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

 

[graybeach]

Favollo,
Is your allowable deflection for a 8 meter long beam 1mm? I am kind of metrically challenged, but isn't that L/8000? What is your application that has such a tight deflection limit?

 

[miecz]

Favollo,

While using Roark's case for fixed ends gives 1.5mm (I get 1.45mm), the case for pinned ends gives 37.6mm (did I do that right?). I'd give close consideration to how rigid your supports are.

 

[Favollo]

Graybeach,

1 mm as a tolerance is not a limit imposed by anybodu, it is just the result that come out first and for some reason I am trying to stick to it.

The fcat is that all I know about elasticity was learnt at school, and if you apply a linear model is stricltly speaking correct only if deflrction are infinitesimal, which is clearly a theoretical abstraction.

I do not have a clue about what a structural engineer considers acceptable, 10,5 or 1% a characteristic length.

The only criteria is not allowing buckling.

 

[youngstructural]

Favollo:

Deflections are one of the most obscure and "gray" areas of Structural Engineering. This is one of the areas where Structural Engineering is much more art than science.

My best advice to you: Consider your permissible deflection in terms of the length of your beam. Then consider what you area limiting the deflection against, and choose an appropriate limit from the list below:

1) You want to prevent people from seeing the deflections, and
i) your line of sight is along the invert: SPAN/360
ii) your line of sight is accross the invert: SPAN/180

2) You want to prevent cracking of brittle cladding (glass, stucco): SPAN/500

3) You want to minimize any possible vibration problems: SPAN/600 (VERY conservative)

Please note that a proper vibration check is needed (stiffness and source of the excitation are key to a proper check) if you want to be confident of minimizing vibration, however a good short hand is to check the following against EXPECTED (not factored or specified) loads:

Frequency (Hz) = 18/SQRT(Total Deflections in mm)

A result of 8 or greater is desirable, with 15 or greater being quite reliable.

Hope that helps,
Cheers,

YS

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

 

[40818]

Further to Youngstructurals post, in the small deflection theory of elastic bending, the limiting factor is the radius of curvature of the beam rather than related to the thickness of the beam, or span factor. Read timoshenko i recommend. You can also have large displacement but perfectly elstic bending of a beam depending upon such factors as material etc.
From a pure static strength point of view, the deflection will not be the critical factor, but may become so due to other considerations.

 

[hokie66]

I think in this case the focus on deflection has become a red herring. What Favolo has is a compressive strut, with bending only due to self weight. The member required is dependent on the end conditions and whether or not there is any intermediate bracing. It is similar to a horizontal strut in a braced roof plane. I doubt that fixity should really be assumed. The member should be designed as an 8 metre long column with pinned ends. Many engineers ignore the self weight bending in these cases, and it only makes a small difference in member size.

 

[Favollo]

Youngstructural,

your post was enlighting.
I have never thought you people would limit deflections in order for people not to notice them, with even ad hoc factors subject on view angle. Dead crafty.

40818, I see your point which is of course evidenttly right.
This story about the displacements is coming from a post of mine which was rather unprecise, I want to limit the curvature not the deflection per se as well.The two being related explains my poor expression.

Anyhow, the all point of this conversation, by the way the most interesting, was how to calculate the section. Now the focus is on the design criteria, while it seemed to me any agreement on the calculaion method itself, leave the criteria, was far from reached.

However, assuming the calculation is fine, my criteria is simply avoid buckling, whatsoevr the displacements.
In order to use the calculation I propsed the curvature has to bee as small as possible though.

also in analysing buckling linearly deflections are undetermined, so there is no way of using a defklection as a criteria, if you alredy beyond the loss of stability.

I do apologize for the most verbous post and I hope to hear still from all of you.

Have a nice evening

ATB

Favollo

 

[graybeach]

Favollo, it is true that the responses have gone all over the place, making for an interesting conversation. This shows that your post is not really trivial. Anyway, part of the art of structural engineering is knowing how far to go. Instead of spending many hours trying to get the deflection absolutely correct, an experienced structural engineer might make some simplifying conservative assumptions and see how the deflection comes out. If it turns out to less than the allowable, and as long as the assumptions were valid, you are done.

 

[graybeach]

One more thing. The checks to avoid buckling in a beam column involve, in ASD, calculating the stresses and checking them against an allowable that is calculated based on the properties of the section and the relative amounts of bending and compression, or the equivalent procedure in LRFD. In the US, we do this based on the AISC code. You must have something similar in your country.

 

[Favollo]

Graybeach,

needless to say I totally agree with the opinions presented in your posts.

I am also sure in England there is a code equivalent to AISC, but I would not know where to look.

Anyhow the beam has been now designed considering the worst case between Roark's formulas and the Euler Beam column ODE.
Pinned ends have been considered for safety's sake.

The beam is being manufactured at the moment and will be used for one off event middle of July.

I will let this post's aficionados how events progressed...

Thanks to all and have a nice evening

Favollo

 

[apsix]

Favollo
You're a braver person than I am.
You have designed a 8 metre long column (not beam) supporting 40 tons and you don't know if it complies with the steel design code BS5950.

For peace of mine you could check it using downloadable software;

http://www.corusconstruction.com/en...ware/software_sci_corus_interactive_blue_book

NB I haven't tried to download or use it.

 

[Favollo]

Apsix,

you are kind in your irony, I would have accepted being called a fool rather than a brave.

I will certainly check the link at the first occasion.

Do not call the police, it is not a structural application and no damge to people could occur anyhow!

Kindest Regards

Favollo