The reason why the Tacoma Narrows bridge collapsed was due to the frequencies of resonance. The wind traveling at 40 miles per hour coincided with the frequencies of the steel bridge. Which made it swing like a hammock, and eventually the steel gave in.
The length of the bridge had a lot to do with the collapse, because the longer any material is extended, the less resistant it becomes. Eventually with age, the own item's weight will cause the item to give in. Specially an item susceptible to vibration.
When the collapse of the bridge happened, it opened a lot of windows of knowledge to many scientists; to understand the way an object subject to vibration could be affected depending on temperature, movement, wind, and other atmospheric conditions.
Nevertheless, only a highly scientific person can understand a considerable amount of the reasons why the bridge collapsed. It is one of the reasons why nobody expected the bridge to collapse in the first place. Never before had anyone built a bridge a mile long span, over a body of water with capability of changes in wind speed the way the Tacoma Narrows Puget Sound has.
For a more detailed scientific explanation please visit this page: http://www.generalresonance.com/science/index.php5