Mechanical Behavior 1: Calculation Solutions
(70 points)
1. (10 pts) A specimen of aluminum having a rectangular cross section 10 mm  12.7 mm (0.4 in. 
0.5 in.) is pulled in tension with 35,500 N (8000 lbf) force, producing only elastic deformation.
Calculate the resulting strain.
A.
B.
C.
D.
4.1x10^-5
4.1 x10^-3
3.6 x10^-3
3.8 x 10^-5
2. (5 pts) Your co-worker has applied a stress of +300 MPa to a steel rod. Did he load the sample in
tension or compression?
a. Tension
b. Compression
3. (5 pts) Toughness represents:
a. The energy required to break (i.e., fracture) a material
b. The energy required to stretch a material.
c. The area of the test specimen
d. The length of the test specimen
4. (10 pts) A steel bar 100 mm (4.0 in.) long and having a square cross section 20 mm (0.8 in.) on
an edge is pulled in tension with a load of 89,000 N (20,000 lbf), and experiences an elongation
of 0.10 mm (4.0  10-3 in.). Assuming that the deformation is entirely elastic, calculate the
elastic modulus of the steel.
A.
B.
C.
D.
225 MPa
201 GPa
223 GPa
198 MPa
5. (10 pts) For a bronze alloy, the stress at which plastic deformation begins is 275 MPa (40,000
psi), and the modulus of elasticity is 115 GPa (16.7  106 psi). What is the maximum load that
may be applied to a specimen with a cross-sectional area of 325 mm2 (0.5 in.2) without plastic
deformation?
A. 89.4 kN
B. 95.6 kN
C. 78.8 kN
D. 100.1 kN
6. (10 pts) For a bronze alloy that is 115 mm in length, what is the maximum length the bronze
alloy can be pulled to before plastic deformation initiates? Note that the stress at which plastic
deformation begins is 275 MPa (40,000 psi) and the modulus of elasticity is 115 GPa (16.7  106
psi).?
A.
B.
C.
D.
115.28 mm
116.11 mm
115.05 mm
116.08 mm
7. (20 pts) A specimen of ductile cast iron having a rectangular cross section of dimensions 4.8
mm  15.9 mm (3/16 in.  5/8 in.) and is deformed in tension. Using the load-elongation data
shown in the following table, complete parts (a) through (d). You will need to plot this data as
engineering stress versus engineering strain to complete this problem.
Load
Length
N
lbf
mm
in.
0
0
75.000
2.953
4,740
1,065
75.025
2.954
9,140
2,055
75.050
2.955
12,920
2,900
75.075
2.956
16,540
3,720
75.113
2.957
18,300
4,110
75.150
2.959
20,170
4,530
75.225
2.962
22,900
5,145
75.375
2.968
25,070
5,635
75.525
2.973
26,800
6,025
75.750
2.982
28,640
6,440
76.500
3.012
30,240
6,800
78.000
3.071
31,100
7,000
79.500
3.130
31,280
7,030
81.000
3.189
30,820
6,930
82.500
3.248
29,180
6,560
84.000
3.307
27,190
6,110
85.500
3.366
24,140
5,430
87.000
3.425
18,970
4,265
88.725
3.493
Fracture
(a) Compute the modulus of elasticity (5 pts).
A. 207 GPa
B. 197 GPa
C. 200 GPa
D. 212 GPa
(b) Determine the yield strength at a strain offset of 0.002. (5 pts)
A. 167 MPa
B. 280 MPa
C. 325 MPa
D. 235 MPa
(c) Determine the tensile strength of this alloy. (5 pts)
A. 410 MPa
B. 359 MPa
C. 485 MPa
D. 520 MPa
(d) What is the ductility, in percent elongation? (5 pts)
A. 24.2%
B. 18.4%
C. 14.6 %
D. 12.8 %