deflection formula by committee

February 5, 2016 § 1 Comment

Lecture 7 Enlightenment.001Big and Tall is off to a fine start this year.  We’ve managed to get through the first 2000 years or so of western building (fun stuff) in a couple of weeks and now we’re getting to the Enlightenment (more fun stuff).  What happens when building culture goes from a purely empirical approach–we could pile this many stones on top of one another, so maybe we could pile (this many +1) stones on top of one another?–to something that involves the process of experimentation–observation, hypothesis, testing, rinse, lather, repeat?  There are a bunch of moments in the 15th through 19th century where some insight becomes part of the collected wisdom and the models get more and more useful to actual builders.


Richard Betts, “Structural Innovation and Structural Design in Renaissance Architecture,” JSAH, 52:1, March, 1993.  13.

To talk about this, we start with the fact that ‘structural engineering’ in medieval and renaissance building relied largely on quadrature, the process of tracing out geometrical relationships between circles and squares, and using the resulting line segments to size buttresses, walls, etc.  This was basically rule-of-thumb advice codified, but it had the appearance of divine mathematical rigor.  Thicknesses of supporting walls were given a dimensional relationship to the roofs, domes, or vaults they supported, but why this worked was never established–or really questioned.  While this gives the appearance of a structural theory, it was simply a way to replicate the proportions of existing structures–really a fancy way of keeping track of how many stones the last pile had held.

Leonardo (1452-1519) is often seen as one of the pioneering figures of statics, but his observations on beams and columns were very much stuck in this medieval mindset.  He relied heavily on authority–on quadrature for his unbuilt church designs, and on Aristotle for his insights into beam theory in particular.  To stick with this, Leonardo’s “Principle of Levers” was a rudimentary theory of bending moments–that the deflection of a beam was related to the magnitude of the load it was being asked to carry, and the span–or lever arm–between that load and the support.  From his sketches it’s apparent that Leonardo thought of these both as linear relationships.  And while that’s true for the load, a simple experiment would have shown that it’s not at all true for the span.  That, in fact, is an exponential relationship.  To wake students up at this point, I like pounding the desk and saying that while Leonardo may have been a great Renaissance artist, he was still, profoundly, a medieval scientist.

GalileoThat insight had to wait for Galileo (1564-1642), who had nothing better to do during his famous house arrest then to test out and refine his own theories of statics.  Galileo was the first of the great experimenters, devising ways to actually put ideas about how things work into the world to see whether they were right or wrong.  That’s a profoundly different attitude than relying on the authority of Aristotle, or the Church, or quadrature–part of what got him in trouble in the first place.  But it also produced refinements that took Leonardo’s observations and hypotheses and a) proved them qualitatively correct but mathematically wrong, and b) made refinements to them that produced a useful mathematical model.  Galileo recognized that the span of a cantilever was in fact exponentially more important to deflection than load was.  And, importantly, by looking at actual beams under load he recognized that the depth of a beam also mattered.  In the very SCI-TECH observation above, a flat beam carries far less (or deflects far more) than the same shape turned on its edge.

Lecture 7 Enlightenment.006From there, our understanding of deflection underwent several further refinements.  Robert Hooke recognized the relationship between stress and strain, making the whole idea of a deflection formula meaningful.  Euler’s work on bending gave us the Modulus of Elasticity (E), and wove the importance of material strength and stiffness into the equation.  Finally, Navier and Fairbairn, working in iron at the turn of the 19th century, began to refine Galileo’s recognition of “depth’s” importance.  Moment of Inertia (I) measures not just the depth of a beam, but where the area of a beam is located in its cross section.  This, of course, made little sense when nearly every architrave or beam was hewn from wood or stone, with little labor spent on sculpting cross sections.  But in iron or steel, where quantity mattered and could be easily controlled by rolling, Moment of Inertia becomes something easy to play around with and to fine tune.  Materials and form influence one another, and the way we think about one often leads to insights about the other.

So, that’s a nice story, and it’s a good way to teach deflection–bringing students along one variable at a time.  But it also shows that our knowledge usually proceeds by refinement.  If you’re trying to explain to a layperson how a beam works, Leonardo’s “Principle of Levers” still works.  But if you want to know how this particular beam design will work under these conditions, you want something more than a qualitative model, and the scientists who came after Leonardo each refined that basic idea into quantitative models that allowed us to confidently predict what shapes and sizes would be necessary to achieve the spans and loadings that we desired.  The formula isn’t just a useful tool, it’s an historical document, one that shows how, despite the mythology of the great figures, what we know about building (or, really, anything else) has been a long-distance, long-term collaboration.


best civic space in chicago?

January 27, 2016 § Leave a comment

Daley Plaza? Federal Center? For me the civic space that defines the city is the Lakefront Trail, especially in the morning. Curbed just linked to the video above, showing an intrepid biker hyper-lapsing the just-renovated section through Lincoln Park.  When the weather is good (i.e., better than now), a morning run up the lake is my standard routine when I’m in town and it never fails to be a great mashup of the city and its residents.  Glad this section is re-opened–for a couple of years now it’s been a pothole- or orange fence-dodge and this should make the bike/jogger/stroller ballet that much more enjoyable…

the more things change…

January 20, 2016 § Leave a comment

Brick and concrete in Thursday’s Big and Tall class, and in brushing up on my Vitruvius this passage comes up:

17. The laws of the state forbid that walls abutting on public property should be more than a foot and a half thick. The other walls are built of the same thickness in order to save space. Now brick walls, unless two or three bricks thick, cannot support more than one story; certainly not if they are only a foot and a half in thickness. But with the present importance of the city and the unlimited numbers of its population, it is necessary to increase the number of dwelling-places indefinitely. Consequently, as the ground floors could not admit of so great a number living in the city, the nature of the case has made it necessary to find relief by making the buildings high. In these tall piles reared with piers of stone, walls of burnt brick, and partitions of rubble work, and provided with floor after floor, the upper stories can be[57] partitioned off into rooms to very great advantage. The accommodations within the city walls being thus multiplied as a result of the many floors high in the air, the Roman people easily find excellent places in which to live.

18. It has now been explained how limitations of building space necessarily forbid the employment of brick walls within the city.

The translation here seems kind of weird, but the comment at the start of paragraph 18 makes it clear that Vitruvius’ objection is to walls of unfired brick, which was only half as strong as fired brick.  If that’s the case, the point here is that unfired brick requires piers that are too large to meet the city’s building code.

Here’s the same argument, nearly 2000 years later, for why brick isn’t a suitable material for a tall urban building:

“The carrying strength of street walls for masonry construction is the carrying strength of the piers; that is, that part of these walls measured between the windows, and this fact limits the height of masonry buildings. The horizontal area of the piers either takes floor space or window area, and both alternatives are objectionable…. The lower floor piers are seven feet thick, in spite of using vitirified brick and cement mortar in their construction, figured to carry eighteen tons per square foot, dead and live load. The windows of these buildings might be better if they were wider, and the floor space taken in the lower floors by the walls is very valuable.”

Corydon T. Purdy, “The Evolution of High Building Construction.” Journal of the Western Society of Engineers, XXXVII, no. 4. August, 1932.  204-205.  Note the “in spite of using vitrified brick,” then the strongest available.

nipigon river bridge (update)

January 11, 2016 § 1 Comment!/fileImage/httpImage/image.jpg_gen/derivatives/16x9_620/nipigon-river-bridge-fails-in-cold.jpg

Oh, here’s a doozy…The Trans-Canada highway has been closed this morning because of a bridge failure over the Nipigon River in Ontario.  Not, as you can see, the most spectacular failure, but pretty tough to get the family sedan over that rather abrupt change in level.

Two SCI-TECH principles come immediately to mind.

First, it’s pretty clear what happened.  Although no one’s saying anything yet, you can see that the failure happened at an expansion joint (note the ‘teeth’ drooping from the edge of the deck).  The only thing authorities have mentioned so far is that they’re blaming “extreme cold conditions” for the failure.  Concrete’s coefficient of thermal expansion is a pretty benign 14-ish 10-6/°C, about the same as steel, which is one of the reasons we use steel and not, say, aluminum for reinforcement.  But it got down to -24°C in Thunder Bay last night, or a good 45°C colder than room temperature.  The bridge is listed as spanning 252 meters.  Assuming that’s measured at 21°C, at its coldest last night the bridge would have shrunk by a solid 15.8 centimeters from its design length (14 cm/cm x 10-6/°C x 252m x 45°C), or about 6 inches.  Thermal expansion (or, in this case, contraction) is a powerful force, and it’s easy to imagine that amount of pull fracturing whatever pins were holding that joint together.  You can see, too, the results of diagonal tension members in a cable-stayed bridge–the deck is not only pulled up, it’s also pulled back since the deck suddenly became a very skinny horizontal column.  It’s buckling, but very gently.

Second point:  Redundancy and resilience.  The Trans-Canada is apparently the only automotive route between the eastern and western halves of the country.  So today, if you want to drive from Toronto to Vancouver, you’re going to be stuck going around the southern edge of the Great Lakes.  The Nipigon River Bridge is being replaced by a double-span, which would provide the kind of backup you’d expect in a system so reliant on a single node.  But, of course, that backup would have been subject to the same forces of thermal contraction, and if both spans had been designed to the same standard, they could both have ended up looking like this.

Anyway, to any neighbors to the north enjoying a leisurely drive through the Midwest today, wave and smile, and enjoy the extended tour of the U.S., brought to you in this case by the laws of physics…

Update, 12 January 2016: 

A multimillion-dollar bridge on the Trans-Canada Highway, the sole east-west route across part of northern Ontario, has partially reopened after sustaining serious damage over the weekend, provincial officials said Monday.

“The Ontario Provincial Police and the Ministry of Transportation confirmed that one lane of the Nipigon River Bridge has reopened.

“A statement from Transportation Minister Steven Del Duca said the lane is available to cars and regular-weight transport trucks, but that engineers are still working to determine whether it can sustain the weight of oversized trucks.”

integrated design studios coast to…

December 15, 2015 § Leave a comment

…well, not exactly coast to coast, but central North Carolina to Kansas, at any rate.  ‘Tis the season…

OK, to get back on that soapbox from last week for just a minute…The National Architectural Accreditation Board made a fundamental change to its list of Student Performance Criteria last year, re-organizing and re-emphasizing the couple of dozen aspects of architectural design and practice that any school needs to demonstrate to receive accreditation.  On one level we’re sort of casually interested, since we received an eight-year re-accreditation in 2012.  But Comprehensive Design was one area that we were flagged for, and so we’ve watched as the accreditation criteria have changed.  It’s a bit self-serving to say so, but to my eyes the revision matches more closely what we’ve always done, and what we’ve consistently battled NAAB over for the last 15 years.

At the risk of boring the readership, here’s the language that schools used to be held to:

Comprehensive Design: Ability to produce a comprehensive architectural project that demonstrates each student’s capacity to make design decisions across scales while integrating the following SPC:
A.2. Design Thinking Skills
A.4. Technical Documentation
A.5. Investigative Skills
A.8. Ordering Systems
A.9. Historical Traditions and Global Culture
B.2. Accessibility
B.3. Sustainability
B.4. Site Design
B.5. Life Safety
B.8. Environmental Systems
B.9. Structural Systems

So, in effect, students had to produce projects that would fully meet all of these criteria–demonstrably code-legal, environmentally efficient, structurally sound, and historically/culturally conscientious.  Nothing wrong with that, but in practice Comprehensive studios became the place where visiting teams could score easy points–a door swinging the wrong way in one project, for instance (bitter?  Not me), and the whole program could fail.

We had always made big noises about how Comprehensive studio should be comprehensive, and to incorporate the vast range of criteria involved we took an integrative approach.  Do your doors swing the wrong way?  OK, that’s a problem, but if that’s part of an overall project that’s looked for ways to blend a reasonable exiting strategy with everything else, we thought that met the spirit of the law, was forgivable in the grand scheme of the studio, and in hindsight we were pretty obstinate (too obstinage, apparently) about that when visiting teams showed up.  Other programs met this criteria by having students basically do construction drawings for super-reductive programs (two-story suburban office parks, e.g.), and we thought that kept the bar for design unconscionably low.

So when the 2014 revisions came out, my colleagues and I couldn’t wait to page through and find the new Comprehensive criteria, because the word on the street had been that our objections, along with a couple of dozen other schools, had been heard.  And, in fact, the whole notion of a “Comprehensive” project got shelved–when you think about it, asking a 23-year old with maybe a summer or two of practice to design a perfect project is pretty ridiculous (disagree?  Well, then I assume you do your own mechanical engineering?  Never hired a code consultant?).  Instead, NAAB even adopted a new title that reflected a more holistic approach that suggested looking for the forest in addition to the trees:

Integrative Design: Ability to make design decisions within a complex architectural project while demonstrating broad integration and consideration of environmental stewardship, technical documentation, accessibility, site conditions, life safety, environmental systems, structural systems, and building envelope systems and assemblies.

Total win.  “Broad integration and consideration” ring far truer in terms of a design student’s abilities, knowledge, and–frankly–how we educate architects today.  Any project in an Integrative Design Studio still needs to show that code, environment, structure, and cladding have all been part of the design strategy, but the “tick-in-the-box” mindset has all but disappeared.  If a door swings the wrong way it can still get called out and discussed, but it no longer invalidates the entire project.

Christensen Mueller_Page_4

King Street Station Hotel, ARCH 603 project by Frank Mueller and Nick Christensen

So, Integrative Design Studios are now a thing, and last week I was lucky to sit on juries for three good ones–our own ARCH 603 reviews as well as those at UNC-Charlotte and at Kansas State.  And while there’s still a range of approaches evident, including a few construction drawing sets in the mix, there are also more and more presentations that go back and forth between diagrams and renderings, system drawings and models–that do that binocular vision thing where the forest and the trees both get documented, and the relationships between one and the other get explained, proving that they’ve also been thought about.  This, to me, is what any design education is all about.  Do you understand the basic vocabulary of forms, elements, components, and systems, and do you understand the rules–the grammar, maybe–that determines how all of these have to relate?  That takes enormous cognitive attention and labor, and that, more than anything else, is what I hope our students leave us with; an understanding of the architect’s role as orchestrator and the immense effort and responsibility that takes.



King Street Station Hotel, ARCH 603 project by Bryan Johnson, Nathan Peters, and Thomas Thatcher

And, of course, this also jibes with the immense brainpower that now sits on student desktops.  Data-driven design is no longer a buzzword, it defines how a whole generation of students tackles a complicated project.  Get critiqued on daylighting?  Run a quick Sefaira model to find out whether you or the crit (or neither of you) are right and adjust accordingly.  All of that brainpower, of course, is uncoordinated–so far, though Grasshopper is now also a legitimate cognitive assist in studio–so the integration still has to take place in the discussions, sketches, and noodling around that (thankfully) still goes on around the desktop.


Finally, while there’s no requirement for it in the new criteria, it’s cheering to see that the final results still get held to the basic scrutiny of human experience.  All the correct decisions in the world can still easily lead to a design that sucks, and that subjectivity will keep juries, studio critics, and designers contentedly arguing no matter what evidentiary backup gets produced.  Good to see over the last week that students remain passionate about creating things that touch our souls even as they meet the ever more demanding criteria for demonstrating fluency in the stuff of building.  Heading off to break feeling humbled by the great work I’ve seen this past week and recharged by the energy, thought, and flat-out joy that’s been on display in these three programs…

Elliott Vansice 24

King Street Station Hotel, ARCH 603 project by James Elliott and Kyle Vansice

uncc reviews

December 9, 2015 § Leave a comment

IMG_125835 minutes from alarm to gate this morning…Charlotte’s legendary traffic isn’t nearly as impressive at 5:00am.  A good day yesterday reviewing projects at UNC-Charlotte.  Our programs have been nicely hybridized over the last ten years or so–we’ve traded faculty and made enough connections that there’s been a good bit of healthy sharing, and it’s been nice to get out here for the first time in a few years and review Comprehensive Design projects for former colleague Chris Beorkrem.

(I meant, of course, Integrated Design.  NAAB’s change in nomenclature is significant, and it represents a shift in what this accreditation requirement means…no longer do students have to show mastery of every technical detail, they have to show that they understand how various systems interact and how a holistic approach to engineering, construction, function, climate, life safety, etc. needs to account for each of these.  This isn’t without controversy, but it jibes very well with what we’ve emphasized at ISU.  Specialists do the math, we do the orchestrating, and while you need to anticipate what sort of solutions the number crunching is going to give you, we need to get it 90% right to begin with.  And, since a 15-week project isn’t really any more than schematic design, it’s getting to this 90% that’s most important–not drilling down and getting one or two systems 100% right and having no time to think about the rest.  Soapbox being put back in its place).

IMG_1266Anyway.  A lot of 90% being done right in Prof. Beorkrem’s graduate studio review yesterday.  By happy coincidence, they’ve been working on a high rise in downtown Charlotte that’s a similar scale as, and on a similar site to our Seattle project, so it felt very comfortable sliding into their world.  As you can see, they’ve emphasized all the usual elements–structure, cladding (this one’s got a Ned Kahn-inspired fluttering wind screen).  But Chris also asked them to incorporate some parametric aspect into the processes, so there were interesting forms that came about as results of programming, solar, and circulatory responses.  What your data come up with are often richer and more interesting than anything that comes out of your aesthetic instincts…but it takes those instincts to make sense of the data.  Lessons worth repeating.

IMG_1252IMG_1251UNCC has had an incredible decade and a half or so.  It’s gone from being a commuter school to being a powerhouse of design, computation, and fabrication (one of the world’s few degrees in motorsports engineering, e.g.), and any visit means seeing what the new toys are.  Robot arm?  Check.  They live and breathe the philosophy that these are studio toys, though, not lab toys, so instead of being locked away in a clean room the cutters, routers, robot arms, and high-end processors are all in the same suite of rooms that double as classrooms and studios.  So students get familiar with the equipment on a day-to-day basis instead of having to run across campus to have a grad assistant run their models for them.  As a result, there are some really innovative projects going on, including this one that produced precisely deformed steel sheets by having the robot arm draw with a ball-bearing ‘finger.’  With very carefully calibrated differences in pressure the arm slowly, patiently presses the sheet into forms that could be ornamental, or could stiffen curtain wall panels, etc., etc.  Pretty stuff, and nicely complemented by morning reviews of projects in a combined design/computation master’s program that looked at software and hardware ‘nudges’ to change energy-intensive behaviors.

Oh, and the reviews were held in their fifth year graduate suite, housed in the brand new Kieran Timberlake satellite campus downtown, pictured above.  Every hip school in the U.S. these days is building a new KT building, of course…

old home week–lego style

December 5, 2015 § Leave a comment

I’ve hit the point in my academic career where there’s a “circle of life” moment every so often–a former student who suddenly shows up as a colleague, for instance.  This week was a pretty glorious example.

Dan Winger graduated from our B.Arch. program in 2003, after surviving one of my first studio teaching experiences (our inaugural Comprehensive Design studio, in fact).  Dan was a brilliant drafstman–his sketches were consistently amazing but it was clear that his interests lay well beyond architecture.  We kept in touch a bit after he graduated, and after a couple of years of–by his own account–waiting tables he was accepted to the Art Center College of Pasadena in their industrial design program.  Where, obviously, he did well.

Winger has been with LEGO almost ever since, and he’s now a Senior Concept Designer for the LEGO Future Lab, an R&D branch that produces things that, as he admits, he can’t really talk about.  But he did talk about some of the projects he’s worked on that are on the market now, including some of the company’s digital innovations.  LEGO Worlds, for example, which is basically an infinite digital LEGO kit.

Scratch almost any architect and you’ll find a one-time LEGO maniac under the surface.  Like me, Dan grew up with a tub of random parts (but I’ll bet he doesn’t remember when they started including wheels in sets…me and LEGO go back pretty far).  I think that a lot of the appeal has always been the low-context nature of the bricks.  Nothing you can build in your playroom has the verisimilitude that, say, a ready-made plastic toy has.  Your mind always had to fill in the blanks, and I think that sort of engagement made the bricks that much more interesting…to some of us.

LEGO today, of course, has taken the 2×4 brick and turned it into an empire…robotics, digital and board games, etc.  LEGO Worlds turns that around–even though the company got beaten to the punch by Minecraft (and, arguably, by SimCity), the idea of a never-ending supply of bricks online finally satisfies that part of my brain that was always–always–looking for one more red 1×2.

Dan spent the afternoon in our studios, interested in the digital tools we use today and talking about the links between industrial design and architecture.  Architectural education often seems like a good liberal design education that can be translated into any number of fields, and our graduates have gone on to careers in law, medicine, urban planning, development, software design, and–yep–product design after their time with us.  Seeing the LEGO-architecture inspiration go full circle was particularly rewarding.

And, just to show that the apple doesn’t fall that far away, my 15-year old son joined me in the audience for the lecture.  Afterwards I suggested that we download LEGO Worlds and mess around with it.  Turned out he’d been playing with the beta version for months already…


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