Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

p13.3 The thin rectangular plate shown in Figure P13.3/4 is uniformly
deformed such that ε x = 120 µε, ε y = −860 µε, and γ xy =
1,100 µrad. If a = 25 mm, determine
(a) the normal strain ε n in the plate.
(b) the normal strain ε t in the plate.
(c) the shear strain γ nt in the plate.
a
a
a
a
t t′
B
y
O
D
x
A
n
p13.7–p13.10 The strain components ε x , ε y , and γ xy are given
for a point in a body subjected to plane strain. Determine the strain
components ε n , ε t , and γ nt at the point if the n−t axes are rotated
with respect to the x−y axes by the amount, and in the direction,
indicated by the angle θ shown in either Figure P13.7 or Figure
P13.8. Sketch the deformed shape of the element.
t
y
FIGURE p13.7
θ
n
x
a
C
y
t
a
n′
a a a a a a
FIGURE p13.3/4
p13.4 The thin rectangular plate shown in Figure P13.3/4 is
uniformly deformed such that ε x = −890 µε, ε y = 440 µε, and γ xy =
−310 µrad. If a = 50 mm, determine
(a) the normal strain ε n′ in the plate.
(b) the normal strain ε t′ in the plate.
(c) the shear strain γ n′t′ in the plate.
p13.5 The thin square plate shown in Figure P13.5/6 is
uniformly deformed such that ε n = 660 µε, ε t = 910 µε, and γ nt =
830 µrad. Determine
(a) the normal strain ε x in the plate.
(b) the normal strain ε y in the plate.
(c) the shear strain γ xy in the plate.
a
D
y
C
t
x
θ
FIGURE p13.8
Problem Figure ε x ε y γ xy θ
P13.7 P13.7 −1,050 µε 400 µε 1,360 µrad 36°
P13.8 P13.8 −350 µε 1,650 µε 720 µrad 14°
P13.9 P13.7 −1,375 µε −1,825 µε 650 µrad 15°
P13.10 P13.8 590 µε −1,670 µε −1,185 µrad 23°
p13.11–p13.15 The strain components ε x , ε y , and γ xy are
given for a point in a body subjected to plane strain. Determine the
principal strains, the maximum in-plane shear strain, and the absolute
maximum shear strain at the point. Show the angle θ p , the principal
strain deformations, and the maximum in-plane shear strain
distortion on a sketch.
n
x
A
FIGURE p13.5/6
p13.6 The thin square plate shown in Figure P13.5/6 is
uniformly deformed such that ε x = 0 µε, ε y = 0 µε, and γ xy =
−1,850 µrad. Using a = 650 mm, determine the deformed length
of (a) diagonal AC and (b) diagonal BD.
B
n
Problem ε x ε y γ xy
P13.11 −550 µε −285 µε 940 µrad
P13.12 940 µε −360 µε 830 µrad
P13.13 −270 µε 510 µε 1,150 µrad
P13.14 670 µε −280 µε −800 µrad
P13.15 960 µε 650 µε 350 µrad
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