Seismic Base Shear — ELF Procedure
Determine the seismic design base shear V = Cs·W using the Equivalent Lateral Force (ELF) procedure per ASCE 7-22 Section 12.8. Computes the seismic response coefficient Cs from the design spectral accelerations SDS and SD1, then distributes the base shear vertically over each story based on the height and weight distribution per Section 12.8.3.
What this calculates
Seismic response coefficient Cs per Section 12.8.1.1 (bounded by Cs,max, Cs,min, and Cs for long periods), design base shear V = Cs·W, vertical distribution of lateral forces Fx = Cvx·V per Section 12.8.3, story shears, and overturning moments. Also computes the approximate fundamental period Ta = Ct·hn^x per Section 12.8.2.1.
Inputs
Design spectral acceleration at short periods (in units of g)
Design spectral acceleration at 1-second period (in units of g)
Response modification coefficient per Table 12.2-1
Seismic importance factor per Section 11.5.1
Total effective seismic weight of the structure
Height above the base to the highest level
Approximate period coefficient per Table 12.8-2 (e.g. 0.028 for steel moment frames)
Approximate period exponent per Table 12.8-2 (e.g. 0.8 for steel moment frames)
Long-period transition period from ASCE 7-22 maps (seconds)
Outputs
Approximate fundamental period (seconds)
Seismic response coefficient
Total seismic design base shear
Lateral force at each story level
Overturning moment at the base
Methodology
Per ASCE 7-22 Section 12.8: Cs = SDS/(R/Ie), but need not exceed Cs = SD1/(T·(R/Ie)) for T ≤ TL, and Cs = SD1·TL/(T²·(R/Ie)) for T > TL. Cs shall not be less than 0.044·SDS·Ie ≥ 0.01 per Equation 12.8-5. For structures with S1 ≥ 0.6g, additional minimum Cs = 0.5·S1/(R/Ie). Approximate period Ta = Ct·hn^x per Table 12.8-2. Vertical distribution: Cvx = wx·hx^k / Σ(wi·hi^k) where k depends on period (k=1 for T≤0.5s, k=2 for T≥2.5s, interpolated between).
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