Physical properties of just a giant tower of solid metal

Factual Questions
21

In general, one bound on the height of a cylindrical tower is that the yield strength at the base must be greater than the pressure. If you crunch the numbers, this works out to be

\text{max. height} = \frac{\text{compressive yield strength}}{\text{(density)} g}

where g is the acceleration due to gravity. Note that this is independent of the cross-sectional area (though of course changing the cross-sectional area will affect this tower’s stability to other failure modes.)

This means that you can place a bound on the height of a tower just by knowing the properties of the material it’s made of. For copper this works out to be anywhere between 500 and 5000 meters depending on the alloy in question (see Table 2).

22

My back-of-the-envelope calculation indicates that a 20-degree F temperature difference between the two sides (unlikely in a metal that conducts heat as well as copper) would make the sunny side around an inch longer.

23

There’s also self-buckling to consider, when a column experiences buckling under its own weight. A free standing column with density p , Young’s modulus E, and cross-sectional area A, will buckle under its own weight if its height exceeds a certain critical value defined by:

max height = (7.8373 * (EI / pg*A))^1/3 , where g is gravitational acceleration and I is the second moment of area of the cross section.

24

What units are those in?

25

That magic number 7.83735 is just a dimensionless constant, unless I misunderstood something.

26

Correct.

27

Just keep the units consistent, Si or English for everything. 7.8373 is a dimensionless constant.

28

I went ahead and ran the self buckling calculations for a 5m (16.4ft) solid copper cylinder. If my math is mathing, the critical height before it will buckle under its own weight (all other factors notwithstanding) is approximately 303m (995 ft).

29

I’m getting there. My copper tower is at 275 metres.

30

Remove the bottom layer of blocks and place them at the top, leaving the entire 52 million kilogram structure hovering in the air like some Wile E. Coyote project, violating everyone’s OCD. When they complain, tell them it’s a space elevator in geostationary orbit.

31

The joys of Minecraft.

Copper: 298 metres
Gold: 47 metres
Iron: 139 metres

Coal is at 98 metres but the concept of cubic metre blocks of solid coal doesn’t make as much sense.

32

Aside: Minecraft Steve can carry 45,660 tons, based on inventory, stack limits, and the mass of a cubic meter of gold.

There are heavier calculations out there on the Internet, but they’re all based on the (IMO unfounded) assumption that a crafted item weighs as much as the sum of all of its ingredients.

33

The addition of shulker boxes means you can carry way, way more than that. They are in effect portable chests, so each can carry 27 more stacks.