What’s the minimum shank diameter that could safely handle a 416 Rem? Is 1.16 inches too small? I’ve seen standard contours up to 1.2 and 1.25 inches.

uhm
when you say shank, you mean the thread portion inside the action, right?

rugers, mausers, remingtons, and winchesters are all way less than 1.2 --

remember, the 416 rem is no more pressure than a 7 rem,

No, I’m referring to the straight portion coming out of the receiver. So maybe breech is the correct term.

Shank is the correct term, from which the threads are cut, and some sticks out in front of the receiver. Some call it a cylinder.
Breech is technically, the part of a cannon (barrel) behind the bore) Some call anything at the ass end of a barrel the breech, but none of that is germane here. What we call it is not important; the question was, how big does it need to be.
It is more for balance, the ability to have a thread shoulder (albeit Savage doesn't have one and many new rifle designs use the barrel nut method, so the shank is the same diameter as the threads) or rigidity than strength; after all, you just reduced your thread OD to inch didn't you? Do not think that the receiver provides any radial strength when you fire a rifle.
And modern CM steel is very strong.
Whelen turned the shank of a Springfield down to .1 inch wall thickness; no issues noted until he fired some proof rounds. Do not do that. And that was not even Chrome Moly steel.
Look at modern double rifles (not all are low pressure); then you will see some very small shank/breech diameters.
Bottom line; the answer is 1.15. (just for discussion)

The portion just in front of the ring, where it is full diameter is called the reinforce.

On a cannon barrel.
Especially when they are made from two or more pieces. And on a Parrot Rifle where a wrought iron band is wrapped around the breech.
On rifles, it is more common to call it the breech, breech end, shank. Fat part. Other technical terms.
But I have also called it a reinforce.

to answer your question,
mausers are typically 1.2 for a bit, depending, and 1.16 isn't a great deal different

i'd done 458 winmag on small ring mausers

Actually all (99%) military Mausers are 1.1, thread diameter, for about .21 inches, then drop down to .960 and they aren't even CM steel.
Small thread 98s and most pre 98 ones, have a .980 thread OD.

I like doing the math.

Head diameter is 13.03mm.
Max Pressure (SAAMI) is 450MPa
Yield stress for 4140 is 750MPa or greater (depends on heat treat).
Ignoring the cartridge case, but without any additional safety factor gives a minimum diameter of 20.8mm (0.819").
Personally, I would want at least 1", for a safety factor of 1.6.

PS, I know this are as the Knox Form?

Actually Nock developed a flat place on the barrel shank to make fitting easier; so, Knock's form, a flat spot. You can see it on the Lee Speeds and others. Rigby. Usually mis spelled.
Anyway, next time do the math in English so I can understand it; but your shank OD of one inch would be fine. But since that is the same diameter as threads on Winchesters and Ruger, and they have no inner shoulder, it has to be larger, at least for a narrow band. Or use a barrel nut.
Just shows that CM steel is very strong. Barrels aren't really heat treated; they are stress relieved (Douglas does it twice).
Certainly not hardened.

Thanks for the history lesson! Will try to remember it.

Sorry about the metric units. It's the language I grew up with, and the spreadsheet I used to do the calculations on is quite complicated, so I didn't feel like translating the whole thing. Will translate more of the figures next time.

I realize that barrels are not hardened, which is why I used the words "heat treat" instead. Thus, 750MPa (65.267ksi) is the highest practical figure to use.

The can of worms here is the thread root diameter. There are no internationally-recognized standards for firearm design. However, there are piles and piles of standards for other types of pressure vessels. My own field of professional expertise is valve design, and as a result I know a few of the design standards for valves fairly well. In the ASME standards (yours in other words), it is clearly stated that in a situation where you have a sleeve inside a cylinder, the sleeve is supposed to be strong enough to handle the pressure as if the outer cylinder is not there.

That in effect means that, should you follow these design standards, than the root diameter of the barrel thread should be large enough to handle the design pressure. Furthermore, the country I live in requires all new firearms to be proof-tested at a pressure 50% higher than the design pressure.

Now, as said before, these design standards are not applicable to firearms, and also you guys are in the lucky position that proofing is not required, so you can, if you want to, sail a bit closer to the wind. Personally I like playing it a bit safer.

Obviously, bigger is better, so increasing the size in order to get a good seating shoulder or for other aesthetic reasons. The only negatives are weight and perhaps how low a scope can be mounted. Once past the chamber, the barrel can be thinned down a fair amount, so the weight penalty is actually quite small.

I know you guys use Metric, but the only things Metric here are one liter pop bottles.
As for threads; I might have said this, and you alluded to it; the thread shank must support 100% of the load; no radial pressure is transferred to the receiver. That would not be a good idea. And it shows just how good 4140 steel is. Like above, the 458 on a small thread mauser. .980 thread OD with at least .1 less at the roots. Inches I mean.
Look at a Marlin 336/1895 thread shank sometime; they are paper thin on the fat cartridges; no problem though.

I ran the numbers for g33/40 action GMA for a 416 Rem on our integral barrels (we are building a 338 winmag on the g33/40). Used barrel minor thread of 0.866", Per Krieger, their yield strength is 125.8Kpsi (858 Mpa), barrel pressure curve from Quickload and
Saami MAP for the remington.
As shown below, there are 2 locations of min. safety factor, the shank and then end of the radiused barrel.

Don't let some guys here know you are using a Mauser action for actual shooting! It sends them into a tizzy fit.

Steve, just as a matter of interest, what inside diameter(s) are you using for the calculation?

For the barrel, 0.416”
Have not run the receiver ring, barrel shank.