Fillet Weld Size⚠ unverified

Understanding the Parameters

• Applied load $F$ — the service load the weld must transmit. In shear-on-throat design the direction of $F$ is deliberately ignored; the throat is checked in shear regardless, which is conservative for transverse loading (a transverse fillet is actually ~50 % stronger than a longitudinal one).

• Weld length $L$ — the effective length, i.e. the sum of every weld line resisting the load. Short welds lose a start/stop crater length; wrap-arounds and returns add length. Double the value for a weld on both sides of a plate.

• Allowable shear stress $\tau_{\text{allow}}$ — the throat stress limit. In AISC/AWS practice it is a fraction of the electrode tensile strength: $0.30\,E_{XX}$ (e.g. $0.30 \times 480\,\text{MPa} \approx 145\,\text{MPa}$ for E70 wire) times a resistance/safety factor. The registry default $100\,\text{MPa}$ is a round placeholder.

• Leg size $h$ — the fabrication dimension the welder controls. It is specified in standard increments (e.g. 3, 5, 6, 8, 10 mm). Codes set a minimum size tied to the thicker plate (to ensure the arc fuses it) and a maximum at plate thickness (minus 2 mm along an edge $\ge 6$ mm thick).

Derivation (Approaching a Proof)

Model the fillet as an isosceles right triangle with equal legs $h$. The throat is the perpendicular from the root corner to the hypotenuse (the exposed face). For a $45^\circ$ triangle that distance is

$$t = h\,\sin 45^\circ = h\,\cos 45^\circ = \frac{h}{\sqrt 2} = 0.707\,h.$$

The failure surface is the throat plane running the length of the weld, so its area is

$$A_{\text{throat}} = t\,L = 0.707\,h\,L.$$

The design assumption (AWS D1.1 / AISC) is that the weld fails in shear across this plane, so the throat shear stress is $\tau = F / A_{\text{throat}}$. Setting $\tau = \tau_{\text{allow}}$ and solving for the leg:

$$\tau_{\text{allow}} = \frac{F}{0.707\,h\,L} \;\Longrightarrow\; h = \frac{F}{0.707\,L\,\tau_{\text{allow}}}.$$

Dimensional check. $\dfrac{F}{L\,\tau_{\text{allow}}} = \dfrac{\text{N}}{\text{m}\cdot\text{Pa}} = \dfrac{\text{N}}{\text{m}\cdot(\text{N}/\text{m}^2)} = \text{m}$ — a length, as required for a leg size.

History and Development

Arc welding matured as a structural joining method in the early 20th century (Slavianoff and Kjellberg's coated electrodes, ~1900–1907), displacing riveting in ships, pressure vessels, and buildings by the 1930s. The shear-on-throat convention and the $0.707$ throat factor were codified by the American Welding Society (AWS D1.1 Structural Welding Code) and the AISC steel specification, giving designers a single, conservative rule that sidesteps the far messier true stress state at a weld toe. Electrode strength classes (E60, E70, …, the number being the tensile strength in ksi) let $\tau_{\text{allow}}$ be read directly from the filler specification.

Related Concepts: Fillet Weld Capacity, Throat Thickness, Weld Throat, Weld Size, Weld Throat Stress, Shear Stress

Notes: Registry uses shear-on-throat design (direction-independent, conservative). $L$ is the effective throat length — sum all resisting weld lines. Apply the code resistance/safety factor to $\tau_{\text{allow}}$; observe minimum/maximum leg-size limits. Real welds carry size tolerance and inspection requirements.