Observed rotation rates of small asteroids [point to a limit](https://physics.stackexchange.com/questions/26476/can-a-minimum-ultimate-tensile-strength-uts-for-an-asteroid-be-established-bas) on the material strength of these bodies. This limit is not very high

But that's only part of the picture, because an upper limit on rotation rate only tells you about the *global mechanics* of the body. There's also the question of whether we expect collisions to cause high rotation rates which stress the bodies in the first place.

Given the fact that we have direct observations of asteroid material (falling from the sky all the time), what material quality could we expect? It's simple to look up [values for ordinary Earth rocks](http://www.stanford.edu/~tyzhu/Documents/Some%20Useful%20Numbers.pdf). Compare the two, there is 3 orders of magnitude difference.

* Asteroid rotation rate based limit: 20 kPa
* Granite, Basalt, Quartzite, etc tensile strength: around 20 MPa

The most obvious use of asteroids seems like it could be cutting it into beams, and using those for station construction, like what we do with certain kinds of lumber or granite counter-tops on Earth. If we did that, would these materials be worth a darn? Do we have a measured range of asteroid material strengths? Would the rock be too fragmented to use? 

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Also note that the target for [NASA's Asteroid Redirect Initiative](http://www.youtube.com/watch?v=rzOHVQA4dqA) is intended to be soft rock. This eliminates some dangers of losing its (unstable) orbital location and falling to Earth, although I do not know if it's the reason for the requirement.