The most common failure points on an umbrella are the little rivets holding the component parts of the stretchers together. All you need, to fix the stretchers, is some wire, a pair of scissors and a sailing knot.
This is my second mend it instructable. As last time, I mended something and then thought, 'I should make that into an instructable.' So, here is a retrospective look at what I did...
You can see other green things I do at http://www.ecopunk.org.uk
Step 1: "Ingredients"
You will also need a pair of scissors.