Calculate the required area of reinforcing steel for a concrete column with a gross area of 400 square inches, given that the minimum steel ratio is 1% and maximum is 8%.
Correct Answer
C) 4 to 32 square inches
Minimum steel area = 0.01 × 400 = 4 sq in. Maximum steel area = 0.08 × 400 = 32 sq in. Therefore, required range is 4 to 32 square inches.
Why This Is the Correct Answer
ACI 318 specifies that longitudinal reinforcement in columns must fall between 1% and 8% of the gross cross-sectional area. Minimum: 0.01 × 400 = 4 sq in. Maximum: 0.08 × 400 = 32 sq in. Therefore, the allowable steel area range is 4 to 32 square inches.
Why the Other Options Are Wrong
Option A: 4 to 64 square inches
Option A uses the correct minimum (4 sq in) but an incorrect maximum of 64 sq in. A ratio of 64/400 = 16%, which is double the ACI maximum of 8%. This is a distractor for students who double the correct maximum.
Option B: 8 to 32 square inches
Option B uses an incorrect minimum of 8 sq in (which would imply a 2% minimum ratio) and an incorrect maximum of 32 sq in. The maximum is correct but the minimum is wrong.
Option D: 1 to 8 square inches
Option D uses values of 1 to 8 sq in, which correspond to ratios of 0.25% to 2% — far below the actual ACI-required range. These numbers appear to use the percentage values as square inch values directly, a common arithmetic error.
Memory Technique
Column rebar limits: 1% min, 8% max — remember '1 and 8 for the column's fate.' Then simply multiply each percentage by the gross area: 0.01 × Ag and 0.08 × Ag.
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