Design of Slabs MCQ with answer and solution

Concept

Calculation of steel percentage in RC slab

Formula

Pt = (Ast / (b × D)) × 100

Step-by-step solution

1. Area of steel per meter width is Ast = (1000 / 200) × (π × 10² / 4) = 392.7 mm². 2. Total cross-sectional area of concrete per meter width is A = 1000 mm × 150 mm = 150,000 mm². Answer: A

Explanation

The cross-sectional area of steel per meter width provided by 10 mm bars at 200 mm spacing is about 392.7 mm². Dividing this steel area by the total gross concrete area of 150,000 mm² gives a ratio of 0.0026. Therefore, option A is correct.

Why the other options are wrong

B) 0.0036 corresponds to a larger bar spacing than the specified 200 mm interval. C) 0.0046 represents an undercalculation of the reinforcement percentage for the given bar dimensions and spacing.

Shortcut

Steel ratio = Ast / (1000 × D): (78.54 × 5) / (1000 × 150) ≈ 0.0026.

Common mistake

Expressing the steel ratio as a decimal fraction without proper percentage conversion or using effective depth instead of total depth.