Weld Throat Stress⚠ unverified
Mechanical / Joints · Compute the shear stress on a weld throat
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| F | F | N | 1.0 | Applied load on the weld |
| L | L | m | 1.0 | Length of the weld |
| throat | throat | m | 1.0 | Weld throat dimension |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | τ | Pa | Shear stress on the weld throat, in pascals (Pa). Returns 0.0 when the throat dimension ``throat`` is not positive |
The science & history
Understanding the Parameters
- Applied load $F$ — the direct load carried by the weld; direction ignored (shear-on-throat, conservative).
- Weld length $L$ — the effective throat length resisting the load.
-
Size input ("throat" / leg $h$) — because of the $0.707$ in the formula, this must be the leg size for the result to be a correct throat stress. Passing the true throat double-counts the factor (see note).
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Effective throat $0.707\,h$ — the load-bearing thickness of the fillet (Throat Thickness); the shear area is $0.707\,h\times L$.
Derivation (Approaching a Proof)
For an equal-leg fillet, the effective throat is $t = 0.707\,h$ (Throat Thickness), so the throat shear plane over the weld length has area
$$A_{\text{throat}} = 0.707\,h\,L.$$
Under a direct load $F$, assuming uniform shear on the throat (the AWS/AISC convention),
$$\tau = \frac{F}{A_{\text{throat}}} = \frac{F}{0.707\,L\,h}.$$
This is the inverse of the capacity relation $F_{\text{cap}} = 0.707\,h\,L\,\tau_{\text{allow}}$ (Fillet Weld Capacity) and of the sizing relation Weld Size — the same physical statement in stress form. (The $0.707$ is correct here only because the size symbol denotes the leg $h$; if it denoted the throat $t$, the correct expression would be $\tau = F/(L\,t)$.)
Dimensional check. $\tau = \dfrac{F}{0.707\,L\,h} = \dfrac{\text{N}}{\text{m}\cdot\text{m}} = \dfrac{\text{N}}{\text{m}^2} = \text{Pa}$ — a stress, as required.
History and Development
Throat shear is the governing check of the AWS/AISC fillet-weld method: reduce any fillet to its effective throat, assume uniform shear there, and compare against an electrode-based allowable. The recurring confusion between leg and throat in tools and tables — exactly the ambiguity this card's input label raises — is why codes are explicit that the "size" of a fillet is its leg, while the strength is referred to the throat ($0.707\times$ leg).
Related Concepts: Weld Size, Fillet Weld Size, Fillet Weld Capacity, Throat Thickness, Weld Throat, Shear Stress
Notes: Input labelled "throat" must be the leg $h$ (the $0.707$ converts it); passing the true throat overstates $\tau$ by ~41%. Inverse of Fillet Weld Capacity / Weld Size. Shear-on-throat basis.