sm8 48

_______________________________________________________________________
PROBLEM (*8.48) The state of stress at a point A in a structure is shown in Fig. P8.48.
Determine the normal stress
σ
and the angle
θ
.
*SOLUTION
x
’
σ
y
’
θ
36 MPa
x
16 MPa
A
'' yxyx
σ
σ
σ
σ
+=+
MPa12;36408
−
=
−−=−−
σ
σ
'840840
36 cos2 12sin2
22
x
σ
θθ
−− −
=− = − −
or
θ
θ
2sin122cos1612 −=− (1)
'' 840
16 sin2 12cos2
2
xy
τ
θθ
−+
=− =− −
Multiply by
:43−
θ
θ
2cos92sin1212 += (2)
Add Eqs. (1) and (2),
θ
2cos250 =
or
oo 45,902 ==
θθ
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