Tenon half the depth of the beam? You have a quarter of the strength

(½)² = ¼. And the fix costs one saw cut.

A beam does not fail in bending. It fails in HORIZONTAL SHEAR, along the neutral axis — and once the split starts, complete failure is likely. Chappell calls it “the primary cause of beam failure”.

When you cut a tenon on the underside, the neutral axis rises from the centre of the beam toward the centre of the tenon. The factor is (d/h)². A tenon half the depth: (½)² = ¼. You have a quarter of the shear strength left.

In the book's own numbers: a white pine 6×6 with a 3 in tenon carries 510 lb. The same 6×6 with a 4½ in tenon — three quarters of the depth — carries 1,147.5 lb. Nearly double, for 1½ in more wood.

And here is what almost nobody applies: if the shoulder is cut on a BEVEL instead of square, the strength returns to the net depth of the tenon. The (d/h)² factor no longer applies at all. Same timber, same tenon, one more saw cut.

The generator applies the penalty, and tells you when the bevel makes it vanish.

Source : chappell-calcul-assemblages-gros-bois.md §2