Determining the Value of the Lever Arm on a Spherically Dished Cover
hR represents the lever arm for the radial component of the membrane load of the spherical segment Hr. This field is only required for the design of a spherically dished cover for Figure 1-6(d). The magnitude of the moment arm is most easily determined by reviewing the mentioned figure: it is the axial distance from the centroid of the flange thickness to where the mid thickness of the dish intersects the flange.
If the mid-thickness of the dish is closer to the gasket face of the flange (in the axial direction) than the centroid of the flange is to the gasket face, the sign of hR is positive; otherwise, it is negative. It may be more or less conservative to determine this value in the corroded condition.
The sign of the moment arm is based on whether or not the moment (Hr*hR) causes rotation of the flange around the bolt circle in the same direction as the gasket reaction. The gasket reaction will cause the flange to want to rotate around the bolt circle in such a fashion that the flange will want to open up into the vessel with the bolt circle acting as a hinge. Since Hr acts in an inward radial direction, we know that if the mid-thickness of the flange is closer to the flange face (in the axial direction) than the centroid of the flange thickness is to the gasket face, the resulting rotation will want to open the flange face into to the vessel with the bolt circle acting as a hinge. As this is the same direction of rotation as the gasket reaction, hR would be positive in this case.
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