Distortion — where it appears
Named by 7 essays across 2 fields — each of them below, with the objects they name alongside it.
The section that will not keep its shape
A box girder is closed, so torsion costs it almost nothing. What an eccentric load actually does to it is something a torsion calculation contains no term for — the rectangle becomes a parallelogram, in its own plane, along the whole length of the span.
One diaphragm is nearly none
A box girder's distortion decays over a length the section decides, and on a sixty-metre span that length is twenty-four metres. So a single diaphragm at midspan sits further from each end than the distortion can reach and removes a third of the problem; three diaphragms remove nine tenths. The spacing rule is not span over five — it is a property of the plates.
Twice the moment, four times the brace
A lateral brace has to be on the right flange and its demand is very nearly linear in the load. A torsional brace has no flange to be wrong about, and its demand is exactly quadratic — so the restraint that is indifferent to where it is attached is the one that gets expensive fastest.
Three actions on one web
A load applied off the centreline of a box girder is three actions at once, and every textbook decomposes it into them. What the decomposition does not say is that all three land on the same piece of plate — added on one web and subtracted on the other, so the two walls of one section differ by a factor of ten.
The diaphragm that is a few angles
A box girder's diaphragm holds its section square against the distortion an eccentric load drives. It does not have to be rigid; it has to be stiff against the girder's own resistance to a point racking load, which is small — twice the section's frame stiffness times its decay length. A cross-frame of two 1,000 mm² diagonals is twenty-six times that and holds the warping stress at the rigid value, while a 10 mm plate is five hundred times it. The cross-frame lets the section rack three times as far as a plate, which leaves the walls bending at 5 N/mm² instead of 1.5, against 275 with no diaphragm at all. And its diagonals carry nearly a rigid diaphragm's force whatever their stiffness, so it is sized for strength.
The deck whose frame is its crossbeams
A steel box girder resists distortion as a beam on an elastic foundation, the foundation being its walls' transverse bending. When the top flange is an orthotropic deck, that foundation is almost absent between the crossbeams and concentrated at them, so the box sits on a row of springs, not a bed. Smeared into a bed, the springs give the right answer to within a few per cent as long as they are closer together than the bed's own decay length — and the rule holds for every crossbeam stiffness on one curve. Past that spacing the frames act as separate diaphragms and the warping stress between them doubles.
The stiff frame among soft ones
A steel box girder with an orthotropic deck is held in shape by a frame at every crossbeam, and its designers usually add a stiffer frame — a pair of diagonals across the box — at every few crossbeams as well. Whether the soft frames between can be left to do the work depends on one length: how far a distortion reaches along a box held by the soft frames alone. Ring frames welded into the webs and bottom flange hold it to six and a half metres, and then cross-frames twenty metres apart barely change the distortion and add a peak of warping stress at each one, where a stiff frame grips a box that was distorting gently. Crossbeams that are only tees under the deck reach twenty-one metres, and then the box between the cross-frames distorts as if the crossbeams were not there.
Named alongside it
The objects these essays reach for when they reach for this one.
WarpingBox girderDiaphragmCharacteristic lengthElastic foundationLoad pathShear flowTorsionDecay lengthEccentricityFatigueOrthotropic deck