The Equivalent Lateral Force (ELF) procedure in ASCE 7-22 Chapter 12 is the workhorse seismic analysis method for buildings that meet the regularity requirements of Table 12.6-1. It replaces the dynamic response of a structure with a static lateral force whose magnitude is calibrated against the design spectral response. Once you understand how the seismic response coefficient Cs is built up, the rest is bookkeeping.
Worked example — the building
- Two-story steel moment frame
- Plan 80 ft × 50 ft, story heights 14 ft / 12 ft → hn = 26 ft
- Site Class D (default)
- Risk Category II → Importance Factor Ie = 1.0
- Mapped values: SS = 1.10 g, S1 = 0.40 g (Salt Lake City foothills, illustrative)
- Seismic weight W = 1,250 kips
Step 1 — Site coefficients and design spectral accelerations
From Tables 11.4-1 and 11.4-2 (Site Class D, ASCE 7-22):
- Fa = 1.0 (interpolated, SS = 1.10)
- Fv = 1.7 (interpolated, S1 = 0.40; note Site Class D-default may also trigger MCER ground-motion requirements per 11.4.8)
Maximum considered earthquake (MCER) spectral accelerations:
SMS = Fa·SS = 1.0(1.10) = 1.10 g
SM1 = Fv·S1 = 1.7(0.40) = 0.68 g
Design values (two-thirds of MCER):
SDS = (2/3)·1.10 = 0.733 g
SD1 = (2/3)·0.68 = 0.453 g
Step 2 — Approximate fundamental period Ta
Ta = Ct · hnx
For steel moment-resisting frames, Table 12.8-2 gives Ct = 0.028 and x = 0.8. With hn = 26 ft:
Ta = 0.028 · 260.8 = 0.028 · 13.71 = 0.384 s
Step 3 — Seismic Design Category and R
SDS = 0.733 with Risk Cat II → Table 11.6-1 SDC D. SD1 = 0.453 → Table 11.6-2 also SDC D. For SDC D, choose a Special Moment Frame: R = 8, Ω0 = 3, Cd = 5.5.
Step 4 — Seismic response coefficient Cs
Cs = SDS / (R/Ie) = 0.733 / (8/1.0) = 0.0916
Check upper bound (T ≤ TL, take TL = 8 s for most Western US sites):
Cs,max = SD1 / [T·(R/Ie)] = 0.453 / [0.384(8)] = 0.1474
Check lower bound (Section 12.8.1.1):
Cs,min = max(0.044·SDS·Ie, 0.01) = max(0.0323, 0.01) = 0.0323
Cs = 0.0916 is between the bounds → use Cs = 0.0916.
Step 5 — Base shear V
V = Cs·W = 0.0916(1,250) = 114.5 kips
Step 6 — Vertical force distribution
Section 12.8.3 distributes V to each level using Cvx = wxhxk / Σwihik. For T < 0.5 s, k = 1. Assume floor weights w1 = 700 k at 14 ft and w2 = 550 k at 26 ft:
- Σwihi = 700(14) + 550(26) = 9,800 + 14,300 = 24,100 k-ft
- F1 = (9,800/24,100)(114.5) = 46.6 kips
- F2 = (14,300/24,100)(114.5) = 67.9 kips
Check: 46.6 + 67.9 = 114.5 k ✓
Drift check
Story drifts are computed from the elastic analysis, then amplified by Cd/Ie. Allowable drift Δa from Table 12.12-1 for Risk Cat II buildings is 0.020hsx. For hsx = 14 ft = 168 in, Δa = 3.36 in.
When ELF is NOT permitted
ASCE 7-22 Table 12.6-1 prohibits ELF when:
- Building has irregularities listed in Table 12.3-1 (specific types)
- SDC D, E, F structures over 160 ft with certain irregularities
- Structures with T > 3.5 Ts in SDC D, E, F
If any apply, you owe a Modal Response Spectrum Analysis (Section 12.9).
Speed up the design
Once you have lateral forces at each level, the next steps are sizing the lateral system. Our beam calculator handles the gravity + seismic combined cases, the column buckling calculator sizes axial-flexural members, and the base plate calculator handles the moment-bearing connection at the foundation where most of the seismic demand lands.
Closing
ELF is essentially: build up Cs, multiply by W, distribute by floor mass and height. The discipline is in the bound checks and in confirming the building is actually regular enough to use the method. Get those right and you have a defensible base shear in 30 minutes.