Monthly Mechanics: Risk

Rosencrantz and Guildenstern Are Dead, a play by Tom Stoppard, opens with a scene in which the protagonists flip a fair coin 80-something times, and the coin comes up heads every time. I like this scene because it illustrates one of the tenets of engineering: the difference between improbable and impossible. A coin coming up heads 80 times in a row is like an 8.0-magnitude earthquake striking Vermont: it’s not impossible, but it’s sufficiently improbable that you can safely ignore the possibility.

No matter how well a structure is built, it cannot last forever. Every building, every bridge, every dam, every tunnel has a risk of failure, and it’s the job of the engineer to make that risk sufficiently small that it can be ignored. Armed with a couple centuries of reliable atmospheric and seismic data, engineers today have a better understanding of risk than ever before.

People sometimes ask me if there are any bridges that I’m afraid to drive on. The answer is no. All bridges in the US are inspected regularly, and they’re closed for repairs or posted for load limits before any risk of failure becomes probable. For some perspective, over the last decade, bridge failures killed 14 people in this country. In the same ten years, drunk driving incidents killed over 100,000 – an average of 27 people every day. When you are on the road, the biggest threat to your well-being by far is the motorists around you. (Fortunately, Google X and Tesla are working on this.)

Another risk-related question structural engineers often field is, “What is the factor of safety?” Answer: it’s complicated. To begin with, structures are complex arrangements of materials. A bridge might have concrete abutments, elastomeric rubber bearings, steel stringers, and a composite deck. The loads on each component are different, and may include self weight, live loads, snow, wind, earth pressure, seismic, and impact forces.

It’s too conservative to add together these forces as if they all occur simultaneously (for example, a bridge is unlikely to be loaded curb-to-curb with heavy trucks when it’s also under two feet of snow), so instead engineers compare numerous load combinations. I might multiply the dead load by 1.2 and the live load by 1.6, which certainly changes the safety factor, though it’s not clear by how much.

Safety is also built into the strength of materials. Engineers might specify a minimum compressive strength for concrete, say 4000 psi. But concrete continues to cure – and strengthen – many years after it’s placed. (It’s said the concrete in the Hoover Dam, placed in the 1930s, is still cooling off.) Moreover, contractors often need to provide test samples of their concrete mix, and if failing the test means delaying the project then they’ll err on the side of caution. Thus, the actual strength of most materials is far greater than the engineers assume for their calculations.

The safety factor is complicated, but it’s high enough to keep risk small. So, to quote another piece of literature that explores extreme improbability: Don’t panic!

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