sm8 40

_______________________________________________________________________
PROBLEM (8.40) Given the stresses acting uniformly at the edges of a block (Fig. P8.40),
calculate:
(a) The stresses
x
σ
, y
σ
, and
x
y
τ
.
(b) The maximum shearing stresses with the associated normal stresses.
Sketch the results on properly oriented elements.
SOLUTION
5sin30 2.5 5cos30 4.33
oo
yxy
M
Pa MPa στ =− =− = =
(a)
2.5 AΔ(0.866)
AΔxA
σ
Δ
(0.5)
30o
4.33 A
Δ
(
0.866
)
4.33 A
Δ
(0.5)
15 A
Δ
,
∑=Δ+Δ+Δ−= 0)866.0(33.45.015:0 AAAF xx
σ MPa
x5.22
=
σ
(b) 22
max 22.5 2.5
( ) 4.33 13.23
2
M
Pa τ
+
=+=
x
’
13.23 MPa
y
’
35.5o
10 MPa
x
10 MPa
122.5 2.5
2 tan [ ] 70.9
2(4.33) o
s
θ
−+
=− =−
MPa10)5.25.22(' 2
1=
−
=
σ
'' 22.5 2.5sin( 70.9 ) 4.33cos( 70.9)
2o
xy
τ
+
=− − + −
11.81 1.42 13.23
M
Pa=+=
Thus,
' 35.5o
s
θ =−
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