Transverse shear — notched beam ends and integral joinery

Chapter 1 sized the roof beam for bending in the middle of its span, where moment is highest. But beams don't just fail in the middle — they can fail right at the support, in a completely different way: horizontal shear, where the beam tries to slide along its own grain.

The formula: τ = VQ/(Ib), where V is the shear force (highest right at the supports, not the middle), Q is the first moment of area of the part of the cross-section above the point being checked, I is the moment of inertia, and b is the width. For a solid rectangular beam, the maximum horizontal shear stress lands at the neutral axis (the center), not the top or bottom edge — which is the opposite of where bending stress is worst.

Why this is the Ogopogo joint chapter

A notch cut into the bottom of a beam end (common in traditional joinery, and relevant to how the Ogopogo modular joints seat) removes material right where shear is highest and reduces the beam's effective depth right at the point of maximum shear stress — a notched end can fail in horizontal shear at a load a full-depth end would shrug off. This is the mechanism behind a failure mode that looks like nothing (no visible bend) until the beam splits lengthwise along the grain near a notch or bolt hole. It's also the reason integral joints (mortise-and-tenon, French cleats) need their bearing shoulder sized generously rather than cut thin to save material — the shoulder is carrying shear, not just holding shape.

Open items for a later pass

Exact notch/joint geometry for a specific Ogopogo connection, once a real joint detail exists to check against. Breyer Chapter 3 works the notched end with the NDS rules (a notch on the bottom face may not exceed a quarter of the beam depth, and the shear capacity falls with the square of the depth ratio), and the calculator on this page uses that form.