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In my world, there is a forest of giant trees on both poles. The trees create a canopy that is perpetually covered in ice. This frozen canopy extends so high that it supports a "land" of frozen clouds. There live the Yeti of this world.

How strong could this frozen cloud land be? Is it strong enough to support a village of 100 humans (although they are Yetis instead of humans)?

I'm imagining it will be more like frozen snow, instead of a block of ice, but I can be wrong. The strength of the canopy is assumed to be strong enough for any mass of the solid ice needed.

This frozen cloud would have some parts extending away from the canopy. My main concern is how strong this extension will be, and how to calculate the minimum thickness of the extension and how far it can be.

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    $\begingroup$ I have some fundamental problems with this concept including the following. Trees that survive in permanently cold snowy climates tend to be of a pointy type that shed snow and don't really have a canopy, specifically to stop this situation arising. The snow would block the light and kill the trees. But don't let that stop you. $\endgroup$ – Separatrix Nov 20 '17 at 8:12
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    $\begingroup$ I see your profile gives your location as Indonesia, so I suspect you haven't experienced this first hand, but it's perfectly possible to have below-freezing temperatures and dense fog. Wreaks havoc with most things. I think it's safe to say that if you want something based in real-world science, that is essentially your "ice cloud". There are ways to make it more extreme than this, for example as discussed in the answers to my old question Can whiteout/snowstorm conditions be coupled with heavy fog?, but it's still basically the same thing. $\endgroup$ – a CVn Nov 20 '17 at 10:28
  • $\begingroup$ Snow is made of ice crystals. There isn't a clear point where densely packed snow stops being snow and starts being a block of ice. $\endgroup$ – sphennings Nov 20 '17 at 15:54
  • $\begingroup$ Another problem is that the trees aren't going to support the weight of ice. Even normal ice storms or heavy snowfalls will typically bring down a number of trees, or break branches. $\endgroup$ – jamesqf Nov 20 '17 at 19:08
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A solution can be found in Canada:

During the Second World War, G. Pyke proposed that an iceberg be used as an aircraft carrier in the Atlantic. When it became apparent that natural icebergs were too small, proponents then launched a plan to build a giant "bergship." They found that the mechanical properties of ice were not up to the task, howeverthe tensile strength was too low, and the ability to withstand ballistic impacts and explosions was unacceptable. In February 1943 it was discovered that wood pulp could solve the problem; for instance, the addition of four percent Canadian spruce more than doubled the strength and, on a weight-to-weight basis, increased the shock resistance to that of concrete.

Source: http://www.tms.org/pubs/journals/JOM/9902/Schulson-9902.html

Since you already have trees, you could come up with an explanation as to why some wood pulp would be in the ice. Perhaps the yetis added it?

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    $\begingroup$ ‘Gaze upon my pycrete fortress, ye traveller, and despair!’ $\endgroup$ – Joe Bloggs Nov 20 '17 at 18:10
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    $\begingroup$ It's hard to imagine trees pushing wood pulp up into the ice, but maybe they grow a thick mesh of thin, root-like branches up into the ice. $\endgroup$ – Luke Nov 20 '17 at 23:27
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No Yeti Castles in the Clouds

The frozen canopy is basically a giant ice sheet that's arbitrarily thick; thick enough that we can forget about the trees that are under it.

Clouds are made up of water vapor or ice crystals. They stay suspended because they are small enough to stay suspended in the air. Once they reach a certain size/density the air currents that kept them suspended are no longer able to support them and they fall in the form of some kind of precipitation.

It's certainly plausible that the Yetis live on the ice sheets and are frequently enveloped in fog of some kind (freezing fog is especially unpleasant) but the micro-currents in the air aren't going to be able to support a full weight human in any way.

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I would be curious about how it formed (did the tree tops grow through the ice somehow? did the ice cloud form only after the trees were that high, how do the trees get light?), but I think your question is answerable.

Ice has a tensile strength of 0.7 - 3.0 Mpa and a compression strength of 25Mpa. In comparison, concrete is 2.2 - 4.2 Mpa tensile, and 17-28 in compression. It will fail in tension, so it would be better if you can use something as tensile reinforcement (such as tree branches).

Interestingly, ice is 1g/cm3 and concrete is 3g/cm3. What does this mean? Combined with the difference in strengths, it means that a structure made from ice should be twice as thick as if it were made from concrete, and then it will have about the same total mass and the same sort of strength.

So if you think your trees are strong enough to hold up a 100m platform of concrete, then they can also hold up a 100m platform of ice. And we have built boats out if concrete, so, at least with engineering(!) someone could build a sky-ice-city.

Note that this answer assumes a solid block of ice.

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