Buckling Capacity by Newmark's Numerical Procedures 2

[WoodDesignCat]

thread507-267603
thread507-278129
I'm trying to learn to use Newmark's Numerical Procedures for calculating buckling capacity of a column with varying cross section.

In the thread507-267603 user BAretired said he posted some notes, but it looks like the were removed when the thread was closed? Can someone repost those notes for me please?

I'm currently looking at Theory of Elastic Stability 2nd Edition by Timoshenko & Gere, section 2.15. The Determination of Critical Loads by Successive Approximations,

http://www.kstr.lth.se/fileadmin/ks...ity_by_S._Timoshenko_and_J.M._Gere__1963_.pdf

which refers out to
"N. M. Newmark,Numerical Procedure for Computing Deflections, Moments and Buckling Loads, Tram. ASCE, vol. 108, p. 1161, 1943."
Does anyone know where to find a copy of this article? I'm having trouble finding it.

I've also been looking at a thesis paper by Charles E. Riley, "ELASTIC BUCKLING LOADS OF SLENDER COLUMNS WITH VARIABLE CROSS SECTION BY THE NEWMARK METHOD".

http://files.engineering.com/downlo...73c96fd89c&file=Variable_Section_Buckling.PDF

Where he applies the method by spreadsheet, but often when he references elsewhere in the paper it's an outdated reference that has since been changed to a new figure or column, and I'm not positive everything is done correctly. I followed through his pinned pinned example, which he starts outlining on page 38. I was able to replicate the table he produced in the Appendix, but to do so I had to use different equations than the one he referenced in figure 3.2 (called out as 3.1 in the explanation),and had to change the first and last "Nodal Concentration" to be something that I think is incorrect. He also set-up his sheets specifically for tapered columns, so for stepped columns I think I will need to add revised equations.

I also found thread507-278129 where user IDS points to an Excel calculation tool that he developed to do this. I was able to download that, I haven't tried going through it yet to see how it works, I plan on doing that and see how it matches up to the Timoshenko text as my next attempt to understand the calcs more.

I'm going to be applying the calculations to a stepped column, I want to try to understand the method more fully before running with what I have.

 

[IDS]

I had a look through my personal collection of pdfs on column buckling, and the best I found from a quick search can be downloaded from:

https://archive.org/stream/nasa_techdoc_19690025320/19690025320_djvu.txt

It's quite old, but looks pretty comprehensive.

I thought I had downloaded the paper originally linked by BAretired (now no longer available on-line), but I can't find it.

If I recall correctly (which I may not) I developed my spreadsheet based on the Timoshenko and Gere book. Did you find that it did not fully describe the procedure?

You have probably seen the link to my blog post below, but if not it would be worth a look:

https://newtonexcelbach.com/2010/08/09/buckling-of-columns-with-varying-cross-section/

If you need more details or background on how the spreadsheet works, please ask.



Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[BAretired]

WoodDesignCat,

I still have a dog-eared copy of notes on Newmark's Numerical Procedures. They were removed or lost when the thread was closed. There are 25 pages of notes, some handwritten portions; I do not want to be scanning it on a regular basis, so I think it might be useful if Eng-Tips had a place to store it for posterity. One possibility is SlideRuleEra's storage file, but we would need his permission to store it there.

Too late to start tonight; I will start scanning tomorrow.

BA

 

[JoshPlumSE]

WoodDesignCat -

That AISC design guide has been released.
Design Guide 25: Frame Design of Web Tapered Members

Appendix A has a method termed "Method of Successive Approximation" that I believe you may be looking for. This appendix references both Newmark and Timoshenko / Gere. This is likely the same sort of thing that IDS referenced.

Then Appendix C walks you through a couple of good examples using this method.

 

[rb1957]

My most comprehensive Column analysis text is McCombs "Engineering Column Analysis".

another day in paradise, or is paradise one day closer ?

 

[BAretired]

Well, that wasn't too bad. The last time, I had to feed it in one page at a time. My current printer/scanner allows me to use a feeder. Ain't technology grand?

Here it is. Enjoy.

BA

 

[WoodDesignCat]

Thanks for all of the responses already.

BAretired, thanks for scanning those, I uploaded them to a dropbox file that I labeled to not delete, so hopefully this is a more permanent link to share them by. I'm not sure a better way to make files available online long term without hosting a website.

https://www.dropbox.com/s/jxjuryc8sisqt8k/BAretired_Newmark_Numerical_Process_notes.pdf?dl=0

IDS, I think the Timoshenko book will be enough, it just says the Newmark article presented the material in very complete form, and that it gives more examples with other end conditions, so I thought it would be a good document to review. Also I'm not sure I understand what condition Figure 2-45(c) is showing. "The formulas in Fig.2-45c give the equivalent concentrated loads due to a distributed load between stations n and m only. Thus, these formulas are used when the load changes abruptly at the station point. The ordinate to the M /EI diagram labeled c may be an extrapolated value if, for some reason, no actual value exists." I probably wont need this equation, but if I had a curved profile, then a sudden jump to a different curved profile, would I need to use this equation twice, once for each profile, and have an estimated value for c past the change in profile? I'd be interested in seeing the derivation of 2-45(c). I'll go through those examples, your blog, and your Excel sheet and post if I have more questions.

https://www.dropbox.com/s/1xwf07p7vcegvix/2-45(C).PNG?dl=0

JoshPlumSE and rb1957 I'll check out your resources as well.

I might not be able to get back to this until Monday, I need to switch over to another project for today.

 

[BAretired]

I can explain what 2-45(c) is showing. You will see a similar sketch on p. 23 of the notes I emailed earlier. Think of a cart of length d with an ordinate a, b at each end. The total load on the cart is the area under curve ab. Curve abc is taken to be parabolic. Even when the curve is of higher order, this approximation is pretty good over a short distance.

Rnm and Rmn are reactions of the cart to the load on it. The total load on the left cart is ad/2 + bd/2 + 2hd/3 where h is the ordinate of the curve above the straight line between the ends of the curve at m and n.

The centroid of the triangular loads are at the third point of the cart length. The centroid of the parabolic cap is in the middle of the cart. The height h is one quarter of the rise of the double cart, or h = [b - (a+c)/2]/4. I was thinking while typing, always a dangerous thing, so I hope I got it right, but the reactions are simple geometry.

BA

 

[IDS]

Well, that wasn't too bad. The last time, I had to feed it in one page at a time. My current printer/scanner allows me to use a feeder. Ain't technology grand?

Yes, almost as good as the fax machines of 40 years ago

Thanks for taking the time to do that (I'm not sure if I should confess that I have now found the copy you posted previously).

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[BAretired]

That's okay Doug; if you had posted it I never would have found out about the attributes of my new printer/scanner.

BA