This video shows you how to repair everything, but without all the written instructions included in the steps below.
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Step 1: How to Repair a Cracked / Broken, Bucket or Trash Can
If you have a broken and cracked bottom on a plastic trash can, large or small bucket, it's easily repaired in just a few steps.
Step 2: Structural Fix
Because the plastic has lost its strength, it now needs to be reinforced. Find a piece of scrap plywood around the garage, or go to a home store and buy one. The only requirements to keep in mind is that it must be as wide as the bucket is at it's widest point. I recommend at least 1/2" thick plywood, but 3/4" will work too. Measure the diameter of the bucket and then mark this out on your plywood. Find the middle of this length and mark that too. I used a scrap metal bracket, a nail and a pencil to draw out the circumference, by tracing it out. Push the nail through a hole in the bracket to hold it on the middle point you measured. Put the pencil against the bracket where it meets up with the edge of the diameter and then just swing the bracket around in a circle, tracing it out with the pencil.
Step 3: Cut It Out.
I used a band saw to cut out the shape of the circle, but you can also use a jig saw or hand saw as well. Because the bottom of the bucket is curved, it's a good idea to trim off the bottom edge of the wooden circle at a 45 degree angle. This will allow it to seat snuggly in the bucket. If you can't do this with a saw, some low grit sand paper 40 - 80 or even a wood rasp are good alternatives (they will take longer, but still do a good job).
Sand both sides of the wooden disc to make sure it's smooth and there are no sharp bits sticking up. You should also sand the sides for the same reason. Once smooth, choose which side is the bottom and apply glue all over. I used E6000 glue because it's good for all materials and is a flexible glue, which means it will give a little as the bucket flexes, without breaking. Press the disc into the bucket with both hands, you can even get inside and stand on it for extra pressure.
Step 5: Flip It
Find a smaller diameter object, like a trash can to use as a brace. Flip the bucket over on top of the can so it will prevent the wooden disc from falling out and allow you to apply pressure from the opposite side.
Step 6: Screw the Bottom
Find screws that are shorter than the thickness of the plywood you used. This is important to prevent them from poking through into the bottom of the inside of the bucket. Find a drill bit that is smaller in diameter than the screws (so the threads have something to grab on to) and drill holes around all the cracked parts of the bottom. Screw everything down until it looks flat and secure. Use as many screws as you feel is necessary.
Step 7: Secure the Sides
Now use longer screw for the sides. Drill holes all the way around the bucket, into the sides of the plywood disc. Space them out around every 3 inches. Screw in all your screws to give the bucket added strength from the unbroken sidewalls.
Step 8: You're Done!
You can now fill up the bucket with whatever you want! I needed it for wood scraps in the shop. The wood bottom actually makes it stronger than it was brand new, so it will give you plenty more years of service.