Seismic base shear (ELF)

The seismic base shear and its distribution over the height by the equivalent lateral force procedure of ASCE/SEI 7-22 Section 12.8, with the period, the seismic response coefficient Cs and its limits, story forces, story shears, overturning moments and story drifts.

Inputs of the seismic base shear #

• Seismic hazard: SDS and SD1 (design spectral accelerations, from the ASCE Hazard Tool or 11.4.4), S1 (used for Eq. 12.8-7 when S1 ≥ 0.6 g and for SDC E / F when S1 ≥ 0.75 g), the long-period transition period TL (Chapter 22) and the risk category (Table 1.5-1). Ie comes from Table 1.5-2 (1.00, 1.00, 1.25, 1.50).
• Cs method (12.8.1.1): Method 2 (prefilled) uses SDS and SD1 (Eqs. 12.8-3 to 12.8-5). Method 1 uses the design spectral acceleration Sa at the period T (Eq. 12.8-2) from the multi-period design spectrum you enter (Sa = 2/3 of the USGS multi-period MCER spectrum at the periods of 11.4.5.1, 0 to 10 s): Sa is interpolated linearly, extended beyond 10 s by 11.4.5.1 item 3, and taken as the maximum Sa where T is below the period of the maximum. ASCE 7-22 permits either method where the multi-period spectrum is available; where Exception 2 of 11.4.5 applies (no multi-period values), Method 1 is not used.
• SDS cap of 12.8.1.3 (option): Cs and Ev with SDS = 1.0 but not less than 0.7 SDS. The calculation checks criteria 1 (no irregularities, from the irregularity input), 2 (five stories or fewer; count each mezzanine as a level), 3 (T ≤ 0.5 s), 6 (risk category I or II) and 7 (R ≥ 3); criteria 4 (ρ = 1.0 permitted by 12.3.4.2) and 5 (site class not E or F) are yours. Where a checked criterion fails the calculation is NOT FEASIBLE until the option is cleared.
• SDC by Table 11.6-1 alone (option): the exception of 11.6 where S1 < 0.75 g. Checked: (1) Ta < 0.8 Ts, (2) the period used for drift (the analytical period entered, else Ta) < Ts, (3) Cs by Eq. (12.8-2), that is Method 1, as the 7-22 text reads; condition (4) (rigid diaphragms, or vertical elements not more than 40 ft apart) is yours. When a condition fails, the SDC stays the more severe of the two tables and an advisory names it.
• Structural system: a system of Table 12.2-1 (R, Ω0, Cd, the Table 12.8-2 structure type and the height limits are taken from the table) or Other system, where R, Ω0, Cd, the structure type for Ta and whether it is a moment frame are entered. Flexible diaphragms applies footnote b (Ω0 of 2½ or more reduced by ½). The redundancy factor ρ (12.3.4) is your input: 1.0 in SDC B and C or when one of the conditions of 12.3.4.2 is met, 1.3 otherwise. The irregularity input feeds criterion 1 of 12.8.1.3 only.
• Period: Ta = Ct hn^x (Eq. 12.8-8) or Ta = 0.1N (Eq. 12.8-9: 12 stories or fewer, a system entirely of steel or concrete moment frames, average story height at least 10 ft). An analytical period may be entered; it is capped at Cu Ta (Table 12.8-1). With 0 the approximate period Ta is used.
• Levels: the height of each level above the base, its seismic weight wx (12.7.2) and, optionally, the elastic displacement δxe from the strength-level analysis. Rows may be entered in any order. The allowable drift coefficient Δa / hsx of Table 12.12-1 is an input (0.020 for risk category I or II, "all other structures", is prefilled; 0 = no limit, for the single-story case of note a).

Checks performed #

The drawings (on screen, in the report and as a PDF / DXF sheet) show a schematic building elevation with the levels, their seismic weights wx and the story forces Fx as arrows, the story heights dimensioned and drawn to scale (the building width is not an input and is drawn schematic; a building too tall for 1/16" = 1'-0" is drawn not to scale), and beside it the story shear Vx and the overturning moment at the base of each story. The lateral system, the diaphragms and the horizontal distribution are not part of the calculation and are not drawn.

Limitations #

• SDS, SD1 and S1 (and, for Method 1, the multi-period spectrum) are entered; the site coefficients and the site-specific procedures (Chapter 21) are not computed. For a site-specific spectrum, enter its values.
• Table 12.2-1 values are built in for the 15 listed systems; for any other line choose Other system and enter R, Ω0, Cd. The detailing requirements of the system and the provisions of 12.2.5 are not checked.
• Ta by Eq. 12.8-10 (masonry or concrete shear walls, Cw) is not offered; Eq. 12.8-8 is always permitted.
• The irregularities themselves (Tables 12.3-1, 12.3-2), the redundancy conditions of 12.3.4.2 and their additional requirements are not evaluated; ρ and the irregularity class are your inputs.
• Accidental torsion and its amplification (12.8.4.2, 12.8.4.3), P-delta (12.8.7), diaphragm forces (12.10), diaphragm deformation δdi and the drift with the period free of the Cu Ta limit (12.8.6.2) are outside this calculation; enter δxe from an analysis that includes them. 12.8.6.1 lets that analysis omit Eq. 12.8-6.
• The seismic weight W is the sum of the level weights entered (what 12.7.2 includes is the engineer's).
• The 11.6 exception condition (3) reads "Equation (12.8-2) is used to determine Cs"; in ASCE 7-22 that equation is Method 1 (in 7-16 the same number was SDS/(R/Ie)). The calculation follows the 7-22 text [verify: ASCE 7-22 errata or supplement for the 11.6 cross-reference].

Verification examples #

Verified against ASCE/SEI 7-22 (PDF on file; pages are PDF pages): the tabulated values below are read from the rendered table pages, and the equations, limits and exceptions of 11.4.5.1, 11.6, 12.3.4, 12.4.2, 12.6, 12.8 and 12.12 from the text (PDF pp. 66 and 167 to 195).

Published worked examples to ASCE/SEI 7-22: the AISC Design Examples v16.0 building (Part III), FEMA P-2192-V1 (2020 NEHRP Provisions Design Examples, Chapters 4 to 7) and the WoodWorks five-story-over-podium design example (2nd ed., 2025). The period, Cs limits, base shear, force distribution, overturning and drift are compared with the values printed in each example:

The procedure is also verified against hand calculations in closed form: