Problem 15.14
Given:
An isotropic thin rectangular plate has dimension
a
parallel to the
x
axis and dimension
b
parallel
to the
y
axis.
The
x
parallel edges are simply supported; the
y
parallel edges are free.
Uniform downward
pressure
p
is applied to the upper surface.
What are the principal stresses at the middle of the lower
surface?
What is the lateral deflection at the center of the plate.
Solution:
a
b
Free edge
x
y
When bending occurs making a cylindrical
surface, then the plate acts like a beam with a
uniform distributed load.
A simply supported
beam with a uniform distributed load has the
following deflection formula:
w
5q
L
4
384 E
I
=
We can adapt this to the plate using:
qp
1
()
=
distributed load per unit width
EI
D
=
Et
3
12 1
ν
2
=
q
b/2
qb/2
V
M
y
Lb
=
Thus:
w
60 q
b
4
1
ν
2
384 E
t
3
=
Using a free body diagram, the maximum moment in a simply supported beam at the center is
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 Fall '10
 Folkman
 Cartesian Coordinate System, Polar coordinate system, simply supported beam

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