sm8 47

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PROBLEM (8.47) Consider a point in a loaded body subjected to the stresses shown in Fig.
P8.47. Determine:
(a) The principal stresses.
(b) The maximum shear stresses.
Sketch the results on properly oriented elements.
SOLUTION
(a) 22
1,2 50 30 50 30
( ) 20 40 22.4
22
σ
−− −+
=± +=−±
12 17.6 62.4
M
Pa MPa
σ
σ =− =−
12( 20)
2 tan 63.4
50 30 o
p
θ
−−
==
−+
(b) max 17.6 62.4 22.4
2
M
Pa τ
−+
==
17.6 62.4
'4
20
M
Pa σ
−−
==−
'50 30 50 30 cos63.4 20sin63.4
22 oo
x
σ
+−
=− − −
MPa4.6288.1748.440
−
=−−−=
Thus,
" 31.7o
p
θ =
17.6 MPa
62.4 MPa
22.4 MPa
40 MPa
40 MPa
31.7o
x
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