sm8 34

_______________________________________________________________________
PROBLEM (8.34) For the state of stress given in Fig. P8.34, determine the magnitude and orien-
tation of the principal stresses. Show the results on a properly oriented element.
SOLUTION
MPaMPaMPa xyyx 60,80,50
=
=−=
τ
σ
σ
22
1,2 50 80 50 80
()
22
σ
−+ −−
=± +
60
103.5 MPa
21.4o
73.5 MPa
x
x’
= 46.8815±
MPaMPa 5.735.103 21
−
==
σ
σ
12(60)
2 tan 42.7
50 80 o
p
θ
−
==
−− −
'50 80 50 80 cos( 42.7 ) 60sin( 42.7 )
22 oo
x
σ
−+ −−
=+ −+−
=
MPa5.737.4076.4715 −=−−
Thus,
" 21.4o
p
θ =−
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