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Geometry beats material — page 11

Essays 241 to 243 of 243 on this thread, in the same order.

A deck holds the middle of the span. The twist along an 8 m open section on forks, free to warp, carrying 12 kN/m at 75 mm from its shear centre — 900 Nmm of torque per mm of span. With nothing fastened to it the beam twists 6.25° at mid-span; a deck resisting the top flange's rotation at 5.0 kNm per metre per radian holds it to 4.20°, and one four times as stiff to 2.10°. The deck works where the beam is weakest, in the middle; near the supports the beam's own torsional stiffness does most of the work whatever is fastened to it.

A deck is a spring, not a wall

An open-section beam loaded off its shear centre twists, and the usual reassurance is that the deck fastened to its top flange will stop it. The deck resists the flange's rotation with a stiffness per metre of span, and that stiffness has to be compared with the beam's own. On an 8 m beam a screwed deck of ordinary stiffness removes a third of the twist; on a 16 m beam the same deck removes three quarters, because the beam's torsional stiffness falls with the square of its span and the deck's does not.

Ductile until it was welded. A 2.0 m 6082-T6 member pulled in tension, as supplied and with one weld across it whose heat-affected zone is 60 mm long: the load per unit of parent section against the member's overall strain, to the maximum load, where the weaker part begins to neck. The plain member reaches 310 N/mm² at 7.0% strain, 140 mm of stretch. The welded one reaches 185 N/mm² at 0.62%, 12.3 mm — 8.8% of the plain member's, and the parent never reaches its proof stress of 260 N/mm². (uniform elongations assumed: 7.0% for the parent, 12% for the zone)

Materials

The soft zone that takes all the stretch

The metal beside a weld in heat-treated aluminium is weaker than the rest of the member and more ductile, and it is tempting to read the second fact as a consolation. It is not. A member welded across stretches only where it is weak, and the weak zone is sixty millimetres long; a two-metre 6082-T6 tie that would extend 140 mm before necking extends 12 mm once welded, and the parent metal never yields at all. What decides it is one ratio, the zone's ultimate strength over the parent's, and the ductility returns only when that ratio reaches one.

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.

Connections

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.

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