sm8 49

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PROBLEM (*8.49) Redo Prob. 8.48 for the case shown in Fig. P8.49.
*SOLUTION
'' yxyx
σ
σ
σ
σ
+=+
30 20 18 ; 28
M
Pa
σ
σ −=−+ =
x
’
σ
y’
θ
14 MPa
x
18 MPa
'30 20 30 20
28 cos2 10sin2
22
x
σ
θθ
−+
== + +
or
θ
θ
2sin102cos2523 += (1)
θ
θ
τ
2cos102sin2514
'' +−=−= yx
Multiply this by :5.2−
θ
θ
2cos252sin5.6235 −= (2)
Add Eqs. (1) and (2),
o
13.532,2sin5.7258 == θθ
or
o
6.26= θ
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