Structural Engineering & Statics
where the load goes
Concept

Vortex-shedding — where it appears

The alternate shedding of vortices from a bluff body in a steady flow, at a frequency proportional to the wind speed. When it coincides with a structure's own frequency the two lock in and the response grows until damping limits it, which is a resonance whose forcing frequency the structure partly controls.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

Lock-in: the frequency the wind sheds at, and what it does to the chimney. A 1.2 m cylinder at 0.9 Hz. Vortices leave it at St·U/D, so the critical speed at which they match the structure is 6 m/s — a breeze, met many times a year rather than once in fifty. The upper panel shows the shedding frequency locking on to the structure across a band from 5.1 to 7.8 m/s; the lower shows the amplitude that results. At a Scruton number of 11.2 the peak amplitude is 180.94 mm, which is 15% of the diameter.

The wind that brings its own frequency

Every other load in this subject arrives at whatever rate it happens to arrive at. Vortex shedding arrives at a rate set by the wind speed — so for any chimney, mast or cable there is always a wind speed at which the shedding matches the structure exactly, and it is a breeze rather than a storm.

dynamics · Vortex-shedding What a damper at the anchorage can do, and the ceiling it cannot pass. Modal damping against damper size for a 200 m stay at 4500 kN, with the damper 4 m from the anchorage — 2.0 per cent of the length. Each curve is a mode, found as a complex root of the taut string with a viscous damper in it rather than from a formula. Every one of them peaks at 1.00 per cent of critical, which is x/2L exactly, and the peaks are at different damper sizes — a higher mode wants a smaller damper, because it moves faster at the same amplitude. The curves are flat near their peaks: half the optimum coefficient gives 80 per cent of the ceiling, and so does twice it.

The damper that is too near the end

A stay cable has almost no damping of its own, so it is given a damper — and the damper cannot go where the motion is, because the middle of a two-hundred-metre stay is a hundred metres above the road. What it can supply is then decided by one length, and no amount of damper changes it.

dynamics · Cable dynamics However stiff the ties, a free line stops short. The first three frequencies of stays 180, 150 and 120 m long joined by cross-ties, against the stiffness of each tie from 1.0 kN/m to 1000 MN/m, with the line free at its ends and, dashed, anchored to the deck at both ends with the same stiffness. With the line free the first frequency rises from 0.73 Hz and levels off at 0.82 Hz, however stiff the ties are made — short of the 1.01 Hz of the 120 m stay, which a free line cannot pass. Anchored, the first frequency reaches 1.09 Hz. At the 6.0 MN/m marked, the free line gives 0.82 Hz and the anchored line 1.09 Hz.

The line of ties that stops short

Cross-ties are the one intervention on a stay cable that changes its frequencies rather than damping them, and the usual account says they lift the stays out of the range that excites them. A line of ties that is not anchored to anything cannot lift the first frequency above the shortest stay's own, however stiff the ties are made. What lifts it is carrying the line to the deck.

dynamics · Cable dynamics The chimney that locks in most is tuned above the commonest wind. Lock-in cycles a year at the full lock-in amplitude that do the same damage as the whole band (millions), for 1.2 m cylinders of every frequency in hourly mean winds at the top Rayleigh-distributed with scale 5.5 m/s, against the critical speed as a multiple of that scale. Solid, the count through the amplitude envelope; dashed, EN 1991-1-4's closed form 2·T·f₀·ε₀·(Ucr/v0)²·exp(−(Ucr/v0)²) at band widths ε₀ of 0.1 and 0.3. All three peak at a critical speed of √(3/2) = 1.22 times the scale, 6.7 m/s — above the commonest wind (0.71) and the mean (0.89). The envelope is EN's formula with ε₀ = 0.22. The chimney drawn, at 6.0 m/s, collects 4.6 million a year.

The breeze that uses up a chimney

A chimney that locks in to vortex shedding at a breeze is usually told to accept the motion and check its fatigue. Counting the cycles a real wind climate delivers turns that into arithmetic, and the arithmetic has two surprises. The chimney that collects the most cycles is not the one tuned to the commonest wind but to one a fifth stronger than the climate's scale, so stiffening a chimney can shorten its life. And damping does not lengthen the life in proportion: it ends the count, all at once, at the damping that puts the largest stress range under the detail's cut-off.

dynamics · Vortex-shedding

Named alongside it

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

DampingResonanceCable dynamicsEigenvalueFatigueLock-inMode shapeScruton numberStay cableTaut stringAeroelasticityCross wind response

All concepts