Structural Engineering & Statics
where the load goes
Concept

Creep buckling — where it appears

The slow loss of stability of a concrete member or arch whose deflection grows under sustained load as the concrete creeps. A load well below the short-term critical one can reach it in years, because creep softens the stiffness that resisted the sway.

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

The deflection goes on growing, and sometimes it does not stop. Second-order deflection of a sustained-loaded concrete column against age, on a log time axis. Creep takes the effective modulus down, which takes the buckling load down with it — from 11580 kN on the day to 3309 in the long term, 29 per cent of it — so the amplifier 1/(1 − N/N_cr) grows even though nothing was added to the load. At 2200 kN the column settles: 25 mm of eccentricity on the day and 60 mm at the end, a factor of 2.4 for a load that never changed. At 5294 kN — still only 46 per cent of the day-one critical load — it does not settle, and the divergence arrives at 55 days for no new reason at all.

The column that fails years later

A concrete column under sustained load goes on straining at constant stress, so its deflection grows — and because the second-order moment is the load times that deflection, the demand grows with it. There is a load below which the two settle and one above which they never do.

stability · Creep buckling A concrete rib creeps into snapping long before its prop matters. For the shallow pinned arch of rise 6.0 radii of gyration under a sinusoidal load, propped at its crown by a concrete column of stiffness κc = 3.5, the creep coefficient at which a load that stays on loses equilibrium, against that load as a share of the day's critical load: a steel rib on the creeping column (solid), which loses only the column's share, so that by a creep coefficient of 3 no load below 85 per cent snaps; and a concrete rib whose column creeps with it (dashed), whose lasting load acts as if (1 + φ) times larger, so that it snaps at φ = pcr/p − 1; dotted, a creep coefficient of 2. At half the critical load the concrete arch snaps at a creep coefficient of 1.00, at 70 per cent at 0.43; the steel arch on its column does not snap at either.

The column that creeps under the arch

A shallow arch propped at its crown by a stiff enough column stops snapping — the sideways branch it would have fallen down turns upwards. If the column is concrete, it creeps under the force it holds, and after a decade it holds that force as a spring a third as stiff, well on the side where the arch snaps. But a load that arrives in seconds does not meet the crept column; it meets the column's instantaneous stiffness, from a rest length that creep has merely moved down, and the arch's branch still rises. Creep reaches only the load that stays on, and there it can take back only the column's own share — 13 per cent of it. A concrete rib is another matter: it creeps itself, and a lasting load at half its critical load snaps it before its creep coefficient reaches one.

stability · Snap-through

Named alongside it

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

CreepEffective modulusImperfectionAmplificationArchBifurcationBucklingDivergenceDuration of loadEccentricityFirePost-buckling

All concepts