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
100KN
A force of 100 KN is applied on a column as shown. The
column is made from two materials. [The top one is a
functionally graded material with a linearly varying
modulus and densities. Its length is 2 meter. The density
and elastic modulus of the top material at point A are 2700
А
kg
m3
and 72 Gpa, respectively. The density and modulus of
kg
the top material at point B are 3000 and 100 Gpa. The
m
3
В
kg
bottom material is made from steel (density =7800
and
m2
modulus=200GPA). The length of the bottom material is
1m. The cross-sections of both materials comprising the
column are cylindrical with a diameter of 0.5 m.
C
ID (oijj + bị = 0) and
considering the weight and the applied force determine:
Using equilibrium
while
The stress distribution in both members
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