I am currently fixing a house and it has a beam run down the center of the house with steel support columns. Some of them are just wood resting on stone (old house) and some are steel. At some point I am thinking that one was removed because the beam has a dip in it. Right now I am wanting to replace all the columns with new ones but I wanted to pour footings for them. Anybody got any advice on what size sono tubes I should use and if I should dig down far enough to pour an actual footing for the poured sono tube concrete to sit on? I was planning on using 10" tubes with 4-6" of gravel tamped in a 3' hole. The beam is 6x8 and spans approximately 20'.

If this is a basement you're referring to, there is no need to dig deep footings, and even without looking at your house, I can tell you that 10-inch diameter footings will be insufficient. There is no reason to place gravel under the footings; they should bear on undisturbed soil.

In order to properly size the footings, you need to know exactly how much load is on each column, and you need to have some idea of the soil conditions that the footings will rest on. Determining the loads is a job for a professional, so I suggest you enlist the aid of a competent architect or a structural engineer to do so.

Column footings tend to be square, with a thickness of half the width. As a minimum, basement footings are usually 24 inches by 24 inches by 12 inches thick, and their tops are usually set eight inches below the basement floor level. Depending on the spans of your girder and the loads on each footing, your columns could require larger footings. Be sure to coat the steel columns with bituminous material such as that used for dampproofing where they are below floor level. Do it right and get some help.