sm8 42

_______________________________________________________________________
PROBLEM (8.42) The state of stress at a point is shown in Fig. P8.42. For that point determine:
(a) The magnitude of the shear stress
τ
if the maximum principal stress is not to exceed 70 MPa.
(b) The corresponding maximum shearing stresses and the planes at which they act.
SOLUTION
(a) 22
1060 060
70 ( )
22
σ
τ
+−
== + +
MPa5.26=
τ
(b) 22
max 60
( ) 26.5 40
2
M
Pa τ
−
=+=
60
'30
2
M
Pa σ ==
1060
2 tan [ ] 48.6
2(26.5) o
s
θ
−−
=− =
'' 60sin48.6 26.5cos48.6 40
2oo
xy
M
Pa τ =+ =
Thus,
' 24.3o
s
θ =
x
’
30 MPa
y’
24.3o
30 MPa
x
40 MPa
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