Vertical Distribution of Seismic Forces (ASCE 7 §12.8.3)
The standard hand calc after the base shear: distribute V up the height as Fx = Cvx x V with Cvx = wx hx^k / Sum(wi hi^k), then take the story shears Vx by summing the forces at and above each level (§12.8.4). The exponent k (1 at T <= 0.5 s, 2 at T >= 2.5 s, interpolated between) is the whole story - softening a 3-story from T = 0.4 to 1.06 s shifts nearly 10 of 200 kips up to the roof. Levels enter one per line, bottom-up, as weight and height from the base; the base story carries the full V as the built-in check. Feeds the story shear the drift and P-delta tiles consume. 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; Vx = Sum Fi for i = x..n (forces at and above the level).
ASCE 7-22 §12.8.3 (Eqs. 12.8-11 and 12.8-12, the vertical distribution and its exponent k) and §12.8.4 (Eq. 12.8-13, the story shear), by name.
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