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I have an old (80's I guess) road bike, it is heavy, I'd like to make lighter. is it posible to cut and replace the tubes on the frame by welding aluminum ones?

I would not. Instead I'd strongly recommend you look at buying the bike you want rather than chopping up a working vintage bike. At best you'll come out with something worse than a replacement aluminium road bike, and perhaps slightly better or worse than the bike with which you started.

A used 2000's bike would be a far better bike than some chopped-up monster, and then you have N+1.

Steel and aluminium are dissimilar metals and welding is not possible. You'd be looking at brazing them. If you expected to weld them, then perhaps this is beyond your welding skill level.

If you are paying someone commercially to do the welding, then they will braze or silver solder the work. Check for what their workmanship guarantee is as well.

You will have to paint the whole frame properly afterwards too, the steel parts need protection.

There is a lot more to a bike frame than just weight. If there is one thing early aluminum frames taught us is that straight gauge aluminum rides harsh! Modern aluminum frames typically employ hydroforming to tailor the compliance and ride characteristics of the frame. This is why modern aluminum bikes ride a lot better than 90’s aluminum frames which were often too stiff. You will likely be stuck with overly stiff straight gauge tubes and a harsh ride if you are able to get it to work.

Even if you successfully execute this frame chop up (Criggie’s answer overviews some of the issues - although I assume you would need to bond the tubes), I suspect the Frankenstein frame would have much worse handling as it will be difficult to keep the frame the geometry in check. In all likelihood I suspect some frame dimension will be altered and handling will suffer as a result.

If the only reason you are doing this is to save weight, there are a lot of better options, including selling and buying a used aluminum bike.

If you want to do it to see if it can be done, then giddy up! Getting a bond between aluminum and steel will likely be your hardest task.

I think your question is basically, "Is it possible to build a frame out of different parts?". The answer is yes, because frames exist in the market, and most of them are built of different parts, so it's definitely possible to build them.

On the other hand, a bike frame being something that can get you killed if it suddenly fails, I most definitely would not build (and ride) my own unless I were an expert in bike frame construction. If you had to ask this question you are probably not such an expert. So I'd advise you just buy the bike you need instead.

Unless you're just going to hang the bike on the wall as a decoration, of course. If that's the case, do what you wish with the frame.