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Tubes don’t fail suddenly
The downtube of my Holdsworth definitely did. Was completely unannounced, nothing visually or audibly giving warning. I have the picture somewhere. Clean snap, not hidden under the shifter's collar, but beyond. There was hardly any rust inside the tube... The head tube isn't short either, frame is a 59cm ctc.
I'm not saying it always happens like this though...
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If you look at my post #19 in this thread you will see another old and broken frame.
https://www.lfgss.com/conversations/246092/#comment14256079
Since writing the description of this failure I've heard that breakages at this point are not that rare when the bottom head lug has a straight edge (as this one did) where the down tube goes into the lug.
I'm reluctant to believe that old frames are a serious health hazard - even though I have suffered another potentially more dangerous breakage. Cycling is always going to be a bit risky, but the most serious danger by far comes from motorised road users. Although old frames do fail occasionally, so do new ones. The worst injury I've heard of was caused by a broken handlebar stem, but that was relatively new.
I think the most important component to check are the forks, anything even slightly suspicious and they should not be used.
BTW I am touching wood as I write this!
Tubes don’t fail suddenly, they will always fatigue fracture so you’ll get notice as long as you’re aware and keeping an eye. A key thing you can do is avoid bikes with short head tubes because the bending load on the downtube is far reduced with a longer head tube.