`Roman aqueducts`

Brief contrast — pre-beam-theory construction relied on safety factors of five-to-ten because brittle materials (stone, brick) could not be sized to calculation. Roman aqueducts cited as the canonical example of this oversized-for-safety regime. ## Figures referenced (not cases)

What they knew from the 1850s, 60s, and 70s is, you could measure the force of fracture of a bar of steel, and that would allow you to calculate — because they had developed beam theory — how strong something would be. That way you could size the parts, rather than just making things ten times larger than they needed to be, which is what they did out of stone and brick — the cathedrals and the Roman aqueducts. They actually could calculate to use the least amount of material. They still had safety factors of five and ten because cast iron was sort of brittle, and they knew that.