Sunday, February 26, 2012

Catenary reconsidered

Application of catenary structures must be carefully considered for use in different environments.  A few examples worth looking at include:

·        An environment without gravity.  If a structure is built in space, or acts as a satellite, or is built in conditions of very low gravity (like on an asteroid, or the moon, or even a buoyant ball) then the reasons for a catenary structure practically disappear.  Under these conditions a sphere or spherical dome is the optimal structure.

·         Very high external pressure.  If a structure is submerged to any depth, then an outside compressive force acts on the entire structure.  Under these conditions, again we find that a sphere is the strongest and most stable structure.  A catenary structure under great external pressure is weaker than a spherical structure.  (Do you ever crack an egg at the tip? No, you crack it on the weak side.)

·         Extreme loading from high velocity winds.  Such conditions are found in extreme storms, including hurricanes, typhoons, and tornadoes.  Under these conditions, the exposed surface area per unit volume is minimized by using a spherical form.  The profile is further minimized by using only a smaller segmental section of the spherical form, further reducing the profile of the structure.  A woven tensile geodesic web will help blocks resist suction forces in very high winds.

·         Earthquakes.  A catenary arch results from acceleration due to gravity.  In an earthquake, the ground can move in a sudden sideways fashion.  This results in acceleration in a sideways or lateral sense.   If a chain hangs from a rod, and the rod is tipped or inclined away from horizontal, then the catenary changes relative to the rod: the same way thrust force lines in a dome change relative to the horizontal ground movement during an earthquake. 

This situation is as if the arch was built on an inclined surface; the catenary still exists, but it is like a catenary on an inclined surface.  The direction of the inclined surface is relative to the motion of the ground.  The result of this sideways acceleration is that the catenary arch may eventually touch or exit the wall thickness; a hinge is created and the structure will buckle and collapse. 

Catastrophic failure of masonry arches during earthquakes can be prevented by using tensile elements woven into the arches as great circle arcs.  This geodesic tensile web will prevent the creation of hinges, catenary thrust force lines will not exit the wall thickness due to lateral acceleration.   Structural integrity is maintained if the hinges cannot open.   Tension is provided.

Tensile elements woven into a dome will help hold it together during an earthquake.


  1. I have not spent all that much time with geodesic structures and domes. In general, I see what you are doing as a low cost, easily obtainable material being utilized to not only have superior strength, but also "skin" the dome as well.
    One thing that has always intrigued me was to built a dome structure as a complete sphere, so its circumferential integrity is maintained and then just bury some of the sphere in a round hole. Then the roof, walls and foundation are all of the same sphere.

    1. Yes, a complete sphere is generally stable. If you made one without tensile reinforcement, it would need to be at LEAST half-buried; preferably buried up to the haunch of the top hemisphere (51.82 degrees from vertical). The only difficulty with this is a lot of digging.

  2. Hello,

    I stumbled across your article after googling "catenary architecture typhoon" with the intent of finding an information on a housing structure or design that would be say typhoon proof capable of withstanding wind forces of 200kmh. The story is we live in the Philippines where there are typically 26+ tropical storms and significant typhoons that affect the population and in our case We have a small group focused on educating and helping out local farmers in preserving both their crops in a "metal greenhouse" design and a simple home at the lowest possible cost with the optimal structural benefits to withstand catastrophic winds.

    Anyways, we found a site helping impoverished or catastrophically affected people by providing strong, architected catenary arch home which are amazing from a social perspective, but we are thinking how well these structures would stand against one of our typhoons?

    Anyways, I appreciate your informative article/concepts and would love it if you could provide an opinion of Abod as a shelter from a math perspective.

    Much appreciated and thanks.

    1. Hello Gene,

      Thank you for your interest in this masonry system.

      The system provided by Abod shelters does not appear to be strong enough to handle the full force of a typhoon or other extreme weather. It would certainly not be as strong as a masonry arched structure; however, it is probably somewaht faster to build. Abod claims their structure is assembled in one day, our system is assembled in around 3 days for a similar sized structure. It would be interesting to combine them both, so that a shelter could include a masonry 'safe room' with other parts of the building made from the Abod system.

      From a "math perspective" the Abod system does not have anywhere near the same strength as concrete. Concrete has a very high compressive strength, usually around 4,000 pounds per square inch (psi). The catenary form is ideally suited for masonry, it is inexpensive and easy to assemble. it is also termite proof, will not rot, rust or decay, and has thermal mass benefits (keeping cooler in the heat and warmer in the cold).

      The Abod system is lightweight, and might actually act like a sail, and catch the high winds of a typhoon, making it less stable than a heavy concrete arch.

      I hope this helps. Please let me know if I can answer any other questions.

      Thanks again for your interest.


  3. Thank you for your insightful reply, I'll close the books on that train of thought. :>

    I am curious about your masonry design and system for catenary forms I am sure its wicked solid and gratz to filing your patents, My question is kinda scaling it down in a 3rd world country, is it feasible as a diy project with a number of farmers creating forms, rebar and cement from local hardware stores?

    In regards, to masonry, Your blog is so fascinating to me and it sparks a lot of personal interests and desires from an artistic perspective. I am not sure if you have spent anytime in Asia or the East, they love the use of rebar and concrete block, it kinda drives me crazy honestly, since I am interested in something more sculptural with more complex curves and such.

    I am Filipino-American and I attended an art college in Philadelphia, PA. to pursue a degree in sculpture as personal passion, it seemed based on feedback I had enough skill and the penchant to carve what I visualized in my mind and I am thank for that and lead me to the next question.

    Can concrete be strong, sculptural and a form for a really bad ass house? I wanted to see how that could translate into a housing solution and I started dreaming about really cool sculptural forms combined with solid engineered pre-stressing benefits. This lead me to searching for a solution that here in the Philippines and found nothing remotely even close. Hence, the Internet was my outlet for research and I found a video so interesting that I can't help but ask for your opinion and comments.

    I'd like to share it with you and given your background and talent I hope it provides sparks some ideas.

    Block Research Group - Titled "Heavy Light - Fabric-Formed Concrete Structures"

    This is stewing in my mind, I would love to hear opinion and thanks again I'm a fan of your blog and your work.

    All the Best,

    1. Hi Gene,

      Thanks again for your interest. To try and answer your questions:

      DIY, as made by farmers, etc., is a challenge if they try to make blocks. Instead, we are working to provide this masonry system globally, to make it available wherever you would buy concrete block. We rely on the low cost, high efficiency and high strength of manufactured concrete block, which are available globally. We just change the mold for the machine to produce specialized block. Block are manufactured in around 2 seconds, which make it inexpensive. If you tried to make (cast) your own block, you have to wait overnight for it to cure, for one block. We are currently working to bring this technology to market, stay tuned.

      The whole idea of this technology is to use manufactured block for curved roofs, arches, domes, spheres, etc. I am the only person anywhere (anywhere in the world, as far as I know!) doing this with manufactured block.

      Cool that you went to school in Philly, I'm up in New York State, at Alfred University (also an art school).

      Manufactured concrete block can certainly be used as a strong sculptural form for a concrete house.

      I've seen the video you shared, it's an interesting approach. It may be suitable for certain applications. I think it's a pretty good approach. I personally think actual masonry is more attractive, but that's just my opinion.

      Thanks again for your interest Gene.


    2. Sweet. Solid info for sure. Next year after a few crop cycles, I should get a chance to start playing with the masonry ideas. Thanks a bunch Peter and keep inspiring us. Thanks.

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  5. BenjaminFranklinApril 20, 2016 at 11:19 PM explains about the 'lift' effect on roofs in hurricanes. Basically, less pitched roofs cause more lift than more pitched roofs. Lift is why tie down straps are needed in modern hurricane resistant construction