Weld Segments & Loads
| x₁ (mm) | y₁ (mm) | x₂ (mm) | y₂ (mm) | Throat a (mm) |
|---|
Horizontal force component, positive = rightward.
Vertical force component, positive = upward.
In-plane moment about load point, positive = counter-clockwise.
Weld electrode classification strength. E70XX = 482 MPa, E80XX = 552 MPa.
Live weld group preview
Results
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Centroid (x, y) / Total throat area Aw / Polar moment J
Centroid (x, y)—
Total throat area Aw—
Polar moment J—
Peak stress location—
AISC Elastic Vector
f_r,max—
φRn—
Utilization
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—
AISC ICR Directional
C_θ—
φRn dir—
Utilization
—
—
EN 1993-1-8 Directional
β_w—
f_vw,d—
σ_w—
Utilization
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Default result — Bracket plate preset
Centroid(32.1, 57.1) mm
Total throat area Aw2100 mm²
Polar moment J13.72 ×10⁶ mm⁴
AISC Elastic Vector
f_r,max561.5 N/mm
φRn1301.4 N/mm
Utilization
43.1%
PASS
EN 1993-1-8 Directional
β_w0.9
f_vw,d241.2 MPa
Utilization
38.8%
PASS
Governing — AISC Elastic
Utilization
43.1%
PASS
Worked example — bracket plate weld, eccentrically loaded
An L-shaped weld group (bracket plate): vertical leg 200 mm, horizontal leg 150 mm, throat 6 mm. Load Py = 50 kN at the plate edge, creating moment Mz = 7.5 kN·m at the weld centroid. S355 steel, E70XX electrode (F_EXX = 482 MPa).
Segments
Vertical: (0,0)→(0,200), a=6 mm, L=200 mm. Horizontal: (0,0)→(150,0), a=6 mm, L=150 mm.
Centroid
ΣAw = 6×200 + 6×150 = 2 100 mm². xc = (1200×0 + 900×75)/2100 = 32.1 mm; yc = (1200×100 + 900×0)/2100 = 57.1 mm
J
Ixx = Σ∫ a(y−yc)² ds; Iyy = Σ∫ a(x−xc)² ds; J = Ixx + Iyy
Direct f_r
σ_y = Py/Aw = 50000/2100 = 23.8 N/mm². σ_x = 0
Moment f_r
Mz = 7.5×10⁶ N·mm. σ_x_M = −Mz·(y−yc)/J; σ_y_M = Mz·(x−xc)/J at each point
φRn
φRn = 0.75×0.60×482×6 = 1 300 N/mm (AISC, LRFD)
EN f_vw,d
β_w = 0.90 (S355). f_vw,d = 470/(√3×0.90×1.25) = 241 MPa
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Frequently asked questions
What is the elastic vector method for weld groups?
The elastic vector method (AISC 360-22 §J2.4) treats the weld group as an elastic continuum. Direct shear from Px and Py is distributed uniformly over all throat area. Torsional moment Mz creates stresses proportional to the distance from the centroid, following J = Ixx + Iyy (polar moment of inertia). The worst-case resultant vector sum is the peak design demand.
What is the ICR (Instantaneous Centre of Rotation) method?
The ICR method accounts for the directional strength of fillet welds. AISC 360-22 §J2.4 allows a directional strength increase of Cθ = 1.0 + 0.5·sin(θ)^1.5, where θ is the angle of the force with respect to the weld axis. At θ = 0° (pure longitudinal shear) Cθ = 1.0; at θ = 90° (transverse load) Cθ = 1.5 — a 50% strength gain. This makes the ICR method less conservative than the pure elastic vector method.
What is the EN 1993-1-8 §4.5.3 directional method?
The EN directional method checks the resultant stress per unit throat area σ_w = f_r,max / a against the design resistance f_vw,d = f_u / (√3 · β_w · γ_M2). The correlation factor β_w from Table 4.1 depends on steel grade: S235 → 0.80, S275 → 0.85, S355 → 0.90, S420/S460 → 1.00. γ_M2 = 1.25 per §2.2.
Why do AISC and EN methods give different utilizations?
The AISC φ = 0.75 LRFD factor and 0.6·F_EXX nominal weld strength operate on a different reliability framework from the EN partial factor approach (γ_M2 = 1.25). For E70XX on S355, AISC φRn ≈ 1300 N/mm per 6 mm throat while EN f_vw,d ≈ 241 MPa. The two methods use different load factor conventions, so direct comparison requires caution. Typically AISC LRFD utilizations are comparable to EN ULS checks within ±10% for common geometries.
How is the weld group centroid calculated?
The centroid is the throat-area-weighted average of the mid-point of each segment: xc = Σ(Lᵢ·aᵢ·x_mid,i) / Σ(Lᵢ·aᵢ), yc similarly. For uniform throat, this reduces to the length-weighted centroid. For the worked example L-shaped group with different length legs, the centroid is offset toward the longer (vertical) leg.
What throat thickness should I use?
For fillet welds, the design throat a is the perpendicular distance from the root to the face of the weld — typically 0.707 × leg size for equal-leg fillet welds. EN 1993-1-8 §4.5.2 defines the effective throat as a minimum. AISC J2.2a defines the effective throat for fillet welds the same way. Enter the throat dimension directly in this calculator, not the leg size.