Concrete Worked Examples
Each example follows the same structure: Given → Load combo → Required → Limit states → AISC ref → Formula → Substitution → Decision → Common mistakes.
Compute Ec, fr, and yield strain for an RC beam
f'c = 4,000 psi normal-weight concrete (λ = 1.0); rebar Grade 60 (fy = 60,000 psi).
Singly reinforced rectangular beam — design moment check
Rectangular beam b = 12 in., h = 22 in., d = 19.5 in. Reinforcement: 3 #8 bars (As = 3·0.79 = 2.37 in²). Materials: f'c = 4000 psi (β1 = 0.85), fy = 60,000 psi. Factored moment Mu = 165 k·ft.
Stirrup spacing design for a rectangular beam
Rectangular beam bw = 12 in., d = 20 in., f'c = 4000 psi (λ = 1.0), fyt = 60,000 psi. Factored shear at distance d from support Vu = 45 kips. Use #3 U-stirrups (Av = 2·0.11 = 0.22 in²).
McCormac Example 6.1 — Immediate and long-term deflections of a simple RC beam
Simple span L = 20 ft. Rectangular beam b = 12 in., h = 20 in. (d = 17 in.), 3 #9 bars in tension (As = 3.00 in², no compression steel A's = 0). f'c = 3000 psi (NWC), fy = 60 ksi. Service DL = 1.0 klf (includes self-weight), service LL = 0.7 klf, 30% of LL is sustained for 3 years.
Tension development length of a #8 bottom bar
Bottom #8 bar (db = 1.00 in.) in a beam. f'c = 4000 psi NWC (λ = 1.0), fy = 60,000 psi (Grade 60). Uncoated, adequate cover and spacing.
Axial capacity of a tied square column
Square tied column 18 × 18 in. (Ag = 324 in²) reinforced with 8 #9 bars (Ast = 8·1.00 = 8.00 in²). Materials: f'c = 4000 psi, fy = 60,000 psi. Ties #3 at spacing s.
One-way slab — thickness and reinforcement for a 14 ft span
Interior one-way slab, both ends continuous, L = 14 ft = 168 in. Superimposed dead load DL = 25 psf, live load LL = 50 psf. Materials f'c = 4000 psi, fy = 60,000 psi. Clear cover 0.75 in.