10b. Buckling Considerations (SSES Ch. 10.4) • Transition Zone • Bracing • Bifurcation 
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Consider the rigid post AB of length L, supported at B by a torsional spring of stiffness K_{T}. Axial load P is applied at A. Suppose the post has a slight angular displacement q. The moment caused by the load helps to tip AB; the spring resists the angular motion. Equilibrium gives: For small q, sinq ~ q, so the result reduces to: 
Rigid post AB supported by torsional spring under force P. 
Thus:

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