ECC

Engineering

Euler Column Capacity Calculator

Calculate radius of gyration, slenderness, ideal Euler buckling load, yield-squash load, governing nominal capacity, allowable capacity, and applied utilization.

Effective column length (m)Elastic modulus (GPa)Least-axis second moment (mm4)Cross-section area (mm2)Yield strength (MPa)Entered capacity safety factorApplied axial load (kN)Entered slenderness comparison

Effective length in millimetres-

Elastic modulus in N per mm2-

Radius of gyration-

Effective length divided by radius-

Elastic Euler buckling load-

Area times yield strength-

Lower Euler or squash reference-

Capacity after entered safety factor-

Applied load divided by allowable capacity-

Calculated minus entered slenderness-

Decision view

Idealized column capacity chain

Idealized column capacity chainGeometry becomes slenderness, Euler and squash references, governing capacity, and utilization.

Exact scenario comparisonEffective column length (m) changes while all other entered assumptions remain constant.

Effective column length (m)	Effective length in millimetres	Elastic modulus in N per mm2	Radius of gyration	Effective length divided by radius	Elastic Euler buckling load	Area times yield strength	Lower Euler or squash reference	Capacity after entered safety factor	Applied load divided by allowable capacity	Calculated minus entered slenderness

How to use Euler Column Capacity Calculator

Enter effective length and section properties.
Enter modulus and yield strength.
Set safety factor and applied load.
Compare the two nominal modes and utilization.

Calculator guide

Understanding Euler Column Capacity Calculator

Euler buckling and material squash capacity are different failure references. The lower one governs this simplified screen before an entered safety factor is applied.

Geometry I and area form radius.

Two modes Buckling and squash stay separate.

Governing value The lower nominal reference controls.

Load check Applied load is compared after safety.

Calculation method

How the calculation works

Calculate least-axis radius and slenderness, compare ideal Euler buckling with a simple yield-squash reference, and divide the lower value by an explicit safety factor. Convert length and modulus, derive radius and slenderness, calculate both nominal capacity references, take the lower, and divide it by the entered safety factor.

Detailed calculation process

Compare buckling and squash capacity before applying safety

The default column has an effective length of 3.2 m, E = 200 GPa, I = 92,000,000 mm4, area 5,800 mm2, and yield strength 250 MPa.

General formula: L = 1000L_mE = 1000E_GPar = sqrt(I/A)lambda = L/rP_E = pi^2EI/L^2P_y = AF_yP_n = min(P_E,P_y)P_allow = P_n/SFU = P_applied/P_allow Radius of gyration converts section geometry into a slenderness ratio. Ideal Euler buckling and the simple yield-squash load are calculated independently, then the lower reference is safety-adjusted.

What each symbol means

L_m, L Effective length in metres and millimetres.

E_GPa, E Elastic modulus in GPa and N/mm2.

I, A Least-axis second moment (mm4) and area (mm2).

r Radius of gyration (mm).

lambda Dimensionless slenderness ratio.

P_E, P_y Euler and yield-squash nominal loads (kN).

P_n, P_allow Governing nominal and safety-adjusted capacity (kN).

SF, U Safety factor and applied utilization.

Worked substitution with the default inputs

1. Convert the entered units L = 3.2x1000 = 3,200 mmE = 200x1000 = 200,000 N/mm2 MPa equals N/mm2, so yield strength already matches the system.

2. Calculate section slenderness r = sqrt(92,000,000/5,800) = 125.944706 mmlambda = 3,200/125.944706 = 25.407975 The least-axis geometry controls this simplified comparison.

3. Calculate Euler capacity P_E = pi^2(200,000)(92,000,000)/(3,200)^2P_E = 17,734.445 kN This is the ideal elastic buckling reference.

4. Calculate squash capacity P_y = 5,800x250 = 1,450,000 NP_y = 1,450 kNP_n = min(17,734.445,1,450) = 1,450 kN The simple material reference governs the default arithmetic.

5. Apply safety and reconcile P_allow = 1,450/2 = 725 kNU = 650/725 = 89.655% The applied load is below, but close to, this simplified allowable reference.

The default screen gives slenderness 25.408, a 1,450 kN governing nominal reference, 725 kN allowable capacity, and 89.66% utilization.

Purpose-built visual

Inspect a column capacity mode diagram

A scaled column sketch links slenderness to two capacity bars, a governing marker, and an applied-load utilization gauge.

Column Effective length and buckling shape.

Bars Euler versus squash.

Marker Governing capacity.

Gauge Applied utilization.

Worked situations

Practical examples

Radius of gyration is 125.945 mm.
Yield squash, not Euler, governs the simple default comparison.
The applied load uses about 89.66% of the safety-adjusted capacity.

Better inputs

Useful tips

Use least-axis I for the vulnerable buckling direction.
Verify effective length assumptions.
Use a governing design standard for real members.

Before relying on the result

Limitations and common mistakes

Inelastic and local buckling are excluded.
Imperfections, residual stress, connections, and load combinations are excluded.
This is not code-compliant column design.

Reference

Key terms

Radius of gyration: Square root of I divided by area.
Slenderness: Effective length divided by radius of gyration.
Euler load: Ideal elastic buckling reference.
Squash load: Area multiplied by yield strength.

Important note

Calculated from the entered values using the displayed engineering relationship. Confirm design values, load cases, safety factors, standards, and field conditions with a qualified professional.

Frequently asked questions

Why use the least-axis I?

Buckling tends to occur about the weaker axis.

Why can squash govern a stocky column?

The material limit can be below the ideal Euler reference.

Is 89.66% automatically safe?

No. This simplified screen omits code requirements and many failure modes.

What does effective length mean?

It represents end-restraint effects in the idealized buckling length.