Edge Restraint in Local Buckling of Extruded Shape 1

[Sparweb]

Hi all,

Referring to Bruhn, chapter C5, I've not worried much in the past about the exact definition of the term "epsilon" or ?, the edge rotational restraint coefficient. Most cases have worked well enough with either "0" or "?".

Now that I get down to needing it, however, I fail to find an actual definition of the coefficient. Any pointers? I also have McCombs' supplement, and haven't turned it up there, either.

Steven Fahey, CET

 

[Sparweb]

Apparently the special greek ANSI characters don't always work on screen, even if I can get them on screen when I write the post. Hope my question is clear, regardless.

 

[SuperStress]

SparWeb,

Bruhn says on p. C5.1, right hand column, second paragraph that epsilon is the raio of rotational rigidity of the plate edge stiffener to the rotational rigidity of the plate.

You can see from figures C5.2 and C5.3 that at epsilon equals infinity in C5.3, you have the clamped condition (Curve A) from C5.2. When epsilon equals zero in C5.3, you have the simply supported condition (Curve C) in C5.2.

Hope that helps.
SuperStress

 

[Sparweb]

Superstress:

The extreme values, I remember being discussed in college. It's the finer gradations in between that are hard to pin down. I have continued to pursue the matter, and with a suggestion from a colleague, I have tracked down a definition in an ESDU paper, but not a helpful one. If anyone is familiar with ESDU 02.01.23, please tell me what I'm doing wrong.

I start with the Elastic Stiffness per unit length:

N = E*Ar / (a*b)

where:
E is the modulus of elasticity,
Ar is the area of the flange cross-section,
a is the plate length,
b is the plate width.

With N, the flange's edge restraint is defined:

mu = N*b / (E*t)

where:
t is the thickness of the flange

This can be simplified into one step:

mu = Ar / (a*t)

For the case I'm dealing with, it reduces even further because Ar = b*t

mu = b/a????

If we're applying the compressive load on "b", then according to the formula, the longer flange is the stiffer one - I don't think so!


Steven Fahey, CET

 

[SuperStress]

SparWeb,

Unfortunately, I don't have that ESDU paper, but here are a couple of observations.

The units for 'N' don't seem to work out. If this term is supposed to be stiffness per unit length, the two area terms' units cancel and you're left with units of stiffness.

Also, when computing mu, do your 't' values really cancel out? Isn't one of them your plate thickness, and the other is the stiffener flange thickness? Obviously these COULD cancel, but not necessarily so.

Like you, I've never had to work with intermediate boundary conditions, but basically we are talking about torsional stiffness. Flabel talks about this a little bit in his book "Practical Stress Analysis for Design Engineers" on pp. 488-89, however he never gets around to saying how you calculate it in practice.

The torsional stiffness of the stiffener elements should be pretty straightforward with a JG/L computation, but I'm not sure how you treat the plate. Do you use the entire plate, or some effective width?

Has anyone else seen a reference in a company stress manual or similar?

SuperStress

 

[Sparweb]

Mixing up "t" values could by my mistake. The ESDU papers would benefit greatly from Free Body Diagrams.

Thanks Superstress, and I await the answers to your questions as anxiously as you...

Steven Fahey, CET

 

[alexeu]

Sparweb, you might want to try NACA 733. Most probably you will find what you are looking for. That reference was called out from NACA TN 3781 and Bruhn C5 reference page references TN 3781. Good luck.

 

[Sparweb]

Thanx Alex.

Steven Fahey, CET

 

[Sparweb]

I have been reading through TR733 as you suggested, Alex. Associated are TR 734 and 735, as well as TN 3781. Put togehter they give a very complete answer to my question. Thanks.

Steven Fahey, CET