Civil Engineering Reference
In-Depth Information
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s
s
s
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F
IGURE
7.7
Cube subjected to hydrostatic pressure
7.6 V
OLUMETRIC
S
TRAIN
D
UE TO
H
YDROSTATIC
P
RESSURE
A rather special case of strain which we shall find useful later occurs when a cube
of material is subjected to equal compressive stresses,
σ
, on all six faces as shown in
Fig. 7.7. This state of stress is that which would be experienced by the cube if it were
immersed at some depth in a fluid, hence the term hydrostatic pressure. The analysis
would, in fact, be equally valid if
σ
were a tensile stress.
Suppose that the original length of each side of the cube is
L
0
and that
is the decrease
in length of each side due to the stress. Then, defining the
volumetric strain
as the
change in volume per unit volume, we have
δ
L
0
−
)
3
(
L
0
− δ
volumetric strain
=
L
0
Expanding the bracketed term and neglecting second- and higher-order powers of
δ
gives
3
L
0
δ
L
0
volumetric strain
=
from which
L
0
3
volumetric strain
=
(7.6)
Thus we see that for this case the volumetric strain is three times the linear strain in
any of the three stress directions.
7.7 S
TRESS
-S
TRAIN
R
ELATIONSHIPS
HOOKE'S LAW AND YOUNG'S MODULUS
The relationship between direct stress and strain for a particular material may be
determined experimentally by a
tensile test
which is described in detail in Chapter 8.
A tensile test consists basically of applying an axial tensile load in known increments
