I think calling vaults, arches, and domes, triangles is an oversimplification from a structural engineering or architecture perspective.
You might try looking into catenary curves. This is the curve formed by a hanging cord or string under uniform gravity load. The loads are almost purely tensile along the length of the cord.
I think calling vaults, arches, and domes, triangles is an oversimplification from a structural engineering or architecture perspective.
You might try looking into catenary curves. This is the curve formed by a hanging cord or string under uniform gravity load. The loads are almost purely tensile along the length of the cord.
Arches are the inversion of this. A perfectly inverted catenary curve results in (mostly) compressive forces along the curve.
History shows us many different forms of compression arches (mostly not strictly catenary curves) and not purely efficient in terms of all compressive forces, but the principle is the same. This accounts for the final placement of the ‘keystone’ at the pinnacle of arches, which closes the circuit on the loads.
"I think calling vaults, arches, and domes, triangles is an oversimplification from a structural engineering or architecture perspective."
Yeah, me too. That's why I call them fractalized triangles and show a picture of discrete versus continuous.
"You might try looking into catenary curves. This is the curve formed by a hanging cord or string under uniform gravity load. The loads are almost purely tensile along the length of the cord."
Yes, I know what they are. They are curve optimized for (discrete analog) chain link force distributed among the links. But that's upside down of this physics problem, and instead of the chain link being the unit where force matters, it's the joint or shared surface between two bricks/tiles.
Catenary curves actually pertain to ropes/cords, not just chain link. It is indeed upside down of an arch or dome, but it also points to why domes and arches work.
The hanging chain or rope shows the uniform load distribution of gravity and ends up expressing the linear load path of tension. When this is turned upside down, as in a catenary vault, the load path becomes one of pure compression, which is well suited to materials such as stone, ceramic or concrete, all being fairly weak under tension loads.
Compare this to a horizontal beam or rafter. The gravity loads here cause deflection of the beam and induce tension in the bottom portion of the member, and compression in the upper. This is the primary limitation for the spanning capacity of a member. Materials that can’t handle tension don’t span very far. This is why egyptian stone architecture has closely spaced columns, whereas timber or steel structures can be built with much larger spans.
The genius of arches, vaults, and domes is that the load path becomes oriented closer to a pure compression orientation. This allows for small pieces (stones or tiles, for example) to be linked together since there is typically very little bending or shearing stress under simple gravity loading.
This isn’t the same thing as triangulation, in which the members are still behaving like beams and are subject to bending and deflection. Note that the center portion of the formwork for the catalan vault in the video uses what looks like plywood as the central web—this is because the formwork will take on bending stresses as it is loaded.
The point of this is actually mathematical as well as structural engineering. The uniform load of gravity as it is expressed in bending stress on a beam actually looks a lot like a catenary curve. The grace of curved arches and vaults is that it uses the simplicity of its form to direct the loads into a more efficient form—compression—instead of bending.
Probably nit-picky, but it’s a unique form and structural strategy in architecture and structural engineering, and worth clarifying.
I think calling vaults, arches, and domes, triangles is an oversimplification from a structural engineering or architecture perspective.
You might try looking into catenary curves. This is the curve formed by a hanging cord or string under uniform gravity load. The loads are almost purely tensile along the length of the cord.
Arches are the inversion of this. A perfectly inverted catenary curve results in (mostly) compressive forces along the curve.
History shows us many different forms of compression arches (mostly not strictly catenary curves) and not purely efficient in terms of all compressive forces, but the principle is the same. This accounts for the final placement of the ‘keystone’ at the pinnacle of arches, which closes the circuit on the loads.
"I think calling vaults, arches, and domes, triangles is an oversimplification from a structural engineering or architecture perspective."
Yeah, me too. That's why I call them fractalized triangles and show a picture of discrete versus continuous.
"You might try looking into catenary curves. This is the curve formed by a hanging cord or string under uniform gravity load. The loads are almost purely tensile along the length of the cord."
Yes, I know what they are. They are curve optimized for (discrete analog) chain link force distributed among the links. But that's upside down of this physics problem, and instead of the chain link being the unit where force matters, it's the joint or shared surface between two bricks/tiles.
Catenary curves actually pertain to ropes/cords, not just chain link. It is indeed upside down of an arch or dome, but it also points to why domes and arches work.
The hanging chain or rope shows the uniform load distribution of gravity and ends up expressing the linear load path of tension. When this is turned upside down, as in a catenary vault, the load path becomes one of pure compression, which is well suited to materials such as stone, ceramic or concrete, all being fairly weak under tension loads.
Compare this to a horizontal beam or rafter. The gravity loads here cause deflection of the beam and induce tension in the bottom portion of the member, and compression in the upper. This is the primary limitation for the spanning capacity of a member. Materials that can’t handle tension don’t span very far. This is why egyptian stone architecture has closely spaced columns, whereas timber or steel structures can be built with much larger spans.
The genius of arches, vaults, and domes is that the load path becomes oriented closer to a pure compression orientation. This allows for small pieces (stones or tiles, for example) to be linked together since there is typically very little bending or shearing stress under simple gravity loading.
This isn’t the same thing as triangulation, in which the members are still behaving like beams and are subject to bending and deflection. Note that the center portion of the formwork for the catalan vault in the video uses what looks like plywood as the central web—this is because the formwork will take on bending stresses as it is loaded.
The point of this is actually mathematical as well as structural engineering. The uniform load of gravity as it is expressed in bending stress on a beam actually looks a lot like a catenary curve. The grace of curved arches and vaults is that it uses the simplicity of its form to direct the loads into a more efficient form—compression—instead of bending.
Probably nit-picky, but it’s a unique form and structural strategy in architecture and structural engineering, and worth clarifying.