Structural Engineering & Statics
where the load goes
Concept

Torsional restraint — where it appears

A restraint that resists a beam's twist rather than the sideways movement of one flange — a cross-frame, a diaphragm or a deck connected through the web. It works whatever its height in the section, and its stiffness, not its strength, decides how much buckling moment it buys.

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

A brace on the wrong flange never gets there, however stiff it is. The critical moment of an 8 m beam against the stiffness of a single midspan brace, drawn three times for the three heights the brace could sit at. On the compression flange it climbs from 143 kNm to the two-half-wave plateau of 447 — the beam braced into two 4.0 m beams — and reaches 99% of it at 447 kN/m. At the shear centre it needs 2252 kN/m, 5.0 times as much. On the tension flange it never arrives at all: at the stiffness that would have done the job on the other flange it has bought a factor of 1.068, and a stiffer brace in the same place buys the same nothing. Past the plateau the beam stops using the brace, which is where the idea of an ideal stiffness comes from.

The brace on the wrong flange

A brace on a column has one property that matters, and it is stiffness. A brace on a beam has two, and the second decides whether the first is worth anything: put the identical restraint on the tension flange and it does not reach the answer at any stiffness whatever.

stability · Beam bracing Below its ceiling, a row of braces is only its total. The critical moment of a beam 24 m long whose unbraced critical moment in uniform bending is 837 kN·m, held by one, two, three or five torsional braces equally spaced along it, against the braces' total rotational stiffness. At 4,336 kN·m/rad in all, the rows of two, three and five give 3,815, 3,726, 3,578 kN·m: how the stiffness is divided hardly matters, while one has already stopped. Each row then stops at its own ceiling, where the braces are stiff enough to be nodes and the beam buckles between them in one more half-wave than it has braces: 2,637 kN·m for one, 5,585 kN·m for two, 9,704 kN·m for three, 21,466 kN·m for five. The dashed line is 5,627 kN·m, the moment the beam is asked to carry; one and two cannot reach it however stiff they are.

The stiffness a row of braces shares out

One torsional brace at midspan has a ceiling, the moment at which the beam gives up twisting it and buckles in two half-waves instead. A row of braces raises the ceiling with every brace added, and the stiffness each must have to reach its ceiling rises with the count — seventy-four times as much for eight braces as for one. That is the right answer to the wrong question. Asked for the moment the beam has to carry rather than for its ceiling, a row of braces needs very nearly the same total stiffness however many it is divided between, so each brace gets softer as the count goes up. The count has one job, which is to put the ceiling above the moment; the stiffness has the other.

stability · Beam bracing

Named alongside it

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

Critical momentLateral-torsional bucklingBeam bracingBracingBuckling modeCompression flangeEffective lengthEigenvalueEnergy methodIdeal brace stiffnessImperfectionMode shape

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