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PROBLEM (9.62) For the cantilever beam described in Prob. 9.61 and shown in Fig. P9.61,
determine the principal stresses at point A. Show the result on a properly oriented element.
SOLUTION
Refer to the solution of Prob. 9.61.
The state of stress at point A is found as
27.60
x
M
Pa
σ
= 1.563
xy
M
Pa
τ
=
From the corresponding
Mohr’s circle, we have:
27.6 13.8
22
x
avg
M
Pa
σ
σ
== =
22
()
2x
x
y
R
σ
τ
=+
22
(13.8) (1.563) 13.89
M
Pa=+=
Thus
1,2 avg
R
σ
σ
=
±
or
113.8 13.89 27.7
M
Pa
σ
=+ =
213.8 13.89 90
M
Pa
σ
=− =−
and
1.563
tan2 ' , ' 3.23
13.8 o
pp
θθ
==
σ
2
σ1
σ
avg
'
2p
θ
C
R
y
τ (MPa)
σ (MPa)
x
σ
x
x
σ
A
x
y
τ
90 Pa
3.23o
27.7MPa
x
x’
A
1
/
1
100%