SESKStuff Everyone Should Know
SESK: Stuff Everyone Should Know · sesk.info/eng-buckling-half-length

If a slender pinned column is made half as long, its critical buckling load:

Goes up four times; Euler's buckling load scales with 1 over length squared.

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  1. Doubles
  2. Stays the same
  3. Goes up four times ✔

Why: Long, slender columns in compression fail by suddenly bowing sideways, not by crushing. Euler's formula puts length squared in the denominator, so halving the length quadruples the load it can carry.

Huh, didn't know that: Bracing a column sideways at its midpoint works like halving its length, which is why braced frames are so common.

The dad joke
The tall column buckled under pressure. The short one just shrugged it off.
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References

Answer: Goes up four times. Long, slender columns in compression fail by suddenly bowing sideways, not by crushing. Euler's formula puts length squared in the denominator, so halving the length quadruples the load it can carry.

  1. MIT OCW 3.11 Mechanics of Materials (Roylance): Stresses in Beams (buckling section) ocw.mit.edu/courses/3-11-mechanics-of-materials-fall-1999/96d839b02e4a6c63cf8031800e89cccd_MIT3_11F99_bstress.pdf
    This is equivalent to making the beam half as long, which increases the critical buckling load by a factor of four.
    Checked 2026-10-10.
  2. MIT OCW 3.11 Mechanics of Materials (Roylance): Stresses in Beams (buckling section) ocw.mit.edu/courses/3-11-mechanics-of-materials-fall-1999/96d839b02e4a6c63cf8031800e89cccd_MIT3_11F99_bstress.pdf
    Long slender columns placed in compression are prone to fail by buckling
    Checked 2026-10-10.

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