Web Geometry

h_w — clear web height (mm)

t_w — web thickness (mm)

Material & End Post

Steel grade

γ_M1 — partial factor

η — interaction factor EN 1993-1-5 §5.1(2) Note: η = 1.20 for S235–S460 (recommended). National annex may specify η = 1.0.

End post condition Rigid: full-depth stiffener at end providing moment resistance to the web panel. Non-rigid: standard stiffener or no stiffener at support — conservative.

Transverse Stiffeners / Design Shear Force

a — stiffener spacing (mm, 0 = no stiffeners) Enter 0 for unstiffened web (kτ = 5.34). For stiffened webs enter the panel width. Keep a/hw ≤ 3 for meaningful shear buckling benefit.

V_Ed — design shear (kN)

Include flange contribution V_bf,Rd (Eq 5.8)

Flange contribution is only available when stiffeners are present (a > 0) and MEd < Mf,Rd. Requires minimum flange width, thickness, and moment inputs.

b_f — minimum flange width (mm)

t_f — flange thickness (mm)

f_yf — flange yield (MPa, blank = same as web)

M_Ed — design moment (kNm)

M_f,Rd — moment resistance, flanges only (kNm)

Shear Buckling Results

Intermediate

h_w / t_w — slenderness ratio—

ε = √(235/f_yw)—

k_τ — shear buckling coefficient—

λ_w — non-dimensional slenderness—

Threshold 0.83/η—

χ_w — reduction factor (Table 5.1)—

Resistance

V_bw,Rd — web contribution (kN)—

V_bf,Rd — flange contribution (kN)—

V_b,Rd cap — η·f_yw·h_w·t_w/(√3·γ_M1) (kN)—

V_b,Rd — total shear buckling resistance (kN)—

Export calculation report

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FAQ

What is web shear buckling?

Thin webs in plate girders can buckle under shear before reaching the full plastic shear resistance Vpl,Rd. EN 1993-1-5 §5 provides a tension-field model: post-buckling redistribution increases capacity beyond the linear shear-buckling load. The check is required when hw/tw > 72·ε/η (§5.1(2)) where ε = √(235/fyw) and η = 1.20.

How is the shear buckling coefficient kτ determined?

For webs with no stiffeners: kτ = 5.34 (uniform shear). For stiffened webs (EN 1993-1-5 Annex A §A.3 Eq A.5): kτ = 5.34 + 4.00/(a/hw)² when a/hw ≥ 1; kτ = 4.00 + 5.34/(a/hw)² when a/hw < 1. Adding stiffeners with a/hw ≈ 1 gives kτ ≈ 9.34, roughly doubling the capacity vs. an unstiffened web.

What is the non-dimensional slenderness λw?

λw = (hw/tw) / (37.4·ε·√kτ) per Eq 5.5. It measures how slender the web panel is relative to its theoretical shear-buckling stress. For λw < 0.83/η the web does not buckle before yielding (χw = η). For λw > 1.08 the tension-field action governs and χw = 1.37/(0.7+λw) for rigid end posts.

Rigid vs non-rigid end post — what is the difference?

A rigid end post is a pair of stiffeners (or double-plate) that provides moment resistance at the end of the girder, allowing full tension-field anchoring. It gives a higher χw for intermediate λw (0.83/η to 1.08): χw = 0.83/λw. A non-rigid end post (single stiffener or none) cannot anchor the tension field — χw = 0.83/λw for all λw ≥ 0.83/η, which means it always matches or is below the rigid post curve.

When does the flange contribution Vbf,Rd apply?

Vbf,Rd per Eq 5.8 applies only when MEd < Mf,Rd — i.e. the applied moment is less than the moment the flanges alone can carry. In that regime the flanges can form plastic hinges at the stiffener positions, providing additional shear resistance. The contribution is computed as (bf·tf²·fyf)/(c·γM1)·[1−(MEd/Mf,Rd)²] where c is the distance between plastic hinges along the flange (Eq 5.9). At high moment levels (MEd ≈ Mf,Rd) the contribution goes to zero.

Does this check cover interaction between shear and bending?

No. This calculator covers shear buckling resistance Vb,Rd only. For webs simultaneously subjected to high shear and high bending, EN 1993-1-5 §7 requires an M–V interaction check: η₁ + (2η₃ − 1)² ≤ 1 where η₁ = MEd/Mpl,Rd and η₃ = VEd/Vbw,Rd. The FrameAI full pipeline checks §7 interaction automatically as part of the plate girder verification pass.

Web Shear Buckling Check

FAQ