sm8 27

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PROBLEM (8.27) A thin plate in plane stress is subjected to stresses
x
σ
= 70 MPa, y
σ
, and
x
y
τ
= 25 MPa, as shown in Fig. P8.27. Calculate the largest value of y
σ
so that maximum in-plane shear
stress does not to exceed 100 MPa.
SOLUTION
1
2
22
max [( ) ]
2
xy xy
σ
σ
τ
τ
−
=+
this gives
11
22
22
max
70
[ ] ; [ ] 96.825
22
xy y
xy
M
Pa
σ
σσ
ττ
−−
=− =
Solving,
70 2(96.825) 123.7
y
M
Pa
σ
=− =−
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