sm8 16

_______________________________________________________________________
PROBLEM (8.16) At a point in a loaded steel bracket the stresses are
x
σ
= 50 MPa, y
σ
= -15 MPa,
and
x
y
τ
= -30 MPa , as shown in Fig. P8.16. Determine the stresses acting on an element oriented at an
angle
θ
= 40o from the x axis. Sketch the result on a properly oriented element.
SOLUTION
'11
()()cos2sin
22
xxyxy xy
2
σ
σσ σσ θτ θ =++− +
11
(50 15) (50 15)cos80 30sin80 6.45
22 oo
M
Pa=−++ − =−
'' 1()sin2cos
2
xy x y xy 2
τ
σσ θτ θ =− − +
1(50 15)sin80 30cos80 37.2
2oo
M
Pa=− + − =−
Hence,
''
50 15 6.45 41.4
yxyx
M
Pa
σ
σσσ =+− =−+ =
x
’
29.8 MPa
y’
θ
=
40o
41.6 MPa
x
6.4 MPa
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