skip to main |
skip to sidebar
Today’s
post includes a small piece rejected from a larger research project which
represents - much like how the best science is driven by curiosity - that even
unexpected results can be valuable. The small exercise in Dynamo was initially
supposed to 1) show the connection between geometry and algebra, with geometry,
of course, being central to architecture, and 2) highlight how in the real
world geometry and algebra often diverge from each other.
 |
| Fig.1 |
The starting point was to replicate the Three Square Puzzle - as featured on Numberphile’s YouTube channel and the Trigonography blog - in REVIT using Dynamo. The puzzle asks what the sum of angles A,B,& C are (Figure 1). Intuitively, if one looks at the puzzle, it can be deduced the sum of the three angles should be 90 degrees. And indeed this is the case with over 80 such solutions cataloged in the literature (one of which is illustrated in Figure 2). However, a very curious thing happens when trying to measure the angles and sum them in the real world. Because trigonometry often includes irrational numbers, it becomes impossible to ever achieve a perfect right angle when measuring. That’s what makes it a puzzle; the solutions only exists in an idealized mathematical world.
 |
| Fig. 2 |
After
establishing the geometry and scaling it up to apply steel framing in REVIT, I
measured the angles assuming Dynamo would miss generating a perfect right angle
by an arbitrarily small amount. To my great surprise, Dynamo nailed the
geometry to four decimal places, the maximum precision allowed in Dynamo at this time. It’s possible that with more precision the expected results could be
generated and we’d see the sum of the angles drift away from the theoretically
perfect right angle. Another alternative is that Dynamo overcomes imprecision
by discretizing/quantizing the output leading to nice integer solutions, kind
of like Minecraft’s logical 1m x 1m x 1m block universe.
At
the end of the day, these are the sorts of curious behaviours one can expect to
find when experimenting with computational architecture.
In an effort build constructively I’ve
collected below two articles which illustrate some of the advantages structural
modelling provides even if our shop isn’t currently utilizing each to its full
extent.
Detailing rebar lines in concrete is one of the
first steps in keeping a building upright and an activity I do daily. Detailing
becomes a challenge when 1) the complexity of the structure and 2) demand for a
comprehensive design increases. The linked article follows VK Architects and
Engineers through their advanced structural modelling workflow and as one can
see the results are impressive. Of most use to the structural engineering community
are the 2D views which track and specify the position and type of reinforcement
to be used and can be critical for certain types of building permits and construction
documents (depending on jurisdiction). The automatic creation of reinforcement
schedules is also welcomed. The other views provided by BIM software, while
perhaps not making it onto the final sheets, are of no less value. The ability
to visually distinguish reinforcement categories in 3D, plan or section allows
the designer to quickly orient themselves in regard to the scope of work. The
3D views especially capture the intricate layering of the rebar.
Designing foundation piles, while not strictly
part of my job, does hinge on the engineers’ ability to establish the geometry
and static forces of the pile. But thereafter this information goes to the pile
manufacture to actually design the pile dimensions necessary to resist said forces.
The reason the industry is structured like this, to the best of my
understanding, is because pile design, like other engineering disciplines,
requires very specific knowledge (and perhaps software) to complete. That
interface between engineering disciplines becomes crucial to avoiding extensive
pre/post-processing and rework. In the linked article’s example, the ability to
do calculations in Excel – where engineers are most likely most comfortable -
and then smoothly bring those changes back into the model can save a lot of
time and increase accuracy. Not a lot of deals in life can achieve both so please
raise a glass and toast BIM technology!
With my background in architectural history I was intrigued by AEC Magazine’s article about non-linear structural forms which aim to span a maximum distance with minimal materials because it highlighted several unique architectural examples. If I understand the article correctly, non-linear structural forms are characterized by always being strictly in tension or compression. This includes the use of stretched membranes, flying buttresses, etc. This is in contrast to traditional structural forms like walls, columns and beams which can have a variety of forces acting upon them in combination but whose structural calculations result in linear equations.
Readers lucky enough to make it to the end of the article will have a new word for the day (at least I did): Tensegrity. It’s defined as the structural condition where elements are either in pure tension or compression with no two compression elements (theoretically) in contact. The article uses the wonderful example of Brisbane’s Kurilpa Bridge (pictured) to illustrate this point where it’s easy to see these forces in balance to create the span. Buckminster Fuller developed the theory while the above project was completed by Arup - and though I often give them a rough time on social media in jest - here again their engineering is totally on point. As an interesting side note, Arup used custom written software to integrate their calculations into Oasys’ GSA engineering software which from what I can gather specializes in non-linear statics resulting in a bridge that is truly a unique structure.
Previously I had joked about 3D printing Star Wars figurines at one’s desk and though I still find that image funny
recent news highlights an important safety issue to consider before starting
your 3D printing project: The process of 3D printing polymers produces volatile organic compounds (VOCs) and
ultra-fine particles (UFPs) as a by-product. And while I’m not aware of any
acute health risks of printing indoors – no one is dropping to the floor in
distress – I’m also not willing to take the risk and sit beside one of these things
indoors for months on end – I’d put it in the garage – and so therefore it seemed
only fair to pass along on such information to our readers to make up their own
minds.
It’s been a busy week for architectural 3D
printing news with several good options to discuss but one breakthrough stands
above the others. I was quite happy to see the efforts of the Bartlett School
of Architecture, UK, reported by 3ders.org in regards to their cementitious 3D
printing achievements using a supported extrusion technique. This method begins with the placement of a cementitious material by a robotic head unit similar to that
which is used by other firms but differentiates itself by simultaneously laying
down a granular support material. After manufacturing once removed the process
leaves a distinctive pattern the designers call “Fossilized” and I call
“circuit board”. The process represents progress toward refining cementitious
3D printing technology by allowing for smaller detail tolerances. Unoforunately
factors such as the process’s structural strength and long-term performance are
still underreported and therefore a certain amount of skepticism is still
warranted before calling this technology useful architectural 3D printing. I
also question the qualifications of a group of designers to tackle what is
essentially a mechanical engineering problem. Absolutely their design aesthetic
is beyond reproach but where are they getting expertise in process, control,
chemical and mechanical engineering? Food for thought at this technology
continues to improve.
Agree? Disagree? Share your comments below.
