Floor Response Spectrum
Floor Response Spectrum: Theoretical Foundations
What is a Floor Response Spectrum?
Professor, what is a "floor response spectrum"?
It's the response spectrum at each floor level of a building. The seismic input from the ground passes through the building and is amplified at each floor. It's used for seismic evaluation of equipment.
Flow: Earthquake → Ground → Foundation → Building (amplification) → Floor acceleration at each level → Input to equipment
So the building acts as a "filter" that amplifies the earthquake.
Components near the building's natural frequency are amplified. The amplification is larger on higher floors.
Calculation Method
1. Time history response analysis with the building's FEM model — Seismic wave input → Acceleration time history at each floor
2. Calculate SRS (Response Spectrum) from each floor's acceleration time history — Input spectrum for equipment
3. Seismic evaluation of equipment — Calculate equipment response using the floor response spectrum as input
So it's a three-stage process: building analysis → floor response spectrum → equipment analysis?
In nuclear power plants, the standard workflow is: building (RC structure) seismic response analysis → floor response spectrum → seismic evaluation of equipment (piping, valves, electrical panels, etc.).
Summary
Key Points:
- Response spectrum at each floor of the building — Seismic input for equipment
- Building amplifies the earthquake — Near the natural frequency. Larger on higher floors
- Building time history → SRS → Equipment evaluation — Three stages
- Most important in nuclear seismic design — Complies with NRC Reg Guide
Floor Response Spectrum is the "Earthquake Inside the Building"
The Floor Response Spectrum (FRS) is an index indicating the severity of input that each floor of a building imparts to a single-degree-of-freedom oscillator (equipment) during an earthquake. The concept of a "two-stage analysis," where building analysis results using ground spectrum as input are recalculated at each floor, was proposed by G.W. Housner in 1956. In nuclear facilities, using building FRS for seismic design of equipment and piping has become the world standard (ASCE 4-98, etc.).
Computational Methods for Floor Response Spectrum
Floor Response Spectrum Calculation
Calculate building time history with Nastran SOL 112 (modal transient) or SOL 109 (direct transient), then generate SRS from acceleration at each floor node.
Direct method: Automatic SRS output using Nastran's PARAM,SRS.
Or calculate SRS from acceleration time history using Python/MATLAB.
Broadening (Peak Broadening)
A process to widen the peaks of the floor response spectrum by approximately ±15%. Accounts for uncertainties in building modeling. Specified in NRC Reg Guide 1.122.
So you widen the peaks to be on the conservative side.
The FEM model of the building has about ±10% uncertainty in its natural frequencies. Broadening the peaks ensures the equipment evaluation remains conservative even if the actual peak location shifts.
Summary
FRS Broadening Standard is 15% per US NRC
"Broadening," which widens the spectrum left and right to account for uncertainties (model errors in building natural frequencies, soil-structure interaction, etc.), is standardized at ±15% (i.e., a total width of 30%) in NRC Regulatory Guide 1.122. A similar concept is adopted in Japan's seismic design review guidelines, reducing the risk that actual peak acceleration is evaluated lower than the analysis value.
Floor Response Spectrum in Practice
Practical Application of Floor Response Spectrum
Seismic evaluation of equipment in nuclear power plants is the primary application.
Practical Checklist
Top Floor FRS of Reactor Buildings Can Be 10 Times Ground Input
In nuclear power plant reactor buildings, the amplification effect can cause the top floor FRS acceleration to reach 5 to 15 times the ground input. Analysis by the Central Research Institute of Electric Power Industry after the 1995 Great Hanshin-Awaji Earthquake found cases where FRS back-calculated from actual seismograph records exceeded the design FRS by up to 3 times. This experience prompted the 2006 NRC guideline revision and the formulation of Japan's new seismic design review guidelines.