Structural Engineering & Statics
where the load goes
Concept

Amplification factor — where it appears

The ratio by which a response exceeds the one a slowly applied load of the same size would produce. For a suddenly applied static load it is two, and near a structure's own frequency it is bounded only by the damping.

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

The load that makes itself worse. The amplification of a deflection against the ratio of applied load to buckling load. A structure at half its buckling load deflects twice as far as first-order analysis predicts, and the curve runs away well before the load is reached.

The load that makes itself worse

A structure that has leaned carries its weight off the axis, which makes it lean further. The amplification is one over one minus the load ratio, and it runs away long before the buckling load.

stability · Second-order A column that was never straight. Load against lateral deflection at mid-height, for a column starting with an initial bow of 0.002. There is no critical value to reach: the deflection grows from the first increment, slowly at first and then without bound as the ratio approaches 1.00 — which is the Euler load, and which the column therefore never attains. The perfect column, drawn for comparison, sits on the vertical axis until it arrives there and then has no answer at all.

The column that was never straight

Euler's load is the load at which a perfectly straight column becomes indifferent to being bent. No column is perfectly straight, so no column ever reaches it — and the load it never reaches can still be measured.

stability · Buckling The water that will not run off. Water depth against sag at the middle of the bay, for a roof bay starting with a reversed construction camber of 0.01. There is no critical value to reach: the deflection grows from the first increment, slowly at first and then without bound as the ratio approaches 1.00 — which is the depth at which the bay fills faster than it stiffens, and which the roof bay therefore never attains. The perfect roof bay, drawn for comparison, sits on the vertical axis until it arrives there and then has no answer at all.

The water that will not run off

A flat roof deflects, the deflection makes room for water, the water deepens the deflection. It is the same equation as a buckling column, with rain in place of the axial load.

deflection · Serviceability

Named alongside it

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

Critical loadImperfectionSecond-order effectsBifurcationDeflection limitEccentricityEffective lengthEuler bucklingLimit stateNotional loadP-deltaPonding

All concepts