01-01ChapGere.0021 - diameter ± d What is the magnitude of...

Solution 1.5-3 Nylon bar inside steel tube
SECTION 1.5 Linear Elasticity, Hooke’s Law, and Poisson’s Ratio
21
C
OMPRESSION
d
1
3.50 in. d
1
0.01 in.
d
2
3.51 in.
Nylon: E 400 ksi 0.4
L
ATERAL STRAIN
e ¿
0.01 in.
3.50 in.
0.002857
e ¿
¢ d
1
d
1
(Increase in diameter)
A
XIAL STRAIN
(Shortening)
A
XIAL STRESS
E e (400 ksi)( 0.007143)
2.857 ksi
(Compressive stress)
Assume that the yield stress is greater than and
Hooke’s law is valid.
F
ORCE
P (
COMPRESSION
)
27.5 k
P s A (2.857 ksi)
¢
4
≤
(3.50 in.)
2
e
e ¿
n
0.002857
0.4
0.007143
d
2
d
1
Problem 1.5-4 A prismatic bar of circular cross section is loaded
by tensile forces P (see figure). The bar has length L 1.5 m and
diameter d 30 mm. It is made of aluminum alloy with modulus
of elasticity E 75 GPa and Poisson’s ratio
1
/
3
.
If the bar elongates by 3.6 mm, what is the decrease in