Flat heads formulas

Unstayed flat heads and covers can be designed by very specific rules and formulas given in this subsection. The stresses caused by pressure on these members are bending stresses, and the formulas include an allowance for additional edge moments induced when the head, cover, or blind flange is attached By bolts. Rules are provided for quick-opening closures because of the risk of incomplete attachment or opening while the vessel is pressurized. Rules for braced and stayed surfaces are also provided. 

The ASME design formula from UG-34 for circular flat heads subjected to internal pressure is t = d CP/SEf, where t is the minimum thickness of the head (in.), d is the internal diameter of the vessel (in.), P is the MAWP (psi), S is the allowable stress in the material listed in ASME Section II, and E is the weld joint efficiency. The value of C ranges from 0.10 to 0.75 depending on the method of attachment of the head and the shell dimensions. For preliminary designs, a value of 0.33 for C will lead to a good approximation of the required head thickness. 

The MAP and MAWP for other components, i.e., cones, flat heads, hemi-heads, torispherical heads, etc., may be checked in the same manner by using the formula for pressure found in Procedure 2-1 and substituting the appropriate terms into the equations. 

Flat heads may be circular or non-circular. This section does not cover non-circular heads because this would be a very rare application for a high pressure vessel. The ASME Code, Section Vni, Division 2 has formulas to follow for fixed, non-circular, flat heads. 

ASME CODE FORMULA FOR CIRCULAR FLAT HEADS AND COVERS... 

ASME Code Formula for Circular Flat Heads and Covers... 

Although spherical vessels have a limited process application, the majority of pressure vessels are made with cylindrical shells. The heads may be flat if they are suitably buttressed, but preferably they are some curved shape. The more common types of heads are illustrated on Figure 18.16. Formulas for wall thicknesses are in Table 18.3. Other data relating to heads and shells are collected in Table 18.5. Included are the full volume V0 and surface S as well as the volume fraction V/V0 corresponding to a fractional depth H/D in a horizontal vessel. Figure 18.17 graphs this last relationship. For ellipsoidal and dished heads the formulas for V/V0 are not exact but are within 2% over the whole range. 

The thickness of flat, bolted heads is governed by bending, and not by tension. Thus, the formulas for the design of these components is the same for Division 1 or Division 2. 

---