Throat Thickness⚠ unverified
Mechanical / Welds · Compute the effective throat thickness of a fillet weld
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| h | h | m | 1.0 | Weld leg size |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | t | m | Effective throat thickness, in metres (m) |
The science & history
Understanding the Parameters
-
Leg size $h$ — the measurable dimension of the fillet along each fusion face. For an equal-leg ("mitre") fillet both legs are $h$ and the weld face is the hypotenuse.
-
Effective throat $t$ — the perpendicular from the root to the face. It is effective because it deliberately ignores any extra "reinforcement" (convex bulge) or penetration beyond the root: design credit is taken only for the theoretical triangle. A concave weld can actually have a throat smaller than $0.707\,h$, so this factor is an idealisation that inspection must protect.
-
The $0.707$ factor — this is $\cos 45^\circ = 1/\sqrt2$, valid only for equal legs. An unequal-leg fillet ($h_1 \ne h_2$) has throat $t = h_1 h_2 / \sqrt{h_1^2 + h_2^2}$, and a deep-penetration process may be credited a larger throat under the code.
Derivation (Approaching a Proof)
Take the fillet's cross-section as an isosceles right triangle with the two equal legs of length $h$ meeting at the root, at $90^\circ$. The hypotenuse is the exposed weld face. The throat is the altitude dropped from the right-angle vertex (the root) to the hypotenuse.
For a right triangle the altitude to the hypotenuse equals the product of the legs divided by the hypotenuse. With equal legs $h$ the hypotenuse is $h\sqrt2$, so
$$t = \frac{h \cdot h}{h\sqrt 2} = \frac{h}{\sqrt 2} = h\,\cos 45^\circ = 0.707\,h.$$
Equivalently, the throat subtends $45^\circ$ from either leg, and its length is the leg projected onto the throat direction: $t = h\sin 45^\circ$.
Dimensional check. $t = 0.707\,h$ carries the units of $h$ directly: $\text{m} \to \text{m}$. The $0.707$ is the dimensionless geometric factor $\cos 45^\circ$.
History and Development
The throat concept underlies the entire allowable-stress treatment of fillet welds. When arc welding replaced riveting in structural steel (1920s–1930s), designers needed a single characteristic dimension to attach an allowable stress to; the effective throat — smaller and more conservative than the leg — became that dimension in AWS D1.1 and the AISC specification. The $0.707$ factor turned every fillet-weld calculation into "throat area $\times$ allowable shear", the compact rule still taught today.
Related Concepts: Fillet Weld Size, Fillet Weld Capacity, Weld Throat, Weld Throat Stress, Weld Size
Notes: $0.707 = \cos 45^\circ$ applies to equal-leg fillets only; unequal legs use $t = h_1 h_2/\sqrt{h_1^2+h_2^2}$. Effective throat ignores reinforcement/penetration — a conservative idealisation. Deep-penetration processes may earn a larger credited throat under code rules.