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I'm a structural engineer. I wasn't going to say anything, but I feel there's some facts, figures, and equations getting thrown around here that are all getting quoted out of context. I'm not saying they're entirely incorrect, just that you need to look at the big picture rather than get caught up in detailed formulae[1].
Yes, Young's Modulus (or the Modulus of Elasticity "E") of steel is higher than concrete. More like 5 times higher, not 10, but that's neither here nor there. However it's almost irrelevant unless you're comparing a steel hollow tube with a concrete hollow tube, or a concrete solid column with a solid steel column, and both are the same size and height. Reason is that shape, size, and height also affects stiffness, and to a much higher degree than Young's Modulus alone.
Yes, wall thickness is a factor too. A thicker walled tube will be stiffer than one of the same outside diameter, same shape, same material, same height, but thinner walls. But change any one of those other properties and things change and you're comparing apples and oranges all of a sudden.
Concrete versus steel? I reckon it's more about what you have readily available or have more experience with rather than it's structural performance. Each will work adequately.
Other factors to consider would be what are your ground conditions - sand, clay, gravel? If loose sand or gravel, you'd be best going with a pad footing. If any clay and the sides will stand up, I'd go with a piled footing.
If it was me building a permanent pier, I think I'd go with casting hold-down bolts into a piled footing, then bolt down a steel pier. Reason is you can adjust any out of vertical in the pier, and remove the pier if you ever move so you can just lay a new footing at the next house. But then, I have access to local steel fabricators and would know exactly what I want and how to specify it. If it's exposed to the weather, make sure bolts and pier is galvanised or you use a very, very good paint.
You might prefer to just buy some PVC tube as formwork for the pier, some stock lengths of reinforcement, and pour concrete yourself.
What sized pier would I use? Depends on what you're going to throw on it. Now and in the future. It's too hard to calculate exactly what sized pier to use. Too many variables for precise equations to be worth it. I'd just pick a size by feel, and then maybe double it. Sorry if it sounds vague.
[1] Take care if you decide to go against my advice and try to use that formula rally posted above. The formula itself is correct, although what it calculates is the deflection of a cantilever under a point load - like how much a diving board would deflect down from horizontal if you were standing on the end of it. Not sure it's relevant for what you're trying to achieve. I suspect rally was quoting it to point out the effects of size and shape rather than use it to help you size your pier. I also suspect there's something off in the numbers he quoted for E of conc and steel - looks like one is metric and one is empirical and you shouldn't try to mix and match those.
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