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In this alternate scenario, metropolitan cities are nothing more than titanic, self-sustaining pyramids, connected only via railway bridges and municipal power lines.

Featured here are characteristics of Manhattan Pyramid crucial to the question at hand:

  • A height of 2004 meters.
  • An outer shell of slate bricks.
  • A skeleton of steel structured in x-bracing.
  • Glass windows of only one size--30 inches wide by 52 tall.
  • When finished, a midway between a Step Pyramid (like the Pyramid of Djoser) and a True Pyramid (like Giza or Khufu).

Using the listed information, in a Life After People, how long will Manhattan Pyramid stand before time and the elements reduce it to rubble?

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closed as unclear what you're asking by type_outcast, Brythan, James, bowlturner, Jim2B Jan 7 '16 at 4:55

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    $\begingroup$ You gave no significant structural information. This question cannot be answered in any realistic factor. People will simply make up answers. Also self sustaining mega structures are called "Acrology" $\endgroup$ – Stuart Allan Jan 6 '16 at 5:43
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    $\begingroup$ Define "rubble". For instance consider the Cairn of Barnenez, I would call it ruins, but not rubble... and it is at least 6000 years old, who knows how long would it take for erotion to redue it to "rubble". Btw, there is some important structural information missing: what is the wall material? I would asssume concrete, of what kind? How tick are the walls? Are there any chemical protections on the exterior - aside from, probably, regular paint? $\endgroup$ – Theraot Jan 6 '16 at 6:16
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    $\begingroup$ 3.2 km high pyramids? Wow! The Burj Khalifa is 0.8km, and that's a skinny tower. At 3.2km, you want a man-made Manhattan mountain. By comparison, Mount Everest is only 3.6-4.6km from base to summit! Even an implausibly thin outer shell of 3m thick slate would result in a $1.74\times 10^{11}\,kg$ shell ($2\,300\,kg/m^3$ slate.) I'm not sure how (or if) the mass damper applies to pyramids. I would love to answer, but this is above my engineering pay grade to tell you whether such a structure is even plausible to build. I hope someone smarter than me can answer you! $\endgroup$ – type_outcast Jan 6 '16 at 8:21
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    $\begingroup$ @JohnWDailey you do not provide enough information on construction methods or materials used. As a result the "how long will it last" question could be - not at all, to a very long period of time indeed. Therefore you provide no significant structural information. For example, the phrase "steel structured in x-bracing" is absolutely meaningless. $\endgroup$ – Stuart Allan Jan 6 '16 at 15:00
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    $\begingroup$ @JohnWDailey again you clearly have no understanding of basic engineering, materials science, or physics. Do some research. Slate is NOT a good alternative it is highly brittle. Yes for a 5 story house it could substitute for brick, but any high rise it would crumble under its own weight. Why not slate cladding? You don't even understand what concrete means.... there is no "modern concrete" as there is a huge number of different concrete recipes engineers use depending on the circumstances required. A mass damper has no use in a giant monolithic pyramid - I have no clue why you would include. $\endgroup$ – Stuart Allan Jan 6 '16 at 16:00
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EDIT: The OP indicated that by 'mass damper system' he meant a damper of the kind usually used to stop skyscrapers from swaying. This only adds to the weight of the structure. With that in mind:

As soon as whatever wizardry you're using to support the structure fails.

Seriously. At the dimensions of the structure you've got, either this is some insane super-alloy of steel that is strong when hammered out to wire thinness, or you've got antigravity technology reducing the weight. As a comparison: The Burj Khalifa, standing at a measly 829.8 m, has a dry weight of 500,000 tons. That's a masterpiece of engineering, it's a slender spire, and it's already having to deal with some of the most extreme mechanical stresses we've ever dealt with as a species.

Your pyramid is much taller, much wider and has a cladding of slate for goodness sake (see type_outcast's comment on the question for more on that. I just spotted it.). Regular steel won't hold up under that. It will crumple under its own weight or sink into the bedrock below. Even mountains can't get that tall without other mountains shoring them up, and they're solid all the way through.

Which leaves us with some form of either:

A: Magically strong steel whose mechanical properties are unknown but somewhere on the far side of ridiculous. In this scenario we can't estimate how long your structure will last, since its skeleton is basically badass.

B: A magical anti-gravity device making the whole thing stand up/not get flattened by weather systems which is presumably powered. As soon as the power goes out, this stops operating, causing the pyramid to collapse.

Edit No 2: The OP changed the height of the pyramid (which doesn't help) and suggested that the structure could be supported using a central column.

Just for fun: lets do the maths on a central column. If it's a 1m2 column that's 2001 m high, we can easily work out the force being put on the bottom meter of the steel as 2000 * 8000 * 9.8 (Height * density of steel in kg/m3 * g). This comes out to 156.8 GigaPascals. The highest compressive strength I've been able to find for steel is 152 GigaPascals, which means that even in an ideal world, with no wind, shear stress or additional weight, your supporting column crushes itself under it's own weight. Adding extra columns or support struts won't help, they just make the problem worse. And that's before we get to any of the other architectural problems the pyramid has.

The lower struts of your pyramid are the first to fail, especially on the side that faces the sea. The weight of the structure above them essentially flattens the entire bottom half of your pyramid, heating it by an appreciable amount as it does so, and turning the lower levels to molten slag. The upper levels warp and buckle, slowly sinking and cracking, with those struts nearer the bottom becoming bendy and rubber-like. A wave of semi-solid steel and shattered slate spreads out over the former state of New York, washing everything (buildings, soil and even the top layers of bedrock) before it.

Eventually you're left with the largest, most bizarre piece of modern art ever. At it's heart lies a slowly swinging pendulum that weighs exactly 1852 tons.

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  • $\begingroup$ Again with the incomplete accusation. What was I missing? As for the slate, look here: worldbuilding.stackexchange.com/questions/28399/… $\endgroup$ – JohnWDailey Jan 6 '16 at 14:57
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    $\begingroup$ @JohnWDailey: The part you're missing is how you have a structure with both the dimensions and the weight that you've quoted in your question. I don't have a problem with using slate as a cladding other than it's very heavy, and you've got a lot of slate to put on that thing. $\endgroup$ – Joe Bloggs Jan 6 '16 at 15:03
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    $\begingroup$ Eventually you're left with the largest, most bizarre piece of modern art ever. and the death of anything within an appreciable radius... $\endgroup$ – James Jan 6 '16 at 21:04
  • $\begingroup$ I edited it to be 2004 meters tall, the height of Tokyo's proposed Shimizu Megapyramid. $\endgroup$ – JohnWDailey Jan 7 '16 at 19:30
  • $\begingroup$ @JohnWDailey From the wiki page for the pyramid: "The proposed structure is so large that it could not be built with current conventional materials, due to their weight. The design relies on the future availability of super-strong lightweight materials based on carbon nanotubes presently being researched." and "The external structure of the pyramid would be an open network of megatrusses, supporting struts made from carbon nanotubes to allow the pyramid to stand against and let through high winds,". But your specs still say steel & slate, so we still don't what prevents collapse. $\endgroup$ – LindaJeanne Jan 7 '16 at 21:58
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10 years, once the power is lost. Approximation based on actual weather, since storms and flooding is sporadic.

I was surprised by an answer to a similar question about Manhattan after people: I thought concrete buildings would last a few hundred years? Turns out that water flooding basements is a killer. Once the pumps stop and maintenance ends, all is lost. A major storm with flooding will cripple it and compromise the structure. The next will cause serious damage.

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Since you referenced "Life after People" then you should already know the answer. Structures made with steel or other metals will fail after about 200 years without regular maintenance. Given the size and mechanical stresses of your proposed structure (mentioned in other answers and comments), 200 years may be a generous estimate.

Concrete structures without steel rebar last longer. Roman structures made of concrete are at least 2000 years old and most of them are still clearly identifiable as man made structures and their purpose can be fairly easily discerned. It is estimated the Petronas Twin Towers could last for 500 years without ongoing maintenance since they have a limited amount of metallic reinforcement, but as slender towers they are also under a lot of stress due to wind, temperature changes and potentially earthquakes.

If we redo your structure using modern composite materials and maybe spray painting the exterior to look like slate, the structure becomes much lighter. Because composites are strong in tension rather than compression, the method of building your structure will have to be different, which leads to different modes of failure. The most severe threat would be if the fibres were to degrade or break. This could be caused if the fibres were exposed to sunlight or water (after a century of weathering to remove any protective coatings), but since known fibres are many times stronger than steel per unit weight, this could take a long time. This could be minimized through the use of Honywell M5, a type of super material which is fireproof and impervious to ultraviolet radiation. Another serious mode of failure would be the release of an anchor which holds a fibre or section of the structure under tension.

If the design is dynamically unstable for any reason, the process of fibres breaking or degrading could be sped up as fibres are abraded or torqued. This is almost inevitable in a structure of that size, since without any sort of active countermeasures it will flex through temperature changes (the side exposed to the sun will expand slightly during the day, for example), wind loads and even earth tremors. This will also affect anchor points.

A far more important consideration is what is being used to bind the fibres? The resins which bind composite materials are very strong, but not as strong as the fibres themselves. They too will degrade based on factors like temperature, exposure to water and flexion and torques caused by movements of the structure.

I have not been able to discover estimated MTBF's for materials like M5 or the binding resins, but I will offer a speculation that the Great Pyramid of Manhattan will only last marginally longer if built from composites. While it will be lighter and stronger than a corresponding steel structure, it will also be subjected to a lot of forces, which, without active countermeasures and maintenance will lead to the failure of some of the fibres, resins or anchors. The extra stress will be passed on to other structural members in unplanned and asymmetric fashion, which will lead to cascade failures of segments of the structure, further unbalancing it and redistributing loads in fashions the designers had never intended. The collapse may look more like a series of sails being furled (or a hot air balloon being deflated), which is still impressive on that scale, in a different way.

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  • $\begingroup$ So slate is out of the question. Are there any long-lasting igneous or metamorphic rocks that may be reasonably lighter than slate? $\endgroup$ – JohnWDailey Jan 7 '16 at 2:47
  • $\begingroup$ The real question is mass. You need a structure of that size to be as light as possible, and a covering of rock on that scale will be very massive (and a dead load on the structural elements as well). $\endgroup$ – Thucydides Jan 7 '16 at 11:33
  • $\begingroup$ So it's back to the dried-up clay that fails to guarantee longevity? Because that's what brick is. $\endgroup$ – JohnWDailey Jan 7 '16 at 16:15
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    $\begingroup$ Concrete does not guarantee longevity, reinforced concrete structures fail because the steel inside rusts out. If you want to protect a steel structure of that size, the external coating needs to be as light as possible to minimize the dead loads; you have to paint the structure constantly instead... $\endgroup$ – Thucydides Jan 9 '16 at 2:44
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    $\begingroup$ You want an outer covering, given. Steel and metallic materials (even metallic composites) need protection from the elements, especially water. Paint helps keep water away from the metal structure, and is far lighter than almost any other protective coating that is not magi tech, lessening the dead loads the structure needs to handle. The aesthetic appeal of paint is secondary in this application. $\endgroup$ – Thucydides Jan 10 '16 at 3:03

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