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Funicular Study
  • I want to do a funicular study of various arch designs that I would like to experiment with in compressed earth blocks.

    I think that somebody who has studied some degree of architecture and masonry might be familiar with the procedure - or be able to point me to a reasonably understandable tutorial to do at least a simplified study of an arch design.

    Resources? Pointers?  Help us collaborate to secure the safety of our arch designs!
  • 15 Comments sorted by

    Posted on youtube to get more help with this.
  • My proposed geometry is detailed in this image which is of this model.

  • Vote Up0Vote Down
    October 2011
    would it be better to not have the voussoirs be inside the column? how does it effect the brick layout/structure? could the voussoirs begin from the floor adjacent to the column instead? you could have a keystone type piece made to place on top of the extra bricks for the side that stars 5 foot up.
    ideakeystone.png 88K
  • Contact Phill of P.J.Vittore Ltd. The most knowledgeable on arches + domes. I could not locate him via web search, but CalEarth has contact with him.
  • I'm actually not particularly worried about whether the voussoirs are embedded in the column or not, it doesn't make much difference to me if I create a 'shelf wall' to support the arch between the columns or tie the arch directly into the columns. If an engineer tells me that's better, I'm likely to do it, if they say it doesn't matter, I'm likely not to.

    @dreambuilder thanks for the pointer, I'll see what I can find by that name.
  • Phillip J Vittore appears to be a 70+ year old man living in arlington heights, Illinois.  He's got a construction method patent to his name which is related to the concept of vaults/domes too.  I'm not surprised he doesn't have email.  I wonder if we could impose on any locals to the Chicago area (Allen?) to carry the concept of OSE to him in person and inquire as to any interest (with or without fee) in assisting with the engineering.

    The cosignature on the patent, Harrall Harrington, is the owner of H P Domes (speculation: Harrall + Phillip Domes?) out of Philadelphia, PA.  The patent and the business are involved in the construction of Monolithic Ferrocement Domes (which is particularly serendipitous to me as I have long been fascinated and interested in building concrete domes!)  He might also be somebody who could be a contact or resource in finding this study information.
  • Initial tension calculation.  Purpose: determine if the top of the arch will be under excess compression.

    The effective 'push together' of the top of the arch is relative to the overall triangle of the arch - how far the legs straddle vs. how high it is.

    First, angles.  As I've drawn it (within a couple of degrees) the lower right is 50 degrees, the lower left is 30 degrees.  Draw a 50/30/100 triangle, with the 50/30 side down.

    Draw a vertical line perpendicular to the bottom line intersecting the top point of the triangle.

    The value of this vertical line is a vector with value 15000 - my calculated 'weight per foot thick wall' form my diagram and densities above.

    We want to find out what the vector length of the bottom line of the triangle.

    the 50 degree side is a right triangle where the opposite is 15000 and the adjacent is unknown.

    tan(50) = 15000/x  

    multiply by x

    x*tan(50) = 15000

    divide by tan(50)

    x = 15000/tan(50)
    x = 12605

    Now the other side, with the 30 degrees

    x = 15000/tan(30)

    x = 25980

    25980+12605 = 38567

    each brick has a face of 72 square inches

    38567 pounds/72 square inches=535 Pounds Per Square Inch

    Our previous tests last june on unstabilized earth brick provided a strength of 795 PSI.  That is significantly greater than the 535 PSI we calculate we need - but it isn't what you'd call a tremendous safety margin.

    I notice on that selfsame entry he mentions that the bricks weigh 20 pounds.  I had calculated my densities based on 30 pounds - the actual density of a 20 pound brick wall is only 120 pounds instead of 180, two-thirds what I had thought.

    That brings all the numbers down by 2/3rds, which means the top brick would only be compressed 357 psi - which is still more than the new mexico building code requires for the bricks to be.  

    What does that mean?  This arch design is too flat, but it wouldn't collapse provided we were using blocks that had a good 700 psi in them, by a safety factor of 2.

  • If I made a semi-circular arch (45 degree triangle) the horizontal compression should be about twice the vertical.  this will require less support volume thus dropping the load to 52 cubic feet per foot from the previous 69.  weight of the 52 cubic feet @ 120 pcf = 6240 pounds, plus another 2600 pounds for the roof live load gives us 8840 pounds to support.  thanks to the simplicity of a 45 degree triangle which is iscosles, the top brick will have compression of 8840*2 or 17680 pounds, spread over 72 square inches provides 245 PSI.  If we can get bricks with a 750 psi capability (and there is indication that we can) we would have a 3 fold safety margin.  300 PSI bricks would be adequate, but not provide nearly as much a margin of safety for the uber-conservative.  The loading information I find in the Structural Masonry Designers Manual   indicates safety factors such as 1.6.  1.6 times 245 is 392.

    That brings up the question of 'how can we make sure our bricks have a compressive strength of at least 400 psi?  A testing jig to actually put them under that much pressure?   Quality control seems fairly important for the creation of the Voussoirs.  Here's a picture showing the semicircular arch design against the riser/carry original design.


  • Vote Up0Vote Down
    October 2011
    looking good.

    might be a while before press with rejectable bricks is online, but its definately worth trying out with what we have.
  • Graphical Analysis

    This free google book is about how to do graphical analysis of arches.  I found it because it was referenced in  this book on page 229 which was suggested by an architectural student who is a friend of Brianna, who helped us at factor e farm a few weeks ago!

    If you have the time to use this method against at least one of the two arch designs detailed in this thread, please let me know so we can coordinate - I'll get to it eventually, of course, but if we have some math heads with some time, that could free me up to do other things that are no doubt also important.

  • David the two text books are excellent! 
    About HP Domes I track the entity down to being a company that uses the inflation method, surplus forms available!
  • Vote Up0Vote Down
    October 2011
    This looks interesting, if incomplete: ; it uses Geogabra which is GPL open source.

    Interactive Thrust is very slick but seems to rely on which is proprietary.

    Wow, there are a ton of interactive programs that might be used for graphical static analysis with a few macros etc.:
  • Yes, Dreambuilder, I've been a big fan of Monolithic domes for a long time - I've even designed a few dream houses using that tech - it would be interesting to see how we could adapt the procedure to create a dome out of steel reinforced cob.  The materials of the monolithic structure as presented are very industrial high-embodied energy things.  Thats okay, if you have a need for that kind of power-rigidity and budget to afford it in your project.

    Thanks chuck.  I wish I knew which method will get me to a solution first - trying programs, attempting to learn them and creating a solution - or following the textbook by hand.
  • Re: the original post:

    Lukas Ballo at ETH (associated with Dr. Block) has several nice video tutorials on fundamentals of graphical statics (funicular diagrams), both by hand on the board and using GeoGebra.

    He starts very simply, and works up to iterative (trial and error) solutions for a catenary vault.

    To use GeoGebra, you'll need his template (script file) at the bottom of the page, here:

    This template allows you to place support reactions, which are unavailable in standard GeoGebra.

    Obviously, you could do a similar scheme in almost any drawing package which permits you to do basic Euclidian construction (lines and arcs), but the GeoGebra package lets you "play" with things by dragging loads or structure geometry and watching what happens (it's parametric, after a fashion).

    If you like heavier going (mathematically speaking), Phillip Block's PhD thesis treats of funicular analysis in three dimensions:

    He uses Rhino with scripting.

    Block and Dr. John Ochsendorf (at MIT) have also done some great stuff with thin tile (Catalan or timbrel) vaulting, which is still common in Catalonia and parts of South and Central America, and was once more common in the US until high labor costs made it economically unfeasible. There are some good related resources on analysis, though I can't think of any specific recommendations off the top of my head. Dr. Anne Fitchett at Witwatersrand and Lara Davis at ETH are part of this circle, and have done quite a bit of both hands-on and theoretical thin tile work.

    Guastavino's analysis of thin tile vault strength (as in his "Prolegomena" [sp?]) is bunk. Somehow, he thinks mortaring tile together changes a brittle material into a ductile material, giving it extra tensile strength (I simplify slightly, but that's the jist of it). Nevertheless, he built aesthetically impressive and enduring structures using simple rules of thumb and experimental strength data.

    Santiago Huerta has done quite a bit of analysis of existing structures to assess their stability and also discusses Medieval and Gothic design philosophies, some of which might be helpful.

    Also Satprem Maini of Auroville Earth Institute has a presentation aimed at architects which goes a step further than basic catenary (funicular) analysis and optimizes the thickness of the vault relative to height, so that there is not excessive weight at the top of the vault. I can't find the link immediately, but if you nose around a bit with Google, you'll find it. It's a big file, about 300Mb, IIRC.

    Jacques Heyman's "Coulomb's Memoir on Statics" has some good stuff on the fundamental physical assumptions which underlie funicular analysis (no slip at mortar joints, for instance). It is good to keep these in mind, as they are axiomatic to the method. My local university library has a copy.

    There are dozens of graphical statics books on Google Books, most from a hundred-odd years ago.

    All that being said, I am a neophyte with funicular analysis, in the process of teaching myself. I am not a structural engineer, so don't really feel qualified to offer a professional opinion on any of the above, but is probably a good start, moving from a strictly working analysis to a more theoretical approach.

    Kind of a lot to chew on, but there it is.

  • Just a follow-up to the list of funicular analysis resources: the link to find Maini's discussion of vault design for architects can be found here:

    Just click the "Download Article" button - 209Mb, a little smaller than I recalled. Though alluded to elsewhere, too, within the document, the design analysis begins in earnest on page 55, with physical catenary models and proceeds from there through funicular analysis to his thickness-optimized designs. Since he is using CSEB, the thickness can only be varied according to the module of his bricks, rather than continuously as might be done with poured in place media.


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