The buckling of columns experiment determines the critical load at which a slender column suddenly bends sideways and fails — not by crushing, but by elastic instability. It verifies Euler’s theory of buckling and shows how a column’s load capacity depends on its length and end conditions. This is a core Strength of Materials practical for civil and mechanical engineering students.
Aim of the experiment
To determine the critical (crippling) load of a slender column experimentally and compare it with the theoretical value predicted by Euler’s formula for different end conditions.
Theory: Euler’s buckling load
A short column fails by crushing, but a long, slender column fails by buckling — it deflects laterally and collapses at a load far below its crushing strength. Euler’s formula gives this critical load:
Pcr = π²EI / Le²
where Pcr is the critical buckling load (N), E is Young’s modulus (Pa), I is the least area moment of inertia of the cross-section (m⁴), and Le is the effective length, which depends on how the column ends are held.
Effect of end conditions
| End condition | Effective length (Le) | Relative strength |
|---|---|---|
| Both ends hinged (pinned) | L | 1 (reference) |
| Both ends fixed | L/2 | 4× stronger |
| One end fixed, one hinged | L/√2 | 2× stronger |
| One end fixed, one free | 2L | 1/4 as strong |
The slenderness ratio (Le/k, where k is the radius of gyration) decides whether a member behaves as a column at all — Euler’s theory applies only to long, slender columns above a critical slenderness ratio.
Apparatus required
- Column buckling apparatus (loading frame with adjustable end fixtures)
- Test columns/struts of different lengths and materials (mild steel, aluminium)
- Dial gauge to measure lateral deflection
- Loading arrangement with a load indicator
- Vernier caliper and steel rule
Procedure
- Measure the length, breadth and thickness of the column and calculate I and the cross-sectional area.
- Fix the column in the apparatus with the required end condition (hinged-hinged, fixed-fixed, etc.).
- Set the dial gauge against the mid-span to read lateral deflection.
- Apply axial load gradually in small increments, recording the load and the corresponding lateral deflection.
- Continue until deflection increases rapidly with little added load — this marks the onset of buckling.
- Repeat for other end conditions and column lengths.
Observations and calculation
Plot lateral deflection against axial load; the load at which the curve becomes nearly horizontal (deflection runs away) is the experimental critical load. Compare it with Pcr from Euler’s formula. A common alternative is the Southwell plot (deflection vs deflection/load), whose slope gives the critical load more precisely.
Precautions
- Ensure the load is applied truly axially to avoid premature eccentric failure.
- Clamp end conditions firmly and consistently.
- Do not exceed the elastic limit of the material — Euler’s theory assumes elastic behaviour.
Applications
Buckling governs the design of building columns, transmission towers, ship hulls, aircraft fuselage stringers, and machine connecting rods. Understanding it on a universal testing machine and column apparatus prepares students for real structural design. See related practicals on the deflection of a beam and bending moment vs shear force, and the formula in our engineering lab glossary.
Frequently asked questions
What is the difference between buckling and crushing?
Crushing is compressive material failure in short columns; buckling is sudden lateral instability in long, slender columns at a load well below the crushing strength.
Why does a fixed-fixed column carry more load than a hinged one?
Fixing both ends halves the effective length (Le = L/2), and since Pcr is inversely proportional to Le², the critical load becomes four times higher.
When does Euler’s formula not apply?
It is valid only for long, slender columns that buckle within the elastic range. For short or intermediate columns, Rankine’s or Johnson’s formula is used instead.
Need a column buckling apparatus or UTM for your lab? Request a quote from Scientico India — ISO 9001:2015 certified, CE marked, exporting to 60+ countries, reply within 24 hours.
Lab Equipment Featured in This Guide
Manufactured in-house by Scientico India — ISO 9001:2015 & CE certified, exported to 60+ countries. Request a CIF quote within 24 hours.
Shear Force in a Beam | FortiTestX – 09View details & get quote →
Polariscope | FortiTestX – 19View details & get quote →
Universal Testing Machine 30kN | FortiTestX – 16View details & get quote →
Suspension Bridge Apparatus | FortiTestX – 25View details & get quote →
Deformation of Frame | FortiTestX-42View details & get quote →
Buckling of Bars | FortiTestX-44View details & get quote →