In the sense of the Lagrange–Dirichlet minimum energy stability criterion, the static stability of a strut with one end fixed and the other pinned only at the first bifurcation point is investigated analytically. The second variation of potential energy expressed by the deflection is semi-positive-definite only at the first bifurcation point and vanishes only in the ‘buckling mode’ in small deflection theory. The fourth variation of potential energy is positive in the ‘buckling mode’. The potential energy of the strut at the first bifurcation point is proved to hold a minimum. Based on the Lagrange–Dirichlet stability criterion, the strut at the first bifurcation point is stable.
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