The strength-to-weight ratio of a structural material is defined as its load-carrying capacity divided by its weight. For materials in tension, use a characteristic tensile stress obtained from a stress-strain curve as a measure of strength. For instance, either the yield stress or the ultimate stress could be used, depending upon the particular application. Thus, the strength-to-weight ratio R S / W for a material in tension is defined as R s / w = σ γ in which a is the characteristic stress and 7 is the weight density. Note that the ratio has units of length. Using the ultimate stress σ U as the strength parameter, calculate the strength-to-weight ratio (in units of meters) for each of the following materials: aluminum alloy 606I-T6, Douglas fir (in bending}, nylon. structural steel ASTM-A57.2, and a titanium alloy. Obtain the material properties from Tables [-1 and 1-3 of Appendix I. When a range of values is given in a table, use the average value.
The strength-to-weight ratio of a structural material is defined as its load-carrying capacity divided by its weight. For materials in tension, use a characteristic tensile stress obtained from a stress-strain curve as a measure of strength. For instance, either the yield stress or the ultimate stress could be used, depending upon the particular application. Thus, the strength-to-weight ratio R S / W for a material in tension is defined as R s / w = σ γ in which a is the characteristic stress and 7 is the weight density. Note that the ratio has units of length. Using the ultimate stress σ U as the strength parameter, calculate the strength-to-weight ratio (in units of meters) for each of the following materials: aluminum alloy 606I-T6, Douglas fir (in bending}, nylon. structural steel ASTM-A57.2, and a titanium alloy. Obtain the material properties from Tables [-1 and 1-3 of Appendix I. When a range of values is given in a table, use the average value.
Solution Summary: The author explains the strength-to-weight ratio for each material. A is brittle and B and C are ductile.
The strength-to-weight ratio of a structural material is defined as its load-carrying capacity divided by its weight. For materials in tension, use a characteristic tensile stress obtained from a stress-strain curve as a measure of strength. For instance, either the yield stress or the ultimate stress could be used, depending upon the particular application. Thus, the strength-to-weight ratio RS/Wfor a material in tension is defined as
R
s
/
w
=
σ
γ
in which a is the characteristic stress and 7 is the weight density. Note that the ratio has units of length. Using the ultimate stress
σ
U
as the strength parameter, calculate the strength-to-weight ratio (in units of meters) for each of the following materials: aluminum alloy 606I-T6, Douglas fir (in bending}, nylon. structural steel ASTM-A57.2, and a titanium alloy. Obtain the material properties from Tables [-1 and 1-3 of Appendix I. When a range of values is given in a table, use the average value.
The figure shows the stress-strain curve for a rectangular steel test piece in tension. The test piece is loaded up to point B and then released.
If the test piece was originally 58.9 mm long, estimate its new length (in mm) after it is released?
State your answer in mm without including the units.
Stress
(MPа)
Elastic
Inclastic
strain
strain
473 -
В
408 -
340
272 -
Unload
204 -
Reload
136 -
Plastic
Elastic
68 -
deformation
recovery
0.0020
0.0060
0.0100
0.0000
0.0040
0.0080
0.0120
Strain (mm/mm)
Answer:
Q1: A circular steel rod ABCD is loaded as shown below. Use the following data
to Find the maximum stress and the deformation (AL) of the rod. Take E = 200
GPa.
A
L1
+ Dia. 1
B
В
P1
L2
Dia. 2
P2
L3
D
30 mm o
P3
Dia. 1
Dia. 2
P1
P2
P3
L1
L2
L3
(mm) (mm) (kN)
(kN) (kN)
(mm) (mm) (mm)
60
45
105
40 25
1350
2150 1350
Q2/ In the nucleus pulposus of an intervertebral disc, the compressive load is 1.5 times
the externally applied load. In the annulus fibrosus, the compressive force is 0.5 times
the external load. What are the compressive loads on the nucleus pulposus and annulus
fibrosus of the L5-S1 intervertebral disc of a 90 kg man holding a 50 kg weight bar
across his shoulders, given that 63% of body weight is distributed below the disc?
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