Shear Stress on a Fillet Weld Throat

Everything about fillet weld design turns on one number, and it deserves to be derived rather than memorised.

Look at a fillet weld end-on. Its cross-section is very nearly a right-angled triangle with the two perpendicular sides — the LEGS — lying along the two plates being joined. For the standard equal-leg fillet both legs are the size w that appears on the drawing and on the welding gauge. The weld cannot fail along a leg, because a leg is a fusion face rather than a section through metal. It fails across the THROAT: the shortest path from the root of the joint to the face of the weld, which is the altitude of that triangle from the right angle to the hypotenuse. For an isosceles right triangle that altitude is $w/\sqrt{2} = 0.7071\,w$, and 0.707 is simply $1/\sqrt{2}$ rounded.

The classic error is to compute on the leg. It over-states the weld's capacity by $\sqrt{2}$, which is forty-one per cent, and it is easy to make because the leg is the number on the drawing while the throat is not. Two limits on the 0.707: it holds only for an EQUAL-LEG fillet, and an unequal-leg weld needs its own throat measured on its own geometry; and it is the nominal throat, ignoring root penetration beyond the theoretical root, which codes permit you to count only when the process has been qualified for it.

The other convention that surprises people is that a fillet weld is checked in SHEAR on the throat regardless of which way the load pulls. A transverse fillet is genuinely stronger than a longitudinal one — perhaps thirty per cent, since the throat plane sees a different combination of normal and shear stress — but design practice treats them alike and takes the conservative shear case for both. It is a simplification that has stood up well and it removes a whole class of ambiguity from weld drawings.

The allowable belongs to the weld metal, not to the plate. It comes from the electrode classification, and the AWS structural relationship is public and widely printed: allowable shear on the throat is 0.30 times the electrode's nominal tensile strength, so a 70 ksi electrode gives 21 ksi and an E48 wire about 190 MPa on the equivalent basis. Check the base metal separately — a weld stronger than the plate it sits on does not make the joint stronger, it just moves the failure into the plate.

Two practical limits sit outside the arithmetic. Codes set a MINIMUM fillet size tied to the thickness of the thicker part joined, because a small weld on a heavy plate is quenched by the surrounding metal, cools too fast, and cracks. They also set a MAXIMUM along a plate edge, usually the thickness less about 1.6 mm, so the edge is not melted away. Between those, prefer length to size: a fillet twice as big takes roughly four times the passes and the deposited metal, while twice the length costs twice.