sm8 134

_______________________________________________________________________
PROBLEM (8.134) At a point A on the surface of a loaded bracket, the strain readings are
a
ε
= -200
μ
, b
ε
= -500
μ
, c
ε
= -900
μ
for a
θ
= 0o, b
θ
= 120°, and c
θ
= 240° (see Fig. P8.134). Calculate:
(a) The in-plane principal strains.
(b) The in-plane maximum shear strains.
Show the results on properly oriented deformed elements.
SOLUTION
Equations (8.43) become
μ
ε
200
−
=
x
)866.05.0()75.0()25.0(500
×
−
+
+=− xyyx
γ
ε
ε
(1)
)5.0866.0()75.0()25.0(900
×
+
+=− xyyx
γ
ε
ε
(2)
Subtract Eq. (2) from Eq. (1):
μ
γ
462
−
=
xy
Equation (1) yields then: 20075.050500
+
+
−
=
−
y
ε
,
μ
ε
866−=
y
(a)
866 200
' 533
2
ε
μ
+
=− =−
2
γ
(μ
() 1200, 664)
22 333 231 405R
μ
=+=
1
1 231
' tan 17.4
2 333 o
p
θ
−
==
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.
μ
ε
128405533
1
−
=
+
−
=
μ
ε
938405533
2
−
=
−
−
=
(b)
μ
γ
8102
max == r
Check:
μ
γ
810938128
max
=
+−=
2
ε
R
ε
(
μ
)
1
ε
2'
p
θ
C
O
ε
27.6o
128
μ
533
μ
17.4o
x’
x
810
μ
533
μ
x’
x
838
μ