I am modeling bolting flanged connections in my piping system using anchor (ANC) restraints and CNodes.

Is there a resource for determining an appropriate stiffness for the bolted flanged connection model described above, rather than using the CII default of 1E12?

I'll ask first why you would want to do this. I can't think of a scenario where I'd want to tell the owner "I'm taking credit for flange flexibility to get piping / equipment to pass code."

But maybe you have another reason, so I'll offer some more.

I don't think there's a "great" way to input this into CAESAR using element stiffness.

Let's consider replacing the anchor with Cartesian components, instead.

Consider the compression case - you wouldn't expect the flange face to significantly compress, so that 1e12 is as good as any.

Consider the tension case, delta = tension * length / area * modulus... so k = tension / delta = area * modulus / length, where area is number of bolts * individual bolt smallest cross sectional area.

So you have a non-linearity in the axial component (let's call this x)

You could do similar for shear, but only for Y and Z axes specifically, once input into CAESAR, would mean that the stiffness in arbitrary radial directions (+Y+Z, -Y+Z, etc) aren't going to be equal to the stiffness in either Y or Z, but up to 41% higher than reality.

You could estimate radial sheer stiffness (RX) decently.

But you'd be in another tough position for bending (RY, RZ).

This could be estimated by assuming half the bolts are put into tension, and you're leveraging them about the flange OD. But again, if your bending action is working outside the Y and Z axes, your stiffness could be as high as 41% higher than reality.

So I suppose you could create a CNODE +X, Y, Z, RX, RY, RZ on one with stiffnesses and a CNODE -X on the next without stiffness, and that's pretty accurate.

Granted, 41% over is still a lot closer than 1e12, and maybe you're fine with a cnode anchor with stiffness handling all these situations as it's still better than cnode anchor with 1e12.

Some additional considerations:

Bolt pre-stress would be a consideration, and the friction between faces would impact real world effective stiffness in the shear force and shear moment directions.

Flange deformation would also be a consideration, which would reduce the stiffness.

Alternatively, I suppose you could model each bolt as a piping / rigid element that approximates the stiffness of a bolt...

I am trying to confirm what has been done on a previous model.
Node 2000 is the piping flange node
Node 40 is the equipment flange node

An anchor restraint was applied to node 2000 with a CNode referencing node 40. The CNode connects nodes 2000 and 40 together. A stiffness of 1E06 was then applied to this CNode anchor.

I am trying to verify the use of the stiffness value of 1E06 for the bolted flange connection, but have not found a resource yet.

I am wondering if a software module within PRG FEA performs a stiffness calculation on bolted flange connections that would be applicable?

I know of no module by Paulin that does the flange connection itself, only the nozzle-shell intersection.

With that said, I would speculate that the analyst before was placed in the position of qualifying something they themselves didn't really have much choice in, so resorted in cutting corners while reducing conservatism.

1e6 is a common go-to for bringing down CAESAR's 1e12 from the stratosphere down to the rafters, for a number of scenarios, such as normal restraint stiffness.

If the model features 1e6 on other restraints, it's possible it's an accidental mis-key from the restraint tab.

But I would ask myself, if, in the real world, we subjected this flanged connection to 1,000,000 lbs of force, would the flange move 1", or more, or 1,000,000 ft-lbs of force, would the flange move 1 degree or more, just looking at the flange, and not the piping attached to it?

I don't know the parameters of your flange, but I'd wager yes.

Is it typical? No.
Is it documented somewhere? Not that I've seen.
Is it non-conservative? Probably not.