sm8 121

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PROBLEM (8.121) A 60 x 80-mm rectangular aluminum plate of modulus elasticity E and
Poisson’s ratio
ν
is subjected to the uniform stresses shown on Fig. P8.121. Determine:
(a) The deformation of diagonal AC.
(b) The deformation of diagonal BD.
Given: E = 210 GPa,
ν
= 1/3
SOLUTION
16
tan 36.9
8o
DAC θ
−
∠== =
22 3
60 80 100 , 2(1 1 3) 8
AC BD E
LL mmG== += = =
+E
(a) 6
1 150 350(10 )
(300 )
3
xEE
ε =+=
6
1 300 250(10 )
( 150 )
3
yEE
ε =−− =−
6
100 800(10 )
3
xy GE
γ ==
Taking
'x along AC:
'11
( ) ( )cos73.8 sin73.6
22 2
oo
xxyxy
γ
εεε εε =++− +
66
10
(50 83.7 128) 261.71(10 ) E
E
=+ + =
63
9
261.71(10 )
100 124.6 10
210(10 )
AC
Lm
−m= ×Δ=
(b)
o
1.1439.36180
1=−=
θ
Taking
'x along BD:
6
'10
(50 300cos286.2 133.2sin286.2 )
oo
xE
ε =+ +
66
10
(50 83.7 128) 5.7(10 ) E
E
=+ − =
63
9
5.7(10 )
100 2.7 10
210(10 )
BD
Lm
−m=×Δ=
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