Instant download and all chapters Solutions Manual Mechanics of Materials 9th Edition
Russell C. Hibbeler
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S
0
33.2
45.5
49.4
51.5
53.4
3-2. Data taken from a stress-strain test for a ceramic are
given in the table.The curve is linear between the origin and
the first point. Plot the diagram, and determine the modulus
of elasticity and the modulus of resilience.
Ans.
Modulus of Resilience: The modulus of resilience is equal to the area under the
l i n e a r p o r t i o n of the stress-strain diagram (shown shaded).
140
(ksi)
e (in./in.)
0
0.0006
0.0010
0.0014
0.0018
0.0022
3-3. Data taken from a stress-strain test for a ceramic
are given in the table.The curve is linear between the
origin and the first point. Plot the diagram, and
determine approximately the modulus of toughness.
The rupture stress is sr = 53.4 ksi.
S
Modulus of Toughness: The modulus of toughness is equal to the area under
the stress-strain diagram (shown shaded).
141
(ksi)
0
33.2
45.5
49.4
51.5
53.4
e (in./in.)
0
0.0006
0.0010
0.0014
0.0018
0.0022
Load (kip)
0
2.50
142
Elongation (in.)
0
0.0009
6.50
0.0025
8.50
0.0040
9.20
0.0065
9.80
0.0098
12.0
0.0400
14.0
0.1200
14.5
0.2500
14.0
0.3500
13.2
0.4700
3-5. A tension test was performed on a steel specimen
having an original diameter of 0.503 in. and gauge
length of
2.0
in. Using the data listed in the table, plot the
stress-strain diagram and determine approximately the
modulus of toughness.
143
Load (kip)
Elongation (in.)
0
2.50
6.50
8.50
9.20
9.80
12.0
14.0
14.5
14.0
13.2
0
0.0009
0.0025
0.0040
0.0065
0.0098
0.0400
0.1200
0.2500
0.3500
0.4700
3-6. A specimen is originally 1 ft long, has a diameter of 0.5
in., and is subjected to a force of 500 lb. When the force is
increased from 500 lb to 1800 lb, the specimen elongates
0.009 in. Determine the modulus of elasticity for the material
if it remains linear elastic.
Ans:
E=
144
8.83 (10 3) ksi
Ans:
A = 0.209 in2, P = 1.62 kip
145
* 3-8.
The strut is supported by a pin at C and an A-36 steel guy wire AB. If
the wire has a diameter of 0.2 in., determine how much it stretches when
the distributed load acts on the strut.
B
146
3-9. The s—e diagram for elastic fibers that make
up
human skin and muscle is shown. Determine the
modulus of
elasticity of the fibers and estimate their modulus of
toughness and modulus of resilience.
Ans:
E = 5.5 psi, u t = 19.25 psi, u r = 11 psi
147
s (ksi)
3-10. The stress-strain diagram for a metal alloy having
an original diameter of 0.5 in. and a gauge length of 2
in. is
given in the figure. Determine approximately the
modulus
of elasticity for the material, the load on the specimen
that
causes yielding, and the ultimate load the specimen will
support.
-e
0
0.001
0.002 0.003
0.004 0.005 0.006 0.007
Ans:
E — 30.0(103) ksi, PY — 11.8 kip, Pult — 19.6 kip
148
(in./in.)