Seismic Overturning Stability Ratio at the Foundation
Two of the three checks seismic-overturning-moment hands off. The subtlety is that the dead load available to resist is NOT D: the same vertical acceleration that pushes the building sideways also lifts it, and ASCE 7 carries that as Ev = 0.2 SDS D acting UPWARD in the uplift combination, so LRFD combination 7 leaves (0.9 - 0.2 SDS) D and the ASD pair leaves (0.6 - 0.7 x 0.2 SDS) D. At SDS 1.0 that is 0.70 D, not 0.90 -- and skipping the term is the classic way an overturning check passes on paper and should not. A 5,422 kip-ft demand on a 20 ft footprint with 900 kips of dead load gives a 1.55 ratio after the 12.13.4 soil-interface reduction, yet the resultant lands 6.45 ft off center against a B/6 kern of 3.33, so the base is in PARTIAL UPLIFT even though global stability passes -- the thing a ratio alone hides. The 12.13.4 reduction does not carry up into the shear wall or its hold-downs. Global stability only; sliding, toe pressure, and hold-down forces are separate.
Formula and source
effective dead-load coefficient = 0.9 - 0.2 SDS (LRFD combination 7) or 0.6 - 0.7 x 0.2 SDS (the ASD 0.6D + 0.7E pair); W_eff = coefficient x D; resisting moment = W_eff x lever arm (half the footprint unless entered); design overturning = M0 x 0.7 for ASD x 0.75 when the ASCE 7 12.13.4 soil-interface reduction is taken; ratio = resisting / demand; eccentricity = demand / W_eff, compared to the B/6 kern and to B/2.
ASCE 7 - the 0.9D + 1.0E uplift combination and the ASD 0.6D + 0.7E pair, with the vertical seismic effect Ev = 0.2 SDS D acting upward in the overturning case, and the 25% reduction in overturning permitted at the soil-structure interface by Section 12.13.4.
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