M15 concrete mix has a mix proportion of 1:2:4 of cement, fine aggregate, and coarse aggregate respectively. M15 – M represents Mix and 15 N/mm^{2 }is the characteristic compressive strength of concrete cube at 28 days.

### Required Data M15 Grade Concrete

- Grade of concrete =M15
- Characteristic compressive strength of concrete at 28days = 15N/mm
^{2 } - Nominal maximum size of aggregate = 20mm
- Specific Gravity of cement = 3.15
- Specific gravity of fine aggregate = 2.6
- Specific gravity of Coarse aggregate = 2.65

### Step 1: Calculation of Target Strength

Target mean strength of concrete is derived from the below formula

**f _{t }= f_{ck} + 1.65 s**

Where S = standard deviation which is taken as per below table= 3.5

Grade of concrete | Standard deviation (N/mm^{2}) |

M10 | 3.5 |

M15 | 3.5 |

M20 | 4.0 |

M25 | 4.0 |

M30 | 5.0 |

M35 | 5.0 |

M40 | 5.0 |

M45 | 5.0 |

M50 | 5.0 |

Characteristic compressive strength after 28 days f_{ck }= 15N/mm^{2}

f_{t }= 15 + 1.65 x 3.5

Therefore, target mean strength **f _{t }= 20.775 N/mm^{2}**

### Step 2: Selection of Water-Cement Ratio

Water- cement ratio is selected from the graph plotted between 28-day compressive strength and water-cement ratio which is as per IS10262-2009

**So, W/C ratio = 0.57**

From table 5 of IS 456-2000, the maximum free water-cement ratio for moderate exposure is**W/C Ratio = 0.60**

The final water-cement ration will be taken as the minimum of the above two values,

Therefore, **W/C ratio = 0.57**

### Step 3: Air Content Calculation

Nominal maximum size of aggregate taken is = 20mm

Nominal maximum size of aggregate | Air content (% of the volume of concrete) |

10mm | 5% |

20mm | 2% |

40mm | 1% |

So, from the table entrapped air content in % of the volume of concrete = 2%

### Step 4: Water Content Calculation

For nominal maximum size of aggregate of 20mm, the required water content is selected form the table-

Nominal maximum size of aggregate | Maximum water content |

10mm | 208 |

20mm | 186 |

40mm | 165 |

The aggregate nominal maximum size is 20mm and they belong to zone 2. So, Adjustment for compacting factor is to be applied.

Therefore, water content = 186 + (186 x 3/100) =** 191.6 lit / m ^{3} of concrete.**

### Step 5: Cement Content Calculation

From step 2, Water cement ratio = W/C = 0.57

From step 4, Water content W = 191.6 liters = 191.6kg

191.6 / C = 0.57

Finally, C = 336.14 Kg / m^{3} of concrete

But from table 5 of IS456-2000, Minimum cement content required for moderate exposure condition for M15 grade concrete is = 240 Kg/m^{3} of concrete.

Greater of above two values will be the cement content.

Hence, **C = 336.14Kg**

### Step 6: Aggregate Ratio for Concrete

From the table, ratio of volume of coarse aggregate to volume of total aggregate, for 20mm nominal maximum size aggregate and zone-2 fine aggregate is

Therefore, **P = 0.62**

### Step 7: Aggregate Content Calculation

Volume of concrete (with entrapped air) = 1 m^{3}

From step 3, Entrapped air % = 2% = 0.02

Therefore, volume of concrete (without air content) = 1-0.02 = 0.98m^{3}

Fine aggregate content F.A is determined from below formula,

**V = [W + C/Gc + (1/ (1-P) X (F.A)/Gf)] x 1/1000**

0.98 = [191.6 + 336.14/3.15 + (1/ (1-0.62) X (F.A)/2.6)] x 1/1000

Therefore, amount of fine aggregate **F.A = 673.52kg**

Similarly, Coarse aggregate content C.A is derived from

Therefore, amount of coarse aggregate **C.A = 1120kg**

### Step 8: Final Mix Proportions of Ingredients

W/C ratio = 0.57

Cement quantity = 336.14Kg = 337kg

Fine aggregate quantity = 673.52kg = 674kg

Coarse aggregate Quantity = 1120 kg

Mix proportion for M15 Concrete = Cement : F.A : C.A = 1 : 2 : 3.3

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