Structural Engineering & Statics
where the load goes
Series

Twist serviceability — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The deformation with no limit against it. A 8 m open section carrying 12 kN/m at an eccentricity of 75 mm from its shear centre. The torque is small — 900 Nmm per mm — and the twist is not: 2.55° at mid-span with the ends restrained against warping, against 9.09° if they are not, a factor of 3.57. What that angle does is move the flange tip sideways by 8.9 mm — 62 per cent of the member's own vertical deflection, and 28 per cent of the span/250 that vertical deflection is checked against. The same load on a closed section of the same depth moves it 0.15 mm, 60 times less. No code gives a limit for this quantity, so it is the one movement in the collection that is computed only after somebody has complained about it.

    The movement with no limit against it

    Every code in the world gives a deflection limit. None gives a twist limit — and a beam loaded off its shear centre twists. On an open section a modest eccentricity moves the flange tip sideways by three fifths of the sag that does get checked, and nothing anywhere says whether that is acceptable.

    part 1 · deflection
  2. 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.

    part 2 · deflection
  3. A point at mid-span is worth twice its total spread out. The mid-span twist of an open section 8 m long on forks, carrying 12 kN/m at 75 mm from its shear centre, against the stiffness of one rotational spring at mid-span, logarithmic; dashed, the twist with the uniform deck of 5 kN·m per metre per radian, whose whole restraint is 40 kN·m per radian. A mid-span spring of 19.5 kN·m per radian — 49 per cent of the deck's total — twists the beam as little as the deck does; the deck's whole total at mid-span leaves 3.13°.

    The restraint that works where the twist is

    A deck fastened along a beam's top flange resists its twist a little everywhere. A secondary beam framing in at mid-span resists it a lot at one point. Given the same total stiffness, the point does better — half the deck's total at mid-span holds the beam as well as the whole deck — because it works where the beam twists most. But a point restraint has a price the deck never charged: it takes the torque through one connection, up to three fifths of the whole applied torque, and if it is stiff it moves the worst twist out to the quarter-points rather than removing it.

    part 3 · deflection
  4. A secondary holds more than it twists once its connection passes a few tens of kilonewton-metres per radian. The mid-span twist of the 8 m primary beam of 12 kN/m at 75 mm off its shear centre, with a 6 m 356 × 171 × 51 UB framing in at mid-span whose 60 kN reaction acts 60 mm off the shear centre, against the rotational stiffness of the secondary's connection on a logarithmic scale, in series with the secondary's own 3EI/L of 14,453 kN·m/rad. Dashed, the 6.25° with no secondary. On the deck's side the secondary is worse than none below 33 kN·m/rad and better above it: 9.12° at 10, 3.28 at 100, 0.47 at 1,000. On the far side its torque opposes the deck's (0.89° at 10); as a pair, the torques cancel (1.05° at 100). EN 1993-1-8 calls this secondary's connection nominally pinned below 2,409 kN·m/rad (dotted).

    The secondary beam that twists what it holds

    A secondary beam framing into a twisting primary at mid-span is the best restraint a primary can have — concentrated exactly where the twist is. It is also a load: its reaction arrives on the primary's web, off the shear centre, as a torque at exactly the same place. Which wins is decided by the connection, and the threshold is low: a fin plate stiffer than about 33 kN·m per radian, a seventieth of what still counts as a pin, makes the secondary hold far more than it twists. The bolts' free play is another matter, because the torque acts from the first millimetre and the restraint only once the play is taken up.

    part 4 · deflection

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