How do you stiffen up a c channel frame?

Anything you add to increase the amount of material will increase rigidity. the further that material is from the neutral axis the better. You could weld another C channel onto the open face of the existing c channel. you could also weld flat strap on the top and bottom of the channel, that would increase the strength but only in bending. any off axis loads would still cause it to flex. you could also put square tubing vertically stacked at 6in spacing inside the channel this will increase rigidity, but only marginally since most of the material is near the central axis.
I was thinking about welding two square tubes lengthwise to stiffen it up.
 
A flat piece welded on to close the “C” will help, but make sure you unload the trailer with jacks and blocks prior to doing the welding. If that fails, adding a separate boxed member as mentioned above will increase the stiffness even more.
 
We had discussed some of this here:

 
Cut a big hole in each frame rail, like 3 or 4 inch diameter.

Run a tube through and weld it in.

That's the main thing that truck makers do to add stiffness.

You can also weld x-shaped bracing in (as viewed from above) or even cattle panels diagonally on the top or bottom of the frame rails. We used to do that to stiffen our miatas for autocross.
 
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