Q.3.8
The thin cantilever shown in figure is subjected to uniform shearing stress
t
0
along its upper surface (y = +h) while surfaces y = h and x = L are free of stress.
Determine whether the Airy stress function.
Satisfies the required conditions for this problem.
Y
Fig.
t
0
2h
X
L
Solution:
First, to evaluate the formulae for stresses, we differentiate stress function with x
and y.
)
(
4
2
3
2
0
h
y
h
y
y
x


=
∂
∂
t
f
0
4
4
3
3
2
2
=
∂
∂
=
∂
∂
=
∂
∂
∴
x
x
x
f
f
f
Also,
)
3
2
3
2
(
4
2
2
2
2
0
h
y
L
h
Ly
h
y
x
h
xy
x
y
+
+


=
∂
∂
t
f
)
h
6Ly
h
2L
6xy

.
2
(
4
2
2
0
2
2
+
+

=
∂
∂
∴
h
h
x
y
t
f
)
)
(
6
(
4
2
0
3
3
h
x
L
y

=
∂
∂
∴
t
f
)
y
L.
y
L.
y
x.

y
x

(x.y
.
4
1
2
3
2
2
3
2
0
h
h
h
h
+
+
=
t
f
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document