Column Buckling Calculator – Euler Critical Load & Slenderness

Column Buckling Calculator

Euler buckling analysis for columns: critical load, slenderness, and safety check

Critical Load (P_cr)

Slenderness (λ)

Required I

Safety Factor

End Condition (Effective Length Factor K)

K=1.0 (P-P)

K=0.5 (F-F)

K=0.7 (F-P)

K=2.0 (F-Free)

Current: Pinned-Pinned (K=1.0)

Young's Modulus (E)

Pa GPa ksi

Moment of Inertia (I)

m⁴ mm⁴ in⁴

Column Length (L)

m mm ft

Cross‑section Area (A) – for slenderness

m² mm² in²

Length (L)

m mm ft

Radius of Gyration (r)

m mm in

Young's Modulus (E) – optional for buckling stress

Pa GPa

Required Load Capacity (P)

N kN lbf

Young's Modulus (E)

Pa GPa

Length (L)

m mm

Safety Factor (FOS)

Applied Load (P_app)

N kN

Euler Critical Load (P_cr)

N kN

Yield Strength (σ_y) – optional

Pa MPa

Material Preset (fills E and yield)

Preset sets E and yield strength for applicable modes.

Euler Critical Load (P_cr)

54.38 kN

E=200 GPa, I=8.33e-8 m⁴, L=3 m, K=1.0

Slenderness Ratio λ = 103.9

ShortIntermediateSlender

Euler buckling governs

Formula

π²EI/(KL)²

Buckling Stress

54.4 MPa

Safety Status

Safe

Key Buckling Formulas

P_cr = π²EI / (KL)²

σ_cr = P_cr / A = π²E / λ²

λ = KL / r , r = √(I/A)

K – effective length factor (end conditions)
λ – slenderness ratio
r – radius of gyration

People Also Ask

📌 What is Euler buckling and when does it occur?

📏 How do I choose the effective length factor K?

📊 Slenderness ratio limits for columns?

⚙️ Johnson vs Euler: which formula to use?

🔧 How does lateral bracing affect buckling?

📐 Typical moment of inertia for steel sections?

Understanding Column Buckling

Euler buckling is a sudden lateral deflection that occurs in slender columns under axial compression when the load reaches a critical value. The critical load depends on:

Material stiffness (Young's modulus E)
Cross‑section geometry (moment of inertia I, area A)
Column length (L) and end restraints (K)

Buckling is a stability failure, not a material strength failure. Even a very strong material can buckle if the column is slender enough.

Typical Material Properties

Material	E (GPa)	σ_y (MPa)	Typical λ_transition
Structural Steel	200	250	125
Aluminum 6061-T6	69	276	70
Timber (Pine)	9	30	77
Concrete C30	25	30	128

Detailed FAQs

What is the difference between Euler and Johnson buckling?

Euler applies to slender columns where buckling occurs elastically. For intermediate columns, inelastic buckling (Johnson formula) is used: σ_cr = σ_y - (σ_y/(2π))²·(λ²/E). The transition slenderness λ_t = π√(2E/σ_y).

How do I find the radius of gyration for a section?

r = √(I/A). For standard sections (W‑shapes, tubes), values are tabulated. For a rectangle b×h, r_min = h/√12 (bending about weak axis).