Buckling capacity of twisted plate strut 1

[bugbus]

I saw one of these brackets holding up a kitchen benchtop and it got me thinking about how the buckling capacity of this twisted strut would compare to the equivalent untwisted version?


I suppose it basically boils down to something similar to below (ignoring the twist itself):


Does anyone know if there is an exact solution to the buckling load for a given n? Or even as n -> infinity?

I thought this was an interesting/fun problem, might play around with this over the weekend.

 

[bugbus]

OK, it turns out this could be more straightforward than I first thought

I was playing around with this in a FE software. As an assumption, I modelled the stiffer parts as fully rigid elements. I don't think that would be unreasonable, e.g., for a typical plate with aspect ratio of 5, the relative flexural rigidity is 25x more in the stronger direction.

It turns out that the buckling load can just be calculated based on an effective length equal to the sum of the lengths of the more flexible parts (in this case Lef = 0.5L because the segments are roughly equal). The buckled shape is interesting, the red parts are rigid whereas the blue parts are not.

I suppose if (EI)₁ and (EI)₂ are a little more similar in magnitude, it would be somewhat more of a complicated situation. Might investigate further if I get bored.



Intuitively it kind of makes sense. The rigid red elements preserve the same slope at the ends of the blue elements, so that when all the blue elements are pieced together, it is equivalent to a strut with length L/2.

 

[GregLocock]

You could probably model it as a series of linear flexible joints joined by rigid struts and do an energy balance. that is minimise F in F*d=sum(1/2k*theta_n²)

 

[Smoulder]

Feels like will end up like springs. 1/resultant = 1/stiff + 1/flexible.