If you understand anything about materials properties, try not to roll your eyes at this breathless NBC Nightly News video showing time lapse photography of the Manhattan Bridge flexing under the load of a train.
To the layman, the idea of a bridge flexing is certainly terrifying. Bridges are supposed to be strong, symbols of rigidity, unwavering under the highest of loads. Well, yes, but in order to do that, they have to be flexible. There's an interesting correlation between durability and flexibility. The more rigid a structure, the more susceptible it is to stress fractures, and over repeated duty cycling (like running a train over a bridge) a rigid structure will eventually fail catastrophically because of the inherently brittle nature of rigid structure.
Conversely, flexible structures are much more able to deal with repeated loading, and over the life of a structure, the likelihood of catastrophic failure is significantly lower than a rigid structures, instead, a predictable creep will stretch the structure over time. Think of it this way, take a cheap-o pen made out of plastic and an expensive fancy one made out of rigid lacquer, bend the lacquer pen and it's going to break on the first try, bend the plastic one and it'll give, then return to shape, no worse for the wear. The same holds true for iron girders and steel cables, only we're not used to seeing those kinds of things bend and flex.
So for you New Yorkers apparently scared of taking the Manhattan bridge, relax. The video of the bridge flexing under the load of a train is proof it's working properly. If it wasn't bending like you see in the video, you'd have to worry about it randomly shattering instead of sagging under a load. So look at this video as a tribute to engineering rather than the latest sensationalistic lunacy to be irrationally afraid of.