Seismic Base Shear (ASCE 7 §12.8 Equivalent Lateral Force)
The earthquake demand on a regular building reduced to one equivalent static base shear.
Example
You enter
- Seismic weight W (kips) 200
- SDS, short-period (g) 1
- SD1, 1-second (g) 0.6
- Response-modification factor R 6.5
- Importance factor Ie (1.0-1.5) 1
- Fundamental period Ta (s) 0.3
You get
- Seismic response coefficient Cs 0.1538
- Base shear V 30.8 kips
Checked against published worked examples from: FEMA.
Details, formula, and sources
ScopeCs = SDS / (R / Ie), capped at SD1 / (T x (R / Ie)) for T <= TL and floored at the code minimum, times the seismic weight. In much of the western US the seismic demand, not the wind, governs the lateral system - the shear walls, braced frames, hold-downs, and anchor bolts. A taller, more flexible building draws a smaller base shear because the period cap recognizes it rides the short-period spectral peak less. SDS / SD1 are from the USGS maps; R is from Table 12.2-1. A lateral-demand estimate, not a stamped seismic design.
Formula or tablecs_basic = sds / (R / Ie); cs_cap = sd1 / (period_s x (R / Ie)); cs_min = max(0.044 x sds x Ie, 0.01, s1 >= 0.6 ? 0.5 x s1 / (R / Ie) : 0); cs = max(cs_min, min(cs_basic, cs_cap)); base_shear = cs x weight.
Source and editionASCE 7 §12.8 equivalent lateral force (Cs = SDS / (R / Ie), the cap Cs <= SD1 / (T x (R / Ie)) for T <= TL, the minimum Cs >= max(0.044 x SDS x Ie, 0.01) and, where S1 >= 0.6 g, Cs >= 0.5 S1 / (R / Ie) (Eq. 12.8-6), V = Cs x W), by name.
Free accessThe equivalent-lateral-force base-shear relations are stated in ASCE 7 §12.8; the arithmetic is public. SDS / SD1 are from the USGS seismic design maps.
What governsEstimate. AHJ and licensed professional govern.
API field namesweight_kip, sds, sd1, r_factor, ie, period_s, cs, base_shear_kip
- Response coefficient Cs = SDS / (R / Ie), bounded above by the period cap and below by the code minimumASCE 7 §12.8
- Period cap Cs <= SD1 / (T x (R / Ie)) for T <= TL recognizes a flexible structure rides the short-period spectral peak lessASCE 7 §12.8
- Base shear V = Cs x seismic weight is the lateral demand that sizes the shear walls, braced frames, hold-downs, and anchorageASCE 7 §12.8