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Looking for some advice on increasing bending stiffness of a mild steel 1" x 0.065" round tube.

This is for a motorcycle frame and clearance is an issue. There is a fuel tank above and the engine below this top tube (two running parallel) that I wanted to reinforce against bending.

Tried internet searches on stiffness and learned a little about beams and elastic modulus.

So I came up with this...

The segment that needs to be braced is about 12" long from the rear cross brace in red to where the boxed section ends on the top tubes.

Thanks much in advance!

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# Increasing bending stiffness of a steel tube

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