Structural Engineering & Statics
where the load goes
Concept

Sway frame — where it appears

A frame whose joints can translate sideways as well as rotate, so that its columns' effective lengths exceed their true lengths. Preventing the sway with a single restraint carrying no vertical load can change the critical load by a factor of three.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

The ends decide the length that matters. Four columns of identical height and section, buckling under four sets of end conditions. The effective length factor is the fraction of the column that behaves like a pin-ended one, and the buckling load goes as its inverse square.

The ends decide the length that matters

Four columns of identical height and section, buckling at loads sixteen times apart. Nothing differs but what is holding the two ends.

stability · Effective length One restraint, and several times the load. The same portal — the same columns, the same beam, the same steel — buckling with its head held against sway and with its head free to sway. The braced frame's critical load is 16.46 EI/L² and the swaying one's is 5.69 EI/L², a factor of 2.89, and the effective length factor that comes out of each eigenvalue is 0.774 against 1.317. Both are eigenvalues of the assembled frame at a beam-to-column stiffness ratio of G = 1.00; the buckled shapes are the mode vectors themselves, drawn at 18 per cent of the storey height so that the movement can be seen.

Held, and not held

One horizontal restraint at the head of a storey, carrying no vertical load whatever, moves the critical load of the columns beneath it by a factor of 2.89. Effective length is a property of the frame, not of the member.

stability · Sway stability What the frame notices. An 8 m by 4 m portal whose columns stand on bases of every rotational stiffness, in units of the column's EI/L on a logarithmic scale: solid, the portal's sway under a load at the knee as a multiple of the fixed-based portal's; dashed, the columns' effective length factor in sway (fixed bases 1.13, pinned 2.26). Bolts sleeved 300 mm, 5.3 EI/L: 1.45 times the fixed portal's drift, an effective length factor of 1.30 and 75 per cent of its buckling load; as detailed, 9.1 EI/L: 1.28 times the fixed portal's drift, an effective length factor of 1.23 and 83 per cent of its buckling load; rigid by EN 1993-1-8, 30.0 EI/L: 1.09 times the fixed portal's drift, an effective length factor of 1.16 and 94 per cent of its buckling load.

The fixed base the bolts decide

A column base drawn as fixed is a spring, and the component method says what it is made of: the grout squeezed under the flange, the plate bending under the bolt row, and the anchor bolts stretching over their free length. For a 500 mm plate on two M24 bolts the bolts are three fifths of its flexibility, so the base comes out at nine times the column's EI/L — under a third of what EN 1993-1-8 calls rigid — and no thickness of plate can lift it above fifteen. Leave the bolts free in sleeves for erection tolerance and it falls to five. The frame on it drifts 28 per cent more than a fixed-based one and buckles at 83 per cent of the load.

connections · Base plate

Named alongside it

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

Effective lengthBracingBuckled mode shapeAnchor boltBase plateComponent methodCritical loadEigenvalueEnd restraintJoint classificationPryingRotational stiffness

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