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What are the factors limiting the height of a "tower" made of typical fired brick and mortar?

By "tower", I mean a structure whos point is to be tall, and can support a human standing on or near its top. I'm interested in the self-supporting structural aspects, not limitations of construction techniques, or environmental factors like wind loading, possiblity of earthquakes, etc. I want to understand what limits such a structure mostly from its own weight and properties of the material.

The point is to maximize height for any given land area the thing sits on. I'm trying to leave reasonable latitude for land area to understand the constraints, but let's not get silly like wrapping around the earth or end up with a star made of diamond, as a similar questions mentioned in a comment devolved to. If a maximum is required to avoid silly answers, let's say about the area of a typical Manhattan city block, with reasonable latitude on shape.

I understand this material can handle high compressive loads, practically no tension load, and has a high density as building materials go. My gut feel (I'm a electrical engineer, not so fluent with structural engineering) is that the optimum (least material for highest result) shape would be a circular crossection, probably with exponentially decreasing diameter with height. How well does that scale due to ground loading? What if this is built on bedrock? Wouldn't that be about the same properties, if not better, than the brick and mortar? Would that allow scaling some shape aribtrarily, or do the proportions of the shape change with size?

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  • $\begingroup$ I'm not sure if the questions are similar enough for this to be called a duplicate, but see this question. It doesn't limit the material to brick and mortar, but the points made in the answer still mostly apply to your question. $\endgroup$ – Wasabi Dec 25 '17 at 17:21
  • $\begingroup$ Wasabi: I tried to add some constraints so this question doesn't devolve like the one you linked to. $\endgroup$ – Olin Lathrop Dec 25 '17 at 17:46
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since the structure is loaded only by its own weight, the limiter will be the maximum compressive strength of the material, beyond which the bottom floor gets crushed. as pointed out by others, this can be at least partly mitigated by tapering the sidewalls. in any case, knowing the compressive strength, the density, and the dimensions of the tower, its height at the point of compressive failure of the first floor can be calculated.

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There is a brick building in Chicago that is claimed to be the tallest that brick can build ( without crushing the bottom). It is about 200 ft. But it will have the additional weight of floors and other interior components, so I guess it is not quite an answer.

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