sm8 106 110

_______________________________________________________________________
PROBLEMS (8.106 through 110) The state of strain at particular points in a structure is given in
the table below. Determine the state of strain associated with axes x’ and y’ rotated through the specified
angle
θ
(Figs. P8.106 through P8.110). Use Eqs. (8.35).
-------------------------------------------------------------------------------------
Problem
x
ε
y
ε
z
ε
θ
-------------------------------------------------------------------------------------
8.106 -400
μ
800
μ
1500
μ
30o
8.107 500
μ
1200
μ
-1000
μ
-45o
8.108 200
μ
410
μ
100
μ
40o
8.109 -300
μ
420
μ
200
μ
10o
8.110 -720
μ
-200
μ
240
μ
-30o
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SOLUTION (8.106)
'400 800 400 800 cos60 750sin60
22
oo
x
ε
−+ −−
=+ +
)866.0(750)5.0(600200 +−=
μ
550
=
μ
ε
150650300200
'−=−+= y
oo
yx 60cos150060sin)800400(
'' +−−−=
γ
μ
1789
=
SOLUTION (8.107)
'500 1200 0 500sin( 90 )
2o
x
ε
+
=+−−
μ
1350500850 =+=
μ
ε
350500850
'=−= y
0)90sin()1200500(
'' +−−−= o
yx
γ
μ
700
−
=
Continued on next slide
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SOLUTION (8.108)
'200 410 200 410 cos80 50sin80
22o
x
ε
+−
=+ +
o
μ
3364918305 =+−=
μ
ε
2744918305
'=−+= y
oo
yx 80cos10080sin)410200(
'' +−−=
γ
μ
224
=
SOLUTION ( 8.109)
'300 420 300 420 cos20 100sin20
22
oo
x
ε
−+ −−
=+ +
μ
2443433860 −=+−=
μ
ε
3643433860
'=−+= y
oo
yx 20cos20020sin)420300(
'' +−−−=
γ
246 188=+ 434
μ
=
SOLUTION ( 8.110)
'720 200 720 210 cos( 60 ) 120sin( 60 )
22 oo
x
ε
−− −+
=+ −+−
μ
694104130460
−
=−−−=
μ
ε
226104130460
'
−
=++−=
y
)60cos(240)60sin()200720(
'' oo yx −+−+−−=
γ
μ
330−=
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
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