Stress unalysis 405
Example
X
e = 300 3 sin e = 0.500, COS e = 0.866
:. of = 20 x (0.866)2 + 10 x (0.500)' +2 x 10 x 0.500 x 0.866 = 26.16 MPa
oY, = 20 x (0.500)2 + 10 x (0.866)' - 2 x 10 x 0.500 x 0.866 = 3.84 MPa
zIy = 10 (0.866' - 0.500") - (20 - 10) x 0.866 x 0.500 = 0.67 MPa.
An interesting check of the arithmetic is that
(0, + cy) = (0,. + 43.
So in this case
ox + oy = 30 MPa
and
ox, + = 26.16 + 3.84 = 30.00 MPa.
Notice that T~~~ is very low in comparison to zv. We may be tempted to
ask whether there exists for x'y' an orientation such that zxtyt = 0. Well
there is.
Principal directions and principal stresses
t
't -
.X
From this - To this -