Seismic response spectrum & RRS

The elastic design response spectrum to ASCE 7-16 or TBDY 2018, and from it the required response spectrum (RRS) for shake-table qualification of equipment and other nonstructural components to ICC-ES AC156.

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HOW IT'S CALCULATED · WITH YOUR NUMBERS

Step by step, with your numbers

01
Equilibrium████ ██ ███████ · ██████ = ██.██
02
Reactions████ ██ ███████ · ██████ = ██.██
03
Shear force████ ██ ███████ · ██████ = ██.██
04
Bending moment████ ██ ███████ · ██████ = ██.██
05
Deflection████ ██ ███████ · ██████ = ██.██
06
Stress████ ██ ███████ · ██████ = ██.██

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References: ASCE/SEI 7-16 §11.4; Türkiye Bina Deprem Yönetmeliği (TBDY 2018) Bölüm 2; ICC-ES AC156 (2010) §6.5.1.

ASSUMPTIONS & LIMITS

ASCE 7-16 §11.4: S_S and S_1 are the mapped MCE_R values; the design spectrum is two thirds of the MCE_R spectrum.
5 % damped elastic spectra. No response modification (R), importance or overstrength factor is applied.
Site coefficients are interpolated linearly in the code table. Site class F, and the cells the table refers to a site-specific analysis, are not handled.
The RRS follows ICC-ES AC156 (2010): A_FLX/10 at 0.1 Hz rising to A_FLX at 1.3 Hz, flat to 8.3 Hz, falling to A_RIG at 33.3 Hz, straight lines on logarithmic axes. The 0.1 Hz ordinate is from the paper behind AC156 (Gatscher et al. 2004, eq. 6a), which states it is included in AC156.
The test response spectrum has to envelop the RRS from 1.3 to 33.3 Hz — only down to 3.5 Hz where the resonance search finds nothing below 5 Hz, or to 75 % of the lowest resonance frequency where it does (AC156 §6.5.3). The branch below 1.3 Hz is not part of that requirement, and the RRS is meant for components whose fundamental frequency is above 1.3 Hz.
The corner frequencies 1.3, 8.3 and 33.3 Hz are fixed in AC156 (derived for a Site Class D default); they are not recomputed from the site's T_0 and T_S. The site values are shown in the working for comparison only.
The chart of S_a against T shows the horizontal spectrum and, dashed, the vertical spectrum of ASCE 7-16 §11.9, which is defined up to T_v = 2.0 s and is not taken below half of the horizontal one. That lower bound is the one item not checked against the printed standard.
z is the height of the component's attachment above the base, h the average roof height; z/h runs from 0 at grade to 1 at the roof.
Not covered: site-specific spectra, near-fault effects, and ASCE 7-22 with the AC156 revision that follows it.

DISCLAIMER · For education and preliminary sizing only. Results must be reviewed by a qualified engineer before use in design.

BEYOND THE SPECTRUM

Response-spectrum and time-history analysis of the equipment itself, anchorage included — we run the model.

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