Structural Engineering & Statics
where the load goes
Concept

Modal analysis — where it appears

Decomposing a structure's motion into independent modes, so that a building with many floors becomes a set of separate one-mass problems.

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

five floors · 300 t eachmode 10.6 s · 1.65 Hz88.0% of the massno nodemode 20.21 s · 4.83 Hz8.7% of the massone nodemode 30.13 s · 7.61 Hz2.4% of the masstwo nodes

A structure has more than one period

One mass on one spring has one period. A building with eight floors has eight, each with a shape of its own, and the second one bends the building into a curve nobody drew. They are not harmonics, they do not interfere, and each behaves as though the others were not there.

dynamics · mode shapes eight modes · 2400 ttwo modes reach 90% of itmode 1 · 0.93 s85.6%85.6% cumulativemode 2 · 0.31 s9.1%94.7% cumulativemode 3 · 0.19 s3.0%97.7% cumulativemode 4 · 0.14 s1.3%99.0% cumulativemode 5 · 0.12 s0.6%99.6% cumulativemode 6 · 0.1 s0.3%99.9% cumulativemode 7 · 0.09 s0.1%100.0% cumulativemode 8 · 0.09 s0.0%100.0% cumulative

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

Named alongside it

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

Mode shapeBase shearDegrees of freedomEigenvalueFloor accelerationModal massNatural periodOrthogonalityParticipation factorResponse spectrumSeismic massSoft storey

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