Structural Engineering & Statics
where the load goes
Concept

Clamping force — where it appears

The normal force pressing two surfaces together, supplied by reinforcement crossing a crack or by preload in a bolt, which lets friction or interlock carry a shear. It is a force perpendicular to the sliding plane doing work in a direction nothing is being applied in, and it is what turns a crack from a discontinuity into a joint.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

A check made on a perimeter, not on a section. One bay of a flat slab, 7.2 m square, on a 400 × 400 mm column. The heavy closed line is the control perimeter, 2d from the column face with its corners rounded at that radius — 4427 mm long against 1600 mm round the column itself. The shaded area inside it delivers no shear across it and is subtracted from the load; everything outside arrives through the perimeter. At 12 kN/m² that is 604 kN across 4427 × 225 mm, a shear stress of 0.606 N/mm² against a resistance of 0.658.

A check made on a perimeter, not on a section

Every shear check in this collection is made on a plane cut through a member. A slab sitting on a column has no such plane, because the shear leaves in every direction at once — so the check is made on a closed line, and a line grows with the column while the load grows with the square of the bay.

internal-forces · Punching shear The coefficient is a slope, and that is why it can exceed one. The crack magnified: two rough faces, drawn as a sawtooth at 54° to the plane. Sliding one over the other cannot happen without lifting it, so a shear displacement forces a separation in fixed proportion — the tangent of that angle, which is the number written down as a coefficient of friction and here is 1.40. The bars crossing the plane are stretched by the separation and clamp the faces back together; they are not carrying the shear, they are supplying the normal force that lets the roughness carry it. A bar that is not anchored on both sides supplies nothing.

Shear across a crack that is already there

Every shear calculation in this collection starts from an uncracked solid — a principal stress, a shear flow, a diagonal tension. This one starts after the crack, on a plane with no tensile strength at all, and the coefficient it uses is not a coefficient of friction. It is the slope of the roughness.

internal-forces · Shear friction The bolt force is the larger of two lines. What an M20 bolt in a 25 mm tee flange actually carries, against the tension applied to the flange. Preloaded to 171 kN it starts there and climbs at Φ = 0.185 — the bolt's own stiffness over the bolt's plus the clamped plates', 857 against 3781 kN/mm — so 18 per cent of every kilonewton applied reaches it and the rest is unloading the contact. At 138 kN the contact runs out and the line joins the one an ordinary bolt has followed from the start, climbing at 2.12. The two lines meet, so the strength is the same either way; what differs is the slope, by a factor of 11.5. The flange's own mechanism is at 172 kN, comfortably past the crossing.

The bolt that was already stretched

Prying is a lever that needs the flange to lift before it can act, and a preloaded bolt does not let it. The bolt carries a fifth of every kilonewton applied until the plates part, and everything after that is the ordinary calculation — which is why preload changes the fatigue answer by a factor of a thousand and the strength answer by nothing at all.

connections · Prying 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 Lean a screw and its bending stops mattering. The peak load on an 8 mm fully threaded screw (yield moment 20 N·m, tensile capacity 20 kN) through two 100 mm softwood members of density 350 kg/m³, against the angle it is driven at to the joint: the joint, its two resistances added slip by slip (solid); the thread's alone, resolved along the joint with its friction (dashed); the bending and embedment's alone (dotted); and the square screw with the rope effect, 5.9 kN (thin). At 45 degrees the joint carries 13.4 kN, 2.3 times the square screw, of which the bending gives 1.8; at 30, 19.1. The bending is the larger share only steeper than 85.7 degrees, within 4.3 of square. Withdrawal is taken to peak at 1.5 mm of axial movement and soften after it; bending follows Foschi's curve from EN 1995-1-1's slip modulus — shapes, not measurements.

The screw that is pulled instead of bent

A screw square to a timber joint resists slip by bending, and its thread is engaged only when it has tilted far enough to be pulled. Lean the same screw to 45 degrees and the slip pulls it from the first millimetre. An 8 mm screw through two 100 mm members goes from 5.9 kN to 13.4, reached after 2.2 mm of slip instead of more than twelve, and the bending that Johansen's model is about becomes an eighth of the joint. The price is a joint that holds one way better than the other.

connections · Dowel yield

Named alongside it

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

Aggregate interlockBearingEmbedment strengthFailure surfaceFrictionJohansen modelPlastic hingeShear frictionTimberAnchorageBolt tensionColumn head

All concepts