If a satellite in low-earth orbit has a cross-section of 10 meters, then the timescale for hitting the space elevator is about 300 years.
Given that there are about 3600 satellites in orbit (http://en.wikipedia.org/wiki/Satellite), a satellite would crash into the space elevator about once a month.
Let's do a back of the envelope calculation: https://www.google.com/search?q=(pi%20*%20(radius%20of%20the...
If a satellite in low-earth orbit has a cross-section of 10 meters, then the timescale for hitting the space elevator is about 300 years.
Given that there are about 3600 satellites in orbit (http://en.wikipedia.org/wiki/Satellite), a satellite would crash into the space elevator about once a month.