Structural Engineering & Statics
where the load goes
Concept

Embedment strength — where it appears

The bearing stress at which timber crushes under a dowel pressed into it, taken over the dowel's diameter and the member's thickness. It falls with the dowel's diameter and rises with the timber's density, and across the grain it is half to a third of its value along it.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as johansen model — the same set of essays touches all of them, so they are one junction rather than several.

Six ways for one dowel to fail, and the capacity is the smallest. Johansen's single-shear mechanisms for a 12 mm dowel through 40 and 40 mm members, each drawn as the shape it is: the dowel straight and the timber crushing, the dowel rotating rigidly, one plastic hinge, then two. The capacity under each is that mechanism's own, and the joint's strength is the smallest — 5.02 kN by mode c, which is the dowel rotates rigidly and both members crush. That is the kinematic theorem of plasticity: every mechanism gives an upper bound and the true collapse is the lowest of them. The crushed timber is shaded, and the circles are plastic hinges in the steel.

The smallest of six failures

Everything else in this collection that fails does so in one way at a time. A dowel through timber does not — the wood can crush while the steel stays straight, or one plastic hinge can form in it, or two — and the capacity is the smallest of the six, which is the kinematic theorem of plasticity applied to a joint rather than to a frame.

connections · Dowel yield The modes that tilt, and the ones that do not. Johansen's mechanisms for a 12 mm bolt with washers in single shear through 40 and 40 mm of timber of density 350 kg/m³, each with the rope term the fastener's axial resistance of 6.64 kN adds to it. Modes a and b, where the fastener only translates, gain nothing; the modes in which it tilts gain a quarter of its axial resistance, capped at a quarter of their own Johansen value. The joint's capacity rises from 5.02 kN (mode c) to 6.28 kN (mode c), 25 per cent.

The pull that Johansen left out

Johansen's mechanisms treat a timber fastener as a beam in a bed of crushing wood, bent and pushed sideways and nothing else. A real fastener that tilts across the joint is also pulled along its own axis, and if a washer or a thread resists the pull, it clamps the two members together and adds to what the joint can carry. The addition is a quarter of the axial resistance, it goes only to the modes in which the fastener tilts, and it is capped by fastener type — nothing for a dowel, a quarter for a bolt, all of it for a screw — which is how a screw keeps gaining strength past the thickness at which Johansen's capacity stops.

connections · Dowel yield

Named alongside it

The objects these essays reach for when they reach for this one.

BearingJohansen modelPlastic hingeTimberAnisotropyBound theoremsClamping forceCollapse loadConnection designDowel yieldDuctilityFree body

All concepts