EAS4200C Aerospace Structures Homework #4 (Due: Oct. 2nd)
1. Show that there is no warping in the bar of circular crosssection
Hint: First, calculate the constant C in
2
2
2
2
( , )
1
x
y
x y
C
a
a
φ
⎛
⎞
⎟
⎜
⎟
⎜
=
+
−
⎟
⎜
⎟
⎟
⎜
⎝
⎠
from the compatibility
equation. Second, calculate shear strains
γ
xz
and
γ
yz
from shear stresses
τ
xz
and
τ
yz
. Third,
integrate
w
(
x
,
y
)
from the definition of shear strains:
,
xz
yz
w
u
w
v
x
z
y
z
γ
γ
∂
∂
∂
∂
=
+
=
+
∂
∂
∂
∂
.
2. Consider a straight bar of a uniform elliptical crosssection. The semimajor and semiminor
axes are
a
and
b
, respectively. (a) Show that the stress function of the following form:
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 Spring '09
 Kim
 Expression, Conic section, πa b, Aerospace Structures Homework

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