A concrete column has a cross-sectional area of 144 square inches and is reinforced with 4-#8 bars. What is the steel reinforcement ratio?
Correct Answer
D) 2.2%
Steel ratio = (As/Ag) × 100. Area of 4-#8 bars = 4 × 0.79 = 3.16 sq in. Ratio = (3.16/144) × 100 = 2.2%.
Why This Is the Correct Answer
The steel reinforcement ratio is calculated as (As/Ag) × 100, where As is the area of steel reinforcement and Ag is the gross concrete area. Four #8 rebar have a total area of 4 × 0.79 = 3.16 square inches. Dividing by the concrete cross-sectional area: (3.16/144) × 100 = 2.19%, which rounds to 2.2%. This ratio is critical for structural design and code compliance.
Why the Other Options Are Wrong
Option A: 3.3%
3.3% results from an incorrect calculation, likely using wrong rebar area values or mathematical errors. This percentage is too high for the given parameters and would indicate excessive reinforcement that doesn't match the actual steel area provided.
Option B: 4.4%
4.4% represents a significant calculation error, possibly doubling the correct result or using incorrect rebar properties. This ratio would indicate much heavier reinforcement than actually present in the column design.
Option C: 1.1%
1.1% is exactly half the correct answer, suggesting a calculation error where the steel area was divided by 2 or the concrete area was doubled. This underestimates the actual reinforcement ratio significantly.
Memory Technique
Remember 'Steel over Gross times 100' - As/Ag × 100. For #8 bars, think '8 tenths' (0.79 sq in each). Four bars = 4 × 0.79 = about 3.2 square inches.
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