As per Euler's theory, buckling of the long column occurs when: (Given, P = Applied axial load and Pcr = Crippling load by Euler's theory)
- AP = Pcr
- BP ≥ PcrCorrect
- CP < Pcr
- DP is of any value
Solution
Concept
A long column buckles when the axial load reaches or exceeds the Euler crippling load.
Formula
Pcr = π2 E Imin / Le2
Step-by-step solution
1. Euler's crippling load Pcr is the smallest axial load at which a long column can stay in a bent (buckled) shape. 2. If P < Pcr, the column stays straight and stable. 3. When P reaches Pcr, buckling starts. 4. If P > Pcr, the column is also unstable and buckles. 5. So buckling occurs when P ≥ Pcr.
Explanation
Euler's crippling load is the critical load for a long column. Below this load the column stays straight. When the load reaches or goes above Pcr, the column buckles.
Why the other options are wrong
A: Buckling starts at P = Pcr but also happens for any load above it, so A is incomplete. C: For P < Pcr the column stays straight and stable. D: Buckling does not happen for every load, only for P ≥ Pcr.
Shortcut
Below Pcr the column is safe. At or above Pcr it buckles.
Common mistake
Correct answer: B) P ≥ P_cr