sm8 129

_______________________________________________________________________
PROBLEM (8.129) During a static test of an aircraft panel, a 45° rosette measures the following
normal strains on the free surface (Fig. P8.129):
a
ε
= -400
μ
, b
ε
= -500
μ
, c
ε
= 200
μ
Calculate the principal strains. Show the results on a properly oriented deformed element.
SOLUTION
Using Eqs. (8.44), we have
μ
γ
μ
ε
μ
ε
800)200400()500(2,200,400 −=+
−
−
−
=
=
−= xyyx
Equations (8.36) are thus,
22
1,2 400 200 600 800
()()
2
22
ε
−+
=±−+− 500100
±
−
=
μ
ε
μ
ε
600,400 21 −==
1
1
2800
tan [ ] 26.6
400 200 o
p
θ
−−
==
−−
2' 6001.53sin4001.53cos300100
εμε =−=−−−= oo
x
Thus,
" 26.6o
p
θ =
400
μ
26.6o
x’
x
y’
600
μ
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