# The engineer who designed the Genoa bridge that collapsed and killed forty-three people warned of its corrosion risk thirty-nine years ago

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1. UserFriendlyRobot
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Since I'm bored and you mentioned capitalism, let's do a calculation on how long a bridge needs to last unmaintained in order for it to make economic sense to not maintain our bridges by doing...

Since I'm bored and you mentioned capitalism, let's do a calculation on how long a bridge needs to last unmaintained in order for it to make economic sense to not maintain our bridges by doing Fermi approximations. Suppose the bridge is built at time 0, you spend X on building the bridge and Y per year on maintenance.

Now if the bridge is unmaintained for a period of time T1 until that bridge collapsed, that is a cost of only X over T1, and you would have to build a new bridge after T1 which would last presumably around the same time as T1. Now if you were to maintain that bridge and maintenance over T1 costs Y * T1, it would cost you X+Y*T1 over T1 but you wont have to build a new bridge. So at a certain T1, Y * T1 = X, at which point it costs the same to maintain a bridge or leave it unmaintained, let it break and build a new one.

But wait, what about all the destruction that is caused by the bridge collapsing? Let's call the economic damage of a bridge collapsing D, and let's assume our regulators are reasonable and will impose this cost on the bridging agency. At this, for it to make sense to leave a bridge unmaintained X + D < Y * T1. So if we have X, D, and Y we can find out the amount of time a bridge needs to stay up unmaintained for it to be profitable.

To get a real sense of how much this is, according to this paper (http://www.iti.northwestern.edu/publications/utc/tea-21/FR-4-6-Krizek.pdf) in figure 4, around 50 years of maintenance will cost the same as the initial construction (T1 at which point X = Y * T1). According to Google a bridge will cost \$10000 per sq meter to build (http://www.partnershipborderstudy.com/pdf/Suspension%20Bridge_2.pdf) and according to the measure function on google maps, the Golden Gate bridge is 100,000 square meters, so that's about \$1b for the initial construction cost of the bridge (this is an order of magnitude approximation on "average", the actual number is \$1.5b which is pretty close, this is X). Given that maintenance cost per year of that bridge is the initial construction divided by 50 years, we arrive at 20 million dollars per year (the actual non-approximated value is \$37m which also is pretty close, this is Y).

To find D, I counted 30 cars and 1 bus on 1 quarter of the Golden Gate bridge in Google Satellite view, so that's just say the bridge at any time carries on average 200 people. Averaging these people's current age at 40 and a life expectancy of 80, their lifetime domestic product lost (total economic damage) is 200 * 40 * 60000 (gdp per capital of the US) which is \$480 million dollars (this is D)

So we profitability if T1 > (X + D)/Y, which is (\$1b + \$0.5b)/(\$20m per year) which is 75 years. An unmaintained bridge will be profitable if it can support itself unmaintained for 75 years. I forgot the point I was trying to make, I've completely spaced out by this point, anyways kthxbai.

Edit: I momentarily regained lucidity and remembered the point I was trying to make: capitalism dictates that you should maintain your bridges, but people are either too short sighted or susceptible to short term gains to see the long picture. No one is going to string up a politician or company for failing to repair a bridge if it works just fine every day. But people will string you up if you fail to report profits or cut taxes for them. So we end up in a situation where you take a low risk of ending your career drastically (bridge fails) in order to advance it incrementally (more earnings/cut taxes).