How can I determine spring rate of U-shaped clip?

[Raddy13]

I'm redesigning a small, U-shaped spring clip, similar in shape to this:

To make it fit, I had to increase the radii in the corners from the original design, so I need to validate that it will still have sufficient spring rate/clamp force for our application. I'm trying to figure out how I can do this analytically. It seems like a simple problem, but I can't find anything in my machine design book about U-shaped clips. At the very least, if I know the spring behavior of the original clip, can I predict how increasing the radii will affect it?

 

[OldEngr63]

Go to a Mechanics of Materials text and look up Castigliano's method and related energy methods. You are likely to find a related example there.