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

 

[40818]

Just thought i'd pop a thought in...

The use of software to solve situations such as beam columns requires a non-linear approach, and is greatly more complicated than a simple linear run.

 

[Lion06]

RAM Advanse does a second order iterative, non-linear analysis.

 

[Lion06]

but you will need several nodes along the length of the member as it only captures second order effect from nodal displacements, it doesn't capture second order effects from displacements between nodes.

 

[youngstructural]

Ussuri: No one knows! Tomfh is dead right in saying that this forum is not an appropriate place for Wooten's first and second laws, even if we don't know what they are. Let's just say that Wooten's first and second law are more appropriately developed/proven between two consenting adults.

Sometimes I wonder if we don't have a major problem in our industry caused, for the most part, by software. I have heard of engineers relying blindly on software and ignoring other evidential input as the project progressed. Memory fails which, but there was a stadium case study at University which saw a partially erected roof frame system collapse DESPITE the fact that the engineers were warned by a number of project team members (foreman, steel erector, project manager) that the steel was deflecting too much... And ignored it. It seems that they were relying on a computer model that told them to expect the deflections. They just didn't check that the connections could handle the rotation. They couldn't.

Now, many engineers in my class pointed out that they missed a step of the design process, and that could have been missed in a hand based analysis as well.... BUT, our professor was quite right (in my opinion) when he pointed out that these mistakes are made easier by the laudanum-like effect of computer graphics presenting you with what looks like a ready-made, complete, solution inclusive of your stresses.

Apologies for the long post!

Cheers,

YS


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

 

[40818]

You have hit upon a gripe that has been going on for some time across manu industries.
One thing that stands out in your post was the engineers ignoring others vocal judgement. To do so requires either total confidence or just stupidity and arrogance. It seems the post has taken its own path rather than the op's intentions, however, my opinion is that you should always have an idea as to what you should expect in both numbers and behaviour if your going to do any software analysis (FE, Complicated mathcad, excel with macros etc). Otherwise how do you know if it reflects reality. If any of the engineers who work for me cannot do it by hand, i wont let them do it by black-box approach.

 

[kslee1000]

Hand calculation on small scale structures enhance the understanding of complicate matters. Computer analysis fasten the process, and make some impossible to been possible. At the end, common sense, or so called engineering judgement rules.

 

[Favollo]

Hi there,

this conversation is utterly interesting.

Without fear of being unpolite, I must though admit I am very surprised.
It has been suggested the beam colum should be designed by as tructural engineers.
A few of you, has made their contributions and suggestions range from Roark's formula to non linear analysis, going through various intermediate proposals.

Is it really so difficult that no two of you, among which there are without doubt many experienced and skillful engineers without being sarcastic, have proposed the same idea?

A column with a distributed load and a compressive force? Non linear analysis?


Hope no one misunderstands how much I appreciate your contribution and truly respect any of you.

Best Regards

Muzialis

 

[hokie66]

Muzialis,

Yes, we do tend to waffle on and stray from the original question. The other factor is that people understood your question differently. Perhaps if you gave the actual problem, including the section you are investigating along with the applied loads and support conditions, you would get a more consistent answer.

 

[Favollo]

Hokie66,

you are too right.
I will give some detail with the results I have found so far.

The beam column is loaded with a trnasversal load of 0.33 N/mm, span 8000 m, clamped both end, 4*10^5 N compressive force.

At the momemt I did some calcs for a section with I = 1.532*10^7 mm^4, stell modulus 200 GPa, yield 355 MPa.

Percentage compressive capacity used = 28%

Deflection without compressive force = 1.044 mm

Deflection with compresive force = 1.42 mm
(Found solving the 4th order Euler Beam equaition with EI constant, just to test the numerical accuracy).

Euler Buckling Load = 1.89 * 10^ 6 N

It seems to me the buckling load for the bema column is the same as for the beam, but I have top check this later on.

As soon as I can I will try the energy method.
Might try non linear finite element buckling analysis if I get time and will surely let you know for your imformtation.

Thank al ot to everybody, owe you a drink.

ATB

Favollo

 

[hokie66]

Muzialis,

When you say "clamped", I assume you mean fixed at both ends. That way, I get 1.15 mm deflection with only bending. Are you sure the supports are fixed? With simple supports, the deflection would be 5 times that much.

Based on your numbers, this member is bent about the strong axis. I think the only buckling concern is in the other direction, and without knowing what type of member this is (wide flange, RHS, CHS), it is hard to know whether buckling will control.

 

[Favollo]

Hoki66,

thanks a lot.

The connection is a point I am struggling with.
the intention is to have it fixed through welding to a support, but there might be some deflection of the support as well.
Anyhow, in theory it is fixed.

The section is a squre hollow section, 150 x 1150 x 8.

My deepest gratitude for your comments.

All the Best

Favollo

 

[hokie66]

Yes, fixing the beam could be difficult unless you have a massive column. There will probably be some rotation.

By the way, my tables for a 150 x 150 x 8 SHS give the moment of inertia as 14.1 x 10^6. Did you compute it? If so, the radiused corners reduce this somewhat.

You only have about 14 MPa in bending stress, so this is a column with a bit of bending.

410 kN is too much for this section if the ends are pinned and there is no intermediate bracing, so you have to fix the ends for it to have a chance. I would tend to use a larger section.

 

[csd72]

I am skeptical about you having 2 fixed ends to this beam. supporting members will have some give in them allowing for a small amount of rotation.

I have been doing structural design for well over a decade, and I have never come across a situation where both ends of a beams are truly fixed.

I would try to err on the conservative side and maybe treat it as fixed at one end only.

Fixed both ends is something that only truly occurs in textbooks.

 

[Favollo]

Hokie66, Csd72,

both advices accepted, with one pinned connection I have to incresae trhe section up to 180 * 180 * 10 in order to saty in the region of 1 mm deflection.

Hokie66, yes I did calculate EI myself, did not think about the rounded corners..

Have a nice morning ( I am Europe based!)

Favollo

 

[Tomfh]

250SHS is more appropriate.

You will see a lot more than 1mm deflection with 150 or 180 SHS.

 

[Favollo]

Tomhf,

I do appreciate your comments but it was rather cryptic.

Which method did you use then?

Thanks al ot agin to all of you.

Take care

Favollo

 

[prex]

Favollo,
your figure above for deflection in presence of compressive force seems reasonably correct to me: by using a sheet in the first site below and figures and boundary conditions per your post above at 19:18, I get 1.35 mm with compression and 1.08 without.
Also be careful with buckling: you are allowed to take a fixed-supported scheme only if the two ends are not allowed to displace laterally one relative to the other.

prex

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[Tomfh]

favollo,

I assumed Span/1000 initial camber and d/2 load eccentricity.

 

[kslee1000]

When dealing with beams that subject to axial load, I always try to understand the source of the axial load and how the load is applied (from one end, both ends, in the middle). Also, what is the anticipated movement of the end supports with respect to each other (move in the same direction, opposite directions?) If the supports are been pushed closer to each other, doesn't axial shortening need to be addressed also? Just to throw some mud into this mix to see how it (this topic) develops.

 

[Favollo]

Tomhf,

thanks for letting us know.

kslee1000,

you are very right but axial shortening is not too much of a concern given the application.
The end supports will tend to rotate in opposite senses.
the axial load is applied form both ends as a live load, in the sense that will always remain aligned with the beam (if the beam stays perpendiculor to its sipport).

I have as awell some more results for the both ends fixed situation, just to start with.

Roark's formula (Table 10,shear, slope, moment for beams with simultaneously applied compressive load and transversal load gives a dipslacement at mid span of 1.5 mm, rather close to what said so far.
moments and stresses match nicely as well.

And for curiosity's sake, a non linear analysis with ANSYS using linear beam elements, 400 nodes, gives a deflection of 1.48.Timoshenko elements decrease the deflection to 1.45 mm.The buckling analysis is still running now, will check results tomorrow...

Many thanks to all the contibuters and have a nice weekend.

Regards

Favollo.