Civil Engineering Reference
In-Depth Information
the normal strains
e
x
, e
y
,
and
e
z
can be computed by the
generalized
Hooke's law
,
s
x
- n
1
s
y
+ s
z
2
e
x
=
E
s
y
- n
1
s
z
+ s
x
2
e
y
=
E
s
z
- n
1
s
x
+ s
y
2
e
z
=
(1.3)
E
Sample Problem 1.1
A cube made of an alloy with dimensions of is placed into
a pressure chamber and subjected to a pressure of 90 MPa. If the modulus of elastici-
ty of the alloy is 100 GPa and Poisson's ratio is 0.28, what will be the length of each
side of the cube, assuming that the material remains within the elastic region?
50 mm
*
50 mm
*
50 mm
Solution
e
x
=
[
s
x
- n
1
s
y
+ s
z
2
]/
E
=
[
-
90
-
0.28
*
1
-
90
-
90
2
]/100,000
=-
0.000396 m/m
e
y
= e
z
=-
0.000396 m/m
¢
x
=¢
y
=¢
z
=-
0.000396
*
50
=-
0.0198 mm
L
new
=
50
-
0.0198
=
49.9802 mm
Linearity and elasticity should not be confused. A
linear material's
stress-strain relation follows a straight line. An
elastic material
returns to its
original shape when the load is removed and reacts instantaneously to
changes in load. For example, Figure 1.4(a) represents a linear elastic be-
havior, while Figure 1.4(b) represents a nonlinear elastic behavior.
Loading
Loading
Unloading
Unloading
Strain
Strain
(b)
FIGURE 1.4
Elastic behav-
ior: (a) linear and (b) nonlinear.
(a)
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