013 Lateral Torsional Buckling (Cantilever Beam)

A cantilever I-Beam is subjected to a transversal load at its tip point B, as shown in the figure. When the load P is increased, the beam starts to buckle laterally, which is known as lateral torsional buckling.

1. Write the total potential energy equation considering the beam’s out-of-plane bending, torsion, and warping.
2. Take the deformation functions as reasonable admissible functions.
3. Determine the buckling load based on the location of force P.
4. Compare the results with the available sources like stability books and the Timoshenko equation.

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