As usual, click any photo to bring up a larger version.
Here are two common spindles. These are a pair of standard spindles found in houses just like mine all over the place. They are used on a staircase, under the railing, or along the edge of a mezzanine, or somewhere similar.
One spindle is broken, one is not...
Yet just a short time prior to this photo, both spindles were broken in a similar way. It doesn't take much to break one. At their narrowest point, the spindles are less than an inch thick.
The good news is that repairing a broken spindle can be accomplished fairly quickly without too much grief. All you need is an appropriately sized section of hardwood dowel, a drill press, and a forstner bit. I used 5/8" diameter maple dowel, which is about 1/8-3/16" skinnier than the narrow part of the spindle at the break. I cut a 2" section of dowel, and then sanded the ends to just round them over a bit. I recommend making a test hole in some scrap, to make sure that your dowel and your forstner bit are well matched in size.
Next, turn your attention to the broken spindle. The first step is to cut away some of the rough edges at the break. We've broken four or five spindles in my house over the past 10 years, and most seem to break pretty cleanly at the skinniest spot. Just trim the bare wood pieces, do not cut away at the stained areas. You don't want to shorten the spindle!
Mount the broken piece in your drill press and get it lined up with your forstner bit. As you'll see in the photo, you need a fair bit of height for this operation. It might be tricky to manage this with a benchtop drillpress.
Carefully drill a hole in the end of each spindle. Each hole needs to be at least an inch deep, to accommodate a 2" dowel. I recommend allowing 1/4" extra depth, for glue space.
Unfortunately, I missed taking a picture of the holes, or the test fit with the piece of dowel.
Wipe some glue inside each hole and on the dowel, and then slide the two pieces together. I recommend clamping the spindle along the edge of your bench. In that way you can make sure that the repaired spindle is straight!
A little touch up with sand paper and a dab or two of stain, and this repair will virtually disappear from view.
Here is a close-up of a broken spindle and a repaired spindle.