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.

Radioactive trowels and robots

Today there was an interesting item on the US Nuclear Regulatory Commission's blog about a radioactive trowel.  Here's the item, about how the president almost handled a radioactive trowel:

Uncovering the real story of Joe Ball's trowel required research at the Department of Energy's archives, where I could get more information about the AEC’s move from Washington, D.C., to Germantown, Md., in 1957. The AEC's move was precipitated by the Soviet Union development of thermonuclear weapons. To survive a 20 megaton blast over the capital mall, AEC offices needed to be at least 20 miles away. Germantown was selected over 50 other sites.

This Cold-War move coincided with new initiatives by the AEC to promote civilian nuclear power plant construction. Thus, the dedication ceremony became a chance to highlight the atom's contribution to national defense and its potential peaceful applications.

The AEC created a ceremony heavy in symbolism. Electricity from batteries charged by eight military and civilian power reactors lifted a curtain on a commemorative plaque in the new building lobby. A time capsule was placed behind the cornerstone packed with military and civilian artifacts, such as pictures of the Nautilus and scraps of linen wrappings for the Dead Sea scrolls dated by radiocarbon techniques.

As I found out from the DOE archives, AEC Chairman Lewis Strauss wanted even more symbols for the dedication ceremony. He asked for a trowel with some historical significance and Argonne National Laboratory obliged, including, as mentioned in Part I, creating a blade made from uranium. AEC officials liked the trowel and planned on giving speeches about its symbolism to local groups.

But there was a problem.

The uranium metal had been reused for many years in other experimental reactors, most likely in the CP-2. The uranium was still radioactive, enough that an Argonne official told the AEC to use only the handle and not touch the blade. Hoping to preclude objections from the White House, the AEC medical staff reassured the Secret Service that the trowel was a “unique opportunity” for Eisenhower “to demonstrate under completely safe conditions the proper way to perform an operation involving radioactive material.”

AEC assurances didn't work. Ike's staff refused to allow the president to touch anything radioactive. Stymied, the AEC substituted three silver-plated trowels. The uranium trowel was dropped from the ceremony and the silver-plated trowels that history records were used instead. The fate of the symbolic trowels – of which there were either two or three – were mostly lost to history, with one spending decades in storage at Eisenhower College's old campus.

Joe Ball's unusual auction win find reminds us why we love artifacts—their stories are fun. They teach us about the society that made them. The CP-1 trowel was born out of an optimism in the possibilities of the atomic age, but even in the 1950s radiation concerns proved powerful. Today most people likely sympathize with the White House's fear of radiation, and the trowel probably seems like a questionable use of radioactive material.

And so Argonne's creation reminds us how the nation had changed in the last half century in shifting to a more sober attitude toward nuclear hazards.

Joe Ball has graciously agreed to loan the trowel to the NRC , where it is now displayed in our lobby.

Tom Wellock

NRC Historian

Also today, an item in the news about Chernobyl's new containment structure coming closer to being completed. 

 

 

It seems to me that robots should be the only ones handling radioactive trowels.  

 

Building a water storage tank

Today I'm looking back at the construction of a water storage tank.  It's now all done, and it's interesting to look at how it came together.  This tank is made from manufactured concrete block, using a method which I have several patents on.  I've posted several pictures below showing the construction steps.

This particular tank has an inside diameter of around 7 feet.  It holds around 3,000 gallons.  It is being used as a rainwater harvesting (rwh) tank.  I am using it as a plunging tank to cool off after you take a sauna, which I also built.  The tank has an electric light (LED's) at its bottom center.  There is a ladder which conforms to its spherical inner shape, for easy "in & out."

This tank was easy to build, and should last a very long time.  I hope to be using it to collect rainwater and as part of my wood-fired sauna experience for years to come.  If we assume concrete block cost $1 each, this tank cost me $175, which seems like a pretty good value.  Similar tanks for rainwater harvesting can have many uses: from potable water, to fire suppression systems, to watering crops, etc.  It has a hinged lid to keep insects out and to keep the water clean.  Rainwater is collected from the sauna roof, which is around 1,000 square feet.

I hurt myself (chainsaw accident!) while I was working on this, it took some time to heal.  The actual time to build this entire thing was very short though; less than a week.

The grey plastic pipe was used to run electric wire for the underwater light: thinking ahead.

Some of these mortar joints (especially near the top) are intentionally extra 

thick, this stretches the sphere and makes the water tank deeper. Easily done.

This is the electric light I installed in the bottom center of the tank.  LED's.

The light installed.  It is over 8 feet down to the bottom.

This is the finished tank, with my puppy Bartleby investigating.

Here is the actual sauna room.

 Here's a shower I put in.  The building also has a toilet, sink, bedroom and upstairs deck (outside).

This was a fun project, and I can't wait to use it!

Werner Von Braun and the Civic

Several years ago I made a trip to Alpena, Michigan to meet and speak with Besser Company.  They make machines and equipment to mass-produce concrete products, such as masonry blocks.   They are global leaders in the industry.

I met with an engineer, and tried briefly to explain my ideas.  He interrupted me, and brought in the Vice President.  I began to try to explain my ideas to the Vice President, but he also cut me short.

“Can you give our President a ride to Ann Arbor tomorrow?”

I was taken aback.  Isn’t one of the Lear jets available? I stupidly wondered.

“Sure!”  I said, “I’d be happy to.”

I picked up Mr. James Park at his house, having spent the previous 24 hours cleaning my Honda Civic as best I could.  We began our 4 hour drive, and spoke.  It was the very point of the whole thing.  He is an easy man to talk to.

I described how I thought this masonry system could be used, in various applications.  I went through one application after another.  “What else you got?” he kept asking.

I didn’t want to seem silly or crazy, or goofy; I’m the guy proposing triangular block already.  But I said it anyway.

“Lunar blocks.  Like on the moon.  The cost of sending materials from earth is too great, we should use what’s there, and with robots, this block system would…”

He interrupted by laughing.   He laughed heartily and deeply.  Uh-oh, I thought:  I’ve gone too far.

He then explained his laughter. 

Every year Besser would create a special limited edition hardbound leather book of general interest, and would send this book to their very valued customers, as a sign of appreciation.  One year the subject of the book was Rocketry.  One particular customer of Besser happened to be friends with –none other than- Werner Von Braun, the father of modern rocketry. 

Werner Von Braun was so taken with Besser’s book on Rocketry that he sent them a letter, in which he assured them that when man built on the moon, they would do so in something like the masonry manner which I had just suggested, and that it would be done on Besser equipment. 

We both had a good laugh in my Honda Civic, with Werner Von Braun grinning in the back seat as we pulled into Ann Arbor.

 

Corrugations and ribs in a masonry arch

In a masonry roman arch (or round arch) the arch may be viewed as a horizontal half-cylinder.   The arch is subject to stresses from gravity which are represented by a catenary thrust line, as discussed several times on this blog (here, here and here).   Various techniques may be employed to strengthen the round arch against the thrusting forces of its catenary load.

A cylinder may –in turn- be seen as a shell structure, as also discussed several times on this blog.  An arch as a shell structure is seen as a curved plate.  A plate may employ various techniques to provide it with greater flexural rigidity. 

Flexural rigidity, or increased structural stiffness, may be achieved by providing corrugations in the plate.  Corrugations are defined as a series of parallel ridges or furrows.  One example of this which most people are familiar with is corrugated cardboard. 

Corrugated  paper (also called pleated) was patented in England in 1856 and was used as a liner for tall hats; tall hats which are nothing more than cylinders. 

 

Another example of cylinders being made stronger by corrugations are the tin cans which employ corrugations to give them greater rigidity.

As I discussed earlier in this blog, I have developed triangular block to make cylinders and arches.  There are two types of triangular blocks used to assemble into a cylinder, or section of cylinder, or arch.  I call these two types of blocks “flat” and par” because one has a flat top, and the other has abutting edges which are parallelograms. 

 

Each of these blocks has a “tilt” to it which departs from the vertical.  If the triangle which describes these blocks is lower and wider (more obtuse of a triangle) then the amount of “tilt” or departure from vertical is increased.  If the triangle which describes these blocks is taller and skinnier (more acute of a triangle) then the amount of “tilt” is decreased.

The tilt or “leaning” of the triangular blocks used to assemble a cylinder have the effect of introducing corrugations, or ribs into the arch.  These corrugations or ribs have the much desired and beneficial effect of increasing the flexural rigidity and strength of the resulting arch.  The effect is the same as the corrugations in a tin can, as shown above.  The structure is made much stronger and more robust to any applied force; whether it is gravity, wind loads, hurricanes, tornadoes or impacts.

This feature is a simple artifact of the design of these block, it is something of a “happy accident.”  Thus masonry arches made with corrugations are much stronger, more robust and better than a simple, rounded arch. 

A sauna firebox: planned and being made

Here is a look at a firebox I’m building for a sauna.  Below are two short videos, showing the initial planning and the firebox as almost complete. 

I used old kiln shelves for the horizontal top of the firebox and the flame-wrapping structure above it.

I’ll post another entry when this is all done.  It should look quite different by then.

Planning the firebox:

Firebox almost done:

A new engineering model for a new block

Contemporary engineering analysis of masonry arches provides a model which is not adequate for analysis of the masonry system I’ve been describing on this blog (dual inverse mirror plane, or ‘dimp’).  A new model is required to analyze this triangular interlocking system, which I shall attempt to describe.

The currently accepted engineering model makes three assumptions about masonry arches.   (1)  Masonry units have no tensile strength (2) Masonry units are infinitely strong in compression (3) Blocks (or voussoirs) never slide against each other.  An arch modeled on these 3 assumptions is then viewed in cross section, and a catenary thrust force line is imposed on the wall thickness of the arch.  If the thrust force line touches or exits the wall thickness, then a hinge is formed at that point (between two adjacent blocks or voussoirs) and the arch will buckle and collapse.  If a large force is applied to the arch, the thrust force line will eventually touch or exit the inside (intrados) or outside (extrados) of the masonry arch, and failure will result in a hinging mechanism which causes the arch to buckle and collapse.

The dimp design can employ a tensile element, like a wire or cable within the wall thickness of the block.  This feature gives the arch some tensile strength.  When a large force is applied to this arch, the tensile action of the cable or wire counters this force and keeps the imaginary thrust force line more toward the center of the arch thickness.  In addition to this tensile containment, another feature of the dimp comes in to play.

A large force applied to a dimp arch will first be contained by some of the tensile web, woven as great circle arcs.  Instead of hinges forming when the thrust force line touches the intrados or the extrados, conjugate shearing occurs (as described here).  Control joints allow block faces to slide against each other; they are actually designed to.  This deformation is a strain (movement) resulting from excessive stress (applied force).  The strain relieves the stress, and when the applied force is removed, the structure returns to its original state.  The forces which restore a deformed arch are from gravity and the tensile elements.  There is of course a limit to an applied force, beyond which a dimp arch will collapse, but it is greater than that of a conventional arch constructed from voussoirs of the same thickness.  

Thus the currently accepted method of engineering analysis for masonry arches does not appear to work for the dimp design.  First, an arch made of dimp blocks has tensile strength.  Second, the blocks move (slide) against each other.  Finally, instead of a hinging mechanism there is a conjugate shearing mechanism between blocks.  It is a whole different model.

I am currently working toward a computer model to reflect this different engineering analysis.   I hope to have it available to post here eventually. 

Evolution of a block design

First forced-air wood kiln firing

Earlier on this blog I wrote about a kiln I designed and built, here and here.

Yesterday I fired this kiln as a forced-air (with blower) for the first time, using my improvised firebox.

It worked incredibly well.  I have never fired an easier, faster more efficient wood kiln.  What normally takes 3 days was done in less than 8 hours.  It took less than a face cord of firewood to reach temperature (~1,800 F, bisque firing).  It normally takes around 5 - 10 times that much wood.

I used a Ward burner, hooked up to propane to candle the start-up.  After It had warmed up to around 350 degrees F, I lit the wood and turned off the propane.  The blower from the burner provided the forced air.

Here's a short video showing me stoking the kiln.  It is burning just wood (no propane).

Rainwater storage tank: video update

Here's a short video to show the status of a masonry water storage tank prototype I've been working on.  The tank was made from manufactured concrete block which I designed and had produced on a standard concrete block machine.   This will serve as a "plunging tank" to cool off after taking the sauna.  The same idea will be used to collect potable drinking water.

To see the tank completed, please look here.

No mechanism for failure

As I discussed earlier, if masonry is considered from a contemporary engineering perspective then three assumptions are made about it (none of which are actually true).  First, it is infinitely strong in compression.  Second, blocks (or voussoirs in an arch) never slide against each other, they remain in fixed position.  Third, masonry has no tensile strength.  These three assumptions are useful to the engineer in seeing how a masonry structure will respond to forces and how the structure will bear its load.

This perspective of viewing masonry leads to some interesting insight.  Of particular interest is the idea that for some arch forms there is no mechanism of collapse.  As I discussed here, masonry arches collapse from hinges being formed at the intrados and/or extrados of an arch; where the catenary thrust force line either touches or exits either the intrados or the extrados.

As discussed by Jacques Heyman in his book The Stone Skeleton (Cambridge University Press, 1995) by applying the 3 assumptions of engineering for masonry with the arch forms shown below, a hinge cannot be formed; buckling cannot happen and a mechanism for collapse does not exist.  Of these arch forms, a unique application is that of the flying arch buttress.   While Heyman notes "in passing" that this is the case and assigns little significance to the phenomenon (p.19), it seems quite significant and noteworthy to me.

A flying arch buttress cannot fail; something else has to fail for the buttress to fail.  For example, in any known case of a collapsing cathedral flying buttress, it was either due to settling of soft ground at the foundation, or repeated lightning strikes.  No fault of the flying arch, which has no mechanism for failure. 

Another Clerihew makes it 30

Architect Christopher Wren
redesigned London when
it took a forceful maverick
from ashes hence London brick.

The last brick

Nine thousand nine hundred ninety nine brick:
This last one should do the trick.
I think it will, I think it might
I just have to place it right.

Clerihew

Francis Straub from Pennsylvania
In 1913 had his mania.
He used cinders ‘round the clock
when he invented cinderblock.

She's a brick. House.

When you slam the door to a wooden house

The whole thing shudders just a little

If you pound the door to see who’s home

The whole thing shakes just a little

Sounds and thumps and bumps and shivers

Reverberate and underpin a weaker state

In any wooden home or shop or store.

But a stone or brick or masonry home is

Solid as Ella Fitzgerald.

High and dry

Masonry arches for making roofs
Covered with timbers again and again
Proving again these basic truths
Stone stops fire, wood stops rain.

A masonry arch alone is strong
For centuries it’s not weak
Stone alone will last so long
But is all too prone to leak.

Cathedrals and churches use a roof
both inside arches made of stone
and outside wood and waterproof
Stone stops fire, dry as bone.

This old tested proven approach
Still works well, still today
Another topic for us to broach
Of thermal mass and its way

To keep a building truly warm
Helps if there is radiant heat
Stored in rock or stony form
For this to work, is a feat

Insulating the outside’s needed
For allowing radiant heat to pass
To the inside unimpeded
Bare stone inside: thermal mass.

Fresh water and masonry

People are worried for the future
For themselves, their son or daughter
You may not have enough to suit your
Own and offspring’s need for water.

Rising seas and melting glaciers
Means there’s less than you think
The near future to face yours
Looking for good water to drink

Desalination can use the sea
To make that salty water sweet
But it takes much energy
And pollution we must beat

Far too polluting and unsustainable
So another way is sought
To make fresh water obtainable
So our best ideas are brought

And if a concrete masonry sphere
With very high compressive strength
Is sunk to depth then it is clear
It is an acceptable length

To harvest water through a filter
Using free high pressure of the deep
A concrete sphere, once I built her
To collect that filtered seep

Of freshly filtered sweet clear water
Collected for almost free
For your son or your daughter
If we should do it why can’t we?

Of Circles and Erkels

The strength of an arch is not only found
In a half circle structure over your head
It is also found deep underground
It even occurs deep under seabed.

For an arch is one of those configurations
In a circular tube in a deep long tunnel
Its strength is used to join two separate nations
Like England and France are joined by the Chunnel.

Compression still works in a completed circle
It’s pressed on itself all the way round
You needn’t be a nerd or an Erkel
To know that the arch is the strongest found.

Excavation by denomination

Way back when in olden days
they would build masonry domes
and for support, in a number of ways
they would pile up dirt to support the stones.

When the dome was complete
they’d remove all the dirt,
the dome was left: what a feat
it didn’t fall, nobody hurt

But how’d they get the dirt removed?
it surely was a lot of work
to haul it out so space improved
peasants didn’t want to shirk

responsibility to their king,
so the Lord would hide some money
in the dirt, was the thing
which peasants kept, kinda funny.

Cozy

If you live where I live
then you know how it goes
sometimes April or May give
more of winter’s snows.

But living in a concrete home
can be pretty neat
the efficiency of a block dome
with a masonry stove for heat.

It doesn’t matter which your
preference is for a house
below is today’s picture
and I’m cozy as a mouse.