sm8 14

_______________________________________________________________________
PROBLEM (8.14) At a particular point in a loaded machine part (use Fig. P8.9), the stresses are as
follows:
x
σ
= 6 ksi, y
σ
= -4 ksi , and
x
y
τ
= 0. Determine the normal and shear stresses on the plane
whose normals are at angles of -30o and 120o with the x axis. Sketch the results on a properly oriented
elements.
SOLUTION
x
’
4.33 ksi
y
’
30o
3.5 ksi
x
30 :
o
At θ =−
'6464
cos( 60 ) 0
22 o
x
σ
−+
=+ −+ ksi
5.35.21
=
+
=
'' 64
sin( 60 ) 0 4.33
2o
xy ksi
τ
+
=− − + =
:120o
At = θ
'6464
cos240 1.5
22 o
xksi
σ
−+
=+ =−
'' 64
sin240 4.33
2o
xy ksi
τ
+
=− =
x
’
y
’
4.33 ksi
120o
1.5 ksi
x
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