Columns and Buckling MCQ – Objective Questions with Answers
Mechanical Engineering › Strength of Materials | Free practice MCQs with detailed explanations
Last Updated: June 2026
📌 About this MCQ Set
A column is a slender member under axial compression that can fail by buckling rather than crushing. Euler’s theory predicts the critical buckling load for long columns.
These MCQs cover Euler’s formula, slenderness ratio, end conditions and modes of failure.
8 questions • every answer comes with a worked explanation. Click Show Answer to check yourself.
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Columns and Buckling MCQs
Q1. Euler’s critical buckling load is given by:
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Answer: A. π²EI/Le²
Pcr = π²EI/Le², where Le is the effective length and I the least moment of inertia.
Q2. Slenderness ratio is the ratio of:
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Answer: B. Effective length to least radius of gyration
Slenderness ratio = effective length / least radius of gyration (Le/k).
Q3. Long, slender columns primarily fail by:
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Answer: B. Buckling
Long columns fail by elastic buckling well before the crushing stress is reached.
Q4. Short columns primarily fail by:
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Answer: B. Crushing (direct compression)
Short columns fail by crushing/yielding in direct compression.
Q5. The effective length of a column with both ends hinged is:
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Answer: B. L
For both ends pinned/hinged, Le = L.
Q6. The effective length of a column with both ends fixed is:
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Answer: B. L/2
For both ends fixed, Le = L/2, giving the highest buckling load.
Q7. Euler’s buckling theory is valid for:
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Answer: B. Long (slender) columns
Euler’s theory applies to long columns with high slenderness ratio, where buckling is elastic.
Q8. In Euler’s formula, I represents the:
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Answer: B. Least (minimum) moment of inertia
Buckling occurs about the axis of least moment of inertia, so the minimum I is used.
Frequently Asked Questions
What is buckling?
The sudden lateral instability of a slender column under axial compression, occurring before the material reaches its crushing strength.
What is the slenderness ratio?
The ratio of a column’s effective length to its least radius of gyration; higher values mean more susceptibility to buckling.
How do end conditions affect buckling load?
They change the effective length: fixed-fixed (Le = L/2) gives the highest critical load, while free-fixed (Le = 2L) gives the lowest.