Column buckling: direction of failure based on principal second moments of area A vertical column has two principal moments of inertia Ixx and Iyy about orthogonal centroidal axes. Identify the direction in which the column will tend to buckle first under axial compression. Choose the correct option.
Mechanical Engineering
Strength of Materials
Difficulty: Easy
Choose an option
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Aalong the axis of load
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Bperpendicular to the axis of load
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Cabout the axis with maximum moment of inertia
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Dabout the axis with minimum moment of inertia
Answer
Correct Answer: about the axis with minimum moment of inertia
Explanation
ConceptEuler buckling shows that the critical load for a prismatic column is Pcr = π² E I / (K L)². For a given column (same E, L, end condition K), the smaller principal second moment of area I gives the smaller critical load and hence buckling occurs first about that weaker axis.
Why not the others?(a) & (b) mention directions relative to the load line, not stiffness; (c) maximum inertia would raise Pcr, resisting buckling; (d) correctly identifies the weak-axis buckling.
Final Answerabout the axis with minimum moment of inertia