You don't say what welding method is being used also what is the thickness of the tube compared with the bracket thickness ?
It is possible you are getting undercuts which reduce the wall thickness at the point of maximum stress i.e the tube/bracket interface ?
If you put a internal sleeve into the tube and tapered the inside end to spread the stress you would double it's thickness at the point of the weld ?
Don't forget if you make one part stronger and unable flex you just move the forces somewhere less strong , sometimes flex is best
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