Seismic Overturning Moment (ASCE 7 §12.8.5)
The overturning the footing and the hold-downs resist, the next number after the vertical distribution.
Example
You enter
- Base shear V (kips) 200
- Fundamental period T (s) 0.4
- Stories w 1000, h 12; w 1000, h 24; w 800, h 36
You get
- Distribution exponent k 1
- Base overturning moment M0 (kip-ft) 5422.22
- Reduced foundation moment, 0.75 M0 (kip-ft) 4066.67
Details, formula, and sources
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 the base-shear calculation. 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.
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.
The overturning-moment accumulation and the §12.13.4 25% soil-interface reduction are stated in ASCE 7 §12.8.5 / §12.13.4 and reproduced across the public seismic-design literature (FEMA P-1051, the SEAOC design manuals); the arithmetic is public.
Estimate. AHJ and licensed professional govern.
Field names used by the API: base_shear_kip, period_s, stories, k, m_base_kipft, m_base_reduced_kipft
- Base moment M0 = Sum(Fi hi) from the §12.8.3 story forces; the moment about level x sums only the forces above x times their height above xASCE 7 §12.8.5
- Foundation reduction §12.13.4 permits a 25% reduction of the ELF overturning moment at the soil-foundation interface (not to the structure above); reported as 0.75 x M0ASCE 7 §12.13.4
- Separate checks the resisting dead load, the overturning stability ratio, and the shear-wall hold-down design are separate checks this tile does not performASCE 7 §12.8.5