The Brooklyn Bridge is the ultimate example of over-engineering to compensate for lack of good theory/modeling. It is both a cable-stayed bridge and a suspension bridge, each system of which is independently capable of carrying the entire load of the bridge. And it's also a truss bridge, though that system alone won't hold up its entire deck.

Modern calculations are usually multiplied with several 'security factors'[0], anywhere between 1,1 and 1,5 as far as I can remember now (at least in Germany through a DIN [norm], and now Europe-wide via EN). These design factors come in at many different stages of the calculations, from materials to static load distribution (not sure if these are the correct terms in English)

[0] https://en.wikipedia.org/wiki/Factor_of_safety

Well, it is not like "earlier calculations" didn't take into account such safety factors, but the debate is not about existance of safety factors or their amplitude (1.3 to 1.5 has been used as far as I can remember in concrete constructions) but rather on redundancy.

To give a different example elevators/lift (those using rope cables) have usually cables that have a factor of safety 5, but they have nonetherless additionally at least one set of independent brakes.

Back to bridges and more generally reinforced/pre-stressed concrete structures, in my experience modern methods of calculation are more precise than old ones, and allow usually - given the same loads/hypothesis - to save (i.e. there is less rebar steel and cable steel) between 5% and 10% steel and/or concrete.

In practice with old methods of calculation there was a 1.05/1.10 "implied" and "hidden" additional safety factor.

This is not so much a matter of safety factor than redundancy.

Safety factor = "it only fails if the bridge is full of heavy trucks and they all are overloaded 2X"

Redundancy = "we have 6 stays and any single one can snap and the bridge will stay intact"

Airplane wings cant have either. Because safety factor higher than 1,2 would make the plane too heavy to fly. And redundancy from multiple wings would make the system aerodynamically so unstable that snapping a single wing would still cause a crash.

In those cases you need to have very good testing program before installing the structure. And then you need a good inspection program to protect against fatigue and corrosion. The latter was missing in this case.

Better understanding of materials, and better recognition that “once in a century” events do happen.

The once in a century thing is much less troubling than say one failure cascading into multiple catastrophic failures.

Once-in-a-century actually means 1% chance per year. If you build thousands of bridges, you need a lot better than once-in-a-century, or you will have adverse events all the time.

I would think that depends on what kind of once-in-a-century events you’re talking about. If it is a big earthquake, chances are that, if one strikes one bridge, several others will be hit on the same day. You could have adverse events ‘only’ about every 50 years, but lose half your bridges on such days.

Isn’t that affected by age and maintenance, rather than randomness? For sure bridges have finite useful lifespans, so we know in advance they need to be rebuilt or retired.

No. You can (in theory) design a bridge so that it is strong enough to withstand a 1000 year event and has a life expectancy or a single day.

An engineer may say things like “if you build it this way, do this maintenance, it will withstand 100 year events for its service life of 50 years”

You see that (in a slightly different form) with storage media. A SSD drive with a mean time between failures of a million hours typically will have an life expectancy that is significantly shorter (https://www.controleng.com/single-article/learn-or-review-th...)

Earthquakes and other natural disasters follow a random distribution over time.

I don't think an assumption of uniform random distribution is fair.

They didn’t have the capability of the time to do cascading failure analysis of that type.