sm8 135

_______________________________________________________________________
PROBLEM (*8.135) The strain readings at a point on the free surface of a steel bracket subjected
to plane stress (see Fig. 8.134) are
a
ε
= 400
μ
b
ε
= 350
μ
c
ε
= 800
μ
for a
θ
= 0o, b
θ
= 45°, and c
θ
= 135°. Calculate:
(a) The maximum in-plane shearing strains.
(b) The true maximum shear strain (
ν
= 1/3).
Show the results found in part (a) on properly oriented distorted element.
*SOLUTION
Equations (8.43):
μ
ε
400=
x
)5.0()5.0()5.0(350 xyyx
γ
ε
ε
++= (1)
)5.0()5.0()5.0(800
−
++= xyyx
γ
ε
ε
(2)
Subtract Eq. (2) from Eq. (1):
μ
γ
450
−
=
xy
Equation (1) yields
2255.0200350
−
+= y
ε
,
μ
ε
750
=
y
(a)
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instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
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400 750
' 575
2
ε
μ
+
==
22 175 225 285R
μ
=+=
1
1225
" tan 26.1
2175 o
p
θ
−
==
max 2 570 , " 18.9o
s
r γμθ == =
μ
ε
860285575
1=+=
μ
ε
290285575
2
=
−
=
Continued on next slide
O
(400, 225
)
3
ε
ε(μ
)
2"
p
θ
10
2
ε
1
ε
γ
(μ)
2'
ε
x
C
R
y

(b) 313 (400 750) 575
113
z
ε
εμ ==− + =−
−
max
( ) 860 575 1435
a
γ
μ =+=
18.9o
575
μ
570
μ
575
μ
x’
x
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.