How can we find critical moment due to lateral torsional buckling in a laterally unsupported beam using any software like ansys or abaqus?

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Mir Aamir Abbas

How about eigen value buckling analysis? Apply unit moment and multiply the unit load by the eigen value you get in the solution to calculate the buckling load. However, since it eigen value buckling actual buckling load in a nonlinear static analysis might be lower.

Shantunu Chowdhury

Use a dummy elastic wire with low stiffness to reduce its impact. Embed it where you need to measure the moment for accurate results. Good luck!