Quiz 4 – solution
An aluminum [
E
= 10,600 ksi;
G
= 4,000 ksi] plate is subjected to
biaxial stress (Fig. P13.56). The normal stress in the
x
direction is
known to be twice as large as the normal stress in the
y
direction. If
the strain gage measures a normal strain of +560
in the
indicated direction, determine
(a) the magnitudes of the normal stresses
x
and
y
acting on the
plate.
(b) the inplane principal strains,
p
1
and
p
2
(c) the maximum inplane shear strain
max
in the plate.
Fig. P13.56
Solution
Derive an expression for
from Eq. (13.18):
1
2(1
)
2
EE
G
G
Determine Poisson’s ratio from this expression:
10,600 ksi
1
1
0.325
2
2(4,000 ksi)
E
G
(a)
A strain transformation equation [Eq. (13.3)]
22
cos
sin
sin cos
n
x
y
xy
can be written for the normal strain in the direction of strain gage:
560
με
cos (40 )
sin (40 )
sin(40 )cos(40 )
x
y
xy
Note that the shear strain
xy
is related to the shear stress
xy
by Eq. (13.22):
1
xy
xy
G
Since
xy
= 0, the shear strain
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '11
 Weng
 Force, Strain, Stress, Shear strain, ksi, inplane shear strain

Click to edit the document details