Seismic Overturning Moment (ASCE 7 §12.8.5)
The overturning the footing and the hold-downs resist, the next number after the vertical distribution: from the story forces Fx = Cvx x V, the base overturning moment M0 = Sum(Fi hi), the moment about each floor level (Sum of the forces above it times their height above it), and the 25% reduced foundation moment §12.13.4 permits at the soil interface. A 3-story with Fx = 37 / 74 / 89 kips at 12 / 24 / 36 ft carries 5,422 kip-ft at the base, 4,067 reduced. Levels enter one per line, bottom-up, as weight and height from the base; V and T come from seismic-base-shear. The resisting dead load, the foundation stability ratio, and the shear-wall hold-downs are separate checks. A design aid; the engineer of record governs.
Formula and source
k = 1 for T <= 0.5 s, 2 for T >= 2.5 s, 1 + (T - 0.5)/2 between; Cvx = wx hx^k / Sum(wi hi^k); Fx = Cvx x V; M0 = Sum(Fi hi); Mx = Sum over i above x of Fi (hi - hx); M0_foundation = 0.75 x M0.
ASCE 7-22 §12.8.5 (Overturning) with the §12.8.3 vertical distribution (Eqs. 12.8-11 / 12.8-12) and the §12.13.4 25% reduction of the ELF overturning moment at the soil-foundation interface, by name.
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