_______________________________________________________________________
PROBLEM (8.46) The state of stress on the horizontal and vertical planes at a point is only not
completely known, as shown in Fig. P8.46. However, at the point stresses 2
σ
and max
τ
are prescribed
as -7 and 8 ksi, respectively. Determine stresses
σ
,
τ
, and 1
σ
. Show the results on properly,
oriented elements.
SOLUTION
1
max 1
7
8;9
2ksi
σ
τσ
+
== =
We have
975 ; 3
ksi
σ
σ
−=+ =−
22
53
8 ( ) ; 6.93
2ksi
ττ
+
=+=
12(6.93) 5 3
2tan 60, ' 1
53 2
o
pksi
θσ
−
−
===
+=
'53
1 cos60 6.93sin60
2oo
x
σ
+
=+ +
=
ksi9621 =++
Thus,
'30
o
p
θ
=
7 ksi
9 ksi
30o
1 ksi
x
8 ksi
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