Check plate buckling per EN 1993-1-5 §4 for flat compression elements. Computes the buckling factor kσ (Tables 4.1/4.2), plate slenderness λ̄p (Eq. 4.2), reduction factor ρ (Eq. 4.1 internal / Eq. 4.3 outstand), and effective width beff distribution. Covers web plates, flange outstands, box girder flanges. S235–S460. Stress ratio ψ from −1 to +1.
Internal element (ψ=1.0): uniform compression. Green = effective strips b_e1, b_e2. Red dashed = ineffective void.
| Plate width b | 300 mm |
| Plate thickness t | 8 mm |
| b/t ratio | 37.5 |
| ε = √(235/f_y) | 0.8136 |
| k_σ (Table 4.1/4.2) | 4 |
| λ̄_p (Eq. 4.2) | 0.8115 |
| Threshold | 0.673 |
| ρ (Eq. 4.1/4.3) | 0.8982 |
| b_eff = ρ·b | 269.5 mm |
| b_e1 (compressed edge) | 134.7 mm |
| b_e2 (other edge) | 134.7 mm |
| Width reduction | 10.2% |
Step 1 ε = √(235 / f_y) = √(235 / 355) = 0.8136
Step 2 b/t = 300 / 8 = 37.5
Step 3 k_σ = 4 (ψ = 1, internal element, Table 4.1)
Step 4 λ̄_p = (b/t) / (28.4·ε·√k_σ) = 37.5 / (28.4 × 0.8136 × √4) = 0.8115
Step 5 λ̄_p = 0.8115 > 0.673 → ρ = (λ̄_p − 0.22) / λ̄_p² = (0.8115 − 0.22) / 0.8115² = 0.8982
Step 6 b_eff = ρ·b = 0.8982 × 300 = 269.5 mm → b_e1 = 134.7 mm, b_e2 = 134.7 mm
Enter your email to receive a formatted plate buckling report with clause references.
FrameAI Pro extracts all plate girder webs and flanges from your PDF and runs full EN 1993-1-5 effective section checks automatically.
View Plans →EN 1993-1-5 §4 covers the effective width method for plated structural elements under direct stresses (compression and bending). It applies to Class 3 and Class 4 cross-sections where the slenderness of a compression plate element is high enough that elastic buckling occurs before yielding. The standard derives a reduction factor ρ (≤ 1.0) applied to the gross width b to get an effective width b_eff. Where ρ < 1.0, the cross-section is Class 4 and the effective section must be used in resistance calculations.
k_σ depends on the element type and stress ratio ψ. For internal compression elements (webs between flanges), EN 1993-1-5 Table 4.1 gives: ψ ≥ 0 → k_σ = 8.2/(1.05+ψ); ψ < 0 → k_σ = 7.81 − 6.29ψ + 9.78ψ². For outstand elements (flange cantilevers), Table 4.2 gives: ψ ≥ 0 → k_σ = 0.578/(ψ+0.34); ψ < 0 → k_σ = 1.7 − 5ψ + 17.1ψ². These formulas reflect the different boundary conditions (simply supported on both sides vs. one free edge).
ψ is the ratio of the compressive stress at the less-stressed edge to the stress at the more-stressed edge of the plate. ψ = 1 means uniform compression; ψ = 0 means the stress at one edge is zero (e.g. a web with N only, no M); ψ = −1 means equal and opposite stresses (pure bending, so σ₁ is compressive, σ₂ is tensile). For a web under combined N+M, compute the stresses at both edges from the applied axial force and moment and take their ratio.
λ̄_p = (b/t) / (28.4·ε·√k_σ) per EN 1993-1-5 Eq. (4.2), where ε = √(235/f_y). For internal elements, ρ = 1.0 when λ̄_p ≤ 0.673; for outstands, ρ = 1.0 when λ̄_p ≤ 0.748. Above these limits, ρ = (λ̄_p − 0.22)/λ̄_p² for internal (Eq. 4.1) and ρ = (λ̄_p − 0.188)/λ̄_p² for outstands (Eq. 4.3). A Class 4 cross-section results whenever any element has ρ < 1.0.
For internal compression elements under uniform compression (ψ = 1): b_eff = ρ·b, split as b_e1 = b_e2 = 0.5·b_eff. For non-uniform stress (ψ < 1): b_e1 = 0.4·b_eff (more compressed edge), b_e2 = 0.6·b_eff (less compressed edge). The two effective strips are placed at each supported edge; the void in the middle is excluded from the effective cross-section. For outstand elements, the full effective width b_eff = ρ·b is placed at the supported edge.
No — γ_M0 is the partial factor on the cross-section resistance and is applied when computing the design resistance (e.g. M_Rd = W_eff·f_y/γ_M0). The plate buckling check itself only determines ρ and b_eff from geometry and material; γ_M0 is not used in the λ̄_p or ρ formulas. DE NAs set γ_M0 = 1.0 for standard steel structures; IT sets γ_M1 = 1.05 for plate buckling mode. EN recommended values are γ_M0 = γ_M1 = 1.0.