sm8 122

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PROBLEM (8.122) An element at a point on a loaded frame has strains as follows:
x
ε
= 600
μ
y
ε
= 1000
μ
x
y
γ
= -1400
μ
Calculate:
(a) The principal strains.
(b) The maximum shear strain.
(c) The absolute maximum shear strain.
SOLUTION
1()
2
avg x y
ε
εε =+
2
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1(600 1000) 800
2
μ
=+=
22
(800 600) 700
2
R− =+
γ
(μ
60
)
0
728
μ
=
(a) 1,2 avg
R
ε
ε =±
1800 728 1528
ε
μ =+=
2800 728 72
ε
μ =−=
(b) max 2 2(728) 1456R
γ
μ == =
(c) max 1 3 1
() 0
a
γ
εε ε =−=− 1528
μ
=
2
ε
R
ε
(
μ
)
1
ε
O
C
800