Structural Analysis Fundamentals / module 18
Structural instability
Why slender columns fail long before the material runs out of strength.
What you will understand
- Distinguish a strength failure from an instability failure
- Use the Euler formula for a slender column
- Apply effective length to different end conditions
- Explain why buckling happens about the weak axis
- State the limits of Euler theory and why real columns differ
Lessons
Deriving the Euler buckling load
Why a strut fails suddenly at a particular load — an eigenvalue problem, solved from scratch.
Strength versus stability
Two completely different ways for a column to fail.
Effective length, slenderness and the limits
How end restraint helps, which axis buckles, and where the theory runs out.
Real columns, and buckling by energy
Why no column reaches its Euler load, and how to estimate one that has no formula.
Beam-columns: bending and buckling together
What happens when a member carries transverse load and axial compression at once.
Module summary
- Buckling is a stability failure: the column moves sideways rather than crushing
- Pcr = π²EI/Lₑ², so length matters far more than anything else
- Effective length depends on the end restraints: K = 1.0, 2.0, 0.5 or 0.7
- Buckling occurs about the axis with the smaller I — check the weak axis
- Euler applies to slender columns only; short ones fail by yielding
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesCheck your understanding
Check yourself
Which change would most increase a slender column's buckling capacity?
Practice
A column is 6.0 m long and fixed at one end, free at the other. What is its effective length in metres?
Check yourself
Why do real columns buckle at loads below the Euler prediction?