After ten years, things have cycled around to give my colleague Rob Whitehead and me half-course elective slots at the same time, so we’ve pooled our resources and put together what we’ve always talked about as our ideal structures class–one long session every Friday morning dedicated to hands-on structures labs. These have always been our favorite parts of teaching structures and, we think, the most effective since they get concepts off of the whiteboards and out of the textbooks and put them into the real world. Breaking stuff and getting students to talk about how and why failures happen is inherently messy and something of a tightrope act, but that mimics the real world, where nothing is ever quite as pure as the formulas make it seem.
Structures Zoo has been colossal fun to scope out and start to put together. We had our first class yesterday, which was basically our thesis statement–that structural knowledge and awareness comes from our interaction with the actual world, and that we make the most progress (as a species and/or as students of the discipline) when we take a rigorous approach to assessing what works and how. We set the first class up as a structured set of four labs, each tied into the history of the deflection formula. Starting with Archtyras and Archimedes, there’s a very neat history-of-science approach to how we understand the deformation of a beam under load–I’ve written before about using this as a way of showing that structures has always been a scientific enterprise, subject to revision and addition as new technology (including Arabic numerals, algebra, calculus, etc.) has come on-line.
The final lab of the day tried to drive home how efficient the scientific method can be, and how quickly it can produce actionable and testable knowledge. The “E” in the formula above is Modulus of Elasticity or a numerical measure of stiffness (also called Young’s Modulus). That’s an intimidating name, but it’s really just a simple ratio of stress to strain–in other words, how much a material deforms under a given load.
In column theory this is most useful in helping to understand how a “long” column will buckle–you want a stiff material that will resist the tendency to get out of the way of a load and start a death spiral of deflection, increased bending forces, further deflection because of those forces, and failure. But in “short” columns–those not vulnerable to buckling because of their stout, hockey-puck-like proportions–“E” is really simple to measure if you have an accurate enough rig.
Or a squishy enough material. If you’re trying to do deflection calculations on steel, you’re dealing with a Young’s Modulus of something like 29,000,000psi. Here at Big State U., we do not have testing rigs in the Architecture department that can impart millions of pounds of pressure, so we have to scale things down. As it happens, there’s a very convenient kitchen staple that can put us in the desktop range of deflections and loads quite easily:
Jello’s natural squishiness (or, in technical terms, very low Modulus of Elasticity) means that it deflects enough to assess with a tape measure and some light weights. We fabricated columns with various concentrations of gelatin (Disclaimer: actual Jell-O is engineered for a much softer mouthfeel, making for an unworkable column, so we switched it up and went with Knox unflavored gelatin instead), all using high-tech formwork (yogurt tubs with the surfaces oiled for easy removal) that produced nice round columns of equal diameter:
To test them, we simply placed one-pound (ish) cans on a bearing plate that let us measure the height of the columns before and after loading. Adding weights one at a time let us plot a rudimentary stress/strain curve. In an ideal world, the slope of that curve is equal to the Modulus of Elasticity, and a simple calculation lets us put a number to that figure.
And, of course, we loaded them to failure, giving us a yield stress that marks the top of the curve:
Depending on the quantity of gelatin in the column, we got Modulus of Elasticity figures ranging from .8 psito 5.4 psi*, but the shape of the curve was interesting–those figures were the average of a slope that changes from a shallow slope to a steeper one. What that means is that the columns deformed more under the initial load, and underwent some kind of “strain-hardening” as loads increased–they got stiffer under higher loads. We hypothesized that this was due to the colloid nature of the gelatin, since the initial loading pressed excess water out of the material. As that water was pressed out, the material consolidated a bit and got tougher to compress. Further research may be necessary.
Doubling the quantity of gelatin made for a pretty stiff column (relatively speaking), but also a strong one–in addition to deflecting the least, it held the final test weight of 15 pounds without failing. Generic blueberry “gelatin dessert” didn’t do much as an additive, as you can see on the right.
All good fun, but with a point. The math behind our most common structural situations can get pretty simple, and the same forces that govern our largest structures can be observed and played around with at any scale. Similarly, we’re able to change any number of variables when we’re building–shape, scale, and material–but we only know how those changes impact what we’re trying to do by testing them out. And, finally, we’re firm believers that while knowledge can come out of textbooks and formulae, wisdom only comes out of taking those ideas into the real world and seeing where they work and what their limitations are. Hoping to take those principles into our weekly Friday sessions each week this semester…
*When we first thought of jell-o columns we were convinced it was an original idea, but a quick online literature search turns up numerous other efforts at determining the material properties of gelatinous desserts. We’re pleased to report that our measurements support conclusions reached by other squishy-column researchers…we stand on the shoulders of giants, etc., etc.