Dish End Calculations as Per ASME Section VII Div 1

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ASME 8 Div 1 Appendix 1 Section 1.4 f Dished Heads With ts/L < 0.002 ASME 8 Division 1:- Torispherical Ends To UG32 and Appendix 1.4 P := 0.2

Design Pressure Mpa

(Note:- 1 Mpa = 1 N/mm^2)

D := 3000

Inside Diameter mm

r := 200

Knuckle Radius mm

L := 2450

Spherical Radius mm

t := 3.4

Min Required Thickness After forming mm

S := 138

Design Stress Mpa

Sy := 165.2

Yield Strength at max design temp Mpa

ET := 184590

Youngs Modulus At Temperature Mpa

E := 1

Joint Factor

___________________________________________________________________ L  3 +  r  M :=

M = 1.625

4

tmin :=

P⋅ L⋅ M

tmin = 2.885 mm

2 ⋅ S⋅ E − 0.2⋅ P

(

if tmin < t , "Acceptable Calculation" , "Head Too Thin" t L

) = "Acceptable Calculation"

= 0.001

Additional rules for thin heads C1 := if 

r

D

> 0.08 , 0.692⋅

r D

t/L < 0.002

+ 0.605 , 9.31⋅

t Se := C1 ⋅ ET⋅   r r

D

> 0.08 , 1.46 − 2.6⋅

− 0.086



C1 = 0.535 3

Se = 1.678 × 10

 

C2 := if 

r D

r D

, 1.25



C2 = 1.25

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ASME 8 Div 1 Appendix 1 Section 1.4 f Dished Heads With ts/L < 0.002 3

a := 0.5D − r

a = 1.3 × 10

b := L − r

b = 2.25 × 10

β := acos

3

a

 b

ψ :=

(

β = 0.955

L⋅ t )

ψ = 0.456

r

c := if  ψ < β ,



, a ( cos( β − ψ ) ) 

a

3

c = 1.48 × 10

3

Re := c + r

Pe :=

Py :=

Re = 1.68 × 10 Se⋅ t

Pe = 0.849

Re C2 ⋅ Re⋅   0.5⋅  − 1 r   

Sy⋅ t

Py = 0.084

Re C2 ⋅ Re⋅   0.5⋅  − 1 r   

Pck := if 

Pe

Pck := if 

Pe

 Py

 Py

≤ 1 , 0.6⋅ Pe , 0.408⋅ Py + 0.192⋅ Pe

Pck = 0.197

> 8.29 , 2.0⋅ Py, Pck

Pck = 0.167





Maximum Design Pressure P Pck Pmax := 1.5

(

if P < Pmax , "Acceptable Calculation" , "Head Too Thin"

Pmax = 0.1114

Mpa

) = "Head Too Thin"

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