Advice on size/thickness of hollow box section aluminium beam

[alligatorlizard]

Apologies for starting another similar thread to the one about angle iron - but thanks to advice given in the previous one, the plan has significantly changed, and the main question is now different:

I have determined hollow box section aluminium beams are what I need for this project, and the basic question is, what cross-sectional size & thickness do I need to adequately support 6kg in the centre of a 3.1m span, "simply supported" at either end?

Have attached plans, and you'll see the overall setup is a bit more complex than that - i.e. two parallel beams collectively supporting 12kg spread over the middle-most 1.2m of their span - but to keep it simple, I think the problem can be reduced to a single beam supporting 6kg dead in the centre (which should also give a bit of a margin for error).

As I understand, so long as I choose a good grade aluminium (the ones I'm looking at are either 6082 or 6063, T6) then strength is unlikely to be an problem (due to light load), but deflection could be significant (due to long span). I have come up with a way of mounting the beams so deflection will not be an issue in terms of causing stress to any mountings, but would still like to keep the deflection to a minimum (say 1cm max), while also keeping weight down as much as possible. Keeping weight down is why I'm looking at aluminium rectangular box section (with larger sides vertical)

I'm looking at something like: 25mmx50mm, 3.2mm thick - with the 50mm sides vertical - several different AI models give me deflections of around 4mm for this. BUT, as discovered in previous thread, AI is not always that intelligent... hence would like some real-word input on whether this sounds realistic!

Other sizes available that might work: 40mm x 30mm, 2mm thick (AI estimates 9mm deflection) - 38.1mm x 25.4, 3.2mm thick – (AI estimates 8mm deflection)

If anyone has any experience with these sort of materials, or a better understanding than me of the formulas involved, could they advice on whether these sizes/thicknesses at least sound in the ballpark?

btw, I can't suspend from ceiling for multiple reasons - I do realise that would be the usual approach here!

Plans below:

Thanks!

 

[Harry Bloomfield]

Sorry, I have lost interest in your threads on this. It's a pointless, endless OCD discussion. As I pointed out - if you want it to be supported, and with no droop in the middle, then look at how a suspension bridge support works.

 

[endecotp]

Using the Engineering Toolbox calculator:

F = 60 N
L = 3100 mm
I = 50000 mm4
E = 70000 N/mm2
y = 0 mm (????)

gives max deflection = 10.6 mm.

Now find an aluminium section with I = 50000 mm^4.

For a square tube of width and height a and thickness t, I = ( a^4 - (a-t)^4 ) / 12

So 50 x 50 mm with thickness 1 mm, I = 40000. Almost strong enough but not quite.

I hope you can work it out from there!

 

[alligatorlizard]

Sorry, I have lost interest in your threads on this. It's a pointless, endless OCD discussion. As I pointed out - if you want it to be supported, and with no droop in the middle, then look at how a suspension bridge support works.

No, it's a simple question, with a very definite answer, and worth asking because to rely on AI calculations (or my own calculations, not having any prior knowledge of structural engineering) would be risky seeing as this thing will right above my head!

I did thank you for your "suspension bridge" suggestion on the prior thread, but it's not practical in this case. To maximise effectiveness of the acoustic panels, they should be mounted with about a 10cm gap between them and the ceiling - it looks like I'll need a beam that's about 5cm on the vertical edges, so I will only have 5cm gap between the top of the beam and the ceiling and I would have to remove or cut away coving in order to secure high tension wire on either side. Could be done if absolutely necessary... but I have heard no reason yet why beams alone (of sufficient size/thickness) would not suffice.

Also, to be clear, I'm not aiming for "no droop" - as said, droop/deflection is less of a problem now I've changed how the beams will be supported. Any significant deflection would move the panels away from their ideal acoustic position, and reduce headroom, but as long as this is only a cm or so, then not a problem.

From endecotp's calculations above, it sounds like a 50mm high cross section, but thicker (i.e. 3.2mm which seems to be a standard size) would be more than sufficient. My next step will be to try and get my head around these formulas and the parameters involved, and run the numbers for available dimensions. If I can get down to 40cm that would make things easier as then I might not have to trim the ends as much, or at all, to fit around coving.

Am still hoping to hear from someone who's worked with these sort of materials though! Everything's always slightly different in practice...

 

[alligatorlizard]

Using the Engineering Toolbox calculator:

F = 60 N
L = 3100 mm
I = 50000 mm4
E = 70000 N/mm2
y = 0 mm (????)

gives max deflection = 10.6 mm.

Now find an aluminium section with I = 50000 mm^4.

For a square tube of width and height a and thickness t, I = ( a^4 - (a-t)^4 ) / 12

So 50 x 50 mm with thickness 1 mm, I = 40000. Almost strong enough but not quite.

I hope you can work it out from there!

I referenced your data and formulas above, and I think I've got it figured out now - key part was understanding moment of intertia (had to find a slightly different formula due to rectangular shape), which is the only variable I need to change here when comparing different size beams. Have used the calculator you linked to, plus another I found, and for a beam 50mm x 25mm, 3.2mm thick (which I can get from Metals4u), I'm getting consistently around 4mm deflection. Of course I need to factor in the weight of the beam itself, and calculating this as a uniformly distributed weight I get 1.51mm. So 5.47mm total deflection. Which should be completely fine.

Can now run numbers for the different sizes that are available to e.g. check if a 40mm height would work. So thanks again for your help, the "teach a man to fish" approach is much appreciated. Should now be able to build the damn thing, which will probably take a fraction of the time it's taken to plan it out