I think the Coade flange calculator is more accurate than any theory based on assumptions.
In the same time, it makes sense to understand what really the equivalent pressure is, why it’s conservative and why it’s the preferred approach.

I’d like to share with you my conclusions.

1. The Kellogg EQP theory is a gasket load equivalence based on some assumptions.
The result depends on these assumptions.

2. We haven’t a clear understanding on the result. For example, a compressive force is "helping" the flange; anyway it’s not acting as a supplementary pressure that loads the flange. This is not clear in the formula interpretation.

In my first posted paper I’ve made a mistake assuming "mathematically" the gasket load as proportional with pressure. Now I guess this mistake has helped me to see what is wrong in our understanding of Kellogg formula. In fact, if we are looking only mathematically to the formula 2*b*Pi*G*(m*p) we can wrong understand that the stress on gasket is pressure proportional. Following this "understanding" we may say "under a bending moment and compressive axial force, the stress on gasket is increasing, so this is as an equivalent pressure is loading the flange". This is wrong because a pressure load is decreasing the gasket load and stress.

In my understanding, the Kellogg theory analyzes (in a specific way) the gasket tightness reserve, and for this reason the "tensile loaded part of the flange" must be considered.
Following this interpretation, the formula is the same, but now F is a tensile force and is acting –correct- as a supplementary pressure that loads the flange. Also the rating pressure as a limit for the gasket tightness makes more sense.
I’m attaching a paper showing "step by step" my interpretation.

3. This interpretation has helped me to understand why the Kellogg formula is so conservative: it’s a gasket load method presuming that the gasket is carrying on all the external loads.
Supposing we have only a bending moment load, this assumption is exaggerated for the tensile loaded part of the flange (and accurate for the compressed loaded part of the flange).
In fact, this is the worst scenario for the gasket load and the result is a very good formula for the Nuclear Code, where the worst scenario must be considered for the safety reasons!

4. In our days knowledge, I think that the Kellogg formula may be corrected by considering

M* [I/(0.3846*Ip+I)]*[G/(C-2*hD)] instead of M.

We would consider the correction... but is not included in a serious paper (or maybe is?).
You would get directly this result comparing the equivalent force in the Kellogg theory with the equivalent force considered by 2007 ASME VIII Div.2.

5. I’ve realized there is a "simple" effective way to create a realistic "by-pass" of the pressure equivalent method, in the same time estimating accurately the gasket tightness reserve.
But we can do this only numerically, case by case.

A structural model analyzing together the flange, gasket and bolts (as the Coade flange calculator is) can be used to find out a realistic minimum load on gasket.
"Minimum" refers to the fact the flange is under a bending moment and the gasket load is variable along the circumference, so has a minimum.

Having this result, we can estimate a simple "safety factor" versus the gasket load at rating pressure.
This safety factor may be defined as:

(minimum_along_circumference_ gasket load in operation)/ (2*b*Pi*G*m*p_rating).

This safety factor must be greater than 1; a safety factor of 1.2 means the minimum gasket load due to internal pressure and external loads is 120% of the value that occurs at p_rating.

In fact, this safety factor is:

(minimum_gasket_ stress in operation)/ (m*p_rating)

and is following exactly the approach of Rossheim, Markl and Taylor Forge’s "Modern Flange Design Bulletin 502".

For this reason, I think the best name of this safety factor is "the Taylor-Forge gasket stress index".
It’s a piping flange specific safety factor.

In my opinion, this index should replace the EQP method. The Kellogg EQP method makes (in a specific way) a similar estimation, but assuming the worst scenario for the minimum gasket load in operation.

6. Now few questions for Coade:
- is the HG force (calculated and shown in "Plot forces") the minimum_along_circumference_ gasket load
or
the maximum_along_circumference_ gasket load?
- is the axial force (introduced as load) a tensile force or a compressive one?
- it would be possible in the next version of this flange calculator to have either tensile force or compressive forces as loads?
-what is the meaning of the "Leak-Proof Joint (Creq)" in the Gasket Compression section results?
Thank you!

7. Last, about an EQP method based on the ASME VIII Div2. My first paper was wrong, my second paper (even correct in a way) is considering a particular gasket load and gives an ultra-conservative result. May be corrected and gives a realistic result, but I was the first saying it’s hard to be counted as a useful approach, just because it’s not more than an alternative calculation. The problem of the limits for this equivalent pressure is very questionable.
Instead, I’m very confident the Coade flange calculator makes the direct calculation better than any theory, because is able to estimate accurately the HG gasket load and not only this!

Best regards.