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                     Section 
                     4 Dished ends subject to internal pressure
                  
                     
                        
                          4.1 Minimum thickness
                        
                           
                           
                              
                              
                              4.1.1 The
                                 thickness, t, of semi-ellipsoidal, and hemispherical
                                 unstayed ends, and the knuckle section of torispherical ends dished
                                 from plate, having pressure on the concave side and satisfying the
                                 conditions listed below, is to be determined by the following formula:
                                 
                               where t, p, Do, c σ and J are
                                 as defined in Vol  2, Pt  8, Ch  2,  1.2 Definition of symbols
                                 
                               
                              
                              
                              4.1.2 For
                                 semi-ellipsoidal ends:
                               
                                 
                                    
                                    
                                    the external height, H ≥ 0,18Do
                                       
                                     where 
                                 
                                    
                                       | D
                                             o | = | the external diameter of the parallel portion of the end, in
                                             mm. |  
                              
                              
                              4.1.3 For
                                 torispherical ends:
                               
                                 
                                    
                                    
                                    the internal radius, R
                                       i ≤ D
                                       o
                                       
                                     the internal knuckle radius, r
                                       i ≥
                                       0,1D
                                       o
                                       
                                     the internal knuckle radius, r
                                       i ≥
                                       3t
                                       
                                     the external height, H ≥ 0,18D
                                       o,
                                       and is determined as follows:
                                       
                                     
                              
                              
                              4.1.4 In addition
                                 to the formula in Vol  2, Pt  8, Ch  2,  4.1 Minimum thickness 4.1.1 the
                                 thickness, t, of a torispherical head made from more
                                 than one plate, in the crown section, is to be not less than that
                                 determined by the following formula:
                                 
                               where t, p, Ri, c σ, and J
                                 are as defined in Vol  2, Pt  8, Ch  2,  1.2 Definition of symbols
                                 
                               
                              
                              
                              4.1.5 The
                                 thickness required by Vol  2, Pt  8, Ch  2,  4.1 Minimum thickness 4.1.1 for
                                 the knuckle section of a torispherical head is to extend past the
                                 common tangent point of the knuckle and crown radii into the crown
                                 section for a distance not less than  mm, before reducing to the crown thickness permitted by Vol  2, Pt  8, Ch  2,  4.1 Minimum thickness 4.1.4 where t = the
                                 required thickness from Vol  2, Pt  8, Ch  2,  4.1 Minimum thickness 4.1.1 
                              
                              
                              4.1.7 The
                                 minimum thickness of the head, t, is in no case to be
                                 less than  mm, where D
                                 i is as defined in Vol  2, Pt  8, Ch  2,  1.2 Definition of symbols. The minimum thickness permitted
                                 for vessels manufactured in corrosion resistant steels will be the
                                 subject of special consideration. 
                              
                              
                              4.1.8 For
                                 ends which are butt welded to the drum shell, see 
                                 Vol  2, Pt  8, Ch  2,  1.9 Joint factors, the thickness of the edge of
                                 the flange for connection to the shell is to be not less than the
                                 thickness of an unpierced seamless or welded shell, whichever is applicable,
                                 of the same diameter and material and determined by Vol  2, Pt  8, Ch  2,  2.1 Minimum thickness
                                 
                               
                     
                        
                          4.2 
                           CROSS-REFERENCES 
                           
                        
                           
                           
                              
                              
                              4.2.1 For shape factors dished ends, see 
                                 Vol  2, Pt  8, Ch  1,  4.2 Shape factors for dished ends
                                 For dished
                                 ends with unreinforced openings, see 
                                 Vol  2, Pt  8, Ch  1,  4.3 Dished ends with unreinforced openings
 For flanged
                                 openings in dished ends, see 
                                 Vol  2, Pt  8, Ch  1,  4.4 Flanged openings in dished ends.
 For location of unreinforced and flanged
                                 openings in dished ends, see 
                                 Vol  2, Pt  8, Ch  1,  4.5 Location of unreinforced and flanged openings in dished ends.
 For dished ends with reinforced openings, see 
                                 Vol  2, Pt  8, Ch  1,  4.6 Dished ends with reinforced openings
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