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.

 

[levanang]

If doing 122 calc's is considered unfeasible, you may consider doing a table approach and take a conservative allowable based on selected t and p values. Example is attached.

Yes This would be perfect for my scenario, however I have different materials also here. I have to check some other method which can be done within Excel.

 

[WKTaylor]

Possibly related...

15.2.11. Inter-Rivet Buckling - Abbott Aerospace UK Ltd

Reference: Abbott, Richard. Analysis and Design of Composite and Metallic Flight Vehicle Structures 3 Edition, 2019. The common method for inter river buckling is based on Euler column behavior and does not include a correction for Poisson’s ratio effect. There is a method defined in...

www.abbottaerospace.com

Cited in the previous link...

 

[rb1957]

how different are these materials ?

could you use conservative material properties (envelop lowest) at least as a quick assessment to see what is most likely the most critical ?
and maybe re-calc with less conservative properties (if close).

but "surely" we're seeing that the applied (357 MPa) is so much greater than the probable allowable (270 MPa, give or take) that this solution is not going to work and needs a re-think ?

 

[LiftDivergence]

I have all the books you mentioned above, what is Alteon I don't know, Please give me full reference.

Alteon was a company that did structural analysis training for engineers and was acquired by Boeing. So it's a Boeing company but they have a lot of training slides/notes out there that are not proprietary material.

Please show one of your calculations and How to calculate F0.7.

In this case I just did it graphically. Use the stress-strain curve, draw a line that's 0.7E and find where it intersects with the curve. Alternatively you can do this mathematically if you have the Ramber-Osgood K and n values or Hollomon parameters for the material.

I'm still a bit confused though, since your applied compressive stress is in excess of both the interfastener buckling strength and the material Fcy.

Of course we don't always consider buckling to be a failure, in most situations a section can be loaded well in excess of buckling before failure. And of course there are plastic buckling methodologies that can be implemented in analysis. But those are primarily for situations where it's possible that the stress at initial buckling is above the yield strength of the material.

I understand we're talking about flat plates between fasteners here, but as a simple analogy let's just consider column buckling (plates & thin-walled structures are essentially the same, just with some tweaks to the methods). You can separate the load vs. L'/rho curve into regimes... for short slenderness ratio you'll either be block compression or crippling critical. Intermediate columns would fail in a complex mix of primary and secondary instability and you'd be using the Johnson-Euler method. For long columns, you'd basically just have primary instability and Euler or Euler-Engesser (if you want to account for plasticity) should be used. In order for the buckling strength to be over Fcy you'd either need a stiffened and supported assembly or a very short slenderness ratio. In that case you'd likely be crippling critical. But I suppose it's possible that since the crippling stress is defined as the average stress at failure, it's possible to have a buckling mode at a stress over Fcy, before crippling of the section occurs. In which case you'd need a plastic buckling method. Johnson-Euler is generally cutoff at Fcy. I guess it's also possible that you could be an intermediate column and want to take advantage of post-buckled strength in your design. So you want to know what happens if you keep loading past the interfastener buckling strength.

But your analysis shows you will elastically buckle first, and then your applied load keeps going all the way well past yield. So in order to show this structure is OK you need to take advantage of post-buckled strength and also show whatever permanent deformation occurs in the buckled state is non-detrimental? Seems like a tall order. I guess I'm still wondering what is being done here and why you're so set on showing this is OK. Seems to me like the design is insufficient.

 

[rb1957]

I thought "post buckled" behaviour referred to shear buckling (and shear buckling with normal stresses). I thought that once a section crippled, well then, that was lights out (at least for that loadpath, if you needed to you could fail that loadpath as see where the load goes to ... basically "fail-safe"). If the skin cripples, or buckles by inter-rivet buckling, then what strength remains in the skin ?

 

[LiftDivergence]

I thought that once a section crippled, well then, that was lights out (at least for that loadpath

This is true, crippling is a failure stress, although to be crippling critical you need an L'/rho usually <20 and this is really only a term used for failure of thin-walled members of stiffened shell structures.

I thought "post buckled" behaviour referred to shear buckling (and shear buckling with normal stresses).

That is one form of post-buckled strength but not the only one. Flat plates in compression don't usually have much capability after buckling (unlike columns). But for thin-walled compression section of stiffened panels in the intermediate regime (~l'/rho between 20 and ~80) often times they can continue being loaded well past the onset of the first primary or secondary buckling load.

I'm just making the distinction that sometimes structures are design such that they don't buckle even at limit or ultimate. But otherwise you'll potentially have to deal with things like large deflections, etc.

If I can refer back to Rivello again, I'd point to:

• Section 15-7 for plate postbuckling behavior
  • Fairly involved, not usually recommended. For simple plates initial buckling might normally be considered a "failure" and no real effort to take advantage of post-buckling is typical.
• Section 15-8 for inelastic buckling of small b/t plates.
  • As I mentioned, this is where a difference with column compression comes in, the "failure" of a plate is not as well separated into regimes as for a column but typically for small b/t the point at which no higher load can be applied is not until a significant portion of the plate is plastic.
• Stiffened panels and thin-walled columns are covered in chapter 16.
  • For these, the behavior can be more easily separated into regimes based on L'/rho and adaptations are made by Gerard and Stowell.
  • Buckling will occur in the intermediate and long regimes and initial buckling is distinct from failure. Intermediate thin-walled column or stiffened panel specific methods for assessing these strengths need to be used as presented but in general these structures can be loaded past initial buckling before they see their peak load capability.

 

[levanang]

I guess I'm still wondering what is being done here and why you're so set on showing this is OK. Seems to me like the design is insufficient.

@LiftDivergence Thanks for your valuable inputs. Since, I am new to this stability analysis, I think I have to go through lot. As of now I am doing these analysis for my Intercostal locations for the repair manual preparations. Already Certification done with the different methodology, they don't want dig deep in loading point of view. As I shown only one example locations shown above which is already having applied load over Fty this is creating more debates. However, out of 62 my analysis locations, I am getting 13 locations low RF. As of know, there no further approach from my customer side.

@Stress_Eng , Thanks for the method which you suggest It makes my work faster. I have created a simple macro to do Goal-seek for my locations, which done within 10min.

@WKTaylor Thanks for your response.

​