Sieve analysis and fineness modulus: a 20 kg coarse aggregate sample is sieved through 80 mm, 40 mm, 20 mm, 10 mm, 4.75 mm, 2.36 mm, 1.18 mm, 600 μm, 300 μm, and 150 μm sieves with masses retained 0, 2, 8, 6, 4 kg respectively (zero on the remaining sieves). What is the fineness modulus (FM) of the aggregate?

Introduction / Context:
Fineness modulus (FM) is an index number expressing the average size of particles in an aggregate sample based on a standard series of sieves. It helps in proportioning concrete mixes and assessing grading consistency for quality control.

Given Data / Assumptions:

• Total sample mass = 20 kg.
• Mass retained (kg) on sieves: 80 mm = 0, 40 mm = 2, 20 mm = 8, 10 mm = 6, 4.75 mm = 4, and 0 on 2.36 mm, 1.18 mm, 600 μm, 300 μm, 150 μm.
• Standard FM definition: FM = (sum of cumulative % retained on the standard sieve series down to 150 μm) / 100.

Concept / Approach:
Compute the cumulative percentage retained at each sieve, sum them, and divide by 100. Because the entire 20 kg is retained by 4.75 mm, all finer sieves show 100% cumulative retention.

Step-by-Step Solution:
Percent retained on each sieve = (mass retained / 20) * 100.Cumulative % retained:80 mm: 0% (0 kg)40 mm: 10% (2/20)20 mm: 50% (2 + 8 = 10 kg → 10/20 = 50%)10 mm: 80% (16/20)4.75 mm: 100% (20/20)2.36 mm and smaller: still 100% (no additional mass).Sum of cumulative % = 0 + 10 + 50 + 80 + 100 + 100 + 100 + 100 + 100 + 100 + 100 = 840.FM = 840 / 100 = 8.40.

Verification / Alternative check:
Coarse aggregates commonly have FM in the range ~6.0 to 8.5. A grading fully retained above 4.75 mm yields a high FM, consistent with 8.40.

Why Other Options Are Wrong:

• 7.30, 7.35, 7.40, 7.45: each is significantly below the computed FM = 8.40 from the provided data.

Common Pitfalls:
Confusing “percent retained” with “percent passing,” or forgetting to include the cumulative values for all sieves down to 150 μm in the FM sum.

Final Answer:
None of these