Structural Engineering & Statics
where the load goes
Concept

Orthotropic deck — where it appears

A steel deck plate stiffened by longitudinal ribs or troughs and carried on crossbeams, with different stiffnesses in its two directions. Its transverse stiffness comes from the crossbeams, so across the box it is concentrated at points.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

One plate, three systems, one stress. The stress at the rib-to-deck weld of an orthotropic deck, split by which system produced it. The main girder contributes 120 N/mm², the crossbeam 34 and the trough 13, and they add to 167 because the deck plate is the top flange of all three at once. A calculation that treats the crossbeam as a support rather than a structure understates the total by 26 per cent. The stress RANGE at that weld is 47 N/mm², which is the number the whole deck is designed by, because the weld is a low fatigue category running the entire length of the bridge.

One plate and three structures

An orthotropic deck is a single steel plate stiffened by troughs, sitting on crossbeams, sitting on main girders. Nothing about that is unusual until it is noticed that the plate is the top flange of all three, so a wheel standing on it loads every one of them at once.

sections · Orthotropic deck Ring frames close together are a continuous foundation. The corner-angle change along a 60.0 m box 4.0 m wide and 2.5 m deep, its top flange an orthotropic deck of 14 mm plate, its webs 14 mm and its bottom flange 20 mm, under 45 kN/m at 2.0 m from its centre line, in milliradians, with ring frames whose crossbeam has a second moment of 1.7 × 10⁹ mm⁴ every 4.0 m and every 12.0 m (solid), and each row smeared into a continuous foundation of the same stiffness per metre (dashed). At 4.0 m the two are indistinguishable, 1.12 and 1.12 at the worst point; at 12.0 m the box distorts between its frames, to 3.45 against 3.33. Without any frames the same deck distorts 145.

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.

sections · Box distortion Whether the cross-frames' spacing matters depends on the crossbeams between them. For the 60.0 m orthotropic box 4.0 m wide and 2.5 m deep under 45 kN/m at 2.0 m from its centre line: the largest distortional warping stress against the spacing of cross-frames of two 1,900 mm² diagonals, with nothing between them (dashed), with open tee crossbeams every 4.0 m (light) and with ring frames every 4.0 m (solid); dotted, the ring frames alone, 4.1 N/mm². At 8 m, 3.8, 3.8 and 3.1 N/mm²; at 20 m, 21.8, 21.7 and 7.1; at 30 m, 60.8, 59.2 and 7.3.

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.

sections · Box distortion

Named alongside it

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

Box girderCharacteristic lengthDiaphragmDistortionElastic foundationWarpingDetail categoryEffective widthFatigueGrillageLoad pathShear lag

All concepts