Steel & Reinforced Concrete Checks

Both codes are strength design: the factored load effect must not exceed the reduced nominal strength, φRₙ ≥ Rᵤ.

Worked: a singly reinforced beam

b = 12 in, d = 20 in, A_s = 3.0 in², f_y = 60 ksi, f′c = 4 ksi. a = 180/(0.85 × 4 × 12) = 4.41 in. Mₙ = 180 × (20 − 2.21) = 3,200 in-kips = 267 ft-kips. c = 4.41/0.85 = 5.19 in, c/d = 0.26, so φ = 0.90 and φMₙ = 240 ft-kips.