Sphere versus Pyramid

[SagaLore]

What is stronger? Which withstands gravity and load stresses better?

A solid half-sphere, or a solid equilateral pyramid?

A dome (interconnected hex and pent, such as C60 buckyball), or pyramid grid (interconnected triangles)?

 

[imported_Spoot]

Probably the half sphere i would asssume. I would think it would be able to distribute the gravity or load a little more efficently across the whole structure. I could be wrong however...that is merely my 2 cents.

 

[CycloWizard]

The answer, as to any good engineering question, is: it depends. What kind of load are you looking at? How do you define "stronger"?

For a uniform pressure, the dome will be superior in minimizing stress. This is because it has the minimum specific surface area (surface area:volume ratio) of any shape (or half-shape; really, a sphere is the ideal). For a single point load applied at the apex, the pyramid might be better, depending on how you define 'better'.

 

[SagaLore]

I want to design an Archology - it is going to be huge; it is going to contain a city inside it.

If any part of the structure is removed, I want the rest of the structure to support itself. I want it to withstand earthquakes and tornadoes.

 

[CycloWizard]

Are you sure you meant archology? Archology: theory of origins is the only entry I can find on that word. I'll assume you mean some structure that will cover a city. For this purpose, you would definitely use a curved structure, probably torispherical in shape (similar to most domed stadiums, like a truncated hemisphere fitted on top of a cylinder). If you went with a hemisphere, it would weight far too much, be too tall, and the benefits would be minimal at best (unless you were planning on enclosing skyscrapers?).

Regardless of the structure, there will always be certain key pieces that will cause the structure to fail if removed unless you overdesign it by a ridiculous factor of safety and just build in redundant pieces for this purpose. This is avoided because of the prohibitive cost and necessity of increased design complexity.

 

[SagaLore]

Originally posted by: CycloWizard
Are you sure you meant archology? Archology: theory of origins is the only entry I can find on that word. I'll assume you mean some structure that will cover a city.

Try Arcology. I've seen it spelled both ways.

The structure won't be covering a city - the structure is the city.

 

[Yeraze]

You might want to look into this : http://dsc.discovery.com/convergence/en...ramidcity/interactive/interactive.html

Saw that on the discovery channel a few months back,

 

[CycloWizard]

Originally posted by: SagaLore

Originally posted by: CycloWizard
Are you sure you meant archology? Archology: theory of origins is the only entry I can find on that word. I'll assume you mean some structure that will cover a city.

Try Arcology. I've seen it spelled both ways.

The structure won't be covering a city - the structure is the city.

Ah, I see what you're saying. Well, in the case where you want to build up instead of out, I would probably go with a hemisphere shape. This will give you more volume for the same footprint relative to a pyramid or other shape.

 

[sdifox]

Probably x-agon, with the number of sides determined by size, number of supports and other factors. Frontier of Construction covered this a while back. Half a sphere doesn't really help you since you are planet bound and you are only using the flat side. Unless you want to completely cover the site. Dyson Sphere would be ideal to use in space, a la ST:TNG.

 

[CycloWizard]

Originally posted by: sdifox
Probably x-agon, with the number of sides determined by size, number of supports and other factors. Frontier of Construction covered this a while back. Half a sphere doesn't really help you since you are planet bound and you are only using the flat side. Unless you want to completely cover the site. Dyson Sphere would be ideal to use in space, a la ST:TNG.

You're living on the flat side, but the spherical section is still load-bearing. The higher your value of x in your x-agon goes, the closer you approach to the sphere. This increase will increase the structural ability of the dome as well as construction cost. As in all things engineering, there is a balance somewhere in the middle. I was just trying to point out the ideal case, which is what I thought he was asking for.

 

[sdifox]

Originally posted by: CycloWizard
You're living on the flat side, but the spherical section is still load-bearing. The higher your value of x in your x-agon goes, the closer you approach to the sphere. This increase will increase the structural ability of the dome as well as construction cost. As in all things engineering, there is a balance somewhere in the middle. I was just trying to point out the ideal case, which is what I thought he was asking for.

only viable spherical construction would be living on the various circumference, by building circle on top of circle, otherwise you are just building a big dome roof for no good reason.

 

[CycloWizard]

Originally posted by: sdifox

Originally posted by: CycloWizard
You're living on the flat side, but the spherical section is still load-bearing. The higher your value of x in your x-agon goes, the closer you approach to the sphere. This increase will increase the structural ability of the dome as well as construction cost. As in all things engineering, there is a balance somewhere in the middle. I was just trying to point out the ideal case, which is what I thought he was asking for.

only viable spherical construction would be living on the various circumference, by building circle on top of circle, otherwise you are just building a big dome roof for no good reason.

That was my point. The spherical shape still offers the most living space for the same footprint of the subset of geometries that might be able to withstand the stresses that he was concerned with (earthquake and such). Otherwise you could go with a cylinder or rectangle, but they're not as structurally sound.

 

[TuxDave]

Originally posted by: CycloWizard

Originally posted by: sdifox

Originally posted by: CycloWizard
You're living on the flat side, but the spherical section is still load-bearing. The higher your value of x in your x-agon goes, the closer you approach to the sphere. This increase will increase the structural ability of the dome as well as construction cost. As in all things engineering, there is a balance somewhere in the middle. I was just trying to point out the ideal case, which is what I thought he was asking for.

only viable spherical construction would be living on the various circumference, by building circle on top of circle, otherwise you are just building a big dome roof for no good reason.

That was my point. The spherical shape still offers the most living space for the same footprint of the subset of geometries that might be able to withstand the stresses that he was concerned with (earthquake and such). Otherwise you could go with a cylinder or rectangle, but they're not as structurally sound.

I think I read somewhere that spherical domes are not the strongest form given a spherical footprint. It was something that looked more like a parabolic dome that gave better structural support.

 

[sdifox]

Originally posted by: CycloWizard
That was my point. The spherical shape still offers the most living space for the same footprint of the subset of geometries that might be able to withstand the stresses that he was concerned with (earthquake and such). Otherwise you could go with a cylinder or rectangle, but they're not as structurally sound.

I am not sure spherical is all that strong, specially if you are talking about earthquake. Only way to survive earthquake is to move with the wave column has more chance of surviving earthquake since you have a reduced aread to be concerned with. Sphere would be strong if it is a full sphere, half sphere is not really that strong.

 

[DrPizza]

Originally posted by: TuxDave

Originally posted by: CycloWizard

Originally posted by: sdifox

Originally posted by: CycloWizard
You're living on the flat side, but the spherical section is still load-bearing. The higher your value of x in your x-agon goes, the closer you approach to the sphere. This increase will increase the structural ability of the dome as well as construction cost. As in all things engineering, there is a balance somewhere in the middle. I was just trying to point out the ideal case, which is what I thought he was asking for.

only viable spherical construction would be living on the various circumference, by building circle on top of circle, otherwise you are just building a big dome roof for no good reason.

That was my point. The spherical shape still offers the most living space for the same footprint of the subset of geometries that might be able to withstand the stresses that he was concerned with (earthquake and such). Otherwise you could go with a cylinder or rectangle, but they're not as structurally sound.

I think I read somewhere that spherical domes are not the strongest form given a spherical footprint. It was something that looked more like a parabolic dome that gave better structural support.

When I first saw a half sphere proposed, my intuition was telling me that with a circular base, the shape may have something to do with some hyperbolic function.

 

[Powermoloch]

sphere FTW.

 

[Leafblighter]

I think I read somewhere that spherical domes are not the strongest form given a spherical footprint. It was something that looked more like a parabolic dome that gave better structural support.

well, the advantage if the shape is more parabolic, is that the loads coming down to the ground from the structure above will be transferred to the ground in more of a vertical direction. this has the advantage of not requiring as much lateral bracing as would be required in an arched structure which is shallower. think of it as the comparison between a roman arch and a pointed arch. both work, but the pointed allows for the forces to flow more vertically downward rather than outward, necessitating less of a horizontal butress to counter the load.

but if you are talking about say, an underwater habitat, where the forces are equal on all sides, then yes, a sphere is the ideal. but since this is above ground and gravity is most important, then you would probably want something a bit more parabolic

you would definately want to stay away from pyramids. if you take a dome and subject it to uniform vertical loading, the advantage to this is that all of the members in the system are subjected to compression. each part is helping shoulder the load equally with the one next to it. now, the problem comes when you need to puncture this wall, but it can be done to a limited extent (see any european domed church). pyramids which would be hollow inside are just intrinsically more complex with the load not being uniform across the whole structure. you would have to deal with compression and tension forces upon the system. I would assume that you would have concentrations at the vertices and would have to protect against the whole structure torquing in response to the wind (which would in this case require substantial crossbracing to counteract). not that it couldnt be done, but at this scale it may become quite impossible.

either way though, this thing would be horrendously expensive and unnecessary

 

[Asymptoke]

Well one thing's for sure; when I place an egg between my palms and squeeze, I can't break it no matter how hard I try.

 

[sdifox]

Originally posted by: Asymptoke
Well one thing's for sure; when I place an egg between my palms and squeeze, I can't break it no matter how hard I try.

You mean sqeezing from the ends, otherwise it is very easy to crack an egg. Like I said above, if you are building for space, sphere would be ideal, but putting up a building is a whole different ball game.