Inter rivet buckling using Tangent modulus

[levanang]

Hi,

I am currently doing the inter rivet buckling analysis. The formula which I am using from Bruhn chapter C7.14 which suggest me to use tangent modulus. My applied stress at the current location is -357MPa, where as my material Fcy is 290MPa. If I try to find the Tangent modulus using Ramberg-Osgood relation (C2.4 of Bruhn) I found Tangent modulus is 296.9MPa, If I use this in my IRB formula, I am getting allowable inter rivet buckling at this locations as 4.6MPa, which looks like very odd. Please suggest me, how to approach this formula for my case.

clamping factor = 4
pitch = 29.22
Ec = 70300MPa
nc= 17
applied = -357.623MPa
Fcy= 290MPa



Thanks in advance.

 

[rb1957]

I don't have my Bruhn handy ... surely thickness is part of Firb ? I forget, is "clamping factor = 4" fixed (protruding heads) or CSK heads ?

Yes, your calculated Firb looks "odd" !

Your Et looks very low, but that could be because your stress is so high.

How did you determine the stress ? directly from FEA (linear FEA ?), in which case it is probably incorrect, particularly in compression. You need to account for effective width. You need to extract the compression load from the model, and apply that to the effective compression area (maybe 30t^2 ?).

 

[LiftDivergence]

So there are a few things that can be a bit confusing about general interfastener buckling methods. What you'll find is that they typically rely on indexing column buckling curves from Euler-Engesser relations rather than starting from derived plate buckling formulas from Gerard or Kuhn, etc. There can also be some confusion because some methods rely on using a compressive tangent modulus (finding the intersection of the interfastener buckling equation slope on the compressive stress-strain curve) whereas other use the tangent modulus from a tensile stress-strain curve, and this is called different things in different references (for example, Peery calls it F1, but then states is corresponds to the intersection of the stress-strain curve with a slope of 0.7E referring to Ramberg-Osgood.) This in itself can be confusing because a simplistic version of the Ramberg-Osgood relation can be given from this. Most people I think are familiar with the version using K and n or the Hollomon parameters. But I suggest you read NACA TN 902 regarding their three-parameter method.

Finally, there can be some confusion because the general form of the buckling curves that are often used are non-dimensional curves for elastic buckling. But then we are computing tangent moduli using Ramberg-Osgood which is all developed for describing non-linear stress-strain behavior. In this case your applied stress is greater than the compressive yield stress.

Here are my personal favorite references on interfastener buckling (in addition to your Bruhn reference):
Aircraft Structures (Peery) Section 14.13
Alteon Part 2
Theory and Analysis of Flight Structures (Rivello) Section16-17 (Very good because it covers wrinkling as well as buckling between fasteners)
Flabel Section 6.2

Remember than checking the interfastener buckling is generally only one part of a compressive instability analysis. It would typically be used to help determine the critical compressive stress of a segmented cross section. For example, checking to make sure the assumed segment compressive allowable can be taken as Fcy and does not need to be capped/limited to a lower value.

I have set something up to repeat your Bruhn calculation with the values provided (I converted them to USCU because I'm a simple American) with each of the other references I listed. However I need some more detail:

What is the thickness of the fastened material?
What material are you using so we can check the tangent modulus computation?
We can't even just check what you did from Bruhn / your E_t of 297 MPa because you haven't showed your work on finding F_0.7 or told us the material.
Where did you get your Nc value? Is it from a tensile or compressive plot?

 

[levanang]

@LiftDivergence , @rb192 Thanks for your replies.

@rb192 The load has been extracted from the grid point of FEM (Analyzing component is Intercostal which is idealized as Tria shell element). The formula used here to calculate at outer flange stress as (Fx/A+MzY/I) As mentioned this idealization looks unrealistic for Inter rivet buckling. I will check and comeback.

Yes I missed some of the information above. Please find those details below.
Thickness = 2mm
Material: 2024-T42_Clad
Fastener at this locations is DAN5-5 which is Protruding head Hi-Lock fastener.

@LiftDivergence Thanks for your explanation. I will refer the other documents which you shared.
The Tangent Modulus formula which I used to calculate is Et = 1/((1/Ec)+(0.002/Fcy)*nc*(Sigma/Fcy)^(nc-1)).

 

[Stress_Eng]

I've put some equations together in Mathcad, as an example on solving for the inter-rivet buckling allowable. Hope it gives you some ideas on an approach.

 

[rb1957]

1) does the node represent only this skin ? (or is the FEM load distributed between two elements (like the skin and a stringer ?)

2) I would neglect bending in thin sheet (particularly if the node is shared with a stringer).

 

[SWComposites]

Did you see my previous reply?
you have: applied stress = -357.623MPa
which is way above the yield point: Fcy= 290MPa
so why would you not expect a low IRB allowable?

please post a picture of the part and the stress distribution in your FEM. IRB should be calculated using an averaged stress across the flange section, not a peak stress at a node. and agree with the above, bending stress should probably not be used, just the mid-plane stress in the flange.

 

[levanang]

@rb192 the load distribution is between intercostal and skin. I don't have the picture right now, I will share it once I got it. I am not clear about their load distribution method, since I am doing a repair analysis for the part which already analyzed. I will discuss those with the person who did this and clarify here.
@SWComposites, Yes as mentioned the applied load is more than my Fcy. Regarding the load distribution I will post the clear image later. Thanks

 

[rb1957]

oh, this is a repair, and you have the original calcs. this should be "QED". What are you repairing ? have you removed a cap, and so reduced the bending stiffness, and are trying not to return the cap ? are you trying not to add a doubler ?? (maybe the skin was damaged, corrosion?, and reduced in thickness ?).

I think you should be talking to your immediate support (rather than random folks on the "interwebs").

The only way we can help answer your specific problem is if you give us everything. But let's start with sketches of the original structure and the repair.

 

[levanang]

I've put some equations together in Mathcad, as an example on solving for the inter-rivet buckling allowable. Hope it gives you some ideas on an approach.

@Stress_Eng Thanks for your calculation. But the assumption you made is Fir and applied stress in Tangent modulus calculations are same which looks ok initially to me. The allowable IRB value also looking ok to me. However, in the second page you created one graph with the relation of Fir vs Et, which shows that, When Tangent modulus decrease, the Fir will increase. But, when you look the Fir equation, the tangent modulus is directly proportional to the Fir which means, if Et decrease, Fir also should decrease.
But the relation which you created to find the IRB allowable looks a bit complicated for me. I will check it once more.

Thanks!

 

[levanang]

oh, this is a repair, and you have the original calcs. this should be "QED". What are you repairing ? have you removed a cap, and so reduced the bending stiffness, and are trying not to return the cap ? are you trying not to add a doubler ?? (maybe the skin was damaged, corrosion?, and reduced in thickness ?).

I think you should be talking to your immediate support (rather than random folks on the "interwebs").

The only way we can help answer your specific problem is if you give us everything. But let's start with sketches of the original structure and the repair.

I am not doing the in-service repair. I am creating the SRM manual using the existing repair task. Where in my case, I am using trying Lightening strike repair, where I have change the rivets, due to that the clamping factor has been changed from previous revision. My previous calculation was done using some other method which couldn't able to find anywhere referred from Airbus HSB document. So, now I am moving to this usual approach.
Yes! I have to check with my Certification report team who already done this.

 

[rb1957]

So you have an existing (approved) repair for, say, corrosion damage, and now want to use that (or something similar) for a lightning strike repair. ok?

You say the clamping factor of the rivets has been changed from the previous repair. You're using a clamping factor of 4, protruding head rivets, so you've increased the clamping factor from the previous repair and so increased the allowable and so ... what's the problem ?

If you're saying you can't replicate the previous calculation with Airbus approved methods, then that's a different problem. If you can't use that analysis method today, why is it still acceptable for the previous repair ?

 

[LiftDivergence]

I went through and calculated critical interfastener buckling strengths based on the references I outlined above and the info you provided. Here are the results:

1. Peery using the Secant Modulus corresponding to Sigma_0.7 (MMPDS-2023 Figure 3.2.4.1.6(i)) on a tensile stress-strain curve to get the yield point and then using the curves for different n (to account for Ramberg-Osgood shape) in his figure 14.18 w/ B replaced as he describes: F_ir = 278.45 MPa

2. Alteon using compressive tangent modulus curve directly (MMPDS-2023 Figure 3.2.4.1.6(i)): F_ir = 288.28 MPa
3. Rivello using his discussion starting with Eq. 16-16 and following substitution for Figure 14.22 as described: F_ir = 281.38 MPa

4. Bruhn as you described... however I used Figure C2.17 which is basically the same as Rivello's Figure but presented a bit different, I get the same value, F_ir = 281.38 MPa

I didn't bother to to Flabel because it's more of the same. I was unable to replicate your calculation leading to 4.6 MPa.

Notes:

• Methods 3 and 4 are both using the same value of secant modulus I computed earlier from MMPDS when going through Peery. I got 42.5 ksi (293 MPa).
• This does not account for the cladding, they are just basic calcs.
• This does not account for substructure. If you are checking buckling in general for a stiffened panel the next step would be to look at the stiffeners and figure out if interfastener buckling is actually the limiting value or if there is another cutoff.

As usual I would have to most highly recommend Rivello. It is the only reference that discusses wrinkling mode in addition to buckling and the only reference that provides a clear manner for dealing with cladding effects. Additionally, it has the clearest discussion / example for stiffened panels and checking the limiting values for assembled structure (see Example 16-6). Peery is also good and in my opinion the most readable, aside from Rivello.

Now, onto the other issues at hand... your applied compressive stress is very large. Regardless of the value we obtain for interfastener buckling you have a problem. F_ir is always going to be lower than F_cy because just like column curves, there is a cutoff at F_cy. If you have a short column / stiffened strip it will be close, like we are, but still lower.

How are your compressive loads so large? Are these ultimate loads (with a safety factor?) Per 25.305 you are not allowed permanent deformation at limit, unless you can show it is non-detrimental, which is not necessarily easy.

Is this a localized point stress or a net section stress?

It's hard for me to figure out what you're doing. You've mentioned and intercostal attaching to the skin and also that you're "creating and SRM". So is this for an STC and you're making a supplemental SRM? And you're trying to adjust the lightning strike repair/allowable damage in the STC-affected area?

Regardless, if your compressive stress is that high because of changes you made to OEM structure for a repair or STC, then the new design is insufficient, or the method you are using to compute the internal stress is hyper-conservative.

I think for any of us to help more we need a much clearer idea of what you're doing.