What Engineering Is Not, Part 2

Mathematics. Engineering is not math* and engineers are not mathematicians. This may seem obvious, but it’s surprising how many people don’t get it.

Math has complete answers. Math has proofs, which use logic to show that something is the way it is because it must be that way. It is beautiful and it is difficult, and even when it allows for randomness it has rigor in the way it defines answers. Probability and statistics are branches of math that deal with uncertainty, and they do so in a certain and predictable way, which is fantastic. Engineering is different.

Engineering gives up that beautiful certainty in order to make room for design. Rather than revealing a natural underlying order** we create our own artificial schemes. It’s a different result created by a different set of tools and, most importantly, a different mindset. We do not deal in certainty. You can design a building exactly to code and it will fail under foreseeable circumstances.***

So far, this is all vague and is an intro to what I really want to discuss: the difficult part of engineering analysis and design doesn’t involve numbers at all. The thing that we have to get right is the conception of a structure: we have to know the load paths, we have to know the structural mechanisms**** that come into play, and we have to know what the boundary conditions are. The last is critical: what’s free to move and what’s not? What movement is expected? Is a footing resting on soil that moves under load or rock that’s relatively inflexible? Where’s the stiffness in the structure, since that’s where the load will collect?

I recently was in a conversation with a well-educated engineer who stated that, first, he “didn’t believe in empirical analysis” and, second, that he “couldn’t say a structure was safe unless he ran numbers on it.” He obviously believed engineering to be applied physics or applied math, where you use calculation to achieve certainty. He is wrong. All of structural engineering rests on an empirical base, which is why the loads and allowable stresses we use are occasionally revised. Empirical analysis and empirical design are written into the codes; anyone who has heard of buildings being red-tagged or green-tagged after a disaster has heard about empirical analysis in action, as the analysis of hundreds or thousands of buildings in days depends on empirical analysis. If you know that a loaded beam deflects and you see minimal deflection in a beam, then you know that beam is minimally loaded. That’s an empirical observation and it is as true as any calculation I’ve ever performed. Empirical design is a perfectly legitimate way to approach many engineering problems.

If I state that brittle materials crack and that, logically, a wall made of brittle masonry and plaster cannot have moved much recently because it is uncracked, I am not relying on calculation in any way. I am relying on the concepts of brittleness versus ductility, of the inescapable link between stress and strain, and of tracing load paths within a structure. That’s engineering.

* “Maths” for speakers of non-American English.

** This is not to say that mathematicians aren’t creative or don’t invent. They are and they do. Their creativity is in the realm of the tools they use to examine the underlying natural order and in the use of that order.

*** A storm may have winds that exceed the values in the codes and and an earthquake may have ground movement that exceeds the values in the codes. The values in the codes are based on the probability of those events occurring so that we don’t have to design for everything that is physically possible.

**** Here’s an example: is a lintel in a masonry wall an arch or a beam? Both are legitimate structural mechanisms to carry load over the opening, but they have different strengths, different support requirements, and will act differently when loaded. This is also a trick example, as the sometimes a lintel is both.