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
  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 Head Material Specification (1 to 7)
   
                                         
    Design Temperature, Td =  °F Allowable Stress Conical Head, 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, tr =  in.  
                                         
          Length of Conical Head, Lc =   in.  
                                         
                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 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, t =  in.   t  = P D                
            2 cos α (S E - 0.6 P)                
                                         
    Minimum required thickness, tr =  in.   tr  = P D + CA            
            2 cos α (S E - 0.6 P)            
    Nominal wall thickness, tn =  in.                                
                                         
    Check If tr ≤ tn                                    
                                         
    Maximum allowable working pressure  [ASME UG-32(f)]                                    
    Maximum allowable working pressure for Conical Head, MAWP =  psig   MAWP = 2 S E nt cos α                
            D + 1.2 nt cos α                
                                         
    Inside Volume =  ft³   Vi  =  1/3*π*Lc(Ri² + ri² + Riri ) / 1728            
    Outside Volume =  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 allowable working pressure, MAWP =  psig      
    Inside Volume =  ft³      
    Outside Volume =  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).