Tilt-Up Reinforced Concrete Arches

Tilt-up Reinforced Concrete Arches

A couple of years ago I began investigating masonry arches intended to compete with wooden roofing trusses. I thought that a masonry arch -made from manufactured concrete sections- would provide a better solution to providing a structure for roofing than conventional wooden trusses. The idea evolved as I began working on it and has resulted in a crude engineering model which proves the idea and serves as the basis for a prototype beyond the initial engineering model.

 

This first engineering model was made from sections designed to approximate units which could be rapidly mass-produced on a concrete block machine. They are 8 inches in height, the typical height of manufactured block. To produce these first samples affordably, relatively easily, and without too much fuss, I simply used 3-inch diameter PVC pipe as the molds. I cut these 8-inch sections with an angled or beveled top, each with a 6⁰ wedge-shape at the top of the mold. Thus 15 sections would assemble into a 90⁰ arched section, with a span of around 9 feet. This was to be my modestly scaled first model.

I wanted to include tensile reinforcement into these arch sections, so I included a hollow core through which rebar could be placed. To make this hollow core, I placed “pex” pipe sections, located in the center of each PVC pipe section. These simple molds were then filled with concrete, one-third filled and compacted, then 2/3 filled and compacted, and filled to the top and compacted a final time, for consistent consolidation of the concrete within the molds. The cast concrete sections were removed from the molds the following day.

As crude as this method was, it allowed me to produce over 150 sections in a pretty short time.  I decided to assemble these using FRP (fiber reinforced polymer) rebar, which is lightweight and can flex and bend easily. This non-metallic rebar does not rust. I used a simple wooden form as a round section (90⁰) to assemble these arch sections. I placed #3 basaltic FRP rebar (3/8-inch diameter) through the core holes of the arch sections and fastened the assembly to the wooden form and affixed a fill cup to both ends of the arch sections.

The assembly was then poured to fill the gap between the #3 rebar and the core hole, with a liquid grout, to cement the rebar to the concrete arch sections. The liquid grout filled this gap between the rebar and the concrete section with a gravity feed. It worked well, and I soon produced 7 arch sections. I realized that for this first test, I wanted a span slightly larger than the 9 feet provided by the 90⁰ arch, so I added 3 additional arch sections to both ends of each arch. By turning each of these added arch section 180⁰ to one another, each arch section’s wedge-shape was oriented in a complementary fashion, thus adding a short, straight section to each arch: which approximates a catenary shape quite closely. The resulting arches could now span over 12 feet, which was close enough to what I desired for this initial test.

 

I decided to build a one-car garage, and to use these arch sections for the roof. The design I settled on was 21 ft. 4 inches in length, as described by 16 concrete block (CMUs). The garage is 14 feet wide, or 10.5 CMUs. The arches were arranged 32 inches O.C. (on center) in accordance with the modular coordination of CMUs.

 

Each arch had an extra length of FRP rebar sticking out from the concrete section, around 3 feet. This extra length of FRP rebar was used to bond the arch sections into the vertical walls of the garage, by inserting this rebar into the hollow core hole of the CMUs and grouting it into place. Each of these vertical core holes (32 in. O.C.) also had vertical rebar placed in them, so that continuous reinforcement was provided from the foundation up into the vertical block wall, into the arch, across the arch, and down into the opposite vertical wall and foundation.

Once the vertical concrete block masonry walls of the garage were assembled, scaffolding was erected and used to help place the arches into position. One very useful feature of these reinforced masonry arches is that they can be tilted up easily into their vertical position. I was able to do this by myself by hand, with no special tools. For larger arches, any hoisting mechanism could be used for the tilt-up operation, such as a crane.

 

 

Much was learned from the assembly of this engineering model. It would be better to have the arch segments made with a rectangular cross section, as opposed to the round cross section used here (the round cross section was done simply for ease of molds made from 3-inch PVC pipe). By using a rectangular shape, the corners can readily be lined up, unlike the round sections, which tended to be less accurately aligned. The dimensions for the next design iteration will be rectangular: 3-inches by 4-inches cross section by 8-inches in length. This size will allow 32 of these arch sections to be made in a 3 at-a-time concrete block mold pallet (this size mold pallet will produce 3 standard 8-inch x 8-inch x 16-inch blocks per cycle). This provides for exceptional throughput, having 32 arch sections produced in around ten seconds. The 4-inch dimension of these arch sections will be aligned in the vertical direction of the assembled arch, to bear the load of the arch under gravity.

Another design consideration from this first experiment is to provide short grooves near the end surfaces of the arch segments. These grooves will house plastic screw anchors, so that a covering (wood, etc.) can be easily attached to the arches. These screw anchors will be cemented in place once the grout is poured into the core holes to cement the rebar to the concrete arch.

Larger arches can be made from thicker arch segments. Multiple core holes can be provided, for greater reinforcement which utilizes more than one piece of rebar per arch. Larger arches will be heavier and more expensive. They can still be tilted up, using the proper equipment. On a larger scale, this system still provides practical, affordable, effective reinforced tilt-up masonry arches.

3D printed concrete can also be used to assemble reinforced tilt-up arches. 3D printing can be used by itself or in combination with concrete masonry units.

Tilt-up reinforced masonry arches can also be post-tensioned. This makes them stiffer and stronger.

Consideration of this design approach has led to a US patent application, which was recently filed. There is a patent pending currently. Here are some patent illustrations which help to show this idea.

 

 

 

 

 

 

 

The size of the market for wooden trusses in the US is estimated at between $10 – 13 billion. By providing an improved system for trusses, a significant opportunity is created. These reinforced concrete trusses can be rapidly assembled at a relatively low cost. By using either arch sections produced on a concrete block machine, or by 3DCP (3-dimensional concrete printing) and incorporating FRP rebar as reinforcement, arches can be produced affordably, quickly and with ease.

While the engineering model shown here has arches separated by spans, they may also be used assembled side-by-side, so that there is a continuous masonry arch roof. These arches may also be configured one on top of the other, for a thicker, stronger masonry arched roof. This design flexibility allows for roofs strong enough to withstand extreme weather events, including hurricanes, tornadoes, wildfires and more.

The benefits of reinforced concrete tilt-up arches include:

·       High strength

·       Affordable

·       Fire safe

·       Termite proof

·       Rot proof

·       Rust proof

·       Easy installation, via tilt-up

The continuing development of this roofing system promises to provide an improved method for making better buildings. There is huge potential here for economic benefit by providing these better buildings to the marketplace.

Making a concrete ping pong table

I recently completed making a concrete ping pong table. It came out pretty well, and I look forward to playing some ping pong!

Here are the basic steps I took to make and assemble the ping pong table.

First, I made wooden molds. There was a mold made for the table surface, a mold made for the central supporting arches, and four molds for legs which spring from the arches to the corners of the tabletop. Here are the molds, shown upside down.

Here is the arch section being made. There are 4 pieces of #3 rebar (3/8 inch diameter) in the arch form.  I used basaltic FRP rebar (fiber reinforced polymer).  All reinforcement was kindly donated by Nick Gencarelle of Smarter Building Systems. Nick is very knowledgeable and helpful.  We just used a bagged concrete mix, specified as having a strength of 4,000 psi after 28 days of curing.

Here are the four legs being made. Each leg also has 4 pieces of #3 FRP rebar.

Next, we set up a form for the base. The same form was used later for the tabletop. We placed #3 FRP rebar inside the form, at 10 inches on-center.  The arch form and leg forms were placed and cast directly in the concrete of the base.

After the base cured for a few days, we set up the mold for the tabletop. The mold was filled with basaltic FRP mesh reinforcement and also #3 FRP rebar, for tensile reinforcement.  The rebar was located so that it aligned with the legs underneath, for strength. The entire mold was greased with Crisco, used as a mold release agent. A sheet of plastic was placed on top of the wooden form, to help the concrete release from the mold.

The mold was then filled with concrete, with particular attention to place some concrete under the rebar, to help provide proper cover.  The concrete was then screeded (spread evenly with a straight piece of wood, moved back & forth as it is drawn across the form).  This surface was then floated, or smoothed out by hand.  The edges of the form were all vibrated. In this case, we did not have a proper concrete vibrator, so we used a "sawzall" reciprocating saw, which worked pretty well.

Properly floating the surface is important to get a nice, smooth, flat finish.  It is worth spending some time and doing this properly.

The form was then covered and allowed to cure for a full week. It helps to cover the concrete with plastic, so that water remains in the curing concrete to form hydration products.

After one full week, the wooden forms were removed. We also did some landscaping, to create a level playing surface on the ground around the table; this involved a retaining wall being placed also.  This work was simply done with a pick, shovel and rake. It took an afternoon. 

Now, it just needs a net! I will also use a sealant to help protect the concrete from the weather, something like Thompson's Water Seal.  This will also make a great picnic table. I expect it should last a long time. We will also plant some grass on the fresh dirt.

This basic concept could be made much larger, to provide an elevated platform to build homes on. We could use my company's masonry arch system to accomplish this, easily and quite affordably.  This would be appropriate for coastal areas which are prone to storm surges and flooding from hurricanes and severe weather. It is stronger than the wooden posts currently used to elevate homes above a storm-surge plain, and will not rust or rot, like wood. It is also more elegant and looks much better than those wooden posts.

This table cost about $150 in concrete.  The rebar is also inexpensive. If anyone wants a concrete ping pong table and would like to borrow my molds, you are welcome to.  Just let me know.

This thing should be fun, I look forward to using it!

A recent video

Recently some dear friends of mine completed a lovely video they made about me, my work and my company.  This work was done by Burton Stein, his daughter Autumn Layne Stein, and Autumn's fiance, Matt Goodwin.  I am very grateful to them for this work. 

Here it is!  

Cover article in Masonry Magazine

I was asked to write an article for Masonry Magazine about my company's (Spherical Block, LLC) technology.  Here it is, the cover story for the August 2020 issue.  A big thank you to the Masonry Contractor's Association of America.  

Article on Concrete Batteries

I was asked to write a short summary about the concept of using potassium geopolymer as an electrical capacitor or battery.  This article was published in STRUCTURE magazine on May 1, 2020.

Anisotropy

Concrete is made of rocks and sand
glued together with cement
the aggregate you understand
is irregular, with intent.

The intention of irregular shape
is tip-to-face contact all throughout
aggregate packed to reduce the gape
of free space between the grout.

Concrete made into block
has aggregate pressed and jostled
irregular aggregate interlock
frozen into position, fossiled.

The axis of this huge compaction
is the one of greatest strength
energy of vibrating action
aligns the rocks along their length.

When measured strength is the same
in all the measured block directions
"Isotropic" is the name
for equally strong strength detections.

When manufactured block's the topic
It's not so strong in sideways view.
It's known to be anisotropic
and highest strength is vertical too.

Proportionality, strength and buoyancy

I have written several times on this blog about how masonry structures are scaleable.  That is, a given masonry structure can be made larger or smaller and will still have adequate strength, so long as the proportions remain intact.  For example, if a round arch is ten feet in radius and has walls which are one foot thick, then the same design will work with one hundred foot radius and walls which are ten feet thick.

The example cited above is a good one to look at because a “thin-shelled structure” is defined as having a ratio of radius-to-wall thickness of ten-to-one.  This ratio of radius-to-wall thickness provides adequate strength for a masonry arch under earth’s gravity.

If we take this example one step further, and consider not just a semi-circular round arch (or barrel vault, or Roman arch) but we look at a complete sphere, such that the arch describes a completed circle, then we have a spherical structure which can have strength adequate to withstand the pressures at great depth, underwater.

Going further still, if we look at the example of a sphere whose wall thickness is one tenth of its radius, we see that such a sphere will always be buoyant in water, no matter what size it is.  A small hollow concrete sphere 2 inches in diameter, with concrete walls 0.1 inches thick, will have the same proportional buoyancy as a sphere 200 feet in diameter with concrete walls 10 feet thick.

Since the volume of a sphere is (4/3) * pi * r³; the density of concrete is around 2.4 g/cc; and the density of water is around 1.0 g/cc, it is a simple matter to show that the buoyant force acting on a hollow concrete sphere with wall thickness equal to one-tenth of its radius will always exceed the weight of the concrete.  Such a sphere will always float, no matter how big it is or how thick its walls get. (I can show the math, but spare the reader here.  It’s simple stuff).

Given that thicker concrete walls are stronger, a larger sphere (following the scaleability rule for masonry) can be made of great size, with great wall thickness, and can be sunk to great depth and can maintain structural integrity under the great forces found there.  Another feature of increasing the radius of such a hollow sphere is the exponential increase in volume.  As the radius increases linearly, the volume is increased as a function of the radius cubed.

These simple facts of proportionality, buoyancy, strength and volume regarding a submerged masonry sphere are really pretty interesting.  It indicates that a sphere can be used at great depth, if it is made large enough.  The increase in scale will simultaneously provide the economy of scale for tasks such as desalination, as described several times earlier on this blog (here, here and here).  Simple yet elegant.

Particle size distribution of Crickcrete

If we consider concrete, the main ingredient is aggregate:  rocks, stones and sand.  I briefly discussed this here on this blog.

Of real importance is the particle size distribution in the aggregate mix.  The goal in good concrete is to get a complete space filling by using different sized particles.

Aggregate (stones, rocks and sand) is generally not spherical, but has a longer dimension and a shorter dimension.  This results in a “tip” which is located at the ends of the longer dimension, and a “face” which is located at the end of the shorter dimension.  One of the keys to good concrete is tip-to-face contact between larger aggregate.

One of the other keys to good concrete is that the gaps between large aggregate are filled with smaller aggregate, so that there are not empty spaces, or gaps, or interstitial sites between aggregate.  This is what is meant by “space filling.”

There is a field of science which concerns itself with space filling between particles.  My own exposure to this science came in studying ceramics, wherein scientists are typically looking at very small particles.  One of  the insights into space-filling came about in 1930, and was proposed by two scientists (A.E.R. Westman and H.R. Hugill) who worked together to develop a diagram which represented space filling as a percentage of volume based on different sized particles, and is known as a Westman-Hugill diagram.

Here is a quote from an abstract of their paper “The Packing of Particles” published by the Journal of the American Ceramic Society, June 12, 1930: “It is axiomatic that the mode of packing of very large volumes of particles of uniform shape and size is independent of the size of the particles, provided they are large enough for the effect of electrostatic forces, air films, etc., to be negligible. An apparatus is described, in which equal true volumes of approximately spherical particles, ranging in diameter from 0.2 to 0.0035 inch, pack practically to the same apparent volume. This apparatus was used in studying the packing of mixtures of two and three sues of particles. By plotting the data so obtained in diagrams of a particularly convenient character, it is shown that the apparent volumes of mixtures containing unit real volume of solid fall between limiting values which can be calculated from simple assumptions, and that their deviation from these limits depends in a definite manner upon the diameter ratios of the component particles. The conditions governing the application of the results of the study to ceramic technology are pointed out.”

While Westman and Hugill were considering spherical particles for their model, the basic ideas hold for irregular shapes, which is what one encounters in concrete mix.

Here is what I find interesting about this whole concept.  If you go outside and scoop up a shovel full of rocky, sandy mix (not soil, but aggregate, such as one finds in a stream or creek bed) then the mix is very close to the ideal particle size distribution one would design if starting from “scratch.”

I find this incredible!  Nature has provided us with a close to ideal particle size distribution for very good concrete.  Almost everyone fails to appreciate this fact.  Everything we make from concrete would be much more difficult to make if this were not the case.  If we lived in a world of only tiny sand, we would be making large rocks to provide large aggregate.  If we lived in a world of only large rocks, we would be making sand (at a huge cost of time and energy).  As it is, nature has provided us with a very close to ideal concrete mix in terms of aggregate particle size distribution.

There is a commercial brand of concrete known as “quikcrete” which is sold in dry bags.  Friends of mine who are aware that a creek bed provides an ideal mix of aggregate particle size also live in the country, where a creek is known as a “crick”.  They call their homemade concrete “crickcrete” and chuckle and guffaw like country bumpkins.

So grab a shovel, head to the creek and make some of nature’s own crickcrete.

Adding fiber to concrete

Fibers are sometimes added to concrete mix. Why is this done?

Concrete is a mixture of aggregate (rocks), sand , Portland cement, and water. Water combines with cement to form hydration products, which glue the mix together.

Upon initial set, there is a volume shrinkage of the cement paste. This small shrinkage may result in micro-cracks; tiny little flaws on the surface of the curing concrete. These cracks occur because wet cement paste has a low tensile strength, and cannot resist the small shrinkage from the initial cure.

Once cement has cured, it forms a brittle material. When any brittle material cracks, it always begins cracking at a small surface flaw, such as those produced on initial set, due to weak cement paste shrinkage. If these micro-cracks can be eliminated, a much stronger and longer-lived concrete is produced.

Micro fibers have a tendril-like structure, where tiny little spirals come out of a larger fiber (commonly polypropylene). When properly mixed, this type of fiber provides anchorage and locking into a wet cement paste. It will provide the necessary tensile strength for the wet cement paste to resist micro-cracking from shrinkage on initial set.  This results in a much stronger and tougher concrete.

Fiber added to concrete mix reduces the workability of the wet concrete to a small degree. It can be difficult to float a surface due to the fibers.

The specifications for fiber concrete show no increase in tensile strength, but those who really know concrete realize that these microfibers provide an actual slight increase in tensile strength of concrete, and also increase its toughness (resistance to crack propagation). Fibered concrete is a little tougher and has more flexural rigidity.

Fiber added to concrete mix makes a better concrete.

Star of David, Merkabah, Duo-Tetrahedra

A tetrahedron is the only regular polyhedron that is its own dual. If a corner is placed at the center of a face on a polyhedron, you get a dual.

For example, take a cube. Put a corner at the center of each face of a cube, and you get an octahedron, not another cube.

If you place the corners at the centers of the faces of a tetrahedron, you get another tetrahedron.  Two tetrahedral superimposed on each other form a curious and notable structure, variously known as a hyperbolic paraboloid, or duo-tet, or a merkabah.

A merkabah is the shape of the chariot by which the prophet Isaiah ascended to heaven. It is supposed to provide a more full realization of the existence of God. Powerful stuff.

If we look at the surfaces between two edges of superimposed duals, they are a least energy surface. Soap bubbles fit these surfaces, and soap bubbles are an accurate representation of least energy (tension vs. strength) surfaces. These least energy surfaces are also as easy as twisted sidewalks in concrete.

Screeding is a method used to spread concrete evenly within a form. Two guide bars are used to direct the screed bar, which is drawn across the concrete in a reciprocating motion, evenly distributing the concrete. Normally, for a flat sidewalk, screed bars would be parallel.

If the screed bars turn through ninety degrees rotation over their unit length, then the edges of the screeded shape assemble into a hyperbolic parabaloid, or duo-tet, or merkabah.  (That's me, above screeding a twisted piece of concrete; that's my sculpture below).

Monolithic Domes

Monolithic Domes are a decent solution to providing a concrete dome. This involves using an inflatable bladder and spraying (or shooting) shotcrete onto the bladder in a few layers. Shotcrete is basically fluid concrete that is sprayed through a high pressure nozzle.

Monolithic domes are energy efficient, high strength, suitable for resisting hurricanes, tornadoes, fires and termites, and can be built on a fairly large scale. Monolithic domes are appropriate for some of the larger applications including municipal buildings, commercial applications and such.

Monolithic domes do require an inflatable bladder, inflation equipment, shotcrete equipment, steel "rebar" reinforcement, and some expertise in applying shotcrete.

The Monolithic Dome website provides an excellent overview of this technology, its application and its various uses and benefits. Check out their website, navigate around and investigate this interesting technology.

This is definitely not masonry, but is a useful and good application of concrete domes which certainly has an architectural niche and is worthy of consideration if anyone is considering building a concrete dome.