Wall Thickness Calculation of Conical Heads Under Internal Pressure
 
  ASME Section VIII Div 1 paragraph UG-32  Formed Heads, and Sections, Pressure On Concave Side
                                   
    (Enter values in yellow cells for calculations and in blue cells as information)
  DATA INPUT
                                         
    Design Conditions     Material      
    Design Pressure, Pd =  psig Conical Head Material Specification    
          Conical Head Material Type
   
    Design Temperature, Td =  °F Allowable Stress Conical Head, S  =  psi  
                                         
    Welding Efficiency, E =   Dimensions      
Large End Inside Diameter, Di =  in.
Corrosion Allowance, CA =  in. Small End Inside Diameter, di =  in.
Undertolerance Allowance (*), U1 =  default value = 0
Nominal wall thickness, tn =
 in.
Length of Conical Head, Lc =   in.
                                         
                If tr ≤ tn acceptable    
    Notes:(*)                                    
    - 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.   
    - 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.  
    - 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 Heads                                    
    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) )              
            Lc              
                                         
    Minimum required thickness, tr =  in.   tr  = P D + CA            
    Nominal wall thickness, tn =  in.   2 cos α (S E - 0.6 P)            
                                         
    Check If tr ≤ tn                                    
                                         
    Maximum working pressure  [ASME UG-32(f)]                                    
    Maximum working pressure for Conical Head, Pc =  psig   P = 2 S E nt cos α                
            D + 1.2 nt cos α                
                                         
    Volume inner =  ft³   Vi  =  1/3*π*Lc(Ri² + ri² + Riri ) / 1728            
    Volume outer =  ft³   Vo  = 1/3*π* Lc(Ro² + ro² + Roro ) / 1728            
                                         
    Weight =  lbs   W = (Vo - Vi) ρm                    
                                         
                                   
  RESULT
    Design Conditions      
   
Design Pressure, Pd =  psig
Design Temperature, Td =  °F
    Material          
Conical Head Material 
    Dimensions          
Large End Inside Diameter, Di = in.
Small End Inside Diameter, di = in.
Nominal wall thickness, tn = in.
Length of Conical Head, Lc =  in.
Maximum working pressure =  psig
Volume inner =  ft³
Volume outer =  ft³
Weight =  lbs
                                         
                                         
    Discussion and References  
    Information about Wall Thickness Calculation of Conical Heads 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 Heads (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 head    
    Feactures    
    - It is used mainly for heads at the bottom of the vessel.
- Limitations:  α ≤ 30°
- A reinforcing ring shall be provided when required by the rule in 1-5(d) and 1-5(e).