Free Tool · EN 1993-1-5 §4 · Flat Plate Buckling

Flat Plate Buckling Check

Unstiffened flat rectangular plate buckling per EN 1993-1-5 §4. Select boundary condition and loading type — get k_σ, σ_cr, λ̄_p, χ_p, σ_x,Rd and b_eff with full step-by-step breakdown.

Plate Geometry

a — plate length in load direction (mm)

b — plate width (mm)

t — plate thickness (mm)

Boundary condition (long edges) Long edges are the sides parallel to the loading direction. Short edges are simply supported by the surrounding structure.

Material & Form

Steel grade

Plate form Hot-rolled plate: α_p = 0.21 (Table 4.2). Cold-formed: α_p = 0.13.

γ_M1 — partial factor

Loading type

N_x,Ed — axial force parallel to a (kN)

N_z,Ed — axial force parallel to b (kN)

V_Ed — design shear (kN)

Flat Plate Buckling Results

Compression — EN 1993-1-5 §4.3

k_σ — plate buckling coefficient (Table 4.1)—

σ_cr — elastic critical stress (MPa)—

λ̄_p — non-dimensional slenderness (Eq 4.2)—

χ_p — reduction factor (Table 4.2)—

σ_x,Rd — design compression resistance (MPa)—

Class 4 slenderness check—

b_eff — effective width (mm)—

Shear — EN 1993-1-5 §4.4 + Annex A.3

k_τ — shear buckling coefficient—

λ_w — web slenderness—

χ_w — shear reduction factor—

V_bw,Rd — shear buckling resistance (kN)—

Export calculation report

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FAQ

What is flat plate buckling?

Flat plates under in-plane compression can buckle at stresses below the material yield stress when the width-to-thickness ratio is large (Class 4). EN 1993-1-5 §4 gives the design resistance σ_x,Rd = χ_p·f_y/γ_M1 using the plate slenderness λ̄_p = √(f_y/σ_cr) where σ_cr is the elastic critical stress.

How is k_σ determined?

From EN 1993-1-5 Table 4.1: for a/b ≥ 1 — simply supported: k_σ = 4.0, clamped: k_σ = 5.0, one-clamped: k_σ = 1.5. For a/b < 1 multiply by (a/b)². The boundary condition reflects how the long edges resist rotation.

What is λ̄_p slenderness?

λ̄_p = √(f_y / σ_cr) per Eq (4.2). It compares the plate yield strength to its elastic critical buckling stress. For λ̄_p ≤ 0.5 + √(0.25−α_p) → χ_p = 1 (no buckling). For higher slenderness, χ_p = (1−α_p(λ̄_p−0.5))/λ̄_p².

Does the boundary condition choice matter much?

Yes. Switching from simply supported (k_σ=4.0) to clamped (k_σ=5.0) increases σ_cr by 25%, reducing λ̄_p and raising χ_p. For a/b=2, simply-supported gives k_σ=4.0 while clamped gives 5.0. The choice should match the actual rotational restraint provided by adjacent structure.

When is a plate Class 4?

A plate is Class 4 slender when b/t exceeds the limit from Table 4.1 (e.g., for S235 simply supported: b/t > 42ε where ε = √(235/235) = 1, so b/t > 42). In Class 4 the effective width b_eff = χ_p·b is used for stiffness and stress distribution calculations per Annex E.

How does the combined N+M check work?

EN 1993-1-5 §4.5 uses von Mises equivalent stress: σ_eq = √(σ_x,Ed² + σ_z,Ed² − σ_x,Ed·σ_z,Ed + 3τ_Ed²). Utilization = σ_eq / σ_x,Rd where σ_x,Rd = χ_p·f_y/γ_M1. σ_x,Ed = N_x,Ed/(b·t), τ_Ed = V_Ed/(b·t). This checks combined axial + shear loading against the compression resistance.