Beam in compression 4

[Favollo]

Hi All,

let me preface I am far from being a structural engineer, which will explain the triviality of my post.

How to calculate deflections for a horizontal beam, both ends clamped, under distributed force (own weight) and compression?

I am looking at the basics, but as you can not superimpose the Euler beam theory solution to a compressive case my repertoire is almost over.

There must be more than one approach for such a common case, I am hoping in your patience!

Thank you and all the best

 

[rb1957]

a column is a "beam" loaded in compression, easily solved by Euler.

a beam is a beam (der) loaded with transverse loads, easily solved by equations of equilibrium.

a "beam column" is the combination of the two. you're right you can't superimpose them ... the bending deflections due to the transverse loads exagerate the column loading. "advanced" structures books, like Bruhn, solve this structure ... it isn't any more complicated than a redundant beam.

clear as mud ?

 

[miecz]

A solution is published in Roark's Formulas for Stress and Strain.

 

[Lion06]

Do you not have an analysis software?

 

[hokie66]

SEIT,

That is not an appropriate suggestion. If he doesn't know how to do it manually, he shouldn't be using software to solve his problem.

 

[NS4U]

A bit off topic, but, how is using software any less than using Roark's??

Personally, I would think a novice has a better chance of screwing up using Roark's than use something like SAP or RAM.

Just because you can write it on a piece of paper doesn't mean you know know it, ya know?

 

[frv]

I suspect very few engineers actually know how to truly solve this problem (beam-column).

We use codes and approximations to come up with safe solutions . But to understand the TRUE behavior of the member requires a solution to a differential equation unique to each problem. In the US, at least, this is not even taught until grad school. And this is only "easy" with "well-behaved" materials. With concrete, good luck understanding the "true" behavior.

I mention this because hokie66's comment seemed to have a self-righteous undertone. If this is not the case, I apologize in advance. I just think we should recognize the limit of our knowledge. Software, as long as one understands it, is a very powerful tool to aid engineers in mundane tasks.

 

[youngstructural]

NO NO NO! NEVER Design by BLACK-BOX methods what you cannot solve to within 30% by HAND!!!

Sorry frv, love your postings, as well as respect your opinion from numerous other threads, but I have to counter-comment on your comment. I doubt there was anything self-righteous in Hokie's comment... And even if it was, that wouldn't change the fact that our transplanted American friend is ABSOLUTELY RIGHT. I do not accept that there is anything inappropriate about telling someone that they should not use software to solve a problem they aren't able to do by hand.

And it's true that beam-column solutions are complex, often requiring higher level analysis methods, however even then, with all of our high-end wizardry, we still CANNOT know the TRUE state of stresses. Wooten's third law still applies my friend.

With utmost respect and with the hopes that no one misunderstands my passion as being arrogance or disrespect,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[frv]

youngstructural-

I gave you a star for disagreeing with me . Primarily because you were so nice about it. Is it the Canadian thing?

I don't misunderstand. In fact, you have a valid point.

Ironically, two of the posters I have come to consider most insightful are you and StructuralEIT. I say "ironically" because it would seem that at the core, you two disagree about this issue. Our current political climate in the US notwithstanding, people can disagree, yet respect one another.

I also respect Hokie66's opinion. It is obvious he has years of experience and is well versed in many aspects of what we do. If my post came off as anything other than respectful disagreement, it was inadvertent, and I again apologize for it.

I wasn't suggesting that someone with NO knowledge of structural behavior attempt to model this. However, I do think that if you know how to properly model something, software can be an invaluable tool. Therein lies the problem. How do you define "know how to properly model"? I think this is where our disagreement lies.

BTW.. I think 30% is excessive. If your hand calculation is 30% off of a computer generated one, you probably didn't catch the second-order effects.

 

[youngstructural]

Thanks frv; I was concerned I would be misinterpreted, and am greatly relieved that you have understood the heart of my concern.

Yes, I suppose being polite is something that many Canadian pride themselves upon. It tends to be a faut-pas to fail to be polite, however we have our fair share of rude & obnoxious people!

I suppose StructuralEIT and I are disagreeing here, althoug I too normally find his (her?) posts insightful; At the end of the day, for this case, you're probably right that we'll have to agree to disagree. However, that said, I think a lawyer would easily chop a designer up on the stand if they blindly followed a computer analysis and were not able to check the results by hand.

With regard to the level of accuracy for a check, 30% is my red flag, do it again until it checks out point. It's the no-go point for my analysis before it goes to the design phase. I normally find I can estimate structures to withing 15%, and am only really happy if my back of the envelope is out less than 10%.

Cheers,
And thanks for the star,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[Favollo]

All,

many thanks to your suggestions.

I found the formula in Roark's book but I am reluctant tu use a formula which I do not the derivation of, hence significance of its assumptions.

The only software I could use is ANSYS, but I would be ashamed of using it for this problem..

Right, the beam column, I could certainly solve a 4th order differential equation numerically (as the EI is varying) but what about buckling?

Yesterday evening I went back to princioples and I am pretty confident that I have found the critical load for a beam in compresion and with one concentrated load in the middle (the maths was easier than the distributed load).

I will assume conservatively this case (will certainly give me a lower critical load) and start from here.

Many thanks to all

ATB

Favollo

 

[asixth]

I was speaking to a colleague today about using design packages, and in my opinion, if the software is going to perform all the calculations that I was going to perform by hand in a fraction of a second, then why not use the design package.

As to the question, if I was to solve this problem by hand, I would first solve my midspan delfection for vertical loads (by emperical formulas) then superimpose the additional deflections that result from P-delta effects.

As for the reduction in buckling capacity that results from the combined presence of moment and axial compression. Unfortunately, I'm not to crash hot on my beam-column theory and like a true engineer, I work by the fudge factors set out in the code a reduce the member moment capacity in proportion to how hard the section is working in compression.

 

[Ussuri]

YS

Slightly off topic. Just out of curiosity what are Wootens First and Second Laws?

 

[Tomfh]

A forum such as this is not suitable for discussing Wooten's first and second laws.

 

[Lion06]

Well, there has been quite a bit of discussion since I last logged on. I certainly didn't mean to imply that anyone should blindly accept output from a computer.
All I was trying to get at is that if you have a difficult problem in which you at least understand the behavior and can tell (at least qualitatively) that the program is doing the right thing that I wouldn't see anything wrong with it.
As an example for the OP, I might try using a minimum potential energy solution assuming a deflected shape. That can still be time consuming (and may not accurately capture the second order effect).
I should also say if I can't analyze the problem completely accurately I would use a conservative analysis and compare that to the computer output knowing that my results are conservative.


Favollo-
You can use a minimum potential energy solution to get pretty close to the buckling load for a fixed end column with a lateral load applied. It will take some work/time to put the equations (for equilibruim) together and solve, but is much, much easier than using a 4th order differential equation and will get you very close (probably within 3% - 5%. Did I mention that it's A LOT easier than going the 4th order DE route?!

 

[miecz]

Favollo-

In your original post, you described yourself as "far from being a structural engineer", and asked for help to calculate "the deflections for a horizontal beam, both ends clamped, under distributed force (own weight) and compression."

In your second post, you are solving for the buckling load using 4th order differential equations on a section with variable EI.

Whew! That's quite a jump. Now it sounds like you're intending to design a beam-column. If that's the case, and you are truly far from being a structural engineer, then you probably ought to find a structural engineer to design it for you.

On the question of Roark vs. computer solution, NS4U raises a valid question, i.e., is using a formula from Roark any different than using someone else's software? One difference I see is that, when using a software package or a purchased spreadsheet, there is a tendency to shift some of the responsibility for the correctness of the result to the software, even though the software license agreement disclaims any responsibility. When one calculates by hand, it's clear where the responsibility lies, so I think, we are more fastidious, resulting in fewer errors. Also, when using Roark, the formulas are there for scrutiny, the text preceding the tables gives insight to the solution, and references to the development of the formulas are also given. That quite a bit different than an input manual or a spreadsheet with cryptic formulas.

 

[graybeach]

One question I have, how much compression is there? If it is as low as 10 to 15% of the total compressive stress, maybe a simple beam calculation would be sufficient.

 

[csd72]

Favollo,

As graybeach has mentioned, the effect will usually be negligible if the axial load is less than 15% of the capacity.

If this is the case then additional deflections from the axial load can usually be ignored.

At higher axial loads the situation is more complex. At first order there is additional moment from the eccentricity of the axial load from the line of force, this causes additional eccentrity which causes additional (2nd order) moments and so on until it reaches equillibrium.

If this is a critical component, then I would definately reccommend that you get it designed by a structural engineer.

 

[Favollo]

Graybeach, Csd72,

the design I am getting at would be loaded at 13.7% the compressive capacity. Still the moment due to eccentricity is more or lss 30% of the moment due to transversal loads, which looked too much.

I have not had time to look at the energy method yet as suggetsed by Structural/EIT, will give it a go later.


Miecz,

when I meant stating I am far from being a structural engineer I intended I do not have any experience of codes, subtitles, empirical formula, fudge factors, basically real world.

I can easily solve numerically a 4th order equation, but would not tell anybody to live under my beam as any ODE is a simplification. What if section are not plane, what if membrane loads are significant, what if linear kinematics is not sufficiently accurate?
That is why I wanted to hear your opinion.

The beam is not a critical component at all, its failure would result only in me being fired!

Many thanks sincerely to all for sharing some knowlegde, very appreciated.

Take Care

Favollo

 

[apsix]

If you have both Roark's and software use one to check the other, without being ashamed.
I certainly wouldn't touch a differential equation, 4th order or otherwise.
I've been given tools, they are widely accepted as being accurate therefore I use them.
Of course an experienced, critical look at the results is required.