3.4. Average Spectral Acceleration

imcalculator.get_saavg(period)

Computes the geometric mean of spectral accelerations over a range of periods centred on a conditioning period.

The period range spans from 0.2 * period to 1.5 * period, sampled at 10 equally spaced points.

Parameters:

period (float) – Conditioning period (s).

Returns:

sa_avg – Geometric mean of spectral accelerations (g) over the defined period range.

Return type:

float

Theoretical Background

The Average Spectral Acceleration (AvgSA) is the geometric mean of spectral accelerations over a period range centred on the fundamental period of the structure (Cordova et al., 2000; Eads et al., 2015).

Definition

For a structure with fundamental period \(T_1\), AvgSA is computed over the range \([0.2\,T_1,\, 1.5\,T_1]\) at \(N\) equally spaced periods:

\[\text{AvgSA}(T_1) = \exp\!\left( \frac{1}{N} \sum_{j=1}^{N} \ln S_a(T_j) \right)\]

This is equivalent to the geometric mean of the spectral ordinates \(S_a(T_1), S_a(T_2), \ldots, S_a(T_N)\).

Motivation

AvgSA captures the spectral shape over the range of periods most relevant to structural response, making it a more efficient and sufficient intensity measure than single-period Sa for structures that exhibit period elongation (e.g. during inelastic response).