# Step-by-Step Mix Design for M40 Grade Concrete as per IS 10262:2009 Given Data: - **Grade of concrete:** M40 (Characteristic compressive strength = 40 MPa) - **Cement type:** OPC 43, Specific gravity = 3.15 - **Slump required:** 150 mm - **Coarse aggregate:** Crushed angular, 20 mm, Specific gravity = 2.74 - **Fine aggregate:** Zone I, Specific gravity = 2.74 - **Exposure:** Severe (for RCC) - **Method of placing:** Pumping - **Degree of supervision:** Good - **Admixture:** Super-plasticizer --- ## 1. Target Mean Strength \[ \text{Target Mean Strength (f_{ck'})} = f_{ck} + 1.65 \times S \] Where \( S \) = Standard deviation (from IS 10262:2009, Table 1, for M40: \( S = 5. \) MPa) \[ f_{ck'} = 40 + 1.65 \times 5 = 40 + 8.25 = 48.25 \text{ MPa} \] --- ## 2. Selection of Water-Cement Ratio - For M40 grade, use Table 5 of IS 456:200 and IS 10262:2009. - For severe exposure, **maximum w/c ratio = .45**. - Use trial value: **w/c = .38** (with super-plasticizer). --- ## 3. Selection of Water Content - For 20 mm aggregate and slump 25–50 mm, max water = 186 kg/m³ (Table 2, IS 10262:2009). - For **150 mm slump** (with super-plasticizer), **reduce water** by 18% due to admixture effect. - Increase by 3% for pumping = net 15% reduction. \[ \text{Adjusted Water} = 186 \times (1 - .15) = 186 \times .85 = 158.1 \text{ kg/m}^3 \] --- ## 4. Calculation of Cement Content \[ \text{Cement Content} = \frac{\text{Water Content}}{\text{w/c Ratio}} = \frac{158.1}{.38} = 416 \text{ kg/m}^3 \] - IS 456:200 for severe exposure: **min cement = 320 kg/m³**, max = 450 kg/m³. - **Use 416 kg/m³** (within limits). --- ## 5. Aggregate Proportion (Volume Method) ### 5.1 Volume of Concrete Total volume = 1 m³ Volume of all ingredients except air = 1 - .02 (air) = **.98 m³** ### 5.2 Volume of Cement \[ \text{Volume of Cement} = \frac{\text{Cement}}{\text{Specific Gravity} \times 100} = \frac{416}{3.15 \times 100} = .132 \text{ m}^3 \] ### 5.3 Volume of Water \[ \text{Volume of Water} = \frac{158.1}{1 \times 100} = .158 \text{ m}^3 \] ### 5.4 Volume of Superplasticizer Assume dosage = 1% by weight of cement: \[ \text{Weight of admixture} = .01 \times 416 = 4.16 \text{ kg} \] \[ \text{Volume of admixture} = \frac{4.16}{1.145 \times 100} = .0036 \text{ m}^3 \] *(Assume specific gravity of admixture = 1.145)* ### 5.5 Volume of Aggregates \[ \text{Total volume of aggregates} = .98 - (.132 + .158 + .0036) = .98 - .2936 = .6864 \text{ m}^3 \] ### 5.6 Proportion of Fine Aggregate (FA) and Coarse Aggregate (CA) From Table 3 of IS 10262:2009: - For 20mm aggregate, Zone I sand, **FA:CA = .35:.65** (by volume of aggregate). \[ \text{Volume of FA} = .35 \times .6864 = .2402 \text{ m}^3 \] \[ \text{Volume of CA} = .65 \times .6864 = .4462 \text{ m}^3 \] --- ### 5.7 Convert Volumes to Mass #### Fine Aggregate (FA) \[ \text{Mass of FA} = \text{Volume} \times \text{Specific Gravity} \times 100 = .2402 \times 2.74 \times 100 = 658 \text{ kg} \] #### Coarse Aggregate (CA) \[ \text{Mass of CA} = .4462 \times 2.74 \times 100 = 1222 \text{ kg} \] --- ## 6. Mix Proportion by Weight (per m³) - **Cement:** 416 kg - **Water:** 158 kg - **Fine Aggregate:** 658 kg - **Coarse Aggregate:** 1222 kg - **Superplasticizer:** 4.2 kg **Mix Ratio (by weight):** Cement : FA : CA :: 416 : 658 : 1222 Or, divide by cement for ratio: \[ 1 : 1.58 : 2.94 \text{ (by weight)} \] --- ## 7. Final Answer (Mix Design) ### **Mix Proportion for M40 Concrete (per m³):** | Material | Amount | |--------------------|---------| | Cement (OPC 43) | 416 kg | | Water | 158 kg | | Fine aggregate | 658 kg | | Coarse aggregate | 1222 kg | | Superplasticizer | 4.2 kg | **Mix Ratio by weight:** **1 : 1.58 : 2.94** (Cement : Fine Aggregate : Coarse Aggregate) --- ## 8. Notes - **Adjust for site moisture/water absorption.** - **Trial mixes should be cast and tested for workability and strength.** - **Admixture dosage may be fine-tuned as per manufacturer’s recommendations.** --- **References:** - IS 10262:2009 "Concrete Mix Proportioning – Guidelines" - IS 456:200 "Plain and Reinforced Concrete – Code of Practice" --- **Final Answer:** > **The mix proportion (by weight) for M40 grade concrete as per IS 10262:2009 is:** > **1 : 1.58 : 2.94 :: Cement : Fine Aggregate : Coarse Aggregate** > with 158 kg water and 4.2 kg superplasticizer per m³.