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Im not hugely experienced, im sure @coldharbour or @skant can give you a more comprehensive answer, but afaik tube stiffness is relative to diameter more than material. So oversize tubing will build a stiffer frame. It is certainly noticeable. I just built a frame with a 38mm dt. Compared to the frame i built prior to this with a 31.8mm down tube it is much stiffer.
Biggles567-
All steel alloys are essentially the same stiffness, its wall thickness and diameter that makes the difference, and wall thickness is much of a muchness with above mentioned tubes. It is perfcetly possible to build a bike that is far too stiff from tubes available to us today, dependent on compnent choice. However, with the availability of good quality higher volume tyres, the definition of too stiff has moved. A 54cm frame, with 44mm dt, 31.8st and tt, 18ss and 17x30cs will be (ive tried it) unbearable on 28c tyres at 100psi, to the point that I wouldnt want to ride for more than a few hours, but will be amazing as far as power transfer is concerned. However, the same tubeset built around maybe 40c's, or even 650b x 48 tyres at low pressures, will be perfectly comfortable for a long time in the saddle, while still very stiff (once tyre squirm point has been passed). The biggest thing to effect frame design in the last ten years (in my opinion) is tyres. People like to make a lot of noise about tubes, but the reason we choose specific ones is nothing to do with shape or alloy, but but length, wall thickness, shape and how hard they are.
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Question for all you frame builders. I'm thinking about getting a custom steel frame built up as a kind of midlife crisis treat, and having being doing a bit or research into builders etc. My question is, what is going to build a stiffer frame- 853 or 853 oversized tubing, Columbus spirit (oversized?) or something with a stainless rear triangle/forks like Columbus XCR? The frame will mostly be used on roads, with maybe a teeny bit of rough off road type cycle tracks etc, but I like something with a bit of stiffness for when I feel like putting my foot down. (that said I am really only comparing this to my old 531 frame sets built with differing widths of chainstay/seatstay tube etc.)
Basically, I can really only afford a custom frame if it's not including XCR or other stainless, but maybe able to afford something more of the peg with some stainless rear traiangle or something, at a push....)