Are you looking for this to be a welded structure of pipes or are you look for it to be smooth and organic? The reason it doesn't shell is because of the multitude of small sliver openings between the branch joints. It will take a different modeling appoach to make this work correctly. I would recommend lofting or sweeping the branches as surfaces (as I see that you have) but instead of thicken then individually, trim, knit and joint them together cleanly and once you've properly done this, cap the ends of the branches and then make in an enclosed solid. At that point you should be able to thicken it. Then add Radii and then shell.
I have tried trimming and knitting them individually but even after that I get an error saying the surfaces cannot be thickened. As I want the ends to be open I didn't cap them. Is there any other way that I can get this done.
Appreciate your help.