How Geometry Can Establish Architectural Form

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.

BIM Technology For Foundation Design

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!

Non-Linear Structural Forms

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.   

Indoor Desktop 3D Printing Warning

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.

3D Printing Industry: How Toxic Are ABS &PLA Fumes?

3Ders: New study shows health hazards of 3Dprinting

Supported Extrusion 3D Printing

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.                                                                                   

Parametric Structural Design

I’ve been excited for this post for a couple of days now. I’ve been all over computational architecture for the last year and this Autodesk example extends that theory further. The ability to quickly test engineering design iterations with Dynamo has all sorts of interesting applications in finding novel and efficient engineering solutions. Dynamo, for those not in the loop, is an open source visual programming add-on for REVIT. But architecture is not the only domain parametric design can be utilized. Autodesk React Structures, based loosely on the REVIT BIM platform, is one of Autodesk’s enterprise level structural engineering applications. The program comes with a build in set of comprehensive programming tools for the analysis of complex structures. But adding the visual Dynamo interface lets designers try many complex structural variations to see if anything interesting or inspiring comes out. Normally to redo these engineering calculations strictly for experimentation is cost prohibitive. Much of the linked example might be over the reader's head - as it was mine - but I thought it a worthy example to squirrel away because it tells a story of where the AEC industry is going. 

Dutch Cementitous 3D Printing Project

I was excited to post this article about 3Dprinting concrete but first the bad news: The technology is still not big enough for what I wanted to use it for. That said, the article is a nice introduction to some of the changes 3D printing is expected to bring to design.

Dutch 3D printer manufacture Opiliones worked with designer Michiel van der Kley to establish Project Next which aims to solve the coveted goal of “a 3D printable bio-concrete and an accompanying 3D printer capable of making complete architectural spaces”. From what I can tell – at least initially – if by “architectural spaces” they mean spaces you’d need to crawl and squeeze into, mission accomplished. So yeah, scalability is still a factor. The project was focused on developing environmentally sustainable concrete and in the process experimented with several mixes including limestone, hemp fibers, flax fibers, etc., but ultimately I see the role of green building materials in architecture as presupposed and not something I need to be convinced of.  

What did catch my eye, however, was designer Van der Kley’s comments about how radically 3D printing will change what forms are possible architecturally. This is an facet of architectural 3D printing I am already engaged in. Sometimes it can be tough to described how architectural 3D printing affects form; therefore it becomes doubly difficult to predict how the technology will change architecture in the future. But that’s where I want to be: already where the crowd is going. And part of how to

get there is to understand theoretically where is going on aesthetically and economically with the technology.

In the piece Van der Kley’s calls for a “new design language”, the main thrust of his argument being that new techniques – such as 3D printing – require a new descriptive language. But here I must disagree with the good designer. When I look at the sculpture I immediately see math. In fact there are a variety of mathematical interpretations of the work: Manifolds defined by differential geometry; hyperbolic surfaces, etc. Nature also has a wealth of examples because anytime a membrane is put under tension it is capable of displaying this type of behavior and probably if I had more time we could narrow down an example from the human body, like the stomach lining or something. I think what Van der Kley really means is explained in the last paragraph, about the acceptance of such forms by the public. But his line of reasoning seems to assume he discovered the end of all possible forms of cementitious 3D printing, neglecting creative ideas from future architects and designers or further advances in the technology. A position which is hard to support.

Now You Finally 3D Print Star Wars Figurines At Your Desk!

Hype for 3D printing was turned up all the way to 11 at this year’s CES in Las Vegas - promising everything including“limitless possibilities”. There appears to be some substance behind the hype with several manufactures showing interest in the field. Strong competition in the sector bodes well for consumers. One of the highlights was ROBO 3D’s new R2 product lineup which introduces a set of mature consumer-friendly 3D printers stylish enough to sit on a desk while being affordable enough to buy for the office. The printer’s small form factor and Wi-Fi connectivity echoes how laser printers shrunk and shed wires during the last 10 years.

So what would if I got one? First off, family and friends would probably receive 3D printed necklaces and broaches on all occasions! But more to the point, one could at least start practicing 3D model making. My first introduction to 3D modeling was a slog. 3D printing has a steep learning curve in regards to 1) understanding the behavior of the printed material (too thin, too thick, etc.) and 2) how to use the complex 3D modelling software. Learning both is an uphill battle and the sooner one starts the sooner one will understand how to model replacement parts for broken things around the house.

Left unsaid in the glowing press coverage is the newly released printer’s failure rate; an important metric in consumer 3D printing. In my experience failure rates are still higher than normal when compared to other consumer goods. It’s a bit random when your continuous printing process fails. Imagine if your toaster burnt your toast 1 out of every 10 mornings; you’d think it’s a piece of junk. But such failures rates are still common in consumer-focused 3D printing, no doubt a facet manufactures are looking to reduce as a selling point. I’d also really like to see a closed looped 3D printer; where the used material can be recycled in the machine again. This – in my opinion - is sort of the holy grail of rapid desktop prototyping. 

2016 AEC Industry Forecast. Now with Comments!

I’m a sucker for forward looking articles. I’m always on the lookout for predictions of substance on topics I’m passionate about. Reading through Engineering News Record’s 2016 construction trends article I found some useful highlights. But first an apology; I’m really really sorry for the forced Christmas song structure the article takes at points. I’m sure it was just meant as light-hearted attempt to make the article more readable at Christmas but for me, it just makes the article longer without adding quality content. And it’s after Christmas. Below are the article’s main suggestions with my comments:

• Economic forecast for North America looks vaguely positive. I vaguely agree.
• Adopt future technology. Chances are if a firm isn’t already planning to do this they have much bigger problems.
• Try to understand global factors. Always good advice but where does one find the time?
• Aging Infrastructure. Did the author really just predict infrastructure would get older in the future?
• Sustainability. I’m so far past this trend. I consider sustainability factors core to all modern building design. 
• Take care of: experienced staff members, long-standing satisfied customers, solid financials and reputation. I don’t get this one. Isn’t this just common sense in the 21^st century marketplace? Nor is this specific to the AEC industry.
• Expect rare events. The author evidently read Nassim Nicholas Taleb’s The Black Swan in 2015.
• More women in the AEC industry. About time. Let’s keep moving forward on this.
• Firms should focus on their social responsibility. This is insightful if one accepts the assumption the values of the marketplace are shifting. Other firms will probably still advocate advertising in newspapers.
• Safety. Yes. Let’s continue to encourage amazingly safe working conditions for all involved in building endeavors.
• Alternative energy will continue to grow in importance. I will only add solar panels are easier to integrate into a good design than windmills.  
• The winning 2016 presidential candidate will have an effect on AEC industry. So think carefully. While trivially true I’d also like to point out the current crop of presidential candidates’ building design credentials are underwhelming.

Any comments from our readers? I know you’re out there. Are these predictions insightful? Too trivial? Cheesy?