃ =

(

120 R³ π sin(α/2) cos(α/2) + 0.25 D₂ R² (α/2)

)

/ 10⁹

V₄ =

m³

V₄ =

(

πd²L₃

)

/ 10⁹

V_i=

m³

V_i =

V₁ + V₂ + V₃ + V₄

Outside Volume

V₁ =

m³

V₁ =

(

πL₁(D₁² + D₁d_o + d_o²)

)

/ 10⁹

V₂ =

m³

V₂ =

(

πL₂(D₁² + D₁D₂ + D₂²)

)

/ 10⁹

V₃ =

m³

V₃ =

(

120 R_o³ π sin(α/2) cos(α/2) + 0.25 D₂ R_o² (α/2)

)

/ 10⁹

V₄ =

m³

V₄ =

(

πd_o²L₃

)

/ 10⁹

V_o=

m³

V_o =

V₁ + V₂ + V₃ + V₄

Weight =

W =

(Vo - Vi) ρm

Note:

(9)

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.

RESULT

Design Conditions

Design Pressure, Pd =

barg

Design Temperature, Td =

°C

Material

Toricónical Head Material

Dimensions

Large End Inside Diameter, D =

Small End Inside Diameter, d =

Minimum specified thickness after forming, tf =

Length of Toriconical Head, X =

Maximum allowable working pressure, MAWP_C =

barg

Maximum allowable working pressure, MAWP_K =

barg

Inside Volume =

m³

Outside Volume =

m³

Weight =

Discussion and References

Information about Wall Thickness Calculation of Conical Heads Under Internal Pressure

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

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 Heads (With Transition Knuckle)

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

In which the knuckle radius is neither less than 6% of the outside diameter of the head skirt nor less than three times the knuckle thickness.

Di = D_c−2R_c(1−cos α)

t =

P Di

2 Cos α (S E - 0.6 P)

The required thickness of the knuckle shall be determined by eq. 1-4(d)(3) in which

L =

D_i

2 Cos α

M =

(

3 + (L/R_c)^1/2

)

t_k =

P L M

2 S E − 0.2 P

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

P =

2 S E t cos α

Di + 1.2 t cos α

Where:

P: Design Pressure, in barg

S: Allowable Stress, in Mpa

E: Welding Efficiency

D_i = inside diameter of the conical portion of a toriconical head

t: Minimum required thickness, in mm

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

L = inside spherical or crown radius, in mm

r = inside knuckle radius

M = a factor in the equations for torispherical heads depending on the head proportion L/r

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).