Design acceleration parameters from a site-specific spectrum (ASCE 7-22 Sec. 21.4)

Derives SDS, SD1, SMS and SM1 from the ordinates of a site-specific response spectrum, per ASCE/SEI 7-22 Sec. 21.4: SDS is 90 percent of the maximum spectral acceleration over periods from 0.2 to 5 s; SD1 is 90 percent of the maximum of the product T * Sa over 1 to 2 s when the average shear wave velocity exceeds 442 m/s and over 1 to 5 s otherwise, but not less than the ordinate at 1 s; SMS and SM1 are 1.5 times SDS and SD1.

Usage

getDesignParameters(Tn, Sa, vs30 = NULL)

Arguments

Tn

numeric, periods (s).

Sa

numeric, spectral ordinates at Tn, same length.

vs30

numeric scalar or NULL. Average shear wave velocity (m/s) selecting the SD1 window: 1 to 2 s above 442 m/s, else 1 to 5 s. NULL (default) uses the conservative wide window.

Value

A list with SDS, SD1, SMS and SM1.

Details

Sec. 21.4 defines the parameters on the design spectrum, which Sec. 21.3 fixes at two thirds of the MCER spectrum. The 1.5 and the two thirds cancel exactly, because taking a maximum commutes with a positive scale factor, so the same parameters follow from either level. Pass whichever spectrum you hold.

These are parameters for the equivalent lateral force procedure, not a response spectrum. Sec. 21.4 permits the site-specific ordinate itself to replace SD1/T in Eq. (12.8-3); nothing in Chapter 21 directs that a spectrum be rebuilt from SMS and SM1.

Evaluation windows are clamped to the period range of the input. The interpolant is piecewise linear, so maxima are searched on the knots plus a dense grid, T * Sa being quadratic within a segment.

Examples

Tn <- c(0, 0.2, 0.5, 1, 2, 5)
Sa <- c(0.4, 1.0, 0.9, 0.6, 0.3, 0.1)
getDesignParameters(Tn = Tn, Sa = Sa, vs30 = 760)
#> $SDS
#> [1] 0.6
#> 
#> $SD1
#> [1] 0.4049999
#> 
#> $SMS
#> [1] 0.9
#> 
#> $SM1
#> [1] 0.6074999
#>