Structural analysis of a horizontally curved, non symmetrically loaded (out of plane) pinned beam.

[Vimukthi]

Hi,

I have solved horizontally curved, out of plane loaded fixed beam for BM and torsional moments using Castigliano's method. But can't get proper results for a pinned beam. If anyone can provide a worked example or anything that can help its very much appreciated.

 

[r13]

Further look into the diagram, I think Mb is induced by the load P in a fix end support system, and varies along the curve (see sketch below), thus produces component forces of M[sub]θ[/sub] and T[sub]θ[/sub], which interact with the component forces due to Tb. For your thinking, you will have to reformulate the base equation per simply support system with clamped ends (for torsion). Make sense?

 

[Vimukthi]

I solved it guys. Turns out Castigliano’s method is not needed at all. All I was missing was the information that torsion at mid is always zero no matter where the load is applied. Applied when Θ=Φ, MΘ=0 and when Θ=Φ/2, TΘ=0 to equilibrium equations and that’s it! But I still wander how to apply Castigliano's theorem to this problem. I have attached the calculation here if anyone is interested or looking for something like this in future. Thank you very much for your valuable time guys!