sm8 6 8

_______________________________________________________________________
PROBLEM (8.6 through 8.8) Redo Probs. 8.3 through 8.5 using Eqs. (8.4).
SOLUTION (8.6)
y
x
’
x
θ
=15o
y
’
80 MPa
'
x
σ
''
x
y
τ
60 MPa
θ
50 MPa
'11
( 50 80) ( 50 80)cos30 60sin30
22 oo
x
σ =−+ +−− +
MPa3.11303.5615 −=+−=
'' 1( 50 80)sin30 60cos30
2oo
xy
τ =− − − +
MPa5.8496.515.32 =+=
SOLUTION (8.7)
30 90
θ
=
+120o =
θ
x
’ 10 ksi
y
’
'
x
σ
''
x
y
τ
30o
25 ksi
'11
(0 25) (0 25)cos240 10sin240
22 oo
x
σ =++− +
ksi09.1066.825.65.12 =−+=
'' 1(0 25)sin240 10cos240
2oo
xy
τ =− − +
10.83 5 15.83 ksi=− − =−
Thus,
''yx
τ
acts in opposite direction to that shown in the figure above.
Continued on next slide
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.

SOLUTION (8.8)
θ
x
’
10 MPa
y
’
'
x
σ
''
x
y
τ
22.5o
40 MPa
θ
=112.5o
x
70 MPa
'11
(70 40) (70 40)cos225 10sin225
22 oo
x
σ =−++ −
MPa8.1607.789.3815
−
=+−=
'' 1(70 40)sin 225 10cos225
2oo
xy
τ =− + −
MPa4607.789.38 =+=
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.