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ACI 318-19 Special Moment Frame Beam — Capacity Design & Strong Column

Probable moment strength M_pr (1.25f_y, φ = 1.0), capacity-design shear V_e (§18.6.5.1), the V_c = 0 rule in the plastic-hinge zone (§18.6.5.2), hoop spacing (§18.6.4.4, Grade 80: 5d_b) and the strong-column/weak-beam check ΣM_nc ≥ (6/5)ΣM_nb (§18.7.3.2). Turkish counterpart: TBDY capacity-design shear and strong-column tools.

Beam

b_w in

h in

d in

A_s top (negative) in²

A_s bottom (positive) in²

f′c psi

Grade

Smallest longitudinal bar

Clear span ℓ_n ft

w_u (gravity with E) kip/ft

P_u in beam kip

Hoop bar

Legs

Strong column / weak beam (optional)

M_nc column above kip-ft

M_nc column below kip-ft

Results

M_pr⁻ · M_pr⁺ kip-ft—

V_e = (M_pr⁻ + M_pr⁺)/ℓ_n + w_uℓ_n/2 kip—

V_c in ℓ_o §18.6.5.2—

V_s required · limit 8√f′c·b_wd kip—

Hoop spacing in the hinge zone—

ΣM_nc / ΣM_nb §18.7.3.2—

§2.3M_pr: 1.25f_y in tension steel, φ = 1.0 → a = A_s·1.25f_y/(0.85f′c·b), M_pr = A_s·1.25f_y(d − a/2). Compression steel neglected (common practice).

§18.6.5V_e from the free body with M_pr of opposite sign at both ends plus factored gravity load; V_c = 0 within ℓ_o when the earthquake part ≥ ½ of V_e and P_u < A_gf′c/20; φ = 0.75

§18.6.4.4Hoop spacing ≤ min(d/4, 6d_b Grade 60 / 5d_b Grade 80, 6 in)

§18.7.3.2ΣM_nc ≥ (6/5)ΣM_nb, nominal strengths (1.0f_y); M_nc at the factored axial force giving the lowest strength — use the P–M tool

VerifyHand calculation (regression test): b = 18, d = 21.5 in, A_s = 4.0 in², f′c = 5 ksi → a = 3.922 in, M_pr = 488.5 kip-ft. Principles: NEHRP Seismic Design Technical Brief No. 1 (NIST GCR 8-917-1, written for ACI 318-08; clause numbers converted to 318-19), STRUCTURE magazine.

ScopeBeams with equal reinforcement at both ends. Column capacity-design shear (§18.7.6) needs column M_pr from a 1.25f_y interaction diagram — not included.

Preliminary calculation tool. Final design requires the full text of ACI 318 and review by a licensed PE. This tool follows ACI 318-19, the edition referenced by the 2021 and 2024 IBC; ACI CODE-318-25 was published in January 2025 and is expected in the 2027 IBC (changes include development length equations and seismic provisions).