This squared torus geometry offers the compressive assets of arches combined with square floor plans. It is a circulating barrel vault shape. Compressive efficiencies are economical and can reduce needs for much more expensive reinforcement methods. It could be made of thick concrete, thin ferro-cement, or other alternative building materials as well. Qualified engineering could adapt it to withstand heavy loads of earth-covering, hurricanes, floods, earthquakes and disasters-generally.  The square donut concept came to me in 2005. After discussing vaults construction on a ferrocement forum. It seemed to me that making a square unit with rounded surfaces would optimize the structure. Despite that most people rather use ordinary, un-optimized materials or methods.  Unoptimized structures are generally adapted by everyone, including ferro cement enthusiasts. I tend to think in terms of geometric optimization and optimized, non-planar surfaces.

Completely un-buried Square Donuts could be adapted with customized arrangements of windows. Below is SquareDonut geometry optimized with true arcs (circles) at both center and along the diagonal joints. This provides both an interesting look and also a compressive-optimization along the mitered joints of the building. The bluish and reddish circles provide a verification of the true-arc geometry

Note that four columns are provided at center to somewhat reduce the longer diagonal span. Longer, clear spans would necessitate more expensive reinforcement. Therefore, shortening this span will effectively reduce the amount of reinforcement material needed to achieve the same amount of support. Column support is more economical than using expensive, long-span-beams. Columns can be inte3gragted

Next below is a version with a broad-flattened roof to provide a longer clear span. Any ceiling or donut made large and flat would require considerable reinforced truss work(in black). The reinforcement- truss version looses the efficiency-advantage of true arcs. True arcs provide the economical ,compressive assets of arches for randomized dynamic stresses. Straight trusses use more expensive reinforcement materials, instead of cheaper compressively strong materials. Overly expensive method:

Next below , a CAD model has wall thickness which is thickest midway between corners. The interior surface remains as in first picture while the outer surface bulges. The top exterior edge is shown thicker as in the Mexican barrel vault. The added bulk departs from pure ferrocement and might be more appropriate where bulkier qualities are desired.

The purely arced-arch evenly distributes strength along all points of a cross section. Arches don't have to be ideal arcs or ideal circles. However, this ideal is a geometric-resource for strength in all arches and any curvature generally. Cheap stone is a compressively strong building material and is exploited by ARCING across open spaces. An arching pillar is easier to use in place of the donut hole, making the whole structure compact. Since the mass production of steel, pure geometry in structure has been less exploited. But as the information age grows and oil declines, efficiency will again call on ideal elements of geometric pattern to solve many structural needs, micro, nano, macro and mega. Ring reinforcement is yet another option which exploits geometric patterns for reinforced structure.

The model above is more applicable for above ground and rammed earth adobe. Next below, the same structure is adapted with underground tunneling. Increased thermal exchange is the main objective along with additional storage space. Passive Annual Heat Storage was researched by a US Government Grant. An underground house was built and has reportedly been remarkably "self-heated" in the cold State of Montana for decades. Self-heating with nothing more than concrete architecture combined with geologic heat storage is a highly disaster resistant concept.

Tunnels do add considerable cost but deserve cost-benefit analysis. The original breakthrough of Passive Annual Heat Storage adopted earth tubes to enhance thermal exchange, instead of tunnels. Concern about condensation with mold has dampened enthusiasm for inaccessible surfaces such as earth tubes. The tunnels provide accessibility to all thermal exchange surfaces. However, other means to enhance thermal exchange can be considered.

Next, below an example of unconnected earth tubes is offered. The pink surfaces are buried insulation which surrounds 3 sides and top of structure. Could this provide sufficient thermal exchange for cold climate house heating and cooling for the summer? Thermal analysis by physics-software may one day be shared here. (Thermal performance analysis is presently an expensive engineering service with utilizes expensive software.)

Next below is a model which can be built more cheaply than the version illustrated above. remove the bottom earth tubes, which are positioned radically and which are difficult to install. They were replaced with larger collector earth tubes at bottom. This option reduces the amount of required excavation, in the event that the vertical insulation is used underground. More detail of this can be seen, (click here).

One further feature was added, namely two small rooms (brownish in color), which open to the outside. These small rooms may be used for nominal proposes, except that they are active parts of the heat storage system. All door and window should be monitored carefully with this type of thermal strategy. Next below is a Square Donut vault doubled in length with three interior columns. Having columns, (made unusually massive on top), enhances thermal capacity and conduction.

Water cisterns could imaginatively fit in the upper portion of the column. Other functional fixtures could be built into the columns. Or arrangements of shelves, cabinets or partitions could altogether integrate within the columns. Below: a photo from the 1800s. Multiple functionality is suggested by these columns:

(Vatican Library Photo: From a collection by John Stoddard, C.1892).  Thick columns splay out at the top. The square donut pillars adopt a similar pattern as traditional intersecting arches. The square donut approach smooths and rounds the seams between arches. Surface optimizing is the objective instead of sharp and hard corners of traditional masonry.

After discussing the advantages of adding a pillar, for a couple of years on the ferro cement forum...   Mexico-Steve sent me this photo, from Mexico, adapting his preferred forming system to an octagonal base. MxSteve might in fact be the world's first and only builder of a square donut structure! (My own effort was stopped when my client abandoned a 2007 project, involving my first square donut project. Such is life).  However, the point of my page is to explore optimized surface geometry and meshes. Factory produced meshes bend easily in one direction only, (planar bending). Factory mesh does dominate markets. Trimming the mesh, or mangling it, can force fit a rounded donut surface (shape). These are non-optimal reinforcement patterns. Yet it is expedient to adapt familiar materials and crews, instead of starting to develop newer compound curve mesh systems. The traditional Mexican and Eurasian barrel vaults normally use planar surfaces and do not form full circles or "donuts", nor significantly rounded corners. Angularity persists, where optimized geometry is not pioneered. Mavericks endure derision and rarely get hired, but this makes time to pioneer optimizations.  Steve Kornher and his Mexican maestros build remarkably beautiful vaults and other inspired works in Mexico.

Thanks to continued email from the the www-web, i am asked to try "test fit" (design) arrangements and construction methods . Above: square donuts are tested in mixed configurations.

Competitive Concepts For Building "Green" (Globally Efficient)

A tilt up method for building this type of square donut structure.

HVAC with no monthly bills?

PAHS / AGS / Self Heating / Self-Powered-HVAC .... Buy an existing, pre excavated house site in Maine!

See my nephew's research and discussion page on PAHS and traditional precursors. 

Joe Anderson, PE, through his Prime Design Engineering, has done some interesting thermal modeling and research for self heating houses. (I think Joe coined the term "self heating house"). Joe found, (through some engineering software), that earth tubes can be minimal and even omitted in some cases. In fact varied testimonials can be widely found which seem to agree. Many of the traditional earthen and stone buildings can also be cited but these lack the addition of insulation (needed to achieve colder climate comfort). I interpret that one can theoretically remove floor insulation in a super insulated house and instead insulate the house perimeter, to achieve an rudimentary radiant-heat-flooring, without oil wars or CO2 loading. Well sort of, perhaps, sorting out a few preferences. Through some emails and perhaps unexpectedly, Joe helped jog my thinking, to invent this simple, optimized, square donut surface models.

Here is a Virginia man who achieves self heating without earth tubes, but does depend on an electrical heat exchanger.

Another North Westerner who has designed and built AGS homes reports on his work, but offers few picture-diagrams on the web.

Still the most acclaimed U.S. book on PAHS:  Passive Annual Heat Storage, Improving the Design of Earth Shelters. It can be purchased here: http://www.earthshelters.com/

I would love to discuss a potential project like this. Here is my time saving approach to building strong, style adaptable and cost efficient concrete structures. It is especially suitable for semi-buried or begrimed housing. I can offer discounts on my labor for the first "optimized square donut" project.

I started working on 2 projects like this and the second effort got as far as preparing the house site before being stopped. Stone vaults are just not understood in the New England neighborhood.

Here is my latest on ring reinforcement theory and practice.

Note: These pages are placed in the public domain and are furnished "as is". The author assumes no responsibility for the use or misuse of the concepts in this series. All authorities should be satisfied first, as might be required, by relevant laws, before any building proceeds.

Searching Synergy ........ Free Exchange of Ideas