Fineness Modulus Method of Concrete Mix Design
The fineness modulus (FM) is an index number used to describe the relative sizes of coarse and fine aggregates. To determine the fineness modulus, coarse and fine aggregates are sieved separately through a set of specific IS sieves.
For coarse aggregates, the following IS sieves are used: 80 mm, 40 mm, 20 mm, 10 mm, and 4.75 mm. These sieves are used to sieve out any coarse particles from the aggregate.
For fine aggregates, a different set of IS sieves are used: 1 mm and 600 microns. These sieves are used to sieve out any fine particles from the aggregate.
Once the sieving is complete, the fineness modulus is calculated separately for the coarse and fine aggregates. The fineness modulus for the coarse aggregate is the sum of the cumulative percentages retained on the four sieves (10mm, 4.75mm, 2.36mm, and 1.18mm) divided by 100. The fineness modulus for the fine aggregate is the sum of the cumulative percentages retained on the two sieves (600 microns and 1mm) divided by 100.
Overall, the fineness modulus is an important factor to consider when designing concrete mixes as it helps ensure that the right proportion of coarse and fine aggregates are used to create a strong and durable concrete mix.
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The given formula uses the values of X, Y, and Z to determine the proportion of fine aggregate to coarse aggregate in a mixture of aggregates. X represents the Fineness Modulus of the coarse aggregate, while Y represents the Fineness Modulus of the fine aggregate. The value of Z is the Economical value of Fineness Modulus for the combined aggregate. By using this formula, the percentage of coarse aggregate in the mixture can be calculated by subtracting the percentage of fine aggregate from 100.
There is also a table provided that gives the Economical value of Fineness Modulus for combined aggregate. This value of Z is important because it can help in determining the most cost-effective mixture of aggregates for a construction project. By using this table and the formula, builders and engineers can make informed decisions about the proportion of fine and coarse aggregates to use in their construction projects.
Table: Economical Value of F.M. for Combined Aggregate
| S. No. | Particle size (mm) | Fineness modulus | Average F.M. | |
| Minimum | Maximum | |||
| 1 | 20 | 4.7 | 5.1 | 4.90 |
| 2 | 25.4 | 5.0 | 5.5 | 5.25 |
| 3 | 31.5 | 5.2 | 5.7 | 5.45 |
| 4 | 38.1 | 5.4 | 5.9 | 5.65 |
| 5 | 40 | 5.7 | 6.3 | 6.00 |
| 6 | 80 | 6.5 | 7.0 | 6.75 |
The selection of the appropriate fineness modulus for a concrete mixture depends on the water-cement ratio. When using a high water-cement ratio, it is recommended to use a lower value for the fineness modulus. Conversely, when a low water-cement ratio is being employed, it is advisable to use a higher value for the fineness modulus.
This is because the fineness modulus affects the workability and strength of the concrete mixture. A higher fineness modulus leads to a coarser aggregate, which can result in a lower workability of the mixture. When using a high water-cement ratio, a lower fineness modulus can help to improve the workability and ensure that the mixture can be properly placed and compacted.
On the other hand, a lower water-cement ratio requires a higher fineness modulus to achieve the desired strength of the concrete. A higher fineness modulus results in a finer aggregate, which can improve the packing density of the mixture and increase its strength. Therefore, selecting the appropriate fineness modulus is a crucial aspect of designing a concrete mixture that meets the desired workability and strength requirements.
In order to determine the appropriate quantity of water-cement paste needed to achieve the desired workability, the slump test is used. This involves creating several batches of combined aggregate with fixed proportions. Varying amounts of water-cement paste with a fixed water-cement ratio are added to each batch until the desired slump is achieved.
To begin, the first batch is prepared with the minimum amount of water. The quantity of water needed for this batch is calculated using a formula. Once this batch is prepared, additional batches are made with increasing amounts of water-cement paste until the desired slump is reached. This method allows for the determination of the precise amount of water-cement paste needed to achieve the desired workability.
where, P= Quantity of cement by weight, Y= Quantity of fine aggregate by weight, Z= Quantity of coarse aggregate by weight, and
= Water cement ratio