Structural Engineering & Statics
where the load goes
Concept

Response spectrum — where it appears

The peak response of a family of single-mass oscillators to one ground motion, plotted against their periods. It is a summary of an earthquake rather than a load, and reading a force off it requires a structure's period and its mass.

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

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 three structures · one recordT = 0.3 speak 12.54 mmT = 0.8 speak 46.2 mmT = 1.8 speak 108.95 mmpeak displacementperiod

The spectrum is not a load

A response spectrum looks like a load curve and is not one. Every point on it is the peak of a complete time integration of one particular structure, and the curve is what you get by doing that again for every structure there could be.

dynamics · response spectrum 0123400.20.40.60.81period (s)spectral acceleration (g)fixed baseisolatedbase shear ÷ 10.20123400.050.10.150.20.25period (s)spectral displacement (m)fixed baseisolatedmovement × 2.5five per cent damped, faint; 20 per cent damped, bold

Made weaker on purpose

Everything else in this collection resists a load by being stiff or strong enough for it. A base-isolated building resists an earthquake by refusing to hear it — a layer of bearings under the whole structure with a lateral stiffness a twentieth of the frame's, bought with almost no strength at all.

dynamics · base isolation

Named alongside it

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

Base shearDampingModal massMode shapeNatural periodBase isolationDesign spectrumDuctility demandEnergy dissipationFloor accelerationFree bodyGround motion

All concepts