You likely will need bracing, centrifugal force is strong. In hvac /mechanical applications; hanging units, water tanks, wire loom racks, light-med trolley beams, etc. we often used oposing wire cables for bracing, 30° min, pref. 45° or more. Similar to an elevated lines firming up more than one might expect; I'd guess 4-8 points concentrated around the curves will be all you need. I'd start running a cable set inside the loop's curves and see what i have before adding any to the outside edge (pulls loop together this way). (ask an hvac shop about spring loaded cable stays for one end at least to make it easier than the normal stays.)
If you make a slice down the 2 short walls of the channel only, it can be bent to give a solid channel brace that wont easily bend and two connection tabs (each end) can be bent to the angles needed for mounting. You can also pound the ends of conduit/metal tube until flat, bend flat end into a tab, drill the tab(s). The end may even seam split while pounded but will still be usable most of the time. Cut off bad one and pound again.... bracing lengths and angles can usually be "fudged" before an attachment point is actually made.
