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OT - Physics Question ?
mcerd1 - 13/11/13 at 05:02 PM

nothing like a bit of physics in the afternoon.....


say I've got a long bar of metal thats going to go through lots of hot/cold cycles, but for some reason I've restrained it so that it can move at the ends (i.e. its not allowed to get any longer or shorter)
and its also held by clamps at several points along its length to prevent it moving out of line (these clamps can also provide a bit of friction to further restrain the axial expansion/contraction)

what force would be seen at the ends and what force would be seen at the clamps ?

matt_gsxr - 13/11/13 at 05:09 PM

The same as if you compressed it to that length from the length that it would like to be.

matt_gsxr - 13/11/13 at 05:15 PM

I think if you do the numbers then the force is linear in

Cross-sectional area
Temperature change
Coefficient of linear expansion
Young's modulus


Rather neatly it is independent of the length


Might have missed something though.

bi22le - 13/11/13 at 05:55 PM

It would also be the same at each join and could be considered as lots of shorter bars fixed between 2 imovable points.

britishtrident - 13/11/13 at 06:02 PM

In engineering this is what is called a compound bar problem, but from the very fuzzy discription it is very far from clear what is actually being asked " a bit of friction" ? Restrained at the ends ?

As already mention by you just work out the theoretical change in length per unit length due to the change in temperature for free bar.
This is equivalent to the Strain for a perfectly restrained bar then feed this into Hookes Law to get the Stress.

adithorp - 13/11/13 at 06:44 PM

quote:
Originally posted by matt_gsxr
The same as if you compressed it to that length from the length that it would like to be.


...or to put it another way.. A fecking lot and somethings going to give.

http://i.telegraph.co.uk/multimedia/archive/01249/railway-lines_1249034i.jpg

dhutch - 14/11/13 at 05:46 AM

quote:
Originally posted by adithorp.


...or to put it another way.. A fecking lot and somethings going to give.

http://i.telegraph.co.uk/multimedia/archive/01249/railway-lines_1249034i.jpg


Yes, depending on the dimensions and the material (although, most metals are going to be rather high) the axial forces get very big very quickly.

Theoretically if it perfectly straight the side forces are zero and it will stay put. But in practice nothing is perfect and even the slightest bend/curve will result in a side force, and if you can maintain length for the large axle forces, even the side forces become quite significant , and as per the photo can make things like pushing a number of large concrete sleepers sideways through gravel look likes child's play.

Otherwise the other common thing is that the brackets don't contain the axial forces, and it grows in length breaking or deforming the brackets/mounts or causing it to slide in any clamps. If the brackets don't break first time round, but go beyond there elastic limit they end up being bent, and even if they don't go beyond there elastic limit, if they go far enough often enough will fatigue and fail over time.

Or in summary, typically, ignore it at your peril!


Daniel

mcerd1 - 19/11/13 at 02:22 PM

cheers guys you've confirmed my thinking so far



if the bar was swapped for a stranded cable (all be it a very stiff one, say 1200mm˛ aluminium, so it will act a bit like a solid bar with a very low modulus) that way its almost guaranteed to 'snake' a bit - how would you take account of the reduction in the axial force / workout how much it would snake ?


also if you were to take that cable around a corner (using the cleats as formers) - what happens to the axial expansion load and how would you calculate that ?