At http://dinonline.org/2017/01/07/opening-a-foldingcollapsing-bima-on-shabbos/, Rav Zidell writes the following:
“You may open or close the bima without hesitation on Shabbos. The reason for this is since it was made to open and close, it isn’t considered making an ohel. Another permitted factor here is that the bimah is not meant to cover anything, and it is made for what will be put in top of it.
The fact that it is for a mitzvah doesn’t really help us here, and the fact that it is large is not a problem, this may even be done to a collapsible chuppah.”
Why can a collapsible chuppah be set up? We’re not allowed to use umbrellas. There doesn’t seem to be a big difference. Presumably the intent is for shade and not for a wedding as the latter is of little use on Shabbos.
Your asking a good question, on one hand we a collapsible item is usually permitted to open and close, on the other hand almost all poskim prohibited opening an umbrella, and even using one that was opened before shabbos? There are various reasons given by the poskim. The Chazon Ish O:CH 52-6 asks your question, and he says that technically our umbrellas might be permitted, however there it appears to be tikun mana, and uvdin d’chol, and not in the spirit of shabbos, therefore the poskim forbade it, and that is the accepted custom.