Seismic Base Shear Calculation Step by Step — ASCE 7-22 Equivalent Lateral Force Worked Example

What you will see

• Adding the Seismic Loads module from the dashboard, and Steps 1 through 8 walked in order
• Step 1 — each level's seismic weight wx and each story height hsx, one story at a time
• Step 2 — Table 20.2-1 site classification, then the seven spectral parameters from the ASCE hazard tool: the mapped Ss and S1 (Section 11.4.3), the site-adjusted SMS and SM1 (Section 11.4.3), the design values SDS and SD1 (Section 11.4.4), and the long-period transition TL (Section 11.4.5, Figures 22-14 through 22-17)
• Step 3 — Risk Category from Table 1.5-1, seismic importance factor Ie from Table 1.5-2, and the Seismic Design Category assigned by entering BOTH Table 11.6-1 (on SDS) and Table 11.6-2 (on SD1) and taking the more severe letter, per Section 11.6
• Step 4 — Table 12.2-1 reproduced book-style: under A. Bearing Wall Systems, row 16, light-frame (wood) walls sheathed with wood structural panels rated for shear resistance, which sets R = 6.5, the overstrength factor Omega-0 = 3 and Cd = 4, alongside the SDC height-limit columns (no limit in B and C, 65 ft in D, E and F)
• Step 5 — the approximate fundamental period Ta = Ct x hn^x (Eq. 12.8-8), with Ct and x read from Table 12.8-2 and hn taken from the story heights
• Step 6 — Cs written out with every bound: the Method 2 Eq. 12.8-3, the Eq. 12.8-4 upper bound for T at or below TL, the Eq. 12.8-5 upper bound above TL, the Eq. 12.8-6 floor, and the Eq. 12.8-7 floor that applies when S1 is at least 0.6 g — then V = Cs x W (Eq. 12.8-1), with a plotted design response spectrum showing Ts and the project period
• Step 7 — vertical distribution: the exponent k, Cvx, story force Fx, story shear Vx and overturning moment Mx (Sections 12.8.3 and 12.8.5), tabulated side by side as E for strength design and 0.7E for allowable stress design
• Step 8 — diaphragm design forces: the Eq. 12.10-1 column, the minimum column 0.2 x SDS x Ie x Wpx (Eq. 12.10-2), the maximum column 0.4 x SDS x Ie x Wpx (Eq. 12.10-3), and the governing Fpx at each level

The building in this example

Two stories, 40,000 lb of seismic weight and 10 ft of height at each level — W = 80,000 lb, hn = 20 ft. Site Class D, with Ss = 1.0 g, S1 = 0.6 g, TL = 8 s, SMS = 1.0 g, SDS = 0.667 g, SM1 = 0.6 g and SD1 = 0.4 g. Risk Category II, so Ie = 1.0, and both SDC tables return D. Light-frame wood shear walls give R = 6.5, Omega-0 = 3 and Cd = 4. Ta = 0.02 x 20^0.75 = 0.189 s, well below Ts = 0.60 s, so Eq. 12.8-2 governs: Cs = 0.667/6.5 = 0.1026 and V = 8,209 lb (0.7V = 5,746 lb for allowable stress design). With k = 1 the base shear splits into Fx = 2,736 lb at the lower level and 5,473 lb at the upper level. At the top diaphragm Eq. 12.10-1 governs at Fpx = 5,473 lb; one level down the equation gives only 4,105 lb, so the Eq. 12.10-2 minimum of 0.2 x 0.667 x 1.0 x 40,000 = 5,336 lb takes over — the floor that usually controls ordinary wood diaphragms.

Codes referenced: ASCE 7-22 Sections 11.4, 11.6, 12.8 and 12.10; Tables 1.5-1, 1.5-2, 11.6-1, 11.6-2, 12.2-1, 12.8-2 and 20.2-1; Equations 12.8-1, 12.8-3 through 12.8-8, 12.8-12 through 12.8-14, and 12.10-1 through 12.10-3.