I forgot to add - are the brackets you've used, Marcos, the "London
Pattern" stamped-out-from-sheet-metal things (like Screwfix catalogue
number 17536)? If so, you'll find them rather less stiff than the
mitred pattern they also sell (and which should be available in a
d-i-y warehousey place too), like their part number 14870 for the
35x35cm largest size. Pricier, but *much* stiffer in my experience.

HTH - Stefek