Structural Engineering & Statics
where the load goes
Generator

The response-spectrum generator

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
The response spectrum of that record, at one damping ratioThe peak pseudo-acceleration of a single-degree-of-freedom structure against its natural period, for the record above, at 5% damping. Each curve is 44 complete time integrations — one structure per point. At zero period the structure is rigid and rides the ground, so the curve starts at the peak ground acceleration of 3.5 m/s²; it peaks at 7.07 m/s² at a period of 0.37 s, an amplification of 2.02.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,00.511.522.5302468natural period (s)spectral acceleration (m/s²)the ground's own peak, 3.5 m/s²5% damping — peak 7.07 m/s² at 0.37 s

3 essays call response-spectrum. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

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 Dynamics

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.

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

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.

 02468101214161820-60-40-20204060time (s)displacement (mm)a ground motion of 3.5 m/s² peakelastic, and the same frame at a 4th of its strengthelastic: peak 57.71 mmyielding: peak 65.46 mmleft 14.13 mm off plumb Dynamics

The earthquake asks for a displacement

A structure a quarter as strong as the elastic demand does not deflect four times as far. It deflects almost exactly as far, yields on the way, and survives — which is why no ordinary building is designed for the force an earthquake would apply if it stayed elastic.

The library, page 3 of 4 — where response-spectrum sits