I am designing 2ft x 6ft planter boxes to be set on concrete. I'd rather not have to install a bottom. Could drainage be provided by using 1 inch PVC pipe with multiple holes drilled in them lengthwise in the bottom? Maybe use some weed barrier fabric over the pipe to prevent dirt from clogging?
It sort of depends on what you want to grow in there and if your plants are susceptible to root rot or not. I do have a hard time envisioning what the pvc pipe with holes would look like for drainage, so providing a picture would help! But I have done experiments with having large solid rocks in the bottom so the water can drain and go between the rocks so you could try that as an easy and cheap option.
You can find 4" PVC pipe with holes drilled in it already at hardware stores in the drainage area. If you layer landscape fabric or geotextile fabric over it that should allow water to drain.
There are some "buts" that go with this. If the concrete slab does not have any slope which is typical then the water will not drain anywhere. By the time water has gone through soil it will pick up dissolved salts and then having it sit on concrete could cause discoloring or spalling like you see on a garage floor. Depending on the type of winters you have you could find yourself doing concrete repair a few years from now.