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Aerospace Structural Composites I
Homework 6
Anirban Chaudhuri
1.
The unidirectional Boron/Epoxy layer of Example 6.2.1 (using E
1
= 204GPa, E
2
= 18.5GPa,
G
12
= 5.59GPa,
12
= 0.23, t = 0.125mm) is to be loaded by combined axial and shear stresses
with
xy
x
r
.
Determine the strength of this layer based on the TsaiHill failure criterion as a
function of the fiber orientation in the range 0
o
≤
≤
90
o
, and plot the strength for
r = 0.05
and
r =
0.2
. Typical strength properties of Boron/Epoxy layers are X
t
= 1260MPa, X
c
= 2500MPa, Y
t
=
61MPa, Y
c
= 202MPa, and S = 67MPa.
Solution:
The stresses in the principal direction can be found by using the equation (1).
22
1
2
12
2
2
x
y
xy
mn
m
n
nm
m
n
mn mn m
n
…(1)
where, m=cos
and n=sin
. We have
y
=0 and
xy
=
r
x
.
So the principal stresses are given below.
1
2
12
()
(1
)
x
x
x
mr
n
nr
m
mn r
…(2)
TsaiHill criterion is given in equation (3) [Eq. 6.2.11 in book]
2
12 1
2
1
2
2
2
111
1
1
tt
t
XYX
S
…(3)
For the case of compressive loading the
X
t
and
Y
t
are replaced by
X
c
and
Y
c
respectively. The
values found in equation (2) are substituted in equation (3) for both tensile and compressive
loading case and the strengths are plotted for
r = 0.05
and
r = 0.2
. The strength (
x
) in each case
is found by solving the equation (3) (after substituting the values) in MATLAB. The MATLAB
code used for this purpose is given in Appendix I.
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View Full Document(a) Tensile loading
(b) Compressive loading
Fig. 1:
Strength for r = 0.05 under tensile and compressive loading
(a) Tensile loading
(b) Compressive loading
Fig. 2:
Strength for r = 0.2 under tensile and compressive loading
2.
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 Spring '08
 PETERIFJU

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