Is tube stiffer than bar?

[T i m]

Hi All,

I am trying to make a lift_and_slide_away storage system for my Daughters 88 key MIDI keyboard.

So you can get an idea re the bigger picture I'll try to describe what I have so far the best I can.

It's based around a 2' length of 3/8" diameter SS bar, held solidly by two sailing dinghy rudder fitting (gudgeon) at either end ..

to the underside of the front right hand edge of her workbench (so it looks like a towel rail, sorta like this but with a SS bar ).

then have a keyboard sized piece of MDF (so ~ 9" x 4'), also with a pair of gudgeon fittings on the (left hand) end and these are also threaded onto the same bar (forming a long pivot / 'sliding hinge' assembly).

With the keyboard base in the horizontal position, one end joined to her bench on this pivot / bar the other end on a stand (yet decided) the keyboard is then placed on top, secured with Velcro so it can be taken away if needed elsewhere.

If she then sits at her desk the keyboard is at the same level as the desk and running down the right hand side of her (and her room) now looking like a mini music studio. ;-)

When she is finished using the keyboard the idea is she lifts up the right hand end of the keyboard (+ it's base, like a public bar door top) till the keyboard is nearly in the vertical position, then slides it back along the 'hinge' until it gets to the wall where it will rest in a suitable stop / support (design yet to be finalised).

I have currently got this all clamped up for testing but have found the 3/8" SS bar is quite 'springy', allowing the fairly heavy keyboard

• base assembly to wobble / bounce about a bit whilst it's being slid back (but it's ok when in the 'play' position).

But it all works (so far) but I wondered if I could replace the SS bar with *tube* (of the same diameter) and would that better / (stiffer)?

Also, if not stainless is there anything else that could be used that would make a nice sliding 'hinge' do you think please (and I don't really want to re-design it all. e.g. silver steel, would that go rusty?) ;-(

I *might* be able to open the nylon inserts up in the ends of the gudgeons and use a larger diameter rod / bar (I would drill / bore them out in pairs to maintain concentricity).

All the best and thanks for your time ..

T i m

[Ian Stirling]

Of the same material, exterior dimensions, and conditioning - no. For the same weight, given the above, yes.

An important thing to know is that all steels have the same amount of springyness - pretty much, up to a limit, depending on the alloying, and heat treatment. Once it gets past this limit for mild steel, it starts to bend permenantly. The key to better steels is that they will bend permenantly only at higher loads.

[Guy King]

The message from T i m contains these words:

No. Tube is stiffer per weight, but not stiffer per diameter. The only way to make it stiffer is to use a stiffer metal or a larger diameter or a different geometry.

[T i m]

Hmm, thanks 'guys' and that makes sense (now I think about it).

Ok, on the geometry then (and this is probably a stupid thought) what about a 'X' section inside a tube (I'm guessing it would still be a function of the overall x sectional area)? This probably sounds like a perpetual motion question ;-)

So, failing a 'yes' to the above, is there a simple formula (rule of thumb) for how much 'stiffer' any particular steel would be for a percentage increase in diameter please?

Say I go from 3/8 to 1/2" for example, would it be 25% or 33% or something else stiffer?

All the best ..

T i m

[Autolycus]

Stiffness is proportional to the fourth power of diameter for a round beam in bending, so 3/8 to 1/2 inch is a factor of 4^4/3^4, or 256/81, or 3 and a bit, as we engineers say (or pi, or root 10).

[Guy King]

The message from T i m contains these words:

Better, but still not as stiff as solid.

[Tony Bryer]

For a solid bar, stiffness is proportional to D^4, bending strength (in simple terms) to D^3 and weight to D^2. For a tube substitute D^x -d^x where D is the OD and d the ID.

So if your tubes are of 1/16" material the numbers are (work in 1/16" for ease of calculation)

3/8: Stiffness 6^4-4^4: 1040 Weight 20 Stiffness/weight 50.2 1/2: Stiffness 8^4-6^4: 2800 Weight 28 Stiffness/weight 100.0

But it's not quite as simple as just making it as big and thin as possible as you reach a point where the tube buckles before its theoretical strength is reached.

Note that no reliance should be placed on any calculations done at this time of night

[T i m]

Ah, cheers!

So (just to make sure understand your results) the 1/2" bar will be ~3x stiffer than the 3/8" one ??

All the best ..

T i m

[T i m]

Doh! ;-)

All the best and thanks (again) ..

T i m

[T i m]

lol.

Thanks and all the best ..

T i m

[Guy King]

The message from "Autolycus" contains these words:

In other words - make the tube a bit fatter and it'll be a /lot/ stiffer.

[Weatherlawyer]

I wonder if the imperial system is the reason why the British used to seem so much more inventive than dago/gerry types.

I'm convinced that the love of the game fluxed out once metric became the norm. I supposed it was just me getting older and jaded.

It would explain the inertia in the mature tradesmen when the switch occurred. It wasn't just reluctance to change but revulsion at the digitalising what has always been an analogue sport.

It might also explain why there is so much acceptance of dodgy materials and techniques these days. This may seem kook territory to some but there is a lot to it I feel.

With the imperial system you could think in terms of volume at the same time as you were considering lengths and breadths.

[Robert Laws]

Did not the state of Kentucky once legislate that pi=3?.

Robert

[Guy King]

The message from "Robert Laws" contains these words:

In 1897, the Indiana General Assembly passed a bill from which it could deduced that pi was equal to 3.2 or other incorrect values. The Indiana Senate postponed the bill indefinitely, preventing it from becoming law.

[The Natural Philosopher]

No. A tube is really just a rod with the heavy and low stressed material removed.

You MIGHT find a carbon fibre tube is a bit stiffer..3/8" is 10mm give or take

Try here..

However its not a good bearing surface.

There are custom keyboard sliding mounts and the like made for 19" rack use..

There are radio keyaboards...

For a cantilever, I'd be thinking more in terms of 1/2"-3/4" steel...

[The Natural Philosopher]

Think its broadly proportional to diameter squared.. I.e. the load ends up at a greater diameter spread over a greater area..

Hard steel drill shaft is the least resistant to bending..usually stainlesl too.

And a total pig to cut. No saw will dio it - needs a grinder.

[T i m]

Tool steel or Stainless (I cut the 3/8 ss bar with a blunt hacksaw in about 8 strokes?)?

All the best ..

T i m

[T i m]

Nice description ;-)

I did think of carbon ..

Where? ;-)

I thought of that too. How about CF rod in a SS tube! ;-)

Yeah, I bought a couple of heavy roller draw slides for the MK1 version but the keyboard needs to be quite a long way out into her room (so they would probably need to be multistage / telescopic and I'd have to build something to mount them on etc .. (too many bits in the room to do that easily) ;-(

And there are smaller keyboards! The idea of getting this particular instrument:

because it has it's own built in voices and audio output (so can be played live with just an amp) and USB / MIDI for connecting to a PC / Mac. 88 full sized semi weighted keys mean you can play it like a real piano (without running out of notes) ;-) But it's quite long so needed to be 'hinged' away to fit in her packed box-room (or lifted away but I wanted to keep it plugged in and ready for use).!

Well this 3/8" is *ok* (as in work but not perfect) and if 1/2" is 3 times stiffer (if I understood things correctly?) then that should be sufficient. 3/4" would probably be best of course (or even 5/8") but possibly a bit over engineered and probably would require a complete re-work. ;-(

All the best ..

T i m

[The Natural Philosopher]