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CLARKSON UNIVERSITY
Department of Mechanical and Aeronautical Engineering
AE/ME 350 Aircraft Structural Analysis (Fall 2010)
Homework #2 Solution
1.
A structural member supports loads which produce, at a particular point, a direct
tensile stress of 80 N/mm
2
and a shear stress of 45 N/mm
2
on the same plane.
Calculate
the values and directions of the principal stresses at the point and also the maximum
shear stress, stating on which planes this will act.
The principal stresses are obtained using
σ
x
= 80 N/mm
2
,
σ
y
= 0 (or vice versa), and
xy
=
45 N/mm
2
.
22
,
1
()
4
xy
II
I
x
y
x
y
ss
s
+
=

+
t
The direction of the principal stresses are defined by angle
θ
given by
The first value of
θ
corresponds to
σ
I
while the second value corresponds to
σ
II
.
The maximum shear stress, which acts on planes at 45
0
to principal planes, is given by
1
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View Full Document2.
At a point in an elastic material there are two mutually perpendicular planes, one of
which carries a direct tensile stress at 50 N/mm
2
and a shear stress of 40 N/mm
2
, while
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 Fall '10
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