In a one-way RC slab having an effective depth of 120 mm, 10 mm diameter main reinforcing bars are to be provided at 100 mm centre-to-centre spacing. Due to the non-availability of 10 mm bars, it is desired to replace 10 mm diameter bars with 12 mm diameter bars, then the centre-to-centre spacing of the 12 mm bars in the slab will be
- A120 mm
- B140 mm
- C144 mmCorrect
- D160 mm
Solution
Concept
Equivalence of steel area per unit width in reinforced concrete slabs based on bar diameter and spacing.
Formula
s2 = s1 × (d2 / d1)²
Step-by-step solution
1. Write down the given parameters: old diameter (d1) = 10 mm, old spacing (s1) = 100 mm, new diameter (d2) = 12 mm. 2. Area of steel per unit width is given by Ast = (π/4 × d²) / s. 3. Equate the steel area for both bar sizes: (π/4 × 10²) / 100 = (π/4 × 12²) / s2. 4. Simplify and solve for s2: s2 = 100 × (12 / 10)² = 100 × 1.44 = 144 mm.
Explanation
To replace a given bar size with a larger bar size while maintaining the same area of steel per unit width, the spacing must be increased in proportion to the ratio of their cross-sectional areas. The area of a reinforcing bar is proportional to its diameter squared (d²). Therefore, the new spacing can be found by multiplying the old spacing by the ratio (dnew / dold)².
Why the other options are wrong
A: 120 mm corresponds to a linear ratio of diameters (100 × 12/10), ignoring the cross-sectional area. B: 140 mm is an arbitrary incorrect value. D: 160 mm is obtained by miscalculating the area ratio.
Shortcut
Correct answer: C) 144 mm