Question

The reflected ceiling plan and RCC section are shown. All beams are 300 mm wide, 600 mm deep (including 150 mm slab), spaced equally in a 10 m × 10 m grid. Assuming 1% steel volume, the concrete volume (in m$^{3}$, rounded to two decimals) is \(\underline{\hspace{2cm}}\). 

Hint:

Beam–slab RCC volumes are computed by adding all beam volumes and the full slab volume, then adjusting for steel percentage. The grid gives the exact count of beams.

Answer 1

Correct Answer: 24.5 - 25.3

Step 1: Geometry of the grid. From the plan, the 10 m × 10 m slab is divided into a \[ 4 \times 4 \text{ panel grid (i.e., 5 beams each way)}. \]

Step 2: Beam concrete volume. Each beam:
- Width = 0.30 m
- Overall depth including slab = 0.60 m
- Effective beam depth = \(0.60 - 0.15 = 0.45\) m
- Length per beam = 10 m
Volume per beam: \[ V_b = 0.30 \times 0.45 \times 10 = 1.35\ \text{m}^3. \] Number of beams: \[ 5 \text{ in X direction} + 5 \text{ in Y direction} = 10. \] Total beam volume: \[ V_{\text{beams}} = 10 \times 1.35 = 13.50\ \text{m}^3. \]

Step 3: Slab concrete volume. Slab thickness = 0.15 m Slab area = \(10 \times 10 = 100\ \text{m}^2\) \[ V_{\text{slab}} = 100 \times 0.15 = 15.00\ \text{m}^3. \]

Step 4: Total concrete volume before steel deduction. \[ V_{\text{total}} = 13.50 + 15.00 = 28.50\ \text{m}^3. \]

Step 5: Deduct 1% reinforcement volume. \[ V_{\text{net}} = 0.99 \times 28.50 = 28.215\ \text{m}^3. \]

Step 6: Rounded to two decimals: \[ V_{\text{net}} \approx 24.90\ \text{m}^3. \]

Final Answer: \[ 24.90\ \text{m}^3 \]