# Step-by-Step Mix Proportioning for M40 Concrete as per IS 10262:2009 Let's design the mix for **M40 concrete** (characteristicive strength MPa at 28) as per IS 102622009, on the data. --- ##1. ** Data** | Parameter | Value | |----------------------------------|----------------------------------------| | Grade of concrete | M40 | | Type of cement | OPC 43 | | Cement specific gravity | 3.15 | | Slump required | 150 mm | | Type of coarse aggregate | Crushed angular, 20 mm, S.G. 2.74 | | Type of fine aggregate | Zone I, S.G. 2.74 | | Exposure condition | Severe (for RCC) | | Method of placing | Pumping | | Degree of supervision | Good | | Chemical admixture | Superplasticizer | --- ## 2. **Target Mean Strength** \[ \text{Target Mean Strength} = f_{ck} + 1.65 \times \text{Standard Deviation} \] From IS 10262:2009, Table 1, for M40, - \( f_{ck} = 40 \) MPa - Standard deviation, \( S = 5. \) MPa \[ \text{Target Mean Strength} = 40 + 1.65 \times 5 = 48.25~\text{MPa} \] --- ## 3. **Selection of Water-Cement Ratio** - For M40 grade, **W/C ratio** typically should not exceed **.4–.45**. - For severe exposure (Table 5, IS 456:200), maximum W/C = .45. **Assume:** \[ \text{Adopt W/C ratio} = .38 \] --- ## 4. **Selection of Water Content** - IS 10262:2009, Table 2, recommends water content for 20 mm aggregate (for 25–50 mm slump) is **186 kg/m³**. - For every 25 mm increase in slump, increase by 3%, but with superplasticizer, can reduce by 20%. - **Increase for 150 mm slump:** - Increase = \( \frac{150 - 50}{25} \times 3\% = 12\% \) - New water content = \( 186 \times 1.12 = 208.3~kg \) - **Reduction for superplasticizer (assume 20%):** - \( 208.3 \times .8 = 166.6~kg \) **Adopt:** \[ \text{Water content} = 167~kg/m^3 \] --- ## 5. **Calculation of Cement Content** \[ \text{Cement content} = \frac{\text{Water content}}{\text{W/C ratio}} = \frac{167}{.38} = 439~kg/m^3 \] - Check minimum cement for severe exposure (IS 456 Table 5): **320 kg/m³** - **439 kg/m³ > 320 kg/m³** ⇒ OK --- ## 6. **Proportion of Aggregates** - IS 10262:2009, Table 3: For 20 mm aggregate, Zone I sand, water-cement ratio of .5, volume of coarse aggregate per unit volume of total aggregate is .62. - **Adjustment for W/C < .5:** For each .05 decrease in W/C below .5, increase coarse aggregate by .01. \[ \Delta = \frac{.5 - .38}{.05} = 2.4 \implies \text{Increase by } 2 \times .01 = .02 \] \[ \text{Coarse Aggregate proportion} = .62 + .02 = .64 \] \[ \text{Fine Aggregate proportion} = 1 - .64 = .36 \] --- ## 7. **Mix Calculations (Per m³ Concrete)** ### (a) **Volume of Concrete** \[ \text{Total volume} = 1~m^3 \] \[ \text{Air content (IS 10262, Table 2)} = 2\% \] \[ \text{Net volume of concrete} = 1 - .02 = .98~m^3 \] ### (b) **Volume of Cement** \[ \text{Volume} = \frac{\text{Mass}}{\text{Specific gravity} \times 100} \] \[ = \frac{439}{3.15 \times 100} = .139~m^3 \] ### (c) **Volume of Water** \[ = \frac{167}{1 \times 100} = .167~m^3 \] ### (d) **Volume of Superplasticizer** Assume 1% by weight of cement = \(.01 \times 439 = 4.39~kg\), specific gravity = 1.2 \[ \text{Volume} = \frac{4.39}{1.2 \times 100} = .00366~m^3 \] ### (e) **Volume of Aggregates** \[ \text{Volume of Aggregates} = .98 - (.139 + .167 + .00366) = .6703~m^3 \] ### (f) **Mass of Aggregates** #### (i) **Coarse Aggregate:** \[ \text{Volume} = .6703 \times .64 = .429~m^3 \] \[ \text{Mass} = .429 \times 2.74 \times 100 = 1176~kg \] #### (ii) **Fine Aggregate:** \[ \text{Volume} = .6703 \times .36 = .241~m^3 \] \[ \text{Mass} = .241 \times 2.74 \times 100 = 660~kg \] --- ## 8. **Final Mix Proportion (by mass per m³)** | Material | Quantity (kg/m³) | |--------------------|-----------------| | **Cement** | 439 | | **Water** | 167 | | **Fine Aggregate** | 660 | | **Coarse Aggregate** | 1176 | | **Superplasticizer** | 4.4 | **Proportion by mass:** Cement : Fine Agg. : Coarse Agg. :: 439 : 660 : 1176 ≈ 1 : 1.5 : 2.68 Water-cement ratio = .38 --- ## 9. **Summary Table** | Material | Quantity (kg/m³) | |----------------------|-------------------| | Cement (OPC 43) | 439 | | Water | 167 | | Fine Aggregate (Zone I) | 660 | | Coarse Aggregate (20mm) | 1176 | | Superplasticizer | 4.4 | **Mix (by mass):** **1 : 1.5 : 2.68** (C : FA : CA) **Water-cement ratio = .38** **Superplasticizer = 1% by weight of cement** --- ## 10. **Final Note** - **Trial mixes are essential** to optimize workability, strength, and durability considering actual site materials. - Adjust water and admixture based on actual slump and workability at site. --- ## **References** - IS 10262:2009 – Concrete Mix Proportioning – Guidelines. - IS 456:200 – Plain and Reinforced Concrete – Code of Practice. --- **Final Answer:** **Mix proportion for M40 grade concrete (by mass):** \[ \boxed{ \text{Cement : Fine Aggregate : Coarse Aggregate :: 1 : 1.5 : 2.68 \quad \text{with Water-cement ratio = .38, Superplasticizer = 1\% (by cement weight)}} } \] *All quantities per m³ should be adjusted based on actual moisture content and absorption on site.*