**DISHED HEAD CALCULATIONS**

**Paragraph PG-29.1 states that the thickness of a blank, unstayed dished head with the pressure on the concave side, when it is a segment of a sphere, shall be calculated by the following formula: **

The symbols in this formula are defined as follows:

t = minimum thickness of plates (mm)

P = maximum allowable working pressure (MPa)

L = radius (mm) to which the head is dished, measured on the concave side mm

S = maximum allowable working stress (MPa), using values Table PG-23.1

E = efficiency of the weakest joint used in forming the head (not including the joint that joins the head to the shell) to the shell)

PW-12, Joint Efficiency Factors, states that for welded joints an efficiency of 1.0 (that is, 100%) may be used, provided all weld reinforcement on the joint is removed substantially flush with the surface of the plate. Otherwise a joint efficiency not to exceed 90% shall be used. __Seamless heads have an efficiency of 100%. __

• **Paragraph PG-29.2 states: “The radius to which the head is dished shall be not greater than the outside diameter of the flanged portion of the head.” If two different portions of the head are dished to different radii, then the longer radius shall be used as the value of ‘L’ in the formula. **

• **Paragraph PG-29.3 states that when a head, dished to a segment of a sphere, has a flanged-in manhole or access opening that exceeds 152 mm in any dimension, then its thickness must be 15 %, or 3.2 mm, whichever is greater, more than the thickness of a blank unstayed head as calculated by the formula in PG-29.1. **

• **Note: This would apply to a manhole such as is found on the end of a boiler drum. **

• **Paragraph PG-29.6 states that no head, except a full-hemispherical head, shall be of lesser thickness than required for a seamless shell of the same diameter. **

• **Paragraph PG-29.5 states that in the case of a dished head with a flanged-in manhole, if the dish radius ‘L’ is less than 80% of the diameter of the shell to which the head is attached, then, when calculating the thickness by: **

**the value of ‘L’ must be made equal to 80% of the shell diameter. In addition, the thickness thus calculated must be increased by the greater of 15% or 3.2 mm (PG-29.3) to compensate for the flanged-in manhole. This method of calculation will give the minimum thickness for any form of head having a flanged-in manhole**

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