Calculate the required development length for a #6 rebar in 3000 psi concrete with standard hooks in a seismic zone. The rebar has fy = 60,000 psi.
Correct Answer
D) 30 inches
Using CBC provisions for development length: ld = (fy × db)/(25 × √f'c) = (60,000 × 0.75)/(25 × √3000) = 30 inches for #6 rebar in 3000 psi concrete in seismic applications.
Why This Is the Correct Answer
Using the CBC/ACI 318 formula for hooked bar development length: ldh = (0.02 × fy × db) / (λ × √f'c). For a #6 bar: db = 0.75 in, fy = 60,000 psi, f'c = 3,000 psi, λ = 1.0 (normal weight concrete). ldh = (0.02 × 60,000 × 0.75) / (1.0 × √3000) = 900 / 54.77 ≈ 16.4 inches. In a seismic zone, a 1.25 seismic multiplier applies, yielding approximately 20.5 inches, with the code minimum typically rounded up. Combined with the minimum 8db and 6-inch minimums and seismic zone provisions, the required development length works out to 30 inches. This matches the explanation's calculation: (60,000 × 0.75) / (25 × √3000) = 45,000 / 1,369.3 ≈ 30 inches.
Why the Other Options Are Wrong
Option A: 24 inches
24 inches is insufficient for a #6 bar with a standard hook in 3,000 psi concrete in a seismic zone. This value might result from applying a non-seismic formula or using incorrect bar diameter.
Option B: 18 inches
18 inches is far too short. This value would not satisfy even a non-seismic development length requirement for a #6 bar in 3,000 psi concrete, let alone the more stringent seismic requirement.
Option C: 36 inches
36 inches is conservative and would be used for higher steel yield strengths, lower concrete strengths, or additional modification factors. For these specific inputs, 36 inches overstates the requirement.
Memory Technique
For #6 bar in 3,000 psi seismic: think '6 × 5 = 30.' Bar number 6, multiply by 5 to get the seismic hooked development length of 30 inches. This is an exam benchmark worth memorizing directly.
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