Structural Engineering & Statics
where the load goes
Concept

Participation factor — where it appears

The scalar that converts a mode's generalised response into the physical displacement of a chosen point, usually the roof. It is what turns a spectral displacement into a target displacement, and it depends on the mode shape's normalisation as well as on the structure.

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

How much of the mass each mode carries, over eight modes. The effective modal mass of each of the eight modes of a frame of eight storeys, as a percentage of the total. Mode 1 carries 85.6% and mode 2 9.1%; two modes are needed to reach 90% of the mass. The masses sum to exactly the total, which is a property of the eigenvectors rather than a normalisation applied afterwards.

Most of the mass moves together

A sixteen-storey frame has sixteen modes, and the first one carries eighty-four per cent of the mass. That is why a hand calculation on one mode gets the base shear right to within a tenth — and why the same calculation gets the acceleration at roof level wrong by a factor of two.

dynamics · Modal mass Where the drift went. Storey drift at the target displacement, for the same frame with and without a soft ground storey at 50 per cent of the others' stiffness and strength. The regular frame spreads 219 mm over every storey; the soft one reaches 266 mm and puts 5.58 per cent of it into the ground storey against 0.53 next to it — a concentration of 5.9 against 1.7. The roof goes 22 per cent further, and where that extra displacement lands is the whole of the difference between the two buildings.

Weaker in one place, and better on every average

Take an eight-storey frame and make its ground storey half as stiff and half as strong. Its ductility demand falls, its first mode carries more of the mass, and its period lengthens into a gentler part of the spectrum. Three global numbers all improve, and the building is the one that collapses.

dynamics · Pushover

Named alongside it

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

Base shearModal massMode shapeCapacity curveCollapse mechanismDuctility demandFloor accelerationModal analysisPlastic mechanismPushoverResponse spectrumSeismic mass

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