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ACI 318-19 Special Structural Walls and Coupling Beams

ACI 318-19 amplifies the design shear of special walls for flexural overstrength and dynamic (higher-mode) effects: V_e = Ω_v·ω_v·V_u ≤ 3V_u. This tool also sizes boundary-element confinement and designs coupling beams. Defaults reproduce the FEMA P-2192 22-story ductile coupled wall.

1 · Wall design shear (§18.10.3.1, §18.10.4)

V_u (kips)

M_u (kip-ft)

M_pr (kip-ft, blank = not yet known)

h_wcs (in.)

ℓ_w (in.)

b_w (in.)

Stories above critical section n_s

f′_c (psi)

f_y (psi)

2 · Special boundary element confinement (§18.10.6.4)

Boundary element length (in.)

Width (in.)

Clear cover (in.)

f′_c (psi)

f_yt (psi)

Hoop spacing s (in.)

h_x (in.)

Whether a special boundary element is required, and its length and height, are computed by the ACI 318-19 wall boundary element tool (displacement-based §18.10.6.2), which reproduces the same FEMA example.

3 · Coupling beam (§18.10.7)

Clear span ℓ_n (in.)

Depth h (in.)

Width b_w (in.)

Effective depth d (in.)

V_u (kips)

A_s top (in.²)

A_s bottom (in.²)

Smallest longitudinal bar d_b (in.)

Hoop legs × bar area A_v (in.²)

P_u (kips)

f′_c (psi)

f_y (psi)

Diagonally reinforced route (Eq. 18.10.7.4) — formula only

A_vd per diagonal group (in.²)

Diagonal angle α (°)

Sources and verification

AnchorFEMA P-2192-V1, 2020 NEHRP Recommended Seismic Provisions: Design Examples (2021, public domain), §4.5 — special reinforced concrete ductile coupled wall, 22 stories, f′_c 8,000 psi. Reproduced in tests/aci-special-wall-us.test.js: initial V_e = 1.5 × 1.8 × 576 = 1,555 kips; with M_pr/M_u = 3.64 the cap 3V_u = 1,728 kips governs; ρ_t = 0.0051; A_sh/(s·b_c) = 0.012; coupling beam V_e = 229 kips, V_s = 305 kips, six-legged #4 hoops at 6 in.; ℓ_d ≈ 55 in. ACI 318-19 is cited by section number only.

Not anchoredTwo branches are implemented from ACI 318-19 but not exercised by the FEMA example: ω_v = 0.9 + n_s/10 for n_s ≤ 6, and the diagonally reinforced coupling beam (Eq. 18.10.7.4). They are labelled in the results. M_pr of the coupling beam uses a singly reinforced rectangular approximation (726 kip-ft vs. 724 from the book's section analysis).

Errata foundFEMA P-2192 §4.5.2.3 prints "b ≥ 0.025·c·ℓ_w = 19.3 in." — the requirement is b ≥ √(0.025·c·ℓ_w) and the value is 19.74 in.; §4.5.3.4 evaluates 0.05·A_g·f′_c as "0.05 × 34 × 24 × 4 = 163.2 kips", numbers from a different member — for this 26 × 28 in. beam with f′_c = 8 ksi it is 291 kips. Neither changes the book's conclusions. The book's "M_n = 526 kip-ft" for the coupling beam is the design strength φM_n.