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The Secret to Trusses

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Trusses are simply built out of triangles - and they are actually defined as such.  Some member will be in tension and some members will be in compression (about half).  The trick, and at times difficulty, is to determine which members are in tension and which members are in compression.   We can simplify things by recognizing there are only two types of triangles in trusses.  One that has two tension members, and one has only one tensions member (tension = rope, compression = wood in below image)...

If I extend this into a longer truss and simply replace the compression member with the tension member, we have...

Do you see the two types of triangle?  Also as you can see, the bottom chord is in tension and the top chord is in compression.   The trick to determining which diagonal or vertical member is in tension or compression, is ask if they follow the same curve as a hanging chain would between the two end points.  If they do, they are in tension, if not, they are in compression.HANGING

This is a stable truss for gravity loads...

What is really interesting about changing out the sticks for strings when they are in tension, is the fact that the entire truss can now be folded!   Check it out...

Think about how this can be extend to designing and building folding architecture, temporary construction, or tents etc.

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Build a Lamella Dome

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Lamella structures are created using many pieces of the exact same member shape and connection.   So 1000 pieces of something and stacked in a certain manner...

You can imagine it can get pretty big depending on the size of the individual beams and the quantity.   Here a pic with my RISD class a few years back that we built together from sticks I cut in my basement and eye hooks to temporarily hold the pieces together...

I wrote about the physics of this system as well... Published “Infinite Load Path?” October 2007 Structure Magazine if interested.

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The Perfect Arch

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For a arch to be prefect, it must be shaped such that it is in uniform compression.   Basically the inverse of a hanging chain.   So we can build what Robert Hooke describes in 1675 "as hangs the flexible line, so but inverted will stand the rigid arch".  So, we can hang strings from a sheet of plywood, trace and cut... As the thin shell innovator Heinz Isler would say "One does not actually create the form; one lets it become, as it has to according to its own law".  Also, this is an exceedingly complex mathematical shape called the hyperbolic cosine or catenary.

So we cut ...

Remove...

And build...

Cable Y-Hangs and Pulleys

You can imagine a person hanging from a cable that forms a Y in shape between to cliffs.  What are the forces in the cables?   Well we can build this by adding a wight in the middle of a system, and measuring the cable tension by hanging other weights off pulleys like so...

The more weight you add to each end, the more shallow the cable gets.   In other words, the more horizontal the rope, the more tension it contains.  Can the rope be perfectly flat with a point load in the middle?   The answer is no, you would need infinite cable tension!   If cables are horizontal you have infinite tension, if cables are perfectly vertical, you have half the load carried.

What about uneven loading, or changes in cable angle like so?

The more vertical rope in this case takes more tension than the less steep rope, but why is that?   For discussion (sum forces in X and Y).

 

Platonic Solids from Perfect Triangles

Here are Plato's two perfect triangles from his seminal work "Timaeus" that can create the 5 platonic solids (which are according to him form the elements of earth, air, water, fire ...)

They are worth having as objects in the bookshelf to use and demonstrate how to build platonic solids, geodesic domes, tensegrity structures, etc.  Also they can be used to for statics class to demonstrate simple trigonometry (45/45/90 and 30/60/90 triangles), as well as x and y components of force vectors in statics.

Braced Frames vs Moment Frames

Comparing braced frames to moment frames, is like comparing triangles to squares... The square can easily deform and requires rigid joints if used as a lateral system to resist wind/seismic...

The triangle can only deform if the member itself shrinks or extends axially (along length) - which is difficult to do significantly (PL/AE).   The square with rigid joints does not need to deform axially, it simple needs to bend and it will translate.   So moment frames are about 20 times more flexible than braced frames (+/-10).   To make a moment frame into braced frame, simply add a diagonal...

Composite Beam Stiffness

You can make four strips of wood, say 1" wide by 1/8" thick.   Take a pair and tape the middle together, take another pair and only tape the ends.   Feel the difference in stiffness...

The one you one tape in the middle will act as two separate beams.  The one you taped at the ends will act as one beam with double the thickness.  How much stiffer will the beam that is taped at the ends be?   Since deflection is proportional to moment of inertia, and I is proportional to thickness cubed, it will be 4 times more stiff!  Two cubed is eight, and 1 cubed times 2 members is 2, and 8/2 = 4.  It will be double the strength and 4 times the stiffness - just by taping the ends so it resists horizontal shear and acts as a composite beam.  Go ahead and try this simple experiment.

Harpoon Brewary Takes a New Shape

We redesigned the entrance and created a new opening, grand stair and elevator in the existing waffle slab building.   This allows Harpoon to have more room to host beer tours and contains a large restaurant.   The structure is complete, here are a few pics...

 

Listening is an underrated sense to us Engineers

Seth Horowitz, an auditory neuroscientist at Brown University and the author of “The Universal Sense: How Hearing Shapes the Mind”, wrote a terrific article in the New York Times called The Science and Art of Listening which starts...

"Here's a trick question. What do you hear right now?  If your home is like mine, you hear the humming sound of a printer, the low throbbing of traffic from the nearby highway and the clatter of plastic followed by the muffled impact of paws landing on linoleum — meaning that the cat has once again tried to open the catnip container atop the fridge and succeeded only in knocking it to the kitchen floor."

The slight trick in the question is that, by asking you what you were hearing, I prompted your brain to take control of the sensory experience — and made you listen rather than just hear. That, in effect, is what happens when an event jumps out of the background enough to be perceived consciously rather than just being part of your auditory surroundings. The difference between the sense of hearing and the skill of listening is attention.   [Horowitz, NY Times 11/9/2012]

This trick of asking yourself what are you hearing right now, reminds us of the difference between listening and hearing.   Many of us have no trouble hearing sounds, but listening to meanings with our full attention is another matter.  Can we shut of our internal thoughts and really listen to our design team around us?   Can we listen to the Architect or Contractor or co-worker without assuming what they will say or without interruptions by our own thoughts?

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Science is Applied Engineering

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We were designing and building things long before we had a “scientific” methods and mathematical solution techniques – and we still do today.  Did we need to wait for mathematical understanding of a hanging chain before we could build catenaries?  Of course not.   We didn't need to wait for Galileo and Bernoulli to create architecture.   We didn't need Euler to design columns.  We as structural engineers should recognize that while science and math are critically important to what we do, they do not define us - and history tells us, they never did.  How can we be defined as applied scientists when engineering predates science? I am particularly suspicious of the idea that our masterbuilders, craftmen, and masons of the past did not understand flexure and compression basics (top of beam is in compression for example or rules for column slenderness).    They may not have had the proper formulas but they certainly had a better intuition than we give them credit.  Yes, Leonardo Da Vinci and Galileo were the first to "discover" bending stress by writing it down, but it was used as rules of thumb by our builders well before that time.

In the book "Structural Engineering:  The Nature and Theory of Design" William Addis quotes the following statement from Karl Terzaghi challenging the idea that theorey leads to practice:

History shows us that there is hardly a single concept of practical importance in the field of structural engineering that was not instinctively anticipated and used with success in design and construction by individuals or groups of engineers many centuries before applied mechanics came into existence.

In Henry Petroski's book Remaking the World, he states:

Some of the first modern engineers did not apply science but rather led science.  The science of thermodynamics may be viewed as an application of steam engines, and rational structural analysis as an application of bridge building.   The view of scientific discovery as depending on the ingenious craftsmanship of instruments, and thus following technology, convincingly flies in the face of the conventional wisdom that technology is mere applied science.  [Petroski, 1997, 17]

So according to this, Science is Applied Engineering

Structural Art - Heat Plant at Brown University

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One of the finest examples of structural art in Providence is Brown University's Heat Plant on Llyod Ave.  It is a hidden gem.   The brick facade is sawtooth in plan at the base but straight at the top, creating beautiful hyperbolic brick sections that are repeated throughout. Both the Builder/Mason and the Architect/Engineer should be extremely proud and as a Providence resident I want to express my gratitude, thank you!

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