How can I estimate the bending stress for a hollow tube under uniform load?

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To estimate the bending stress for a hollow tube under a uniform load, one can apply methods suitable for statically indeterminate structures, such as Castigliano's theorem. The hollow tube has a diameter of 38 mm and a thickness of 4 mm, subjected to a uniform distributed load of 500 N/m². For validation, finite element analysis (FEA) in 3D can be utilized alongside analytical methods. Additionally, approximating the bends as rigid or pin-jointed can provide upper and lower bounds, simplifying the problem to that of a simply supported beam. Accurate calculations will depend on the material properties, with mild steel having an elastic modulus of 200 GPa and a Poisson's ratio of 0.3.
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Dear All,

Please see the picture. I need to find the bending stress for that profile.

Its hollow tube dia= 38 mm, 4 mm thick. its is acted with udl of 500 N/m2 on its outer surface.
How can I estimate the bending stress, deformation. Assume it as mild steel with E = 200 Gpa, poission ratio = 0.3.

I am trying to validate this with FEA in 3d.
Kindly share your ideas. Thank you in advance.
 

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It's statically indeterminate so you can use a method for those types of problems. Maybe Castigliano's.

Or, you could get upper and lower bounds by treating the bends as rigid and pin-jointed. Then it's an easy simply supported beam problem.
 

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