sm8 13

_______________________________________________________________________
PROBLEM (8.13) At a critical point A in the loaded member in Fig. P8.13, the stresses on the
inclined plane are
σ
= 28 MPa and
τ
= 10 MPa, and the normal stress on the y plane is zero.
Calculate the normal and shear stresses on the x plane through the point. Show the results on a properly
oriented element.
SOLUTION
θ
x
’
y
’
σ
τ
30o
x
120o θ =
00
28 cos240 sin240
22 oo
xx xy
σ
σ
στ
+−
== + +
xyx
τ
σ
464.3112 += (1)
0
10 sin240 cos240
2oo
xxy
σ
ττ
−
=− =− +
xyx
τ
σ
155.1094.23 +−= (2)
Solving (1) and (2):
MPaMPa xyx 5.586.90
−
=
−=
τ
σ
A
x
58.5 MPa
90.6 MPa
y
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