CA Seismic cheat sheet

Seismic Principles

• Base shear (ASCE 7 equivalent lateral force): V = Cs·W, where W is the effective seismic weight including dead load plus applicable portions of other loads (e.g., 25% of floor live load in storage areas, partition allowances, snow where specified).

• Seismic response coefficient: Cs = SDS/(R/Ie) for short-period structures, but Cs need not exceed SD1/(T·(R/Ie)) for T ≤ TL, and Cs ≥ 0.044·SDS·Ie, with a minimum base shear floor of 0.01W.

• Approximate fundamental period: Ta = Ct·hn^x, with Ct = 0.028 and x = 0.8 for steel moment frames, Ct = 0.016 and x = 0.9 for concrete moment frames, and Ct = 0.020 and x = 0.75 for other structural systems; Cu·Ta caps the computed period.

• Site coefficients Fa (short period) and Fv (1-second period) amplify mapped spectral accelerations SMS = Fa·Ss and SM1 = Fv·S1; design values are SDS = (2/3)SMS and SD1 = (2/3)SM1.

• Vertical distribution of seismic force: Fx = Cvx·V, with Cvx = wx·hx^k / Σ(wi·hi^k); exponent k = 1 for T ≤ 0.5 s, k = 2 for T ≥ 2.5 s, and linear interpolation between.

• Story drift check: Δ = Cd·δxe/Ie must not exceed the allowable drift ratio (commonly 0.020 for Risk Category I–II buildings, 0.015 for III, 0.010 for IV), where δxe is the elastic analysis deflection.

• Redundancy factor ρ = 1.0 when the structure meets the conditions of ASCE 7 §12.3.4.2; otherwise ρ = 1.3, and ρ must be applied to the seismic base shear for structures assigned to SDC D through F.

• Overturning moment at any level is the sum of design lateral forces above that level times their heights above it; the resulting stability coefficient θ = Px·Δ/(Vx·hsx·Cd) must not exceed θmax = 0.5/(β·Cd).