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Hardy Column Analogy 3

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Celt83

Celt83

Structural
Sep 4, 2007
2,084
Does anyone have a go to resource or book for the Hardy Column Analogy?

I've been able to find bits+pieces via some google searches but would love if I could find a textbook or practical example source.

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Excellent thank you!

I've got a 2d frame via moment distribution method program pretty well flushed out but realized trying to extend it to concrete equivalent frames it had some short comings. After various searches I stumbled on the Hardy Column Analogy which seems like it could solve some/all of my discrepancies and by extension have some other applications.

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I came by the method similarly. I wanted to understand the derivation for equivalent columns with drop panels and capitals. My first stop was this book which got into the Hardy Cross method and would be well worth the $4 price tag: Link. It's essentially the hand calc version of what you seem to be attempting.
 
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For anyone else's reference I found the book KootK linked to be OK but not quite what I was looking for so I picked up the full version of the CRSI for the 1971 ACI code which in tandem with the supplement provides some great information as well as reference charts.

Two books I found that so far have some excellent information and touch a bit more in depth on some topics I'm trying to tackle are Moment Distribution by James M. Gere and Indeterminate Structural Analysis by J. Sterling Kinney

CRSI -
Moment Distribution -
Indeterminate Structural Analysis -
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Celt83 said:
Moment Distribution by James M. Gere.
Click to expand...

Might need one of these. Can you post a pic of the table of contents and/or a bit of what you're finding enlightening?

Celt83 said:
...I found the book KootK linked to OK but not quite what I was looking...
Click to expand...

How %?@#ing dare you? If I live to be 1005, I will carry this slight to my grave.

The book below also has some good stuff in this space. Just a few pages mind you. Hoffman has actually authored a lot of the related papers if you poke around. Everybody should really have a copy of this however. Just in general, it's probably the best practical "office concrete design" book that I know of. Even better than Fling I'd say. The older editions are both better and cheaper. All are out of date code wise and, as with most things (including the CRSI manuals), they stopped including some very useful/fascinating things with the advent of personal computing machines.

c01_p79dr0.png
 
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So the Gere book has chapters dedicated to non-prismatic members as well as some good content on sway frames, elastic supports, and slanted columns all relative to the moment distribution method.

The Kinney book has a chapter on the column analogy with some worked examples and a follow up chapter using conjugate beam to accomplish the same thing.

Don't feel too slighted I didn't exactly give some great info on what specifics I was looking for.

Will post some images of the contents when i have the books back in front of me.

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Oh.. don't bother. I already caved and bought both Kinney and Gere. I really need to line up an EIT to travel to Calgary and assume possession of my -- truly unrivaled at this point -- structural engineering textbook library when I die. Baring that, it will be one mighty sad hoarding clean up with all kinds of cool stuff going to the landfill or to the 4/$0.99 table at some used book store that doesn't know what they've got. Of course, by the time that I die, it's entirely plausible that EIT's will no longer know how to read. The work will just be perusing 3D, ETABS virtual reality models with stress contours.
 
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Trenno said:
Just you wait KootK...
Click to expand...

And there it is... neat! What a great learning tool that would be.

Celt said:
KootK so you can plan your reading ahead of time
Click to expand...

Thanks for that. Based on the TOC, I'll not have buyers remorse ($5 + $15 shipping). Wife won't like the extra "dead weight" in the library but I can manage that.

I just realized that the Gere who wrote the MDM book is the same Gere that wrote what is probably my ATF advanced structural analysis book. That bodes well.

c01_xzjbdm.jpg
 
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I think you guys are discussing the Hardy Cross moment distribution method.
I learned this in my senior year at Cal Poly (1960). The version taught also included how to consider haunch members and the distribution factors were provided on a handout by my professor, Mr. Mager. When I took my SE exam in 1970, there was a continuous multi span concrete beam problem with haunches and the State provided the additional factors. But the State's handout sheet was illegible so I pulled out my school copy and used that. (open book test). I eventually wrote a spreadsheet in VisiCalc for the Hardy Cross method to use on my Radio Shack TRS-80 Model II. (Actually met Dan Bricklin who wrote VisaCalc - a new hero). Later I used SAP-80 which I bought from Ed Wilson. It would run on the Model II.
 
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oldrunner:
Yep more specifically though I was initially looking for resources on the Hardy Cross Column analogy which allows you to get the fixed end forces, stiffness, and carry over factors for non-prismatic or even prismatic beams. How I'm understanding it you essentially take your beam and call it a column cross section where each segment has a width of 1/EI and you then load it with the pin-pin moment diagram and utilizing the "section" properties of the analogous column and P/A +/- M/S the resulting +/- stresses are the fixed end moments.

Could accomplish the same thing with conjugate beam, but found a random reference to the method and felt like trying to learn what I could about it.


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For anyone still following along I made a quick python script to calculate the member end stiffness's and carry over factors using the Hardy column analogy.
[URL unfurl="true"]https://github.com/buddyd16/Structural-Engineering/blob/master/Analysis/HardyColumn.py[/url]

It assumes each segment section has consistent E and I values and that consistent units are used within the inputs.

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"Statically Indeterminate Structures" by Chu-Kia Wang, Ph.D. 1953 by McGraw-Hill Book Company Inc. was the reference I used in the 1950's. Chapter IX is devoted entirely to the method of column analogy.

BA
 
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Thanks for that BA...searching for that one on the web I stumbled on another book by Chu-Kia Wang titled Structural Analysis on Microcomputers couple copies on amazon hovering around the US$6.00 mark.

I guess one other benefit of looking into these older hand methods is the textbooks aren't in the triple digits anymore.

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