The M40 grade of concrete indicates a specific mixture with a characteristic compressive strength of 40 N/mm2. In this context, we will discuss the mix design procedure for M40 grade concrete using the ACI Method.
M40 Grade Concrete Mix Design Procedure
1. Required Data
The grade of concrete used is M40, which indicates its strength and durability characteristics. The specific gravity of the cement is 3.15, while the fine aggregate has a specific gravity of 2.65. The coarse aggregate has a specific gravity of 2.7 and a bulk density of 1600 kg/m3. The fine aggregate has a fineness modulus of 3.0, and the maximum size of the aggregate is 25mm. Additionally, the degree of supervision for the project is classified as “very good.” This information pertains to the non-air entrained concrete type being used.
2. Mean Design Strength
The standard deviation value for the required grade of concrete determines the level of accuracy and consistency in its quality. A lower standard deviation indicates a higher degree of uniformity and predictability in the concrete’s properties. This is crucial for achieving a very good degree of super vision, ensuring that the concrete meets the desired specifications and performs optimally in its intended applications. By closely controlling the standard deviation within acceptable limits, engineers and construction professionals can enhance the overall quality and durability of concrete structures.
| Grade of concrete | Standard deviation for different degree of supervisions (N/mm2) | ||
| Very Good | Good | Fair | |
| M10 | 2.0 | 2.3 | 3.3 |
| M15 | 2.5 | 3.5 | 4.5 |
| M20 | 3.6 | 4.6 | 5.6 |
| M25 | 4.3 | 5.3 | 6.3 |
| M30 | 5.0 | 6.0 | 7.0 |
| M35 | 5.3 | 6.3 | 7.3 |
| M40 | 5.6 | 6.6 | 7.6 |
| M45 | 6.0 | 7.0 | 8.0 |
| M50 | 6.4 | 7.4 | 8.4 |
| M55 | 6.7 | 7.7 | 8.7 |
| M60 | 6.8 | 7.8 | 8.8 |
Based on the provided table, the value of s is determined to be 5.6. This value is then used in the calculation to find the mean design strength, fm. The formula for calculating fm is fmin + K.S, where fmin is the minimum design strength, K is a constant, and S is the value of s.
In this case, the minimum design strength, fmin, is known to be 40. The constant K is multiplied by the value of s (5.6) and added to fmin to obtain the mean design strength, fm. By substituting the values into the equation, the calculation is as follows: 40 + (1.65 x 5.6) = 49.24 N/mm2. Therefore, the mean design strength, fm, is determined to be 49.24 N/mm2.
3. Water-Cement Ratio
For the design strength of 49.24 MPa, the effective water-cement ratio is not listed in the table provided. In such cases, it is advisable to consider the minimum water-cement ratio, which is 0.38.
| Mean design strength after 28 days (MPa) | Effective water cement ratio | |
| Air entrained concrete | Non-air entrained concrete | |
| 15 | 0.71 | 0.8 |
| 20 | 0.61 | 0.7 |
| 25 | 0.53 | 0.62 |
| 30 | 0.46 | 0.55 |
| 35 | 0.40 | 0.48 |
| 40 | – | 0.43 |
| 45 | – | 0.38 |
4. Water Content and Air Content
For a slump with a maximum aggregate size of 35mm and 25mm, the water and air contents are chosen from the provided table. The water content is selected as 180 kg/m3, while the air content is set at 1.5%.
| Slump/air content | Water content, kg/m3 of concrete for max size of aggregate | |||||||
| 10mm | 12.5mm | 20mm | 25mm | 40mm | 50mm | 70mm | 150mm | |
| 30-50mm | 205 | 200 | 185 | 180 | 160 | 155 | 145 | 125 |
| 80-100mm | 225 | 215 | 200 | 195 | 175 | 170 | 160 | 140 |
| 150-180mm | 240 | 230 | 210 | 205 | 185 | 180 | 170 | – |
| Air content % | 3 | 2.5 | 2 | 1.5 | 1 | 1 | 0.3 | 0.2 |
5. Cement Content
The cement content in concrete is determined using the water cement ratio (W/C). In this particular case, the W/C ratio is 0.38. Another parameter involved is the 180/C ratio, which is also equal to 0.38. By rearranging the equation, we can calculate the cement content (C) by dividing 180 by 0.38, resulting in 473 kilograms per cubic meter of concrete.
6. Coarse Aggregate Content
The fineness modulus of the fine aggregate is 3.0, while the bulk density of the coarse aggregate is 1600 kg/m3. The maximum size of the aggregate is 25mm. According to the provided table, the bulk volume of the dry rodded coarse aggregate is 0.65.
| Maximum size of aggregate (mm) | Bulk volume of dry rodded coarse aggregate w.r.to fineness modulus | |||
| 2.4 | 2.6 | 2.8 | 3.0 | |
| 10 | 0.5 | 0.48 | 0.46 | 0.44 |
| 12.5 | 0.59 | 0.57 | 0.55 | 0.53 |
| 20 | 0.66 | 0.64 | 0.62 | 0.6 |
| 25 | 0.71 | 0.69 | 0.67 | 0.65 |
| 40 | 0.75 | 0.73 | 0.71 | 0.69 |
| 50 | 0.78 | 0.76 | 0.74 | 0.72 |
| 70 | 0.82 | 0.80 | 0.78 | 0.76 |
| 150 | 0.87 | 0.85 | 0.83 | 0.81 |
The coarse aggregate weight is determined by multiplying 0.65 with the density of 1600 kilograms per cubic meter, resulting in a value of 1039 kilograms per cubic meter of concrete.
7. Fine Aggregate
The quantity of fine aggregate in concrete is determined based on the unit weight of fresh concrete, which can be obtained from the provided table. In this case, the fresh concrete density for 25mm size aggregate is specified as 2375kg/m3.
| Maximum size of aggregate (mm) | Density of fresh concrete (kg/m3) | |
| Air entrained | Non air-entrained | |
| 10 | 2190 | 2285 |
| 12.5 | 2235 | 2315 |
| 20 | 2280 | 2355 |
| 25 | 2315 | 2375 |
| 40 | 2355 | 2420 |
| 50 | 2375 | 2445 |
| 70 | 2400 | 2465 |
| 150 | 2435 | 2505 |
The approximate air content is 1.5%. This means that the weight of the fine aggregate in the concrete can be calculated using the equation: 0.985(2375) – (180+473+1039) = 646kg per cubic meter.
8. Final M40 Grade Concrete Mix Proportion
The given information relates to the proportions and quantities of materials used in a concrete mix. The water-cement ratio is stated as 0.38, indicating the amount of water relative to the weight of cement. The water content is specified as 180kg, while the weight of cement is 473kg. The fine aggregate, represented by sand, has a weight of 645kg, and the coarse aggregate weighs 1039kg. The final mix proportion is described as 1 part cement to 1.3 parts sand to 2.1 parts coarse aggregate.