A building site has been classified as Site Class D soil. The structure is a 3-story office building with a fundamental period of 0.8 seconds. What is the design spectral acceleration parameter SDS if SS = 1.5g?
Correct Answer
A) 1.0g
For Site Class D with SS = 1.5g, the site coefficient Fa = 1.0, and SMS = Fa × SS = 1.5g. Then SDS = (2/3) × SMS = (2/3) × 1.5g = 1.0g.
Why This Is the Correct Answer
The calculation follows ASCE 7 seismic provisions: (1) For Site Class D and SS = 1.5g, the site coefficient Fa = 1.0 (per ASCE 7 Table 11.4-1, Fa caps at 1.0 when SS ≥ 1.5g for Site Class D). (2) SMS = Fa × SS = 1.0 × 1.5g = 1.5g. (3) SDS = (2/3) × SMS = (2/3) × 1.5g = 1.0g. The fundamental period of 0.8 seconds is used to determine SD1, not SDS, making it a distractor here.
Why the Other Options Are Wrong
Option B: 1.5g
1.5g would be correct only if no site amplification adjustment were made (Fa = 1.0 applied to SMS, but the two-thirds reduction for SDS was skipped). SDS always equals (2/3) × SMS, so 1.5g cannot be SDS.
Option C: 0.75g
0.75g would result from applying (2/3) × 1.125g, which would require SMS = 1.125g. This doesn't match the correct calculation path for Site Class D with SS = 1.5g.
Option D: 1.125g
1.125g = (3/4) × 1.5g, suggesting use of a 3/4 multiplier rather than the correct 2/3 multiplier for deriving SDS from SMS. The code formula is unambiguously SDS = (2/3) × SMS.
Memory Technique
Remember the seismic formula chain: SS → (×Fa) → SMS → (×2/3) → SDS. For Site Class D at high shaking levels, Fa = 1.0 (the site doesn't amplify further). Then two-thirds is the 'design fraction' — you design for 2/3 of the maximum considered earthquake.
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