Dynamic Buckling 4

[WARose]

I've got a project where I have to get reacquainted with the concept of dynamic buckling (primarily from axial loads due to a sudden load). Can anyone recommend a resource where I can quickly check sections I have for this? Most of the resources I have (and have found) are really not that useable. Thanks in advance.

 

[Denial]

This problem is one I have very occasionally contemplated over the years, but never pursued.[ ] This post has "piqued my interest" again, and I now have a bit of time to play with it.[ ] I am exploring an energy-focussed approach, and hope to have a tentative offering soon.[ ] The paper KootK referenced (for which, my thanks) is a sound and thorough exposition, but is a long way from being useful to a practising engineer.

Gravityandinertia.[ ] Love your handle, and would also love a look at your first-principles musings.

 

[WARose]

Thanks Denial. I've found some stuff and should post in the next few days myself.

 

[Denial]

I have made some progress building a spreadsheet to solve a grossly oversimplified version of my understanding of this problem.[ ] I attach a zip file that contains both the spreadsheet and a document describing the method used & (some of) the assumptions under pinning the method.

This spreadsheet is, at best, highly preliminary.[ ] It must not be used on any real project.[ ] I am putting it up on Eng-Tips at this stage in the hope that some members of the EngTipsBrainsTrust (you know who you are and the rest of us know who you are) will take a critical look at it.[ ] I would greatly appreciate their views on any aspect of it, including the validity of the assumptions, whether the assumptions are likely to be conservative or unconservative, and any implicit assumptions I have overlooked.

Once I have received some ETBT feedback I will decide whether it would be worthwhile taking the exercise further.

Thanks in advance.

 

[WARose]

You did a lot of work Denial......impressive. One comment I would like to make though (even though I am certainly not part of the BrainTrust here ): what I am finding so far is that slenderness (of local elements) has influence here (as well as imperfections) just like it does for static loads. From a paper I was reading yesterday:

"From a study of the sample problems of stiffened panels and I-section
column, the imperfection-sensitivity and the collapse strength are seen
to be governed by two parameters, i.e., slenderness (B/t or ds/t) of the
stiffening elements and the ratio of Euler to local critical stresses. Under
conditions of the sudden application of load, the load carrying capacity
of the structure is diminished by about 8% and possibly more."

--'COLUMNS: STATIC AND DYNAMIC INTERACTIVE BUCKLING', J. Eng. Mech., 1984, 110(1): 49-65

I'm not sure from seeing your spreadsheet if that is taken into account or not so I thought I'd mention it.

I'm working with the aforementioned paper (and others) to try to get something useable. Will advise.

 

[gravityandinertia]

Denial,

I'm a bit swamped at work at the moment and my work would need to be organized a bit better for someone to follow along, I'm hoping maybe I'll have sometime to do that this weekend and start a dialog with the work that I've done and what you've done.

 

[WARose]

Another interesting paper I have been reading is: 'DYNAMIC BUCKLING OF SIMPLY SUPPORTED COLUMNS UNDER AXIAL SLAMMING', J. Eng. Mech., 1999, 125(5): 513-520, by: Cui, et al.

It takes a look at dynamic buckling (vs. dynamic plastic yielding) for fluid-solid "slammed" columns. The difference between fluid-solid & (direct) solid-solid impact being duration of the event. It classifies fluid-solid impact as a "moderate" event in terms of impact time (i.e. being from 0.015 to 0.022 seconds in their tests).

In any case, they tested a number of square steel "columns" that were roughly about 0.5" x 0.3" (that varied) and about 17 inches long. They determined a "critical" impulse for both the onset of plastic yielding and dynamic buckling.

In cases where the slenderness ratio was less than about 135, the dynamic buckling impulse value was greater than the value needed for the onset of plastic yielding (as you would expect).

With just impulse values.....I needed to back out of this thing with real numbers. With one specimen (i.e. 14.52mm x 12.26 mm x 450 mm), I came out with their dynamic buckling value at 103 ksi. (They give: Fy= 56 ksi & Fult= 82 ksi in the intro.) The allowable static (buckling value I came out with was 9.11 ksi (using Table C-50 in the green book (ASD 9th)). So that's an increase over the static buckling strength by a factor of about 11. (However the onset of plastic yielding happens at 93 ksi.) This is of course by my calculations and assuming a impact time of 0.015 s.

Something else interesting: they confirmed a linear relationship between impact duration and dynamic buckling value (the shorter the duration, the higher the value).

Of course, testing these sorts of sections does not account for local slenderness issues with I-sections and the like.......but I thought I'd post.

 

[Denial]

The spreadsheet I posted above on 09Aug16@08:26 contains an error (in addition to containing a heap of tenuous assumptions).[ ] The error is in equation 3 in the notes that I posted with the spreadsheet, where the expressions for the bending strain energy require an extra 2 in their denominators.

As well as fixing that error, I am tarting the whole thing up.[ ] When this is done I will post the result to my website.

 

[WARose]

Thanks Denial.

Something I would like to add to my last post in this thread (that I forgot to mention before): The Dynamic buckling value I came out with (i.e. from my calculations on that Journal article) compares favorably with the paper Mr. Kootk was kind enough to provide (i.e. 'Dynamic Buckling Estimates', AIAA, 1966, see Figures 5&6). This is approximating the impact load as a rectangular load.

So at the very least we (may) have an idea as to the upper bound (limit) to the problem.

 

[Denial]

The revised spreadsheet I referred to above (five days ago) is now downloadable from my website (

http://rmniall.com).