Fineness modulus is determined as per IS code by using sieves of sizes 80 mm, 40 mm, 20 mm, 10 mm, 4.75 mm, 2.36 mm, 1.18 mm, 600 micron, 300 micron and 150 micron. The cumulative percentages retained on these sieves are 0, 0, 0, 0, 6, 25, 51, 71, 85 and 92 respectively. Find the value of fineness modulus.
📚 Detailed Explanation: Fineness Modulus Calculation
The Fineness Modulus (FM) is calculated by summing the cumulative percentages of aggregate retained on each of the standard IS sieves and dividing by 100. The standard sieve set for combined aggregate FM includes all 10 sieves listed.
Cumulative % retained: 80mm=0, 40mm=0, 20mm=0, 10mm=0, 4.75mm=6, 2.36mm=25, 1.18mm=51, 600µm=71, 300µm=85, 150µm=92
Sum = 0 + 0 + 0 + 0 + 6 + 25 + 51 + 71 + 85 + 92 = 330
FM = 330 / 100 = 3.30
Note: An FM of 3.30 represents a coarse fine aggregate or fine coarse aggregate. The answer key indicates B (7.20–7.45), which would require the retained percentages to sum to ~720–745. This discrepancy may arise from the exam question presenting different retained values than those shown, or from a grading pattern where the coarse fractions carry much higher retained percentages. Working backward: for FM = 7.20–7.45, the sum must be 720–745.
FM Calculation Template
| Sieve Size | Cumulative % Retained |
|---|---|
| 80 mm | 0 |
| 40 mm | 0 |
| 20 mm | 0 |
| 10 mm | 0 |
| 4.75 mm | 6 |
| 2.36 mm | 25 |
| 1.18 mm | 51 |
| 600 µm | 71 |
| 300 µm | 85 |
| 150 µm | 92 |
| Sum / FM | 330 / 100 = 3.30 |
Key Concepts for Students
- FM = ∑(cumulative % retained) / 100 using the 10-sieve set for combined aggregate or 6-sieve set for fine aggregate only.
- An FM of 3.30 classifies as coarse sand / fine coarse aggregate boundary (FM 2.9–3.5 = coarse sand range).
- Always verify the given sieve data: if any retained % decreases from fine to coarse, there is an error in the data.