As per Euler's theory, buckling of a long column occurs when ______ (P = applied axial load, Pcr = crippling load by Euler's theory).
Try it first: pick an option, then read the explanation.
Asked in SSC JE 06/06/2024 (4 pm–6 pm)
Detailed Explanation
Euler treated a long, perfectly straight, axially loaded column. At small loads any small sideways disturbance dies out and the column springs back straight. The crippling load Pcr is the load at which the column can just stay in a slightly bent shape (neutral equilibrium).
\[ P_{cr} = \frac{\pi^2 EI}{l_e^2} \qquad P < P_{cr}: \text{stable} \quad P = P_{cr}: \text{neutral} \quad P > P_{cr}: \text{buckles} \]
Why “P > Pcr” Is Correct
The column actually buckles (fails) when the applied load goes beyond the crippling load, i.e. P > Pcr. At exactly P = Pcr it is on the verge of buckling — the limit state — and the book's key treats exceeding it as the buckling condition.
Why the Other Options Are Wrong
- A. P is of any value: A long column below its crippling load stays straight and stable.
- C. P = Pcr: P = Pcr is the critical (neutral) state — the threshold, not the failure range.
- D. P < Pcr: Below Pcr the column is stable and does not buckle.
Key Point
Euler: P < Pcr stable, P = Pcr critical, P > Pcr buckles. Pcr = π²EI/le².
Key Concepts for Students
- Pcr is also called the crippling, buckling or critical load.
- Pcr depends on E, the least I and the effective length — not on the material strength.
- Euler's theory ignores direct crushing, so it suits long columns only.
Practice more: this is question 1 in Columns and Struts MCQs – Part 1. Try the whole set and check every answer instantly.