# Step-by-Step Solution: Concrete Mix Design for M40 (IS 10262:2009) ## Given Data - **Grade of Concrete:** M40 (Characteristic strength = 40 MPa) - **Cement Type:** OPC 43, Specific gravity = 3.15 - **Slump:** 150 mm (for pumping) - **Coarse Aggregate:** Crushed angular, 20 mm nominal max size, Specific gravity = 2.74 - **Fine Aggregate:** Zone I sand, Specific gravity = 2.74 - **Exposure:** Severe (for RCC) - **Method of Placing:** Pumping - **Degree of Supervision:** Good - **Chemical Admixture:** Super-plasticizer --- ## 1. **Target Mean Strength** According to IS 10262:2009, Target Mean Strength: \[ \text{Target Mean Strength (f_{ck,target})} = f_{ck} + 1.65 \times S \] - \( f_{ck} \) = 40 MPa - Standard deviation \( S \) (for M40, Table 1 of IS 10262) = 5. MPa \[ f_{ck,target} = 40 + 1.65 \times 5 = 48.25\ \text{MPa} \] --- ## 2. **Selection of Water-Cement Ratio** - Table 5 of IS 456: Max w/c for severe exposure (RCC) = **.45** - For high strength and super-plasticizer, assume **w/c = .38** (lower values typical for M40, adjust as per trial). --- ## 3. **Selection of Water Content** - Table 2 IS 10262: For 20 mm aggregate, water content = **186 kg/m³** (for 25-50 mm slump) - For 150 mm slump (pumping), **increase by ~3% per 25 mm above 50 mm**: - Extra slump required = \( 150-50 = 100 \) mm - Increment steps = \( 100/25 = 4 \) - Increase = \( 4 \times 3\% = 12\% \) - Adjusted water = \( 186 \times 1.12 = 208.3 \) kg/m³ - **With super-plasticizer, reduce water by up to 20%**: - \( 208.3 \times .8 = 166.6 \) kg/m³ - **Adopted water content: 167 kg/m³** --- ## 4. **Cement Content** \[ \text{Cement Content} = \frac{\text{Water}}{w/c} = \frac{167}{.38} = 439.5\ \text{kg/m}^3 \] - IS 456 (Table 5): Min cement for severe exposure = **320 kg/m³ (max 450 kg/m³)** - **Adopted cement content: 440 kg/m³** (within limit) --- ## 5. **Proportion of Aggregates** ### Volume of Concrete - Total volume = 1 m³ - Volume of cement = \( \frac{440}{3.15 \times 100} = .140 \) m³ - Volume of water = \( \frac{167}{1 \times 100} = .167 \) m³ - Assume super-plasticizer dosage = 1% by mass of cement: - \( .01 \times 440 = 4.4 \) kg - Specific gravity (assume) = 1.20 - Volume = \( \frac{4.4}{1.2 \times 100} = .0037 \) m³ - Volume of all admixtures = .0037 m³ \[ \text{Volume of aggregates} = 1 - (.140 + .167 + .0037) = .689\ \text{m}^3 \] --- ### Aggregate Proportion (Table 3 IS 10262:2009) - For 20 mm size, zone I sand, volume of coarse aggregate per unit volume = **.62** - For pumping, **reduce coarse aggregate by 10%**: - \( .62 \times .9 = .558 \) - Volume of fine aggregate = \( 1 - .558 = .442 \) --- ### Mass of Aggregates #### Coarse Aggregate \[ \text{Mass} = \text{Volume} \times \text{Volume of aggregates} \times \text{Specific Gravity} \times 100 \] \[ = .558 \times .689 \times 2.74 \times 100 = 1052\ \text{kg/m}^3 \] #### Fine Aggregate \[ = .442 \times .689 \times 2.74 \times 100 = 834\ \text{kg/m}^3 \] --- ## 6. **Summary of Mix Proportion (Per m³)** | Material | Quantity (kg/m³) | |-------------------|-----------------| | Cement (OPC 43) | 440 | | Water | 167 | | Fine Aggregate | 834 | | Coarse Aggregate | 1052 | | Super-plasticizer | 4.4 | ### **Ratio (by mass):** \[ \text{Cement} : \text{Fine Agg.} : \text{Coarse Agg.} = 440 : 834 : 1052 = 1 : 1.90 : 2.39 \] ## 7. **Final Mix Proportion** \[ \boxed{ \text{Cement} : \text{Fine Agg.} : \text{Coarse Agg.} :: 1 : 1.90 : 2.39\ \text{by mass},\ w/c = .38,\ \text{Superplasticizer}: 1\% \ \text{of cement} } \] --- ## 8. **Notes** - **Adjustments** may be needed based on trial mixes and actual site conditions. - All aggregates assumed in SSD condition; if not, adjust for moisture content. - Always check workability and strength with trial batches. --- ## 9. **References** - IS 10262:2009 _Concrete Mix Proportioning – Guidelines_ - IS 456:200 _Plain and Reinforced Concrete – Code of Practice_ --- **Example Calculation Table:** | Material | Quantity (kg/m³) | Specific Gravity | Volume (m³) | |-------------------------|------------------|------------------|-------------| | Cement (OPC 43) | 440 | 3.15 | .140 | | Water | 167 | 1.00 | .167 | | Fine Aggregate (Zone I) | 834 | 2.74 | .304 | | Coarse Aggregate | 1052 | 2.74 | .384 | | Super-plasticizer | 4.4 | 1.20 | .0037 | --- **Final Answer:** \[ \boxed{ \begin{array}{l} \text{Mix Proportion by mass:} \\ \text{Cement : Fine Aggregate : Coarse Aggregate = 1 : 1.90 : 2.39,} \\ \text{Water-cement ratio} = .38, \\ \text{Water content} = 167\ \text{kg/m}^3, \\ \text{Cement content} = 440\ \text{kg/m}^3, \\ \text{Super-plasticizer} = 1\% \text{ of cement by mass} \end{array} } \]