The way you frame and support your containers will depend on what you are using. I made mine with steel because it is cheap and strong and easy to work with, if you have the right tools. Many people use wood, such as common studs of 2×4’s. I will outline what I did below but please add any ideas. The important thing to remember is that water weighs 10 lbs a gallon, so a 55 gallon drum could weigh as much as 500 lbs!!
Check out “Barrelponics” on the web… the author has put together a VERY detailed and comprehensive guide for using barrels in aquaponics. The section on framing and using 2″x4″s to support the system is very good. Here is a link to the PDF