Wall Thickness Calculation of Ellipsoidal Head Under Internal Pressure
 
  ASME Section VIII Div 1 - Appendix 1-4 - Formulas for the Design of Formed Heads Under Internal Pressure (14)
  Appendix 1-4(c) Ellipsoidal Heads
     
    (Enter values in yellow cells for calculations)
  DATA INPUT
                                                   
    Design Conditions     Material      
    Design Pressure, Pd =  barg Head Material Specification (1 to 7)
   
                                                   
    Design Temperature, Td =  °C Allowable Stress Head, S  =  MPa  
                                                   
    Welding Efficiency, E =
  Dimensions      
    See Table UW-12     Inside Diameter of the head skirt, Di =   mm  
    Corrosion Allowance, CA =  mm                                          
          Nominal wall thickness before forming (8), tn =
 mm  
                                               
      Minimum specified thickness after forming (9), tf =  mm  
      Minimum required thickness after forming, tr =  mm  
                                               
     Inside depth of the ellipsoidal head with corrosion removed, h (10) =  mm  
      Head Proportion = Di/2h (11) =    
      Outside Diameter of the head skirt, Do =  mm  
                                               
      Straight skirt length (12)(13), SK =  mm  
                                               
      Check If tr ≤ tn    
      Check If tr ≤ tf    
                                                   
                                                   
                                                   
    Notes:                                              
  (1) S ≤ 66.66% of σy @ temp.  
  (2) S > 66.66% but < 90% of σy @ temp.  
  (3) t ≤ 65  
  (4) 65 < t ≤ 100  
  (5) 100 < t ≤ 150  
  (6) Tensile strength of the Section IX reduced section tension test is not less than 690 MPa.  
  (7) Tensile strength of the Section IX reduced tension test less than 690 MPa but not less than 655 MPa.  
  (8) It is recommended a nominal thickness before forming 15% higher than the minimum specified thickness to ensure after forming thickness is above it.  
  (9) 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.  
  (10) For Ellipsoidal head 2:1 h = Di/4  
  (11) Head Proportion = Di/2h (Ratio between 3 and 1)  
  (12) As per UG-32(k) All formed heads, thicker than the shell and concave to pressure, intended for butt welded attachment, shall have a skirt length sufficient to meet the requirements of Figure UW-13.1, when a tapered transition is required. All formed heads concave to pressure and intended for butt welded attachment need not have an integral skirt when the thickness of the head is equal to or less than the thickness of the shell. When a skirt is provided, its thickness shall be at least that required for a seamless shell of the same inside diameter.   
  (13) As per UG-32(l) Heads concave to pressure,intended for attachment by brazing, shall have a skirt length sufficient to meet the requirements for circumferential joints in Part UB.   
  (14) The formula for the typical 2:1 elliptical head is listed in paragraph UG-32(c) of ASME Code Section VIII, Division 1. The general formula for all elliptical heads within the dimensional scope is addressed in Appendix 1-4. Factor K varies depending on the shape of the ellipse.  
                                                 
  CALCULATIONS
                                                   
    Ellipsoidal Head 2:1                                              
    with tf/L ≥ 0.002                                              
                                                   
    Thickness after forming adjusted for corrosion, nt =  mm   nt = tf-CA                            
    Inner diameter with corrosion removed, D =  mm   D = Di + 2CA                            
                                                   
     Inside depth of the ellipsoidal head with corrosion removed, h  mm   (For Ellipsoidal head 2:1 h = D/4)              
    Head Proportion = D/2h                                            
    Factor K (15)     (The value is obtained from Table 1-4.1)              
    Factor K1     (The value is obtained from Table UG-37)              
    Inside spherical or crown radius, L = k1D  mm                                          
    Inside knuckle radius (16), r =  mm                                          
                                                   
    Wall Thickness  [APPENDIX 1-4(c)]                                              
    Minimum required thickness after forming, t =  mm   t = P D K                          
            2 S E - 0.2 P                          
                                                   
    Minimum required thickness after forming, tr =  mm   tr = P D K + CA                    
            2 S E - 0.2 P                    
                                                   
    Check If tr ≤ tf                                              
                                                   
    Maximum allowable working pressure  [APPENDIX 1-4(c)]                                              
    Maximum alloable working pressure for Ellipsoidal Head, MAWP =  barg   MAWP = 2 S E nt                      
            K D + 0.2 nt                      
                                                   
    Check If MAWP ≥  P                                            
                                                   
    Check                                              
    Limitations: tf/L ≥ 0.002 tf/L ≥ 0.002                                          
                                                   
    Volume =  m³   V = ( π Di³ + π Di² SK ) / 109            
            24 4            
                                                   
    Weight =  Kg   W = (( π (Do³-Di³) + π (Do²-Di²) SK ) / 109) ρm      
            24 4      
                                                   
    Note:                                              
  (15) As per ASME VIII-1 EndNote 90. Ellipsoidal heads designed under K > 1.0 shall be designed using a value of S equal to 20,000 psi (138 MPa) at room temperature and reduced in proportion to the reduction in maximum allowable stress values at temperature for the material as shown in the appropriate table (see UG-23).  
  (16) As per UG-32(c) An acceptable approximation of a 2:1 ellipsoidal head is one with a knuckle radius of 0.17D and a spherical radius of 0.90D.   
     
  RESULT
           
    Design Conditions        
    Design Pressure, Pd =  barg    
    Design Temperature, Td =  °C    
             
    Material        
    Head Material       
             
    Dimensions        
    Outside Diameter, Do =  mm    
    Nominal wall thickness before forming, tn =  mm    
    Thickness after forming, tf =  mm    
    Inner Diameter, Di =  mm    
    Inside spherical or crown radius, L =  mm    
    Inside knuckle radius, r =  mm    
    For Ellipsoidal head 2:1 h =   mm    
             
    Maximum allowable working pressure, MAWP =  barg    
    Volume =  m³    
    Weight =  Kg    
       
                                                   
     
                                       
    Discussion and References  
    Information about Wall Thickness Calculation of Ellipsoidal Head 2:1 Under Internal Pressure    
    ASME Section VIII Div 1 Appendix 1-4(c)    
    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 Appendix 1-4   Formulas for the Design of Formed Heads Under Internal Pressure    
  - ASME Section VIII Div 1 Table UG-37 Value of Spherical Radius Factor K1    
  - ASME Section VIII Div 1 Table 1-4.1 Value of Factor K     
       
    Ellipsoidal Head with ts/L ≥ 0.002                  
                                         
                                         
                                       
                                         
                                         
                                         
                                         
                                         
                                         
                                         
                                         
    Minimum required thickness [ASME VIII.1 App 1-4(c)]    
      t = P D K                      
      2 S E - 0.2 P                      
    Internal design pressure [ASME VIII.1 App 1-4(c)]    
      P = 2 S E t                          
      K D + 0.2 t                          
    Where:    
    P: Design Pressure, in bar (psig)    
    D: Inside Diameter (in a corroded condition), in mm (inches)    
    L =  K1D for ellipsoidal heads in which K1 is obtained from Table UG-37.     
    S: Allowable Stress, in Mpa (psi)    
    E: Welding Efficiency    
    K: a factor in the equations for ellipsoidal heads depending on the head    
         proportion D/2h. K is obtained from Table 1-4.1     
    t:  Minimum required thickness of head after forming, in mm (inches)    
    ts:  Minimum specified thickness of head after forming, en mm (in.) ts shall be ≥ t    
    r = inside knuckle radius, in mm (inches)    
    Feactures    
    - High Availability
- Supports higher pressures than the Torispherical
- Ellipsoidal head has one-half the minor axis, h, equal to one-fourth of the inside diameter of the head skirt, D
- An acceptable approximation of a 2:1 ellipsoidal head is one with a knuckle radius of 0.17D and a spherical radius of 0.90D
- For heads with ts/L < 0.002 see Appendix. 1-4 (f)