Thank you for bringing up the Tacoma Narrows Bridge, Phil, as it is an excellent illustration of what I'm trying to convey about the importance of real empirical data and not just mathematics in engineering.
The original Tacoma Narrows design was reviewed and revised by the same man who designed the Golden Gate bridge, Leon Moisseiff. He designed or collaborated on many other designs at the time, and was considered the leading suspension bridge designer of his day. All of these bridges were designed using the same math that had always worked before.
Unfortunately, in the Tacoma Narrows case, they discovered a new phenomenon that had not been seen before and was not covered in their textbook mathematics of the time. There was no error in Moisheff's calculations, the mathematical models of the day just didn't account for the full physics of what happened because they weren't known. Moisheff had been designing bridges for 20 years at this point.
It is interesting to note that the disasterous oscillations resulting in the bridge's demise were easily detected even during construction of the bridge:
http://www.nwrain.com/~newtsuit/reco...narrows/gg.htm
The bridge was in fact nicknamed "Galloping Gertie" because of these oscillations long before it collapsed. The bridge was in use for four months with oscillations so bad that people of the day made a sport of watching cars appear and disappear as the bridge rocked up and down. As the article notes, several means of strengthening the bridge against these oscillations were tried to no avail.
This was not a case of "under engineering" or going off half cocked, it was a case that the engineering science of the day didn't understand or account for the phenomenon at all. As your link concludes, Phil:
"this bridge disaster still has people talking, well arguing really, as physicists and mathematicians argue about the true reason that the bridge collapsed."
A little more ability to gather and act on experimental data and a little less over confidence in the mathematical models and reputations of the engineers involved safe and sound in their offices might have prevented the disaster.
Pull the pin, watch what happens, if your bridge starts to oscillate, put it back. Phil, you leave your pin in. You've got more engineering calculations to do before you're ready to pull it.
Sincerely,
BW