Engineering is a game of optimization under constraints. Problems are never just “design a beam that can span a hundred feet“, but “design a beam that can span a hundred feet, is made of concrete, weighs less than 40 tons, and is less than five feet tall.” Or, more likely, “design a beam that can span a hundred feet as cheaply as possible”. Problems with only one requirement are easy to solve – it’s the ones with multiple, sometimes conflicting requirements that require clever solutions.
One of the most important of these requirements is “…and design it using only these tools“. This isn’t something that shows up in the design contract, but it’s a necessary reality. The tools humans have invented so far, be they wrenches or word-processors, are a limited subset of what’s theoretically possible to accomplish. And the tools any given engineer will have available are a limited subset of that. Much like MacGyver, we can’t solve engineering problems any way we’d like. We have to use whatever junk happens to be lying around.
What this often means is that the problem we have and the problem we can solve are different. Thus, an important engineering skill is the ability to find a relationship between the two. It’s often necessary to fit a round problem into a square tool.
Here’s a simple, but real-world example. I need to design the basement wall of a building. I know it’ll be made of concrete, but I need to decide how thick it needs to be and how much steel to put in it.
I have a variety of tools I could use to solve this problem (including simply cranking out the calculations by hand), but the one I want to use is Enercalc. Enercalc is sort of an engineering swiss army knife, with a variety of calculation modules that can solve a broad swath of problems. One of the modules is a concrete wall designer, which sounds like it will work perfectly.
However, there’s a snag. This wall is holding back soil, which puts a triangular load onto it. And Enercalc, in it’s majestic and far-seeing wisdom, doesn’t allow you to input a triangular load onto a wall like this – it only allows uniform loads. What to do?
At this point I have a problem I want to solve – the design of a concrete section with a triangular soil load. And I have a problem I can solve – the design of a concrete section with a uniform soil load. All I need to do is figure out the relationship between the two. Fortunately, there are well-known formulas for the forces on a beam in various loading and support conditions. Manipulating them lets me find the uniform load that will have the same maximum moment as the triangular load I have.* I simply input this load into Enercalc, and bingo – it spits out the correct wall design in no time at all.
Thinking about the problem you have vs. the problem you can solve doesn’t necessarily let you solve problems you otherwise couldn’t. But it will almost always let you solve a problem faster than you otherwise could. If I stubbornly insisted on designing the wall by hand, it probably would have taken five times as long.
*Due to the nature of the support conditions, the maximum shear will be different.