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So here's a curious little thing...
I noticed the other day that some of the cars in the showroom were
parked on little metal ramps. Now here's the puzzling thing. My car is
only little, and that weighs 1.25 tonnes. Some of the bigger cars surely
weigh even more than this. So these ramps have multiple tonnes bearing
down on them... and they're made from 2mm steel.
Now obviously somebody far, far smarter than me has carefully calculated
how thick the steel needs to be to hold a given amount of weight. But
these things look so utterly flimsy, it looks like you could bend them
with your bare hands. And yet, you can park a car on them, and they
don't even distort slightly.
I am at a loss to explain this.
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> I noticed the other day that some of the cars in the showroom were parked
> on little metal ramps.
You mean like these:
http://members.iinet.net.au/~mmckenzie/files/VX_CHARGED_S/ramps.JPG
> Now here's the puzzling thing. My car is only little, and that weighs 1.25
> tonnes. Some of the bigger cars surely weigh even more than this. So these
> ramps have multiple tonnes bearing down on them... and they're made from
> 2mm steel.
The bigger cars are probably at most 2000 kg, worst case is say 70/30
front/rear weight distribution, so I'd say max 700 kg on each ramp (if you
put the front wheels on it).
> Now obviously somebody far, far smarter than me has carefully calculated
> how thick the steel needs to be to hold a given amount of weight.
Well it seems to me that there are 4 vertical columns supporting the weight,
so probably max 200 kg or a max force of 2000 N in each column.
There's a neat formula that Engineers use to determine the maximum load a
column can take without buckling, find it here:
http://en.wikipedia.org/wiki/Buckling
A bit of rearranging gives us a formula for I (the required area moment of
inertia):
I = F * (K*L)^2 / (pi^2 * E )
In this case we have:
F = 2000 N
K = 0.5
L = 0.3 m
E = 200 GPa
So I = 2.3 x 10^-11 m^4
This allows you to choose what shape and thickness to use.
For simplicity assume a cylindrical rod is used, the formula for the 2nd
moment of area is:
I = pi/4*r^4
Rearranging:
r = (4*I/pi)^(1/4) = 2.3 mm
So there you go, make it out of diameter 5 mm steel rod and you'll be fine!
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scott wrote:
> You mean like these:
>
> http://members.iinet.net.au/~mmckenzie/files/VX_CHARGED_S/ramps.JPG
Yeah.
> The bigger cars are probably at most 2000 kg, worst case is say 70/30
> front/rear weight distribution, so I'd say max 700 kg on each ramp (if
> you put the front wheels on it).
Does that really work? I mean, can you really just say "oh, this thing
has 4 wheels, so each one only takes 1/4th of the load"?
Also, something like a Prius is 3042 Kg (unloaded). I'm presuming they
make these ramps with a damned wide margin for safety.
> Well it seems to me that there are 4 vertical columns supporting the
> weight, so probably max 200 kg or a max force of 2000 N in each column.
But can you really do that? Can you really just say "there's 4 columns,
so divide the load by 4"? Wouldn't it depend on the angle of the force
being applied? And what about the horizontal elements? They need to not
bend at the points where they're unsupported as well.
> Rearranging:
>
> r = (4*I/pi)^(1/4) = 2.3 mm
>
> So there you go, make it out of diameter 5 mm steel rod and you'll be fine!
Looks thinner tham 5mm to me - but then again, it isn't cylindrical...
Just how strong is steel? I mean, obviously it varies by type, but how
much load can you typically put on steel without bending/shattering it?
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> Does that really work? I mean, can you really just say "oh, this thing has
> 4 wheels, so each one only takes 1/4th of the load"?
Well from experience most cars are pretty equal for left/right weight
distribution, and as I said worst case is probably 70% on the front wheels.
So yes, probably 35% of the total weight is the maximum on any single wheel.
> Also, something like a Prius is 3042 Kg (unloaded). I'm presuming they
> make these ramps with a damned wide margin for safety.
Usually when you buy a pair of those ramps they will be marked as supporting
a certain load. 2 ton per pair of ramps is common. If you go over that
then obviously there is a large risk they will break.
> But can you really do that? Can you really just say "there's 4 columns, so
> divide the load by 4"? Wouldn't it depend on the angle of the force being
> applied?
Of course, I was simplifying to get a rough estimate. In reality you would
have to take the worst case loading condition, which is probably with the
tyre directly on top of a single column.
> And what about the horizontal elements? They need to not bend at the
> points where they're unsupported as well.
You would obviously check for this if you were designing it, but I assume
this wouldn't happen as a tyre usually spreads out the load across an area.
The loading would be concentrated at the tops of the support columns as
these won't budge.
> Looks thinner tham 5mm to me - but then again, it isn't cylindrical...
Yes, something like an I beam or a hollow cylinder is a more efficient use
of the metal.
> Just how strong is steel?
It varies from about 250 - 750 MPa. That's the stress you need to apply to
it before it starts to deform plastically. As an example, my steel ruler
has a cross section of 1mm x 25mm, you'd need to pull on it with between
6-18 kN of force, that's the weight of a car.
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Shape is everything. Metals resist tension better than they do pure buckling.
And think of the keystone bridge. Put this all together and you have an
intuitive explanation for why those ramps are not perfect cubes.
Unfortunately, this IS what I studied in college. :/
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>> Does that really work? I mean, can you really just say "oh, this thing
>> has 4 wheels, so each one only takes 1/4th of the load"?
>
> Well from experience most cars are pretty equal for left/right weight
> distribution, and as I said worst case is probably 70% on the front
> wheels. So yes, probably 35% of the total weight is the maximum on any
> single wheel.
Hmm, interesting. I wouldn't have expected that to work.
> Usually when you buy a pair of those ramps they will be marked as
> supporting a certain load.
Sure. I just meant that they probably design them to easily support more
weight than any common car that somebody might try to put on them.
> Of course, I was simplifying to get a rough estimate. In reality you
> would have to take the worst case loading condition, which is probably
> with the tyre directly on top of a single column.
Isn't the worst-case when you drive the car onto the ramp and the
suspension jiggles it up and down over one support column?
>> And what about the horizontal elements? They need to not bend at the
>> points where they're unsupported as well.
>
> You would obviously check for this if you were designing it, but I
> assume this wouldn't happen as a tyre usually spreads out the load
> across an area. The loading would be concentrated at the tops of the
> support columns as these won't budge.
Looks to me like the tire would usually sit between the two horizontal
struts. One is directly over an upright, but the other is on the middle
of the beam. (Obviously that isn't a problem or they'd have added
another upright...)
>> Looks thinner tham 5mm to me - but then again, it isn't cylindrical...
>
> Yes, something like an I beam or a hollow cylinder is a more efficient
> use of the metal.
A few of those struts seem to be angled. But most of them are just flat.
>> Just how strong is steel?
>
> As an example, my steel
> ruler has a cross section of 1mm x 25mm, you'd need to pull on it with
> between 6-18 kN of force, that's the weight of a car.
Jesus, that's strong! o_O
So... what the hell is the thickness of a tin can then? Those seem to
deform pretty easily.
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>> Well from experience most cars are pretty equal for left/right weight
>> distribution, and as I said worst case is probably 70% on the front
>> wheels. So yes, probably 35% of the total weight is the maximum on any
>> single wheel.
>
> Hmm, interesting. I wouldn't have expected that to work.
What, that a car has more weight on the front wheels than the back? Most
front wheel drive cars on the roads are configured like this. Some rear
wheel drive cars have more 50/50 weight distribution, others (if they have
the engine in the back) can have more weight on the rear wheels than the
front. Of course the car's suspension and so-on is designed for this, so
you probably won't notice much when driving normally.
> Sure. I just meant that they probably design them to easily support more
> weight than any common car that somebody might try to put on them.
You would think so.
> Isn't the worst-case when you drive the car onto the ramp and the
> suspension jiggles it up and down over one support column?
Probably. But I really suspect in the design of these things that they just
make a few and test them. I highly doubt they do some computer simulation
or really complex calculation to figure out what size metal to use - it just
wouldn't be worth it because it's so quick to just make a few and test them.
> So... what the hell is the thickness of a tin can then?
0.2 mm or thereabouts.
> Those seem to deform pretty easily.
You mean by squeezing them on the sides? Well yes, I can bend my ruler too
pretty easily and that's 1mm thick! What you're doing there is essentially
using a huge lever, you are moving your fingers a few cm to cause a
contraction/expansion of a few microns in the surface of the material,
generating a huge stress which causes it to permanently distort. Now try to
permanently stretch a tin can by pulling on each end :-)
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>> Hmm, interesting. I wouldn't have expected that to work.
>
> What, that a car has more weight on the front wheels than the back?
Possibly, once you've got the back wheels up on a ramp. ;-)
I meant more that I wouldn't have expected to be able to just completely
disregard 3/4 the weight of the object just because I'm only looking at
one wheel.
>> Sure. I just meant that they probably design them to easily support
>> more weight than any common car that somebody might try to put on them.
>
> You would think so.
So it's probably rated to 5 tonnes or something.
>> Isn't the worst-case when you drive the car onto the ramp and the
>> suspension jiggles it up and down over one support column?
>
> Probably. But I really suspect in the design of these things that they
> just make a few and test them.
Oh, yeah, probably. More like they figure out approximately how much
load it's supposed to take, then design it to withstand 80% more or
something, and then go check whether it breaks or not.
>> So... what the hell is the thickness of a tin can then?
>
> 0.2 mm or thereabouts.
...my God. You can make metal that thin?? o_O
>> Those seem to deform pretty easily.
>
> You mean by squeezing them on the sides? Well yes, I can bend my ruler
> too pretty easily and that's 1mm thick! What you're doing there is
> essentially using a huge lever, you are moving your fingers a few cm to
> cause a contraction/expansion of a few microns in the surface of the
> material, generating a huge stress which causes it to permanently
> distort. Now try to permanently stretch a tin can by pulling on each
> end :-)
Heh, yeah, well, those horizontal beams may only be 5cm long, but they
have up to 2 tonnes pushing them sideways. That's a lot of force...
PS. Apparently human bones have a higher tensile strength than solid
copper. WTF?
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On Tue, 09 Feb 2010 15:37:05 +0100, Invisible <voi### [at] dev null> wrote:
>
> I meant more that I wouldn't have expected to be able to just completely
> disregard 3/4 the weight of the object just because I'm only looking at
> one wheel.
Why not? Try doing some one-handed push-ups and see if they are not harder
to do than two-handed ones.
>>> So... what the hell is the thickness of a tin can then?
>> 0.2 mm or thereabouts.
>
> ...my God. You can make metal that thin?? o_O
Surely you are joking.
http://en.wikipedia.org/wiki/Aluminium_foil
--
FE
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>> I meant more that I wouldn't have expected to be able to just
>> completely disregard 3/4 the weight of the object just because I'm
>> only looking at one wheel.
>
> Why not? Try doing some one-handed push-ups and see if they are not
> harder to do than two-handed ones.
When I become able to do two-handed push-ups, I'll let you know. ;-)
>>>> So... what the hell is the thickness of a tin can then?
>>> 0.2 mm or thereabouts.
>>
>> ...my God. You can make metal that thin?? o_O
>
> Surely you are joking.
>
> http://en.wikipedia.org/wiki/Aluminium_foil
Damn. I thought that stuff was plastic with a metal-powder coating...
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