Had exactly the same break a couple of weeks ago. Fixed with Gorilla Super Glue, which unlike most variations of super glue is a gel, so it gives you a little more time to manipulate the parts before it sets and it doesn't flow where you don't want it. After the glue dried I wrapped a couple of layers of electrical tape for additional support and because my frames are black it's hardly even noticeable. In fact, since I'm looking at them now I've noticed that the tape is only on the arm and not on the hinge, so it's doing nothing for me and I'm going to take it off.
Gorilla Super glue it is then!
A. It has been shown to work
B. It is available quite cheaply
C. It is so Super they had to include it in the name
D. Gorillas are frickin' cool (nearly as cool as Orangutans but not quite (because not orange)).
So in short, unless there is an Orangutan Super Glue out there I will get some Gorilla Super Glue. Thanks Al-Kizzle 
And I only know of a Gorilla wrecking Skyscrapers, but none running a whole library, so Orangutans are WAY cooler!