Engineering Materials
Homework #2
Assigned date: 3 Apr. 2023
Due date: 28 Apr. 2023 (before 11:59 PM)
1. Sieve analysis of a 1000-g sample of fine aggregate resulted in the following data.
Find the fineness modulus.
Sieve size:
4
8
16
30
50
100
Weight retained (g): 26
130
240
252
210
138
2. A composite material is made by reinforcing a cement paste with steel fibers. The
Young’s modulus of steel fibers E1 and that of the HCP (hardened cement paste) is E2.
The volume fraction of the steel fibers is V1, and that of the HCP is V2.
(a) What’s the value of V1 which would give rise to the largest EU/EL, where EU is the
upper bound and EL the lower bound of the composite Young’s modulus.
(b) What is the area enclosed by (EU - EL) on the composite Young’s modulus versus V1
diagram?
3. Determine the weight percentage of C3S and C2S in the following Portland cement.
(a) C = 64.15%, S = 21.87 %, A = 5.35%, F = 3.62%, S"=2.53%.
(b) C = 63.14%, S = 23.29%, A = 3.61%, F = 6.38%, S"=2.29%.
4. A brittle material has been tested for its fracture strength from a batch of 20 samples.
The volume of the samples was 0.35 m3. Experimental data, in units of MPa, were
obtained as shown in the table below.
(a) What is the failure probability when applied stress is 34 MPa?
(b) For the same failure probability as (a), what is the applied stress on the same
material with a volume of 0.15 m3?
23.2
24.8
26.2
27.7
27.8
28.5
28.9
29.4
30.4
30.8
31.8
32.3
32.4
32.8
33.2
33.8
34.5
35.9
36.1
36.5