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Worked example — welded plate girder, a/h_w = 1.5, rigid end post
A welded S355 plate girder: h_w = 1200 mm, t_w = 12 mm, a = 1800 mm (transverse stiffeners at 1.8 m), flanges 300×25 mm, rigid end post. Determine V_b,Rd.
Inputs
h_w = 1200 mm, t_w = 12 mm, a = 1800 mm, f_yw = 355 MPa, rigid end post, b_f = 300 mm, t_f = 25 mm
V_b,Rd ≤ η·f_yw·h_w·t_w/(√3·γ_M1) = 2 663 kN — web governs
V_b,Rd
V_b,Rd = min(2 663 + 205, 2 663) = 2 663 kN
Automate shear buckling checks for every plate girder
FrameAI Pro reads your structural PDF and runs full EN 1993-1-5 shear buckling checks — λ̄_w, V_bw,Rd, V_bf,Rd, M-V interaction — for every plate girder web automatically.
When is a shear buckling check required per EN 1993-1-5?
EN 1993-1-5 §5.1(2) requires a shear buckling check when h_w/t_w > 72ε/η, where ε = √(235/f_y) and η = 1.20 for S235–S355 (or 1.00 conservatively). For S355 this threshold is about 58.6, so most plate girder webs require a check. Rolled section webs are typically stocky enough to avoid the requirement.
What is the difference between a rigid and non-rigid end post?
A rigid end post (Table 5.1, column 1) consists of a load-bearing transverse stiffener paired with an additional inner transverse stiffener close to the support, providing a stiff boundary that can develop the tension field anchor. A non-rigid end post (column 2) is a single ordinary stiffener at the support and provides less anchorage. Rigid end posts give higher χ_w values for intermediate web slenderness (0.83 ≤ λ̄_w ≤ ∞ vs. non-rigid break at 1.08).
How is the flange contribution V_bf,Rd calculated?
The flange contribution per Eq.5.8 is V_bf,Rd = b_f·t_f²·f_yf / (c·γ_M1), where c = (a/2)·√(1−(M_Ed/M_f,Rd)²) per Eq.5.9, and M_f,Rd is the plastic moment of the flanges only (ignoring the web). When M_Ed ≥ M_f,Rd the flanges are fully utilised by bending and contribute nothing to shear (V_bf,Rd = 0).
What is the M-V interaction check in §7.1?
When both high moment and high shear act simultaneously, EN 1993-1-5 §7.1 Eq.7.1 requires: (2·V_Ed/V_b,Rd − 1)² + M_Ed/M_pl,Rd ≤ 1. This interaction only applies when V_Ed > 0.5·V_b,Rd (significant shear). The check ensures the flanges can carry the bending moment once the web has yielded in shear.
How is k_τ computed for transversely stiffened panels?
Per EN 1993-1-5 Annex A.3: for long panels (α = a/h_w ≥ 1), k_τ = 4.00 + 5.34/α²; for short panels (α < 1), k_τ = 5.34 + 4.00/α². An unstiffened web uses k_τ = 5.34 (the limit as a → ∞). Adding transverse stiffeners significantly increases k_τ and therefore reduces λ̄_w, raising χ_w.
What is the upper bound on V_b,Rd?
Eq.5.1 of EN 1993-1-5 caps V_b,Rd at η·f_yw·h_w·t_w/(√3·γ_M1), which is the plastic shear resistance of the web with the η overstrength factor. This prevents V_bf,Rd pushing the total above the web plastic resistance. The calculator flags when this upper bound is the governing constraint.