Question

In a reinforced concrete slab, 10 mm diameter bars are provided at a centre-to-centre spacing of 150 mm to resist a given design moment. If instead of 10 mm bars, 12 mm diameter bars of the same grade of steel are used, determine the required centre-to-centre spacing (in mm) so that the slab resists the same design moment. (Assume effective depth and other parameters remain unchanged. Enter the numerical value only in mm.)

Hint:

For changing bar sizes in slabs while maintaining the same moment capacity, use the simple relation: \( s_2 = s_1 \left( \frac{d_2}{d_1} \right)^2 \). This is a quick way to find the new spacing.

Answer 1

Step 1: Understanding Area of Steel Equality.
To resist the same design moment with same grade of steel and effective depth, the total area of steel per unit width ($A_{st}$) must be the same. $A_{st} = \frac{\text{Area of single bar}}{\text{Spacing}} \times 1000$.
Step 2: Set up the Equivalence.
$\frac{(\pi/4) \times 10^2}{150} = \frac{(\pi/4) \times 12^2}{s_{new}}$. The constants $\pi/4$ cancel out: $\frac{100}{150} = \frac{144}{s_{new}}$.
Step 3: Solve for New Spacing.
$s_{new} = \frac{144 \times 150}{100} = 144 \times 1.5 = 216$ mm.