Wall Thickness Calculation of Torispherical Head Under Internal Pressure
 
  ASME Section VIII Div 1 - UG-32 - Formed Heads, and Sections, Pressure on Concave Side
  UG-32(d) Torispherical Heads with ts /L ≥ 0,002
     
    (Enter values in yellow cells for calculations)
  DATA INPUT
                                                         
    Design Conditions     Material      
    Design Pressure, Pd =  psig Head Material Specification (1 to 7)
   
                                                         
    Design Temperature, Td =  °F Allowable Stress Head (8), S =  psi  
                                                         
    Welding Efficiency, E =
  Dimensions      
    See Table UW-12     Inside diameter of the head skirt, Di =  in.  
    Corrosion Allowance, CA =  in.                                                
          Nominal wall thickness before forming (9), tn =
 in.  
                                                         
          Minimum specified thickness after forming (10), tf =  in.  
          Minimum required thickness after forming, tr =  in.  
                                                         
          Outside diameter of the head skirt, Do =    
                                                         
          Inside knuckle radius is 6% of the inside crown radius (11), r =  in.  
        Check inside knuckle radius is in no case less than 3 times the head thickness (t)    
                                                         
          Straight skirt length (12)(13), SK =  in.  
                                                         
          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  ≤ 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-32(d) Torispherical heads made of materials having a specified minimum tensile strength exceeding 70,000 psi (485 MPa) 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 tempera ture for the material as shown in the appropriate table (see UG-23).  
  (9) It is recommended a nominal thickness before forming 15% higher than the minimum specified thickness to ensure after forming thickness is above it.  
  (10) 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.  
  (11) 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. The inside knuckle radius of a torispherical head shall be not less than 6% of the outside diameter of the skirt of the head but in no case less than 3 times the head thickness.  
  (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.   
                                                         
                                                       
  CALCULATIONS
                                                         
    Torispherical Head                                                    
    with tf/L ≥ 0.002                                                    
    Thickness after forming adjusted for corrosion, nt =  in.   nt = tf-CA                                    
                                                         
    Inside spherical or crown radius adjusted for corrosion, Lc (14) =  in.   Lc = Do + CA                                    
                                                         
    Inside knuckle radius, r =  in.                                                
                                                         
    Wall Thickness [UG-32(d)]                                                    
    Minimum required thickness after forming, t =  in.   t = 0.885 P Lc                              
            S E - 0.1 P                              
                                                         
    Minimum required thickness after forming, tr =  in.   tr = 0.885 P Lc + CA                        
            S E - 0.1 P                        
                                                         
    Check If tr ≤ tf                                                    
                                                         
    Maximum allowable working pressure  [UG-32(d)]                                                    
    Maximum allowable working pressure for Torispherical Head, MAWP =  psig   MAWP = S E nt                          
            0.885 Lc + 0.1 nt                          
                                                         
    Check If MAWP ≥  P                                                  
                                                         
    Check                                                    
    Limitations: tf/L ≥ 0.002                                
                                                         
    Inside Volume =  ft³   V = ( 0.0847 Di³ + π Di² SK ) /  1728                
            4                
                                                         
    Weight =  lbs   W = (( 0.0847 (Do³-Di³) + π (Do²-Di²) SK ) /  1728) ρm      
            4      
                                                         
    Note:                                                    
  (14) As per UG-32(d) the inside crown radius shall be equals the outside diameter of the skirt [see UG-32(i)]  
                                                         
     
  RESULT
           
    Design Conditions        
    Design Pressure, Pd =  psig    
    Design Temperature, Td =  °F    
             
    Material        
    Head Material       
             
    Dimensions        
    Outside diameter of the head skirt, Do =  in.    
    Nominal wall thickness before forming, tn =  in.    
    Thickness after forming, tf =  in.    
    Inside spherical or crown radius, L =  in. (L = Do)    
    Inside knuckle radius, r =  in.    
             
    Maximum allowable working pressure, MAWP =  psig    
    Inside Volume =  ft³    
    Weight =  lbs    
       
                                                         
     
                                       
    Discussion and References  
    Information about Wall Thickness Calculation of Torispherical Head Under Internal Pressure    
    ASME Section VIII Div 1 UG-32(d)    
    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 - UG-32 - Formed Heads, and Sections, Pressure on Concave Side    
       
    Torispherical Head with ts/L ≥ 0.002    
                                         
    Scan_Pic0004                                    
                                         
                                         
                                         
                                         
                                         
                                         
                                         
                                         
                                         
    Minimum required thickness [ASME VIII UG-32(d)]    
      t = 0.885 P L                          
      S E - 0.1 P                          
    Internal design pressure [UG-32(d)]    
      P = S E t                          
      0.885 L + 0.1 t                          
    Where:    
    P: Design Pressure, in barg (psig)    
    S: Allowable Stress, in MPa (psi)    
    E: Welding Efficiency    
    L: Inside crown radius not greater than the outside diameter of the skirt, in mm (inches)    
    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    
    (*) The required thickness of a torispherical head for the case in which 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. The inside knuckle radius of a torispherical head shall be not less than 6% of the outside diameter of the skirt of the head.    
    r = inside knuckle radius, in mm (inches)    
    Feactures    
    - High Availability
- Limitations: ts/ L ≥ 0.002, L ≤ D+2t, r ≥ 0.06*(D+2t)
- For t calculation will be considered L = D
- For heads with ts/L < 0.002, see Appendix. 1-4 (f) 		   
    - Torispherical heads made of materials having a specified minimum tensile strength exceeding 70,000 psi (485 MPa) 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 (see UG-23).