Definition of Spectral Acceleration (SA)
What is "spectral acceleration" or SA?
PGA (peak acceleration) is what is experienced by a particle on the ground. SA is approximately what is experienced by a building, as modeled by a particle mass on a massless vertical rod having the same natural period of vibration as the building.
The mass on the rod behaves about like a simple harmonic oscillator (SHO). If one "drives" the mass-rod system at its base, using the seismic record, and assuming a certain damping to the mass-rod system, one will get a record of the particle motion which basically "feels" only the components of ground motion with periods near the natural period of this SHO. If we look at this particle seismic record we can identify the maximum displacement. If we take the derivative (rate of change) of the displacement record with respect to time we can get the velocity record. The maximum velocity can likewise be determined. Similarly for response acceleration (rate of change of velocity) also called response spectral acceleration, or simply spectral acceleration, SA (or Sa).
PGA is a good index to hazard for short buildings, up to about 7 stories. To be a good index, means that if you plot some measure of demand placed on a building, like interstory displacement or base shear, against PGA, for a number of different buildings for a number of different earthquakes, you will get a strong correlation.
PGA is a natural simple design parameter since it can be related to a force and for simple design one can design a building to resist a certain horizontal force.
PGV, peak ground velocity, is a good index to hazard to taller buildings. However, it is not clear how to relate velocity to force in order to design a taller building.
SA would also be a good index to hazard to buildings, but ought to be more closely related to the building behavior than peak ground motion parameters. I presume design might also be easier, but the relation to design force is likely to be more complicated than with PGA, because the value of the period comes into the picture.
PGA, PGV, or SA are only approximately related to building demand/design because the building is not a simple oscillator, but has overtones of vibration, each of which imparts maximum demand to different parts of the structure, each part of which may have its own weaknesses. Duration also plays a role in damage, and some argue that duration-related damage is not well-represented by response parameters.
On the other hand, some authors have shown that non-linear response of a certain structure is only weakly dependent on the magnitude and distance of the causative earthquake, so that non-linear response is related to linear response (SA) by a simple scalar (multiplying factor). This is not so for peak ground parameters, and this fact argues that SA ought to be significantly better as an index to demand/design than peak ground motion parameters.
There is no particular significance to the relative size of PGA, SA (0.2), and SA (1.0). On the average, these roughly correlate, with a factor that depends on period.
While PGA may reflect what a person might feel standing on the ground in an earthquake, I don't believe it is correct to state that SA reflects what one might "feel" if one is in a building. In taller buildings, short period ground motions are felt only weakly, and long-period motions tend not to be felt as forces, but rather disorientation and dizziness.
