Life’s Lemmas
Are We Civilized?
In a past column, I may have mentioned that I used an iron while building a desk and bookshelf. Although I’ve closed the book on the iron, there is more to say about the desk.
At first glance, building a desk seems like a straightforward operation. After all, IKEA has already fooled half the college kids in America to assemble their own stuff. But when you really start thinking about it, the natural response when building your own furniture is “Please don’t fall apart,” and perhaps even “I hope I didn’t bite off more than I can chew.”
Now, just like any math, engineering, or physics problem, the first hurdle to jump when building a desk is how many, how much, or how big? Qualitatively, these answers are easy: one, cheap, and colossal. Quantitatively, it is a different story.
I decided to put my small civil engineering background to work and calculated exactly how big I could feasibly make my desk. After a few turns of the crank I had everything I needed: required members, loadings, and deflections. But, the numbers looked fishy. I built the desk and bookshelf, half-copying the dimensions from the IKEA catalogue, and sure enough my numbers were wrong. In fact the loadings weren’t even in the same ballpark.
Apparently I failed the third principle of civil engineering: common sense. I repeated the calculations and sure enough a units conversion screwed me over. Now instead of getting insane answers that suggest my desk is stiffer than an old man on Viagra, I actually had reasonable results. The real difficulty however didn’t lie in the stiffness of the desk, but rather in the bookshelf. There was clearly a frequency response problem. I’m not saying a bad response, like a pole in the right half plane, but bad enough that my siblings were ribbing me over my calculations. Apparently the bookshelf from someone’s high school shop class, which is currently holding the extra toilet paper in our washroom, has its poles in all the right places. My mother came to the rescue, adding her engineering experience as an English major: “Don’t worry, the dynamics will change with a load full of books,” she said.
So here we are in the 21st Century and after my construction experience, I started to realize how much of civil engineering involves convincing the public that everything is all right. Let me elaborate.
Civil engineering was one of my first freshman classes. In fact, during the first 10 minutes of the first lecture we were introduced to the three principles of civil engineering. As mentioned earlier, the third was “common sense” or more precisely: “You must know the answer before you get the answer.”
“You can’t push on a rope” was the second principle and “F = ma” was the first. Yet shortly after introductions we promptly set a = 0. Now every field has its own equations and civ is just F = 0. Seriously! This isn’t even a differential equation anymore. Nevertheless, my brother, a typical civ(il servant), seems perfectly happy, perhaps even proud, with this fortunate state of affairs.
I dare say F = 0 is not for everyone. The following year some adventurous individuals thought it would be fun to set “a” not equal to zero. Their travels directed them up a few rungs on the ivory tower to mechanical engineering (e.g. right under the general assumption that course 6 < 8 < 18, etc. …). But for practicing civs, an accelerating building usually leaves everyone wondering what the “F” happened.
Truth be told, as any civ knows, the problem isn’t just about setting a = 0 or solving F = 0 but convincing the public that a = 0. For example, the general public typically views a building as just that — a static object planted on mother earth. Ask a civ and they’ll tell you a building is really an erect elastic stick. To hammer this point home, even the top of the empire state building, a stiff elastic stick, can sway up to 1.5 inches in a windstorm. Perhaps more dramatically, the golden gate bridge piers bend 1.5 feet from temperature and loading variations. The reason this isn’t too alarming is because we can’t see or feel them. Civs design deflections and accelerations below human observation and sensation. Sure enough, the 22-inch deflections on the golden gate bridge do not saturate the human observation threshold of 1/300th of the 700-foot elevation.
One very elastic structure, which violates the 1/300th rule, is an airplane wing. Next time you’re on an airplane, take note of the large oscillations or deflections and smile that some aerospace engineer has subconsciously convinced you it’s safe. But if you want a tip from your local materials engineer, just make sure you’re not looking through a square window.