sm8 35

_______________________________________________________________________
PROBLEM (8.35) Determine the maximum shearing stresses and the associated normal stresses for
the state of stress of Fig. P8.35. Sketch the results on a properly oriented element.
SOLUTION
MPaMPaMPa xyyx 10,40,70
−
=
−==
τ
σ
σ
22
max 70 40
( ) ( 10) 55.9
2
M
Pa τ
+
=+−=
170 40
2 tan ( ) 79.7
2( 10) o
s
θ
−+
=− =
−
'' 70 40sin79.7 10cos79.7
2oo
xy
τ
+
=− −
x
’
15 MPa
y
’
39.9o
55.9 MPa
x
15 MPa
MPa9.5579.111.54 −=−−=
Thus, " 39.9o
s
θ =
We also have
70 40
'15
2
M
Pa σ
−
==
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