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

Problem e a e b e c E ν
y
c
P13.47 −1,320 me −870 me 340 me 100 GPa 0.28
P13.48 1,400 me 560 me −1,270 me 210 GPa 0.31
P13.49 910 me 720 me 1,200 me 15,000 ksi 0.15
45°
45°
b
x
a
y
b
y
c
FIGURE p13.52
60°
x
a
60°
a
45°
c
FIGURE p13.47 FIGURE p13.48
b
x
Problem ε a ε b ε c E ν
P13.50 −840 µε −1,775 µε 665 µε 9,000 ksi 0.24
P13.51 –680 µε 220 µε –80 µε 17,000 ksi 0.18
P13.52 55 µε –110 µε –35 µε 212 GPa 0.30
a
b
y
45°
45°
FIGURE p13.49
c
x
p13.53 A block of 2014-T4 aluminum [E = 73 GPa; ν = 0.33]
has a width a = 640 mm, a height b = 200 mm, and a thickness t =
160 mm. The block is constrained between two rigid, perfectly
smooth surfaces as shown in Figure P13.53/54/55. The block is
compressed by a normal stress σ x = 210 MPa. Assuming plane
stress, determine
(a) the average normal stress in the y direction.
(b) the change in the width a of the block.
(b) the change in the thickness t of the block.
p13.50–p13.52 The strain rosettes shown in Figures P13.50–
P13.52 were used to obtain normal strain data at a point on the free
surface of a machine component. In each of Problems P13.50–
P13.52,
(a) determine the strain components e x , e y , and γ xy at the point.
(b) determine the principal strains and the maximum in-plane
shear strain at the point.
(c) using the results from part (b), determine the principal
stresses and the maximum in-plane shear stress. Show these
stresses on an appropriate sketch that indicates the orientation
of the principal planes and the planes of maximum in-plane
shear stress.
(d) determine the magnitude of the absolute maximum shear
stress at the point.
c
y
60°
60°
b
a
FIGURE p13.50
60°
x
y
60°
60°
c
a
b
FIGURE p13.51
x
σ x
Rigid
FIGURE p13.53/54/55
y
Rigid
a
x
p13.54 A plate of stainless steel [E = 28,000 ksi; ν = 0.12] has
a width a = 18 in. and a height b = 9 in. The plate is constrained
between two rigid, perfectly smooth surfaces as shown in Figure
P13.53/54/55. After a normal stress σ x was applied, the width a of
the plate was found to have decreased by 0.10 in. Assuming plane
stress, determine the average normal stresses acting on the plate in
the x and y directions.
p13.55 A plate of ductile cast iron [E = 168 GPa; ν = 0.32; α =
10.8 × 10 −6 /°C] has a width a = 420 mm, a height b = 250 mm, and
a thickness t = 30 mm. As shown in Figure P13.53/54/55, the plate
is constrained between two rigid, perfectly smooth surfaces at an
ambient temperature of 20°C. The plate is compressed by a constant
normal stress σ x = 300 MPa. Assume that plane stress conditions
exist.
σ x
b
582