Question

The main reinforcement of a RC slab consists of 10 mm bar spaced at 100 mm c/c. If 10 mm bars are to be replaced with 12 mm bars, then the spacing w.r.t. current spacing would be increased by
1. 2 cm
2. 4 cm
3. 4.4 cm
4. 6 cm
5. 14.4 cm

Answer 1

Correct Answer - Option 3 : 4.4 cm

Concept:

Spacing (S) of reinforcement in slab = \(\frac{{1000}}{{Ast}} \times \frac{\pi }{4}{(ϕ )^2}\)

where ϕ = diameter of bar

Calculation:

Given,

ϕ₁ = 10 mm

S₁ = 100 mm = 10 cm

ϕ₂ = 12 mm

Spacing (S) = \(\frac{{1000}}{{Ast}} \times \frac{\pi }{4}{(ϕ )^2}\)

S ∝ ϕ² ⟹ \(\frac{{{S_1}}}{{{\phi _1}^2}} = \frac{{{S_2}}}{{{\phi _2}^2}}\)

\({S_2} = {S_1}(\frac{{{\phi _2}^2}}{{{\phi _1}^2}}) = 100 \times \frac{{{{12}^2}}}{{{{10}^2}}}\) = 144 mm = 14.4 cm

As in the Question, it is asked spacing w.r.t. current spacing would be increased by

= S₂ - S₁ = 14.4 - 10 cm = 4.4 cm