FE Civil Materials Practice Problems

The current FE Civil specification assigns 5-8 of the 110 exam questions to Materials. Form A contains 6 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A sieve analysis of a concrete fine aggregate gives cumulative percentages retained on the 4.75-mm, 2.36-mm, 1.18-mm, 0.600-mm, 0.300-mm, and 0.150-mm sieves of 4, 15, 36, 58, 78, and 89, respectively. The fineness modulus of the aggregate is most nearly:

(A)0.89
(B)2.80
(C)3.20
(D)3.80

Show worked solution

Answer: (B)

The six cumulative retained percentages total 280, making the fineness modulus 280/100 = 2.80.

Fineness modulus works on cumulative percent retained — not incremental values, not percent passing.

F M = \frac{\sum ( cumulative percent retained )}{100}

4 + 15 + 36 + 58 + 78 + 89 = 280

F M = \frac{280}{100} = 2.80

FE Reference Handbook — Civil Engineering: Aggregate Gradation, Fineness Modulus

Why the other choices appear

(A)Sums the incremental (individual) percentages retained, which totals 89, and divides by 100, giving 0.89.
(C)Sums the cumulative percentages passing (96 + 85 + 64 + 42 + 22 + 11 = 320) instead of retained, giving 3.20.
(D)Adds 100 percent for the pan to the cumulative retained sum, (280 + 100)/100 = 3.80.