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Euler Column: Critical Load from the Onset of Buckling

Known L, E, I and pinned–pinned ends. Sweep the compressive load and report P when the deflection grows sharply.

University / research· 22 min·Related simulator: EngineeringEuler Column Buckling

Goal

Determine P_cr as the load where mid-height deflection blows up. Compare with π²EI/(KL)² for K = 1.

Equipment

  • Pinned–pinned column (known L, E, I)
  • Load jack
  • Dial gauge at mid-height

Experiment

Theory

Euler’s critical load is P_cr = π²EI/(KL)². A small imperfection is magnified as ~1/(1−P/P_cr), so deflection grows slowly and then shoots up near P_cr. The bench hides P_cr, the load ratio and any “buckled” banner. L, E, I and the end condition are known. A live mid-height deflection is the instrument.

Procedure

  1. Length, Young’s modulus, second moment and pinned–pinned ends are fixed and known. You only change the load P.
  2. Watch the live mid-height deflection. Park at the onset of the sharp rise. The bench does not print P_cr.
  3. Record that P. Repeat the hunt at least 6 times (you may start from different P).
  4. Take the mean of the P column and compare with the reference.

Conclusion

The mean onset load agrees with Euler’s P_cr. Main uncertainties: discrete load steps and judging the blow-up by eye.