# Cantilever Slab Design Calculation Summary ## Given Data - **Span (L)**: 2.1 m - **Material**: M-20 concrete, Fe-415 steel - **Concrete strength (\(f_{cd}\))**: 20 N/mm² - **Steel yield strength (\(f_y\))**: 415 N/mm² --- ## 1. Depth of the Slab - **Effective depth (\(d\))**: 21 cm (210 mm) - **Total depth (\(D\))**: 215 mm (initial), reduced to 120 mm at free end --- ## 2. Load Calculations - **Self-weight of slab**: \[ \text{Self-weight} = .5 \times (.24 + .12) \times 25 = 4.5\, \text{kN/m}^2 \] - **Ultimate load (\(w_u\))**: \[ w_u = 1.5 \times 8 = 12\, \text{kN/m}^2 \] --- ## 3. Moment Calculation - **Ultimate moment (\(M_u\))**: \[ M_u = .5 \times w_u \times L^2 = 26.46\, \text{kN·m} \] --- ## 4. Depth Check for Ultimate Moment - **Moment capacity formula**: \[ M_{u} = .138 \times f_{ck} \times b \times d^2 \] - **Calculated depth**: \[ d = \sqrt{\frac{26.46 \times 10^6}{.138 \times 20 \times 100}} \approx 98.9\, \text{mm} \] - **Effective depth selected**: 240 mm (satisfies the design) - **Minimum effective depth**: \[ A_{s\,min} = .0012 \times 100 \times 240 = 288\, \text{mm}^2 \] --- ## 5. Reinforcement Details - **Ultimate reinforcement (\(A_{s\,u}\))**: \[ A_{s\,u} = .87 \times A_{s\,\text{provided}} \times \frac{d}{d_{a}} \times \left[1 - \frac{A_{s}}{f_{cd} \times b \times d}\right] \] - **Using provided data, \(A_{s} = 305.6\, \text{mm}^2\)** --- ## 6. Distribution Steel - **Provided steel**: \[ A_{s} = 288\, \text{mm}^2 \] - **Distribution bars**: 10 mm diameter bars at 270 mm centers --- ## 7. Anchorage Length \[ L_{a} = \frac{.87 \times f_{y} \times \phi}{4 \times 1.2 \times 1.6} \times \frac{415}{100} \times \frac{10}{20} \approx 470\, \text{mm} \] - **Main tension bars extended into the support**: minimum length 470 mm --- ## 8. Check for Deflection Control - **Deflection limit**: \(\frac{L}{250} = 8.4\) - **Actual deflection**: \[ \left(\frac{L}{d}\right)_{max} = 14 \] - **Result**: The slab satisfies deflection limits. --- ## 9. Reinforcement in the Cantilever Slab - **Final reinforcement**: 10 mm bars at 255 mm centers, providing adequate strength and stiffness. --- This summarized calculation confirms the design adequacy for the cantilever slab with the specified parameters.